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Early in this century, post-SARS, and in http://buzzdavidson.com/can-you-buy-cialis-over-the-counter-usa/ a period when China started allowing more students and scientists to study abroad, collaboration and exchange between American and Chinese scientists blossomed generic cialis online for sale. Many of China’s top scientists today were educated in the West. These include generic cialis online for sale George Gao, the head of China’s Center for Disease Control and Prevention, who trained and taught at Oxford and Harvard, and Shi Zhengli, who directs the Center for Emerging Infectious Diseases at the Wuhan Institute of Virology and received her Ph.D. In France.

Many, like Gao, spent more than a decade abroad before returning to China for top jobs and, often, prestigious positions and big salaries. They were great at their bench work, their science was well generic cialis online for sale respected, and top American scientists got to know them well. They became friends with their American counterparts, as is clear from Anthony Fauci’s email correspondence with Gao as the cialis emerged, recently released through a Freedom of Information Act request. But early on in what became a global crisis, when limited and reassuring information was coming out of China about the transmissibility of the novel erectile dysfunction and the extent of its domestic outbreak, misplaced trust among America’s top scientists led some to think the spread of the cialis probably wouldn’t be so bad.

Here’s the problem generic cialis online for sale. Chinese scientists are great scientists, but they work for an authoritarian government where politics, not facts, always comes first. If information they know or discover makes China look bad, it is dangerous to say it — especially to generic cialis online for sale foreign colleagues, especially publicly, and, often, even to their friends or family. That may sound familiar after the presidency of Donald Trump, during which he often mocked and sidelined experts like Fauci.

But the risk for scientists in China is far worse. Loss of your job and your kids’ career prospects, visits by the police, generic cialis online for sale false accusations, even prison. As the country’s leader, Xi Jinping, reminded his scientists in a speech last year. €œScience has no borders, but scientists have a motherland.” Every Chinese citizen knows how to interpret that statement, and I learned, too.

When I was a reporter in Beijing, generic cialis online for sale I got to know Dr. Gao Yaojie, who exposed an epidemic of HIV/AIDS in rural China that had resulted from unsanitary blood collection practices, some state-run. She was a valued source for a series of articles I wrote on the unfolding tragedy, in which nearly the entire adult population of poor farming villages was dying, without any treatment and leaving AIDS orphans behind. Dr.

Gao (no relation to George Gao) was feted by Bill and Hillary Clinton and won international human rights awards for saving perhaps tens of thousands of lives and ending dangerous practices. But in China, that very same work meant Gao spent her retirement under house arrest, often followed and threatened by local officials for embarrassing China. She fled China in 2009 and obtained political asylum in the U.S. And that was at a time when China was less autocratic and more open than it is today.

President Joe Biden had instructed security agencies to investigate the lab leak theory — to figure out whether erectile dysfunction, the cialis that causes erectile dysfunction treatment, emerged from the Wuhan lab or from nature. But if international scientific sleuths are hoping to see a lab log or find a whistleblower, that very likely won’t happen. That kind of information won’t be revealed, even to Chinese scientists’ many American friends and scientific partners, which include the U.S. The Wuhan lab has received more than half a million dollars of funding that originated from the National Institutes of Healthand has worked with many American scientists.

Mistakes happen in science. Pathogens leak out of good containment labs, and not because people are evil. It’s because, for example, the technician performing the bench work forgets an important step or, in a rush to go home, gets sloppy — it takes only a second. Or, for example, if scientists gathering bat samples in remote caves get a bit too comfortable in a dangerous environment — because they’ve been there dozens of times before with no problem and the biohazard suits and masks are suffocating.

So, they pull off the face mask a bit too early as they exit. When that happens, you have to acknowledge the error right away to contain the damage. But Chinese scientists can’t do that, at least publicly. When, in late December 2019, Dr.

Li Wenliang, an ophthalmologist working at one of Wuhan’s major hospitals, raised his concerns to colleagues about patients dying from a strange new cialis, he was punished and told by police to “stop making false comments” and investigated for “spreading rumours.” He died of erectile dysfunction treatment just a few weeks later. In China today, it is dangerous to say what you know if it challenges the official government narrative. People who participated in the protests on June 4, 1989, in Tiananmen Square, which were violently put down by the Chinese army, don’t even tell their children about that bloody day when many hundreds, and possibly thousands, were killed. Kai Strittmatter, a longtime China correspondent for one of Germany’s largest newspapers, told NPR’s Terry Gross.

€œOf course, this generation, they all know, but they were afraid to tell their children. Because, you know, what do you do when your child in school suddenly tells the teacher and asks the teacher about Tiananmen massacre?. € We may never know if the novel erectile dysfunction leaked from a lab or from animal-to-human transmission from a wild animal at one of Wuhan’s live animal markets, as the Chinese first suggested. And that’s exactly the knowledge we desperately need to prevent the next cialis, because the solutions are so different.

If the former hypothesis proved true, U.S. Scientists would need to ensure that collaborations with their Chinese partners involve full transparency — access to log books, internal reports, and all. If the latter, China must fully enforce its ban on the sale of exotic animals (the “intermediate hosts” that carry the cialis) at its wet markets, a ban it promised after the original SARS cialis emerged there from a civet cat nearly two decades ago. But the Chinese government’s control over its scientists makes it unlikely we will learn the truth now — or ever.

Elisabeth Rosenthal. erosenthal@kff.org, @rosenthalhealth Related Topics Contact Us Submit a Story TipSACRAMENTO — Gov. Gavin Newsom routinely boasts that California has “one of the highest vaccination rates in the United States of America.” But Newsom, facing a recall election this fall, rarely mentions that the state’s erectile dysfunction treatment uptake has largely stagnated in Black and Latino neighborhoods hardest hit by the erectile dysfunction, and in rural outposts where opposition to treatments runs rampant. In these communities, deep distrust of government and the U.S.

Health care system has collided with the state’s high-stakes effort to finish vaccinating its 34 million treatment-eligible residents. These are places where state health officials believe they can change a significant number of minds. But the Newsom administration is struggling to do so, public health experts say, hampered by its inconsistent and hastily developed public messaging and outreach campaign that relies too heavily on private advertising firms and companies such as Google and Blue Shield of California. €œMany people don’t trust information being put out about treatments because it’s coming from private companies that have profit-seeking motives,” said Dr.

Tony Iton, a senior vice president at the California Endowment, which focuses on expanding health care access for Californians. Iton served as Alameda County’s public health officer from 2003 to 2009. What actually works, Iton and other public health experts say, are well-funded, locally designed operations led by organizations that have built trust with residents and are capable of going door to door to dispel treatment mythology, such as local nonprofits, county health departments and community clinics. But California’s 61 local public health departments have been stunted by years of declining revenue, budget cuts and staff reductions that have stymied their ability to conduct the expensive and time-consuming public health outreach campaigns necessary to combat treatment skepticism and hesitancy.

€œWhen something like erectile dysfunction treatment comes along, local knowledge is absolutely invaluable in reaching every pocket of that community, particularly in building trust in vulnerable populations,” Iton said. €œThe state doesn’t have that, Google doesn’t have that, and certainly Blue Shield doesn’t have that.” Even the Newsom administration’s internal polling shows its efforts are faltering. €œThe resounding barrier to vaccination,” state officials wrote in the latest survey published in June, “has been confusion as a result of inconsistent, contradictory or insufficient messaging from government and public health officials.” Statewide, nearly 60% of Californians are fully vaccinated, but progress is uneven. Just 39% of eligible Black residents and 40% of Latinos had been vaccinated as of Friday, and local public health officials are intensely worried about regions like the Central Valley, where vaccination rates have stalled, especially given the threat of erectile dysfunction treatment’s dangerous delta variant.

Similar disparities exist by geography, across regions and even among neighborhoods. The state’s treatment holdouts make up a cohort that cuts across political and geographic ideologies and is dominated by Latinos, African Americans, rural residents and young people. Unlike outright treatment “rejecters,” who lean Republican, undecideds align with Democrats, according to state polling. State officials are trying to change the minds of both “undecideds” and “rejecters,” and are relying primarily on treatment lotteries with giveaways totaling $116.5 million or vacation packages, and glitzy advertising campaigns featuring paid social media influencers.

The state has awarded two $40 million contracts to high-dollar ad agencies for treatment outreach and education. Companies including Facebook, Google, Comcast and TikTok are providing free advertising on social media, radio and TV, and making charitable contributions to help the state fund its public education campaigns, state records show. Lackluster vaccination uptake drove the Newsom administration to pursue the more personal approach that public health experts favor, but the still-nascent campaign leaves out large swaths of the state. The administration launched its “Get Out the Vax” campaign in April, enlisting 70 community-based organizations and 2,000 community canvassers, now focused on Los Angeles and Central Valley neighborhoods where vaccinations have plateaued or declined.

But county public health officials say the campaign isn’t big enough to combat the treatment misinformation that has infiated regions such as California’s rural north. €œIt’s terrible,” said Placer County’s health officer, Dr. Rob Oldham, who said misinformation is driving treatments down. €œUnfortunately, the lottery didn’t really help us.

We’re working so much harder to get a dozen people vaccinated, whereas before we were doing close to 1,500 shots a day.” State Health and Human Services Secretary Mark Ghaly acknowledged that the state must boost its presence on the ground and said it “needs to do better and more.” At the same time, he and other state officials argue that the treatment lottery is working and that they are seeing progress in hard-hit neighborhoods. This month the state debuted pop-up treatment clinics at McDonald’s restaurants in 11 counties, and state-funded outreach workers have fanned out in neighborhoods such as South Los Angeles to sign people up for appointments or vaccinate takers from a roving van. treatment canvassers report that the people who don’t want the treatments say they’re concerned about safety or repeat sometimes outrageous rumors, such as the false assertion that treatments turn people into zombies. €œWe’re seeing lots of disinformation and lack of a sense of urgency,” said Yolanda Richardson, secretary of the California Government Operations Agency and Newsom’s “vaccination czar.” “The work that we have left to do is really finding out what each individual person needs to make that jump.” Carnella Marks of Oroville, in Butte County, offers a telling case of how hard public health officials must work to cut through the thick swamp of misinformation and confusion.

Carnella Marks of Oroville, California, pictured with Albert Smith, her late father-in-law, doesn’t believe erectile dysfunction treatments are safe. She says she wants someone to explain how the treatments work but “nobody’s knocking on my door to talk to me or answer my questions.” (Carnella Marks) Marks, 51, who is Black, has deep misgivings about the safety of the treatments that are rooted in the country’s racist history and her personal experience. When she was pregnant with her second child, her doctor suggested she get a hysterectomy even though she wasn’t ready to stop having kids and had no health complications. She wonders if the U.S.

Government is experimenting on Black people, as it did on African American men in the Tuskegee syphilis study from the 1930s into the 1970s. €œWhy do they want us to take the treatment so bad?. € Marks asked. €œWe’ve never been first in line for anything, but now all of a sudden you want to make sure that the African American community gets the treatment?.

€ She had considered getting vaccinated because she thought it might be required for work — until government officials paused the single-dose Johnson &. Johnson shot over concerns it caused blood clots. €œI don’t care what kind of money the governor is shelling out to get me to take the treatment,” said Marks, who wants to discuss the safety of the treatments with someone who knows. But “nobody’s knocking on my door to talk to me or answer my questions.” Public health experts say it could be possible to change the minds of people like Marks with targeted and relentless outreach by trusted members of the community who acknowledge their fears and mistrust of the medical system.

A knock on the door or phone call from an epidemiologist who can explain the science behind vaccinations couldn’t hurt, they added. €œSo many of these people really aren’t treatment hesitant. They’re just trying to figure out the facts for themselves and get their questions answered,” said Oldham of Placer County. But the county can’t afford its own campaign, so Oldham said it “Placerizes” state material, adapting messaging for its residents.

€œWhat we’ve seen from the state, frankly, is a lack of investment and interest in public health,” he said. €œI think it builds trust when you have the resources to call people back and tailor a message, but honestly we don’t really have that capacity.” Santa Clara County has created advertising to persuade residents to get vaccinated.(Santa Clara County Public Health) Some counties have committed scarce funds to develop ads targeting populations among whom distrust runs rampant, an effort they say has helped boost vaccination rates. Santa Clara County, for instance, has plowed at least $8.6 million into an outreach campaign and public service announcements related to erectile dysfunction treatment since March 2020, including Spanish-language ads targeting the county’s large Latino population. Health officer Dr.

Sara Cody said the county has also enlisted the help of local health clinics, nonprofit groups and county employees of various ethnicities to develop messages that might persuade people to get vaccinated. €œWe are extraordinarily fortunate,” Cody said. €œThat investment turned out to be one of the most useful. People do have fears, and we want to hear them.” About 73% of the county’s population is fully vaccinated, while other counties with fewer public health resources, like Placer, have struggled to mount effective campaigns.

There, about 48% of residents are fully vaccinated. treatment canvassers say they are making progress by using personal stories and discussing the science behind the treatments. Ricardo Márquez, a state-funded treatment outreach worker in South Los Angeles, said he has changed minds. €œSometimes facts and science work, but sometimes people who don’t believe change their minds when I tell them people are dying, like my sweet grandma,” Márquez said.

This story was produced by KHN, which publishes California Healthline, an editorially independent service of the California Health Care Foundation. Angela Hart. ahart@kff.org, @ahartreports Related Topics Contact Us Submit a Story TipThe week before Brian Colvin was scheduled for shoulder surgery in November, he tested positive for erectile dysfunction treatment. What he thought at first was a head cold had morphed into shortness of breath and chest congestion coupled with profound fatigue and loss of balance.

Now, seven months have passed and Colvin, 44, is still waiting to feel well enough for surgery. His surgeon is concerned about risking anesthesia with his ongoing respiratory problems, while Colvin worries he’ll lose his balance and fall on his shoulder before it heals. €œWhen I last spoke with the surgeon, he said to let him know when I’m ready,” Colvin said. €œBut with all the symptoms, I’ve never felt ready for surgery.” As the number of people who have had erectile dysfunction treatment grows, medical experts are trying to determine when it’s safe for them to have elective surgery.

In addition to concerns about respiratory complications from anesthesia, erectile dysfunction treatment may affect multiple organs and systems, and clinicians are still learning the implications for surgery. A recent study compared the mortality rate in the 30 days following surgery in patients who had a erectile dysfunction treatment and in those who did not. It found that waiting to undergo surgery for at least seven weeks after a erectile dysfunction treatment reduced the risk of death to that of people who hadn’t been infected in the first place. Patients with lingering erectile dysfunction treatment symptoms should wait even longer, the study suggested.

But, as Colvin’s experience illustrates, such guideposts may be of limited use with a cialis whose effect on individual patients is so unpredictable. €œWe know that erectile dysfunction treatment has lingering effects even in people who had relatively mild disease,” said Dr. Don Goldmann, a professor at Harvard Medical School who is a senior fellow and chief scientific officer emeritus at the Institute for Healthcare Improvement. €œWe don’t know why that is.

But it’s reasonable to assume, when we decide how long we should wait before performing elective surgery, that someone’s respiratory or other systems may still be affected.” The study, published in the journal Anaesthesia in March, examined the 30-day postoperative mortality rate of more than 140,000 patients in 116 countries who had elective or emergency surgery in October. Researchers found that patients who had surgery within two weeks of their erectile dysfunction treatment diagnosis had a 4.1% adjusted mortality rate at 30 days. The rate decreased to 3.9% in those diagnosed three to four weeks before surgery, and dropped again, to 3.6%, in those who had surgery five to six weeks after their diagnosis. Patients whose surgery occurred at least seven weeks after their erectile dysfunction treatment diagnosis had a mortality rate of 1.5% 30 days after surgery, the same as for patients who were never diagnosed with the cialis.

Even after seven weeks, however, patients who still had erectile dysfunction treatment symptoms were more than twice as likely to die after surgery than people whose symptoms had resolved or who never had symptoms. Some experts said seven weeks is too arbitrary a threshold for scheduling surgery for patients who have had erectile dysfunction treatment. In addition to patients’ recovery status from the cialis, the calculus will be different for an older patient with chronic conditions who needs major heart surgery, for example, than for a generally healthy person in their 20s who needs a straightforward hernia repair. €œerectile dysfunction treatment is just one of the things to be taken into account,” said Dr.

Kenneth Sharp, a member of the Board of Regents of the American College of Surgeons and vice chair of the Department of Surgery at Vanderbilt University Medical Center. In December, the American Society of Anesthesiologists and the Anesthesia Patient Safety Foundation issued these guidelines for timing surgery for former erectile dysfunction treatment patients. €¢ Four weeks if a patient was asymptomatic or had mild, non-respiratory symptoms. €¢ Six weeks for a symptomatic patient who wasn’t hospitalized.

€¢ Eight to 10 weeks for a symptomatic patient who has diabetes, is immunocompromised or was hospitalized. €¢ Twelve weeks for a patient who spent time in an intensive care unit. Those guidelines are not definitive, according to the groups. The operation to be performed, patients’ medical conditions and the risk of delaying surgery should all be factored in.

€œLong erectile dysfunction treatment” patients like Colvin who continue to have debilitating symptoms months after 12 weeks have passed require a more thorough evaluation before surgery, said Dr. Beverly Philip, president of the society. Now that erectile dysfunction treatment has been brought to heel in many areas and treatments are widely available, hospital operating rooms are bustling again. €œIn talking to surgical colleagues, hospitals are really busy now,” said Dr.

Avital O’Glasser, medical director of the outpatient preoperative clinic at Oregon Health and Sciences University in Portland. €œI’ve seen patients with delayed knee replacements, bariatric surgery, more advanced cancer.” At the beginning of the cialis, surgical volumes dropped dramatically as many hospitals canceled nonessential procedures and patients avoided facilities packed with erectile dysfunction treatment patients. From March to June 2020, the number of inpatient and outpatient surgeries at U.S. Hospitals was 30% lower than in the same period the year before, according to McKinsey &.

Company’s quarterly Health System Volumes Survey. By May 2021, surgical volumes had mostly rebounded, and were just 2% lower than their May 2019 totals, according to the May survey. Oregon Health and Sciences University clinicians developed a protocol a year ago for clearing any patient who had erectile dysfunction treatment for elective surgery. When obtaining patients’ medical history and conducting physical exams, clinicians look for signs of erectile dysfunction treatment complications that aren’t readily identifiable and determine whether patients have returned to their pre-erectile dysfunction treatment level of health.

The pre-op exam also includes lab and other tests that evaluate cardiopulmonary function, coagulation status, inflammation markers and nutrition, all of which can be disrupted by erectile dysfunction treatment. If the assessment raises no red flags, patients can be cleared for surgery once they have waited the minimum seven weeks since their erectile dysfunction treatment diagnosis. Originally, the minimum wait for surgery was four weeks, but clinicians pushed it back to seven after the international study was published, O’Glasser said. €œWe are still learning about erectile dysfunction treatment, and uncertainty in medicine is one of the biggest challenges we face,” said O’Glasser.

€œRight now, our team is erring on the side of caution.” At Memorial Sloan Kettering Cancer Center in New York, doctors don’t follow a specific protocol. €œWe’re taking every patient one at a time. There are no hard-and-fast rules at this institution,” said Dr. Jeffrey Drebin, chair of surgery.

Clinicians work to find a balance between the urgency of the cancer surgery and the need to allow enough time to ensure erectile dysfunction treatment recovery, he said. For Brian Colvin, whose right rotator cuff is torn, delaying surgery is painful and may worsen the tear. But the rest of his life is on hold, too. A sales representative for an auto parts company, he hasn’t been able to work since he got sick.

His balance problems make him reluctant to stray far from his home in Crest Hill, Illinois, the Chicago suburb where he lives with his wife and 15-year-old son. Some days he has more energy and isn’t as short of breath as others. Colvin hopes it’s a sign he’s slowly improving. But at this point, it’s hard to be optimistic about the cialis.

€œIt’s always something,” he said. Michelle Andrews. andrews.khn@gmail.com, @mandrews110 Related Topics Contact Us Submit a Story Tip.

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The revised Kia Kaha, Kia 10mg or 20mg cialis Māia, Kia Ora Aotearoa. erectile dysfunction treatment Psychosocial and Mental Wellbeing Plan provides a framework for actions to support the mental wellbeing of New Zealanders as we respond to the impacts of erectile dysfunction treatment. The original version of Kia Kaha was published on 16 May 2020. The Ministry invited feedback to inform a new version of the plan and received feedback from almost 150 10mg or 20mg cialis stakeholders. Key changes to the plan include strengthening alignment with Whakamaua.

Māori Health Action Plan 2020-2025 and providing updated information on actual and anticipated impacts of erectile dysfunction treatment on mental wellbeing. The framework in Kia Kaha is intended to support alignment across all organisations nationally and locally that contribute to mental wellbeing. To provide more clarity about national priorities, the new version of Kia Kaha outlines key government initiatives that supported mental wellbeing 10mg or 20mg cialis during 2020, as well as cross-government actions planned through to December 2021. Kia Kaha also provides guidance for organisations during higher erectile dysfunction treatment Alert Levels. Kia Kaha represents the first stage in our longer-term pathway to implement the Government’s response to He Ara Oranga.

Report of the Government Inquiry into Mental Health and Addiction and to transform New Zealand’s approach to mental wellbeing.

The original generic cialis online for sale version of Kia Buy cialis with prescription Kaha was published on 16 May 2020. The Ministry invited feedback to inform a new version of the plan and received feedback from almost 150 stakeholders. Key changes to the plan include strengthening alignment with Whakamaua. Māori Health Action Plan 2020-2025 and providing updated information on actual generic cialis online for sale and anticipated impacts of erectile dysfunction treatment on mental wellbeing. The framework in Kia Kaha is intended to support alignment across all organisations nationally and locally that contribute to mental wellbeing.

To provide more clarity about national priorities, the new version of Kia Kaha outlines key government initiatives that supported mental wellbeing during 2020, as well as cross-government actions planned through to December 2021. Kia Kaha also provides guidance for organisations during higher erectile dysfunction treatment Alert Levels. Kia Kaha represents the first stage in our longer-term pathway to implement the Government’s response generic cialis online for sale to He Ara Oranga. Report of the Government Inquiry into Mental Health and Addiction and to transform New Zealand’s approach to mental wellbeing. This version replaces the previous version of the plan – Kia Kaha, Kia Māia, Kia Ora Aotearoa.

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MIPP reimburses them for their Part B premium because they cialis eli lilly australia have “full Medicaid” (no spend down) but are ineligible for MSP because their income is above the MSP SLIMB level (120% of the Federal Poverty Level (FPL). Even if their income is under the QI-1 MSP level (135% FPL), someone cannot have both QI-1 and Medicaid). Instead, these consumers can have their Part B premium reimbursed through the MIPP program. In this article cialis eli lilly australia.

The MIPP program was established because the State determined that those who have full Medicaid and Medicare Part B should be reimbursed for their Part B premium, even if they do not qualify for MSP, because Medicare is considered cost effective third party health insurance, and because consumers must enroll in Medicare as a condition of eligibility for Medicaid (See 89 ADM 7). There are generally four groups of dual-eligible consumers that are eligible for MIPP. Therefore, many MBI WPD consumers have incomes higher than what MSP normally allows, but still have full Medicaid with no spend down cialis eli lilly australia. Those consumers can qualify for MIPP and have their Part B premiums reimbursed.

Here is an example. Sam is age cialis eli lilly australia 50 and has Medicare and MBI-WPD. She gets $1500/mo gross from Social Security Disability and also makes $400/month through work activity. $ 167.50 -- EARNED INCOME - Because she is disabled, the DAB earned income disregard applies.

$400 - $65 = cialis eli lilly australia $335. Her countable earned income is 1/2 of $335 = $167.50 + $1500.00 -- UNEARNED INCOME from Social Security Disability = $1,667.50 --TOTAL income. This is above the SLIMB limit of $1,288 (2021) but she can still qualify for MIPP. 2 cialis eli lilly australia.

Parent/Caretaker Relatives with MAGI-like Budgeting - Including Medicare Beneficiaries. Consumers who fall into the DAB category (Age 65+/Disabled/Blind) and would otherwise be budgeted with non-MAGI rules can opt to use Affordable Care Act MAGI rules if they are the parent/caretaker of a child under age 18 or under age 19 and in school full time. This is referred to as “MAGI-like budgeting.” Under MAGI rules income can cialis eli lilly australia be up to 138% of the FPL—again, higher than the limit for DAB budgeting, which is equivalent to only 83% FPL. MAGI-like consumers can be enrolled in either MSP or MIPP, depending on if their income is higher or lower than 120% of the FPL.

If their income is under 120% FPL, they are eligible for MSP as a SLIMB. If income is above 120% FPL, then they can enroll in MIPP cialis eli lilly australia. (See GIS 18 MA/001 - 2018 Medicaid Managed Care Transition for Enrollees Gaining Medicare, #4) When a consumer has Medicaid through the New York State of Health (NYSoH) Marketplace and then enrolls in Medicare when she turns age 65 or because she received Social Security Disability for 24 months, her Medicaid case is normally** transferred to the local department of social services (LDSS)(HRA in NYC) to be rebudgeted under non-MAGI budgeting. During the transition process, she should be reimbursed for the Part B premiums via MIPP.

However, the transition time can vary based on age cialis eli lilly australia. AGE 65+ Those who enroll in Medicare at age 65+ will receive a letter from their local district asking them to "renew" Medicaid through their local district. See 2014 LCM-02. The Medicaid case takes about four months cialis eli lilly australia to be rebudgeted and approved by the LDSS.

The consumer is entitled to MIPP payments for at least three months during the transition. Once the case is with the LDSS she should automatically be re-evaluated for MSP, even if the LDSS determines the consumer is not eligible for Medicaid because of excess income or assets. 08 OHIP/ADM-4 cialis eli lilly australia. Consumers UNDER 65 who receive Medicare due to disability status are entitled to keep MAGI Medicaid through NYSoH for up to 12 months (also known as continuous coverage, See NY Social Services Law 366, subd.

4(c). These consumers should receive MIPP payments for as long as their cases cialis eli lilly australia remain with NYSoH and throughout the transition to the LDSS. NOTE during erectile dysfunction treatment emergency their case may remain with NYSoH for more than 12 months. See here.

EXAMPLE cialis eli lilly australia. Sam, age 60, was last authorized for Medicaid on the Marketplace in June 2020. He became enrolled in Medicare based on disability in August 2020, and started receiving Social Security in the same month (he won a hearing approving Social Security disability benefits retroactively, after first being denied disability). Even though his Social Security is cialis eli lilly australia too high, he can keep Medicaid for 12 months beginning June 2020.

Sam has to pay for his Part B premium - it is deducted from his Social Security check. He may call the Marketplace and request a refund. This will continue until the end of his cialis eli lilly australia 12 months of continuous MAGI Medicaid eligibility. He will be reimbursed regardless of whether he is in a Medicaid managed care plan.

See GIS 18 MA/001 Medicaid Managed Care Transition for Enrollees Gaining Medicare (PDF) When that ends, he will renew Medicaid and apply for MSP with his local district. See GIS 18 MA/001 - 2018 Medicaid Managed cialis eli lilly australia Care Transition for Enrollees Gaining Medicare, #4 for an explanation of this process. That directive also clarified that reimbursement of the Part B premium will be made regardless of whether the individual is still in a Medicaid managed care (MMC) plan. Note.

During the erectile dysfunction treatment emergency, those who have Medicaid through the NYSOH cialis eli lilly australia marketplace and enroll in Medicare should NOT have their cases transitioned to the LDSS. They should keep the same MAGI budgeting and automatically receive MIPP payments. See GIS 20 MA/04 or this article on erectile dysfunction treatment eligibility changes 4. Those with Special cialis eli lilly australia Budgeting after Losing SSI (DAC, Pickle, 1619b) Disabled Adult Child (DAC).

Special budgeting is available to those who are 18+ and lose SSI because they begin receiving Disabled Adult Child (DAC) benefits (or receive an increase in the amount of their benefit). Consumer must have become disabled or blind before age 22 to receive the benefit. If the new DAC benefit amount was disregarded and the consumer would otherwise be eligible for SSI, they can cialis eli lilly australia keep Medicaid eligibility with NO SPEND DOWN. See this article.

Consumers may have income higher than MSP limits, but keep full Medicaid with no spend down. Therefore, they are eligible for payment of their cialis eli lilly australia Part B premiums. See page 96 of the Medicaid Reference Guide (Categorical Factors). If their income is lower than the MSP SLIMB threshold, they can be added to MSP.

If higher than the threshold, cialis eli lilly australia they can be reimbursed via MIPP. See also 95-ADM-11. Medical Assistance Eligibility for Disabled Adult Children, Section C (pg 8). Pickle & cialis eli lilly australia.

1619B. 5. When the Part B Premium Reduces Countable Income to Below the Medicaid Limit Since the Part B premium can be used as a deduction from gross income, it may cialis eli lilly australia reduce someone's countable income to below the Medicaid limit. The consumer should be paid the difference to bring her up to the Medicaid level ($904/month in 2021).

They will only be reimbursed for the difference between their countable income and $904, not necessarily the full amount of the premium. See GIS 02-MA-019. Reimbursement of Health Insurance Premiums MIPP and MSP are similar in that they both pay for the Medicare Part B premium, but there are some key differences. MIPP structures the payments as reimbursement -- beneficiaries must continue to pay their premium (via a monthly deduction from their Social Security check or quarterly billing, if they do not receive Social Security) and then are reimbursed via check.

In contrast, MSP enrollees are not charged for their premium. Their Social Security check usually increases because the Part B premium is no longer withheld from their check. MIPP only provides reimbursement for Part B. It does not have any of the other benefits MSPs can provide, such as.

A consumer cannot have MIPP without also having Medicaid, whereas MSP enrollees can have MSP only. Of the above benefits, Medicaid also provides Part D Extra Help automatic eligibility. There is no application process for MIPP because consumers should be screened and enrolled automatically (00 OMM/ADM-7). Either the state or the LDSS is responsible for screening &.

Distributing MIPP payments, depending on where the Medicaid case is held and administered (14 /2014 LCM-02 Section V). If a consumer is eligible for MIPP and is not receiving it, they should contact whichever agency holds their case and request enrollment. Unfortunately, since there is no formal process for applying, it may require some advocacy. If Medicaid case is at New York State of Health they should call 1-855-355-5777.

Consumers will likely have to ask for a supervisor in order to find someone familiar with MIPP. If Medicaid case is with HRA in New York City, they should email mipp@hra.nyc.gov. If Medicaid case is with other local districts in NYS, call your local county DSS. See more here about consumers who have Medicaid on NYSofHealth who then enroll in Medicare - how they access MIPP.

Once enrolled, it make take a few months for payments to begin. Payments will be made in the form of checks from the Computer Sciences Corporation (CSC), the fiscal agent for the New York State Medicaid program. The check itself comes attached to a remittance notice from Medicaid Management Information Systems (MMIS). Unfortunately, the notice is not consumer-friendly and may be confusing.

Some "dual How much renova cost eligible" beneficiaries (people who have Medicare and Medicaid) are entitled to receive reimbursement of their Medicare Part B premiums from New York State through the Medicare Insurance Premium Payment Program (MIPP) generic cialis online for sale. The Part B premium is $148.50 in 2021. MIPP is for some groups who are either not eligible for -- or who are not yet enrolled in-- the Medicare Savings Program (MSP), which is the main program that pays the Medicare Part B premium for low-income people.

Some people are not eligible for an MSP even though they generic cialis online for sale have full Medicaid with no spend down. This is because they are in a special Medicaid eligibility category -- discussed below -- with Medicaid income limits that are actually HIGHER than the MSP income limits. MIPP reimburses them for their Part B premium because they have “full Medicaid” (no spend down) but are ineligible for MSP because their income is above the MSP SLIMB level (120% of the Federal Poverty Level (FPL).

Even if their income is under the QI-1 MSP level (135% FPL), someone cannot have generic cialis online for sale both QI-1 and Medicaid). Instead, these consumers can have their Part B premium reimbursed through the MIPP program. In this article.

The MIPP program was established because the State determined that those who have full Medicaid and Medicare Part B should be reimbursed for their Part B premium, even if they do not qualify for MSP, because Medicare is considered cost effective third party health insurance, and because generic cialis online for sale consumers must enroll in Medicare as a condition of eligibility for Medicaid (See 89 ADM 7). There are generally four groups of dual-eligible consumers that are eligible for MIPP. Therefore, many MBI WPD consumers have incomes higher than what MSP normally allows, but still have full Medicaid with no spend down.

Those consumers can qualify for MIPP and have their Part B premiums generic cialis online for sale reimbursed. Here is an example. Sam is age 50 and has Medicare and MBI-WPD.

She gets $1500/mo gross from Social Security Disability and also makes $400/month through generic cialis online for sale work activity. $ 167.50 -- EARNED INCOME - Because she is disabled, the DAB earned income disregard applies. $400 - $65 = $335.

Her countable earned income is 1/2 of $335 = generic cialis online for sale $167.50 + $1500.00 -- UNEARNED INCOME from Social Security Disability = $1,667.50 --TOTAL income. This is above the SLIMB limit of $1,288 (2021) but she can still qualify for MIPP. 2.

Parent/Caretaker Relatives with MAGI-like Budgeting generic cialis online for sale - Including Medicare Beneficiaries. Consumers who fall into the DAB category (Age 65+/Disabled/Blind) and would otherwise be budgeted with non-MAGI rules can opt to use Affordable Care Act MAGI rules if they are the parent/caretaker of a child under age 18 or under age 19 and in school full time. This is referred to as “MAGI-like budgeting.” Under MAGI rules income can be up to 138% of the FPL—again, higher than the limit for DAB budgeting, which is equivalent to only 83% FPL.

MAGI-like consumers can be enrolled in either MSP or generic cialis online for sale MIPP, depending on if their income is higher or lower than 120% of the FPL. If their income is under 120% FPL, they are eligible for MSP as a SLIMB. If income is above 120% FPL, then they can enroll in MIPP.

(See GIS 18 MA/001 - 2018 Medicaid Managed Care Transition for Enrollees Gaining Medicare, #4) When a consumer has Medicaid through the New York State of Health (NYSoH) Marketplace and then enrolls in Medicare when she generic cialis online for sale turns age 65 or because she received Social Security Disability for 24 months, her Medicaid case is normally** transferred to the local department of social services (LDSS)(HRA in NYC) to be rebudgeted under non-MAGI budgeting. During the transition process, she should be reimbursed for the Part B premiums via MIPP. However, the transition time can vary based on age.

AGE 65+ Those who enroll in Medicare at age 65+ will receive a letter from their local district asking them to "renew" Medicaid generic cialis online for sale through their local district. See 2014 LCM-02. The Medicaid case takes about four months to be rebudgeted and approved by the LDSS.

The consumer is entitled to MIPP payments generic cialis online for sale for at least three months during the transition. Once the case is with the LDSS she should automatically be re-evaluated for MSP, even if the LDSS determines the consumer is not eligible for Medicaid because of excess income or assets. 08 OHIP/ADM-4.

Consumers UNDER 65 who receive Medicare due to disability status are entitled to keep MAGI Medicaid through NYSoH for up to generic cialis online for sale 12 months (also known as continuous coverage, See NY Social Services Law 366, subd. 4(c). These consumers should receive MIPP payments for as long as their cases remain with NYSoH and throughout the transition to the LDSS.

NOTE during erectile dysfunction treatment emergency their case may remain with NYSoH for more than generic cialis online for sale 12 months. See here. EXAMPLE.

Sam, age 60, was last authorized for Medicaid generic cialis online for sale on the Marketplace in June 2020. He became enrolled in Medicare based on disability in August 2020, and started receiving Social Security in the same month (he won a hearing approving Social Security disability benefits retroactively, after first being denied disability). Even though his Social Security is too high, he can keep Medicaid for 12 months beginning June 2020.

Sam has to pay for his Part B premium - it is deducted from his generic cialis online for sale Social Security check. He may call the Marketplace and request a refund. This will continue until the end of his 12 months of continuous MAGI Medicaid eligibility.

He will be reimbursed regardless of whether he is in a generic cialis online for sale Medicaid managed care plan. See GIS 18 MA/001 Medicaid Managed Care Transition for Enrollees Gaining Medicare (PDF) When that ends, he will renew Medicaid and apply for MSP with his local district. See GIS 18 MA/001 - 2018 Medicaid Managed Care Transition for Enrollees Gaining Medicare, #4 for an explanation of this process.

That directive also clarified that reimbursement of the Part B premium will be made regardless of whether the generic cialis online for sale individual is still in a Medicaid managed care (MMC) plan. Note. During the erectile dysfunction treatment emergency, those who have Medicaid through the NYSOH marketplace and enroll in Medicare should NOT have their cases transitioned to the LDSS.

They should generic cialis online for sale keep the same MAGI budgeting and automatically receive MIPP payments. See GIS 20 MA/04 or this article on erectile dysfunction treatment eligibility changes 4. Those with Special Budgeting after Losing SSI (DAC, Pickle, 1619b) Disabled Adult Child (DAC).

Special budgeting is available to those who are 18+ and lose SSI because they begin receiving Disabled Adult Child (DAC) benefits (or generic cialis online for sale receive an increase in the amount of their benefit). Consumer must have become disabled or blind before age 22 to receive the benefit. If the new DAC benefit amount was disregarded and the consumer would otherwise be eligible for SSI, they can keep Medicaid eligibility with NO SPEND DOWN.

See this article generic cialis online for sale. Consumers may have income higher than MSP limits, but keep full Medicaid with no spend down. Therefore, they are eligible for payment of their Part B premiums.

See page 96 generic cialis online for sale of the Medicaid Reference Guide (Categorical Factors). If their income is lower than the MSP SLIMB threshold, they can be added to MSP. If higher than the threshold, they can be reimbursed via MIPP.

See also generic cialis online for sale 95-ADM-11. Medical Assistance Eligibility for Disabled Adult Children, Section C (pg 8). Pickle &.

1619B. 5. When the Part B Premium Reduces Countable Income to Below the Medicaid Limit Since the Part B premium can be used as a deduction from gross income, it may reduce someone's countable income to below the Medicaid limit.

The consumer should be paid the difference to bring her up to the Medicaid level ($904/month in 2021). They will only be reimbursed for the difference between their countable income and $904, not necessarily the full amount of the premium. See GIS 02-MA-019.

Reimbursement of Health Insurance Premiums MIPP and MSP are similar in that they both pay for the Medicare Part B premium, but there are some key differences. MIPP structures the payments as reimbursement -- beneficiaries must continue to pay their premium (via a monthly deduction from their Social Security check or quarterly billing, if they do not receive Social Security) and then are reimbursed via check. In contrast, MSP enrollees are not charged for their premium.

Their Social Security check usually increases because the Part B premium is no longer withheld from their check. MIPP only provides reimbursement for Part B. It does not have any of the other benefits MSPs can provide, such as.

A consumer cannot have MIPP without also having Medicaid, whereas MSP enrollees can have MSP only. Of the above benefits, Medicaid also provides Part D Extra Help automatic eligibility. There is no application process for MIPP because consumers should be screened and enrolled automatically (00 OMM/ADM-7).

Either the state or the LDSS is responsible for screening &. Distributing MIPP payments, depending on where the Medicaid case is held and administered (14 /2014 LCM-02 Section V). If a consumer is eligible for MIPP and is not receiving it, they should contact whichever agency holds their case and request enrollment.

Unfortunately, since there is no formal process for applying, it may require some advocacy. If Medicaid case is at New York State of Health they should call 1-855-355-5777. Consumers will likely have to ask for a supervisor in order to find someone familiar with MIPP.

If Medicaid case is with HRA in New York City, they should email mipp@hra.nyc.gov. If Medicaid case is with other local districts in NYS, call your local county DSS. See more here about consumers who have Medicaid on NYSofHealth who then enroll in Medicare - how they access MIPP.

Is cialis a blood thinner

Another strong is cialis a blood thinner melting event discover this info here struck the ice sheet in mid-August. There had never been such a large melting day so late in the season, according to NSIDC. Then, on Aug.

14, scientists reported a shocking event at the National Science Foundation’s Summit Station, a research outpost perched near the highest point is cialis a blood thinner on the Greenland ice sheet. It was raining. It was the first time in recorded history that rain had ever been observed at the summit, around 2 miles above sea level, where temperatures rarely rise above freezing.

After the mid-August melting event, satellite images and aerial research flights is cialis a blood thinner revealed deep-blue melt ponds scattered widely across the white surface of the ice sheet. €œOn the transit to Kangerlussuaq, we flew over [a] set of massive melt ponds and rivers that had begun to refreeze,” tweeted NASA scientist Josh Willis, shortly after the melt event. €œOur Captain Jim Haffey, who’s flown the ice sheet for 25 years, said it was more melt than he’d ever seen.” Greenland’s biggest melt years on record were 2019 and 2012.

Melt rates were highest in 2012 is cialis a blood thinner. But the total amount of ice loss was higher in 2019, likely because snowfall was unusually low that year. Scientists estimate that the ice sheet lost about 532 billion tons of ice in 2019.

Scientists project is cialis a blood thinner that strong melting events will become more common on the Greenland ice sheet as the Arctic climate continues to warm. That’s a concern for coastal communities all over the world. As ice melts and runs into the ocean, it raises global sea levels.

The snowfall from Larry, while unusual, is a welcome addition to the Greenland ice sheet’s mass balance after such strong melting is cialis a blood thinner earlier this summer. €œGood news for the ice sheet where no significant melt or rainfall is forecasted,” tweeted Xavier Fettweis, a climate scientist at the University of Liège, as the storm approached Greenland over the weekend. €œOnly snow!.

€ Reprinted from E&E News with permission is cialis a blood thinner from POLITICO, LLC. Copyright 2021. E&E News provides essential news for energy and environment professionals.When Decio Eizirik began treating patients with type 1 diabetes in the 1980s, he was pretty sure about what was behind the disease.

An immune system gone is cialis a blood thinner haywire. People with the illness lacked insulin, a crucial hormone, because beta cells in the pancreas—the body’s insulin factories—were being attacked and destroyed by immune system cells. €œAt that time, the idea was that if you could control the immune system, perhaps you could prevent diabetes” says the endocrinologist, who now has research appointments at the Indiana Biosciences Research Institute and at the Free University of Brussels in Belgium.

(He no longer sees patients.) This was the classic model of is cialis a blood thinner an autoimmune disorder. Protector cells that turn on their bodily kin. Although treatments with extra insulin could keep people with diabetes alive, the immune assault on innocent beta cells was the root of the problem.

€œPeople saw beta cells as being like the corpse is cialis a blood thinner at a funeral. It’s the focus of a lot of attention, but it’s doing nothing,” Eizirik recalls. Now, however, those beta cells are not looking quite as innocent, and the immune system is looking like it has gotten an unfair share of blame.

Over the course of several decades Eizirik—and a number of other is cialis a blood thinner researchers—has become convinced that beta cells can actually trigger the disease. The way beta cells do this began to emerge in the late 1990s, when Eizirik measured levels of chemical signals from the cells in the pancreas. Those experiments showed that in certain circumstances the cells produce their own inflammatory chemicals, which act as flares that draw the attention, and ire, of immune system cells.

Exactly what sets off these flares is still not clear—it could be a viral or some kind of damaging stress—but this work and more recent experiments by several other scientists is cialis a blood thinner strongly suggest that beta cells play an active role. €œIt all starts at the target tissue,” says Sonia Sharma, an immunologist at the La Jolla Institute for Immunology in California. €œWhat we know now is that the target tissue is not merely a bystander.

It’s an active participant in the damaging inflammation.” Type 1 diabetes is just one autoimmune disease, but now evidence is starting to suggest that other cellular targets in other ailments also can bring about their own is cialis a blood thinner demise. Recent genetic studies indicate that cells afflicted in rheumatoid arthritis and multiple sclerosis have overactive genes that code for disease-related proteins, and immune cells home in on such targets. Sharma says there could be 10 steps between an initiating event and the ultimate attack on a target tissue by immune system cells.

€œWe’ve been looking at step 10, whereas we should be looking is cialis a blood thinner at steps one, two and three,” she says. €œIt’s almost like we’ve been working backwards.” If researchers could understand those early steps, she says, that could lead to better treatments, cures or even measures to prevent disease. It is hard to fault researchers for concentrating initially on the immune system end.

Autoimmune diseases seem like betrayals by an exquisitely sophisticated defense system that evolved not only is cialis a blood thinner to protect us from invading pathogens but also to monitor cells that threaten to turn cancerous and to clean up the cellular aftermath of an injury. It is the sentinel in our bodies that stands between us and chaos. And clearly, key parts of the immune system, particularly B cells and T cells, are critical players in autoimmune diseases.

Treatments, Eizirik says, will require “a two-hit approach” aimed at these cells is cialis a blood thinner and at their targets. €œThe immune system is persistent, and it has an elephant’s memory,” he says. Once T cells have learned to recognize molecules on these target cells, he says, “they will keep coming.” Agents of Self-Destruction Much research of the past 50 years has focused on a classic hallmark of autoimmune disease.

Autoantibodies. Antibodies are tiny proteins produced by B cells in the immune system, and they bind to proteins called antigens on foreign invaders such as bacteria and cialises. When attached in this way, the antibodies mark such invaders for destruction.

Auto-antibodies, however, bind to so-called self-antigens on the surface of our own cells. There they act as homing beacons for specialized assassins called cytotoxic, or killer, T-cells. These cells are the actual agents of destruction, so scientists investigating autoimmunity look for these T cell–autoantibody pairs.

What scientists have recently learned is that although the killer T cells and autoantibodies are signs of an autoimmune problem, their location seems more important than the mere fact of their existence. Healthy people can have these T cells in their blood, for example, without becoming ill. In 2018 immunologist Roberto Mallone of INSERM in France and his colleagues published a study that compared people with type 1 diabetes, others with the type 2 version of the disease (a nonautoimmune disorder in which insulin is produced but works badly), and people without either disease.

The levels of killer T cells in the bloodstream were remarkably similar across all three groups, including the nondiabetic people. Everyone had them. By this measure, Mallone says, “we are all autoimmune.” But it was a different story in the pancreas.

There, Mallone and his colleagues found, autoreactive T cells were present at much higher levels in people with the type 1 version of the disease. Mallone, like Eizirik before him, suspects that they are there not coincidentally but because of a problem with the target tissue, the beta cells. Another reason researchers are considering target cells as major players in autoimmune diseases comes from genetic studies, which have shown that genes influencing these diseases are expressed not just by immune cells but also by target cells.

Starting in the early 2000s, the complete sequencing of the human genome made it possible to do genome-wide association studies (GWAS), which revealed many genes that, when mutated, were linked to higher risk of autoimmune disorders. And those genes turned up not just in Bcells or T cells but also in cells that were not part of the immune system, Sharma says. For example, nonimmune cells have genes that allow them to release cytokines and chemokines, chemical messengers that summon an immune response.

This activity is quite important for cellular health. All cells are susceptible to transformation into cancers, for instance, or to . When such harmful changes happen to cells, Sharma explains, they need to be able to tell the immune system that they are in trouble.

But mutations in those genes may create apparent distress signals when the cells are not really damaged. The immune system will react as if they are and swoop in. Credit.

David Cheney. Source. €œNew Insights into the Role of Autoreactive CD8 T Cells and Cytokines in Human Type 1 Diabetes,” by Christine Bender, Sakthi Rajendran and Matthias G.von Herrat, in Frontiers in Endocrinology, Vol.

11. 2021 (reference) Signs of Vulnerability A study by Eizirik and his colleagues published this past January in Science Advances provides examples of misleading target cells in multiple autoimmune diseases. The scientists examined published genome association research and found that more than 80 percent of identified genetic variants were expressed by target cells in type 1 diabetes and three other autoimmune diseases.

Multiple sclerosis, lupus and rheumatoid arthritis. The study showed not only that target cells contain disease-related genes but also that in people with disease, they make more of those proteins than in healthy people. Eizirik and his colleagues mined genetic databases created from biopsies of affected tissues from people with autoimmune disease.

Pancreas cells of people with diabetes, joint tissue from people with rheumatoid arthritis, kidney cells from those with lupus and even autopsy samples from the brains of people with multiple sclerosis. Their analysis showed that many candidate genes were exceptionally active in the targeted tissues, and many of these active bits of DNA appeared in multiple diseases, pointing to common threads. Among the top genes showing extra activity were those related to interferons, a class of proinflammatory cytokines that cells release to flag down immune cells when there is a problem such as a viral .

Many of the target cells in autoimmune disease also share nongenetic features that make them exceptionally vulnerable to assault. €œThese cells have at least three intrinsic weaknesses,” Mallone says. First, many of them reside in glands such as the thyroid and pancreas, where “they are hormone factories, pumping out hormones at high rates, which creates a lot of stress.” Because they are already under a lot of strain, a little additional cellular stress could flip the balance toward malfunction and pathology, alerting an immune system cleanup crew.

Second, the cells secrete hormones and other peptides directly into the bloodstream. Such molecules travel throughout the body, which means that, as signatures of these cells, they “can sensitize the immune system from a distance,” Mallone says. A third weakness for target cells is that they are penetrated by lots of blood vessels, making them easily accessible.

€œThis means that once the immune cells are sensitized, they have an easy job to get to [the targets],” he concludes. On top of those vulnerabilities, target cells may react to an outside threat—damage from a cialis, for example—in ways that bring on a strong immune response. Some cells self-destruct when infected by a cialis, taking themselves out before the harm can spread and before immune system intervention is needed.

But certain cells afflicted in autoimmune diseases, such as neurons and beta cells, are in limited supply. Simply dying off after a viral is not an option for them, Eizirik says. €œIf too many cells die, we’re cooked,” he says.

Instead they stick around, and the immune system starts interpreting the molecules they release as signs that all cells of that class are in trouble. Then an autoimmune attack ensues. One striking example of a weakness in target cells that leads to an immune response comes from the blood vessel disease vasculitis.

The disorder is not a classic autoimmune disease, because it does not rely on autoantibodies. Rather it is an example of an autoinflammatory disease in which a cell class known as myeloid immune cells goes after other cells that form arteries, veins and capillaries. A rare, aggressive form in children results from a mutation in a gene for a metabolic enzyme called adenosine deaminase 2.

The enzyme regulates activity in both the attacking cells and the attacked ones, according to a 2020 study led by Sharma and published in Science Advances. €œWhen they lose this enzyme, the whole system becomes deregulated,” Sharma says. €œThe end result is that the target cells start producing cytokines, and this has a bystander effect to activate the myeloid cells.

What we’re talking about is the target cell causing its own problem.” Outside Triggers But even cells with inherent weaknesses do not get into autoimmune trouble all by themselves. Remember that in nondiabetic people, Mallone found T cells that could have assaulted beta cells, but they held their fire. Something tips the balance, initiating events in target tissues that seem to start immune system interference.

Many scientists think that thing is often a passing viral or perhaps exposure to toxic chemicals, and it may occur years before an autoimmune disorder becomes obvious enough to be detected. One long-suspected culprit in type 1 diabetes is the Coxsackie cialis, a common pathogen. It usually causes a mild illness that shows up as passing skin rashes and mouth sores.

But Coxsackie can attack the pancreas under the right circumstances, Mallone says. €œThese cialises can infect beta cells, so they can kill some if there’s enough of a viral load.” That could lead to inflammation that draws more immune cells to the place where beta cells are dying. In their death throes, the betas could release signature self-antigens that sensitize nearby immune cells, causing them to go after other beta cells, because such cells have similar antigen signatures.

That multipart mix is crucial, Mallone says. €œBasically, you need three ingredients. Self-antigen, an inflammatory environment and autoimmune predisposition,” he says.

€œAnd these ingredients have to meet at the same place and the same time. This is probably one reason it’s so difficult to identify environmental triggers. Because we’re all exposed, but it depends on specific conditions.” This view is replacing an older idea.

That cialises trigger autoimmune reactions when the viral proteins look, molecularly, a lot like self-antigens, leading immune cells to get confused by the similarity and attack the self. Support for this idea, called viral mimicry, began to crumble as researchers amassed evidence that such molecular doppelgängers are fairly common but very rarely cause disease. There are a number of molecules in human bodies and infectious agents that look like one another, and they are called cross-reactive.

€œCross-reactivity is extremely abundant. You can find it everywhere,” says DeLisa Fairweather, an immunologist at the Mayo Clinic in Jacksonville, Fla. If cross-reactivity led to illness, she says, “we should see diseases at higher levels.

It’s not the answer.” Thus, the idea has gained currency that a cialis kills some target cells and creates some inflammation, and in the middle of all this, some immune cells become sensitized to the dying cells’ proteins. A Rising Count Other irritants from outside the body, such as drugs and other chemicals, can create these inflammatory conditions, providing more occasions for encounters with immune system sentinels to go wrong. Some scientists think encounters with such substances can explain a spike in autoimmune disease frequency over the past few decades.

In 2020 rheumatologist Frederick Miller of the National Institute of Environmental Health Sciences and his colleagues published an analysis that tracked the prevalence of antinuclear antibodies, a subset of autoantibodies that go after proteins in a cell’s nucleus. The study followed more than 14,000 participants in the U.S. Over a 25-year period.

Between 1988 and 1991, 11 percent of those tested carried the antibodies. That number stayed roughly stable through 2004, with a small rise toward the end of that period. But by 2012 the data showed a big jump in the number of people carrying the antibodies, to nearly 16 percent of participants.

The rise was particularly striking in adolescents, Miller says, “which to me was the scariest thing.” That could indicate a coming wave of autoimmune diseases. What has changed to cause the increase?. “We don’t know yet,” Miller says.

He can, however, rattle off a number of possible environmental and behavioral factors. During the time span of his study, approximately 80,000 to 90,000 new chemicals have been approved for use, he says. €œWe have a completely different diet,” he continues.

€œOur use of electronics, while handy and useful, has also meant we’re not getting enough sleep.” People have also encountered increases in air, water and food pollution. €œThere are hundreds of differences in our lifestyle and exposure in the past 30 years,” Miller says. Another, somewhat paradoxical idea is that our immune systems now get too little exposure to the outside world and consequently overreact when they encounter relatively benign molecular representatives from it.

The theory is related to a notion called the hygiene hypothesis, put forth in the early 2000s, which was based on changes to sanitary conditions. This iteration is more closely tied to changes in our intestinal bacteria, our gut microbiome, that come with the habits of modern society. A quirk of geopolitics has presented a unique opportunity to study this effect.

After World War II, a region in northeastern Europe called Karelia was split into Finnish and Russian territories. The populations are genetically similar, but Finnish Karelia rapidly modernized after the war, whereas living conditions in rural Russian Karelia remained similar to those of 60 years ago. You might think an improvement in living conditions would reduce the burden of disease, but that has not happened with autoimmune illnesses.

In fact, the reverse effect has been observed. The incidence of type 1 diabetes in Finland is the highest in the world and about six times that in Russian Karelia. Rates of other autoimmune diseases such as celiac disease are also six to 10 times higher in Finland compared with Russia.

Mikael Knip of the University of Helsinki and his colleagues think these changes in disease prevalence can be tied to changes in the microbiome in the Karelian populations. Our internal ecosystem of gut bacteria becomes established during infancy and is heavily influenced by our surroundings. For a 2016 study published in Cell, Knip’s team collected stool samples from infants on both sides of the Finnish-Russian border for the first three years of their lives.

€œWhen we analyzed the data, we did see a clear difference between the infants in Finnish and Russian Karelia,” he says. The microbes in Russian children were dominated by a nonpathogenic form of Escherichia coli. Finnish children, in contrast, were home to high levels of a bacterial genus called Bacteroides, which typically does not prompt a strong immune reaction.

€œExposure to various microbes in the environment has an effect on training the immune system, particularly in the first year of life,” Knip says, and it looks as if the Finnish systems did not get very rigorous training. The Finnish microbiomes also lacked the variety seen among the Russians. Although Knip emphasizes that it is too soon to cement a cause-effect relation between any drop in microbiome diversity on the Finnish side and the rise in autoimmune problems, he does think there is a connection.

€œI’d say we need to rename the hygiene hypothesis to the biodiversity hypothesis,” Knip says. Sharma agrees that gut biodiversity is important, and exposure to variety—for example, by eating nonprocessed foods or at least much less heavily processed versions—is key for training the immune system. €œThat makes our gut flora more abundant and more diverse,” she says.

And it gives our immune system a chance to get used to molecules that are not inherently dangerous so that it does not overreact when it encounters them. Ultimately a better understanding of the causes of autoimmune diseases—and improved treatments for them—will come from an approach that is quite different from narrow studies of immune cells or target tissues or the microbiome, Miller says. It will come from a more holistic view.

Much like in the old Indian parable, he says, “everyone’s looking [at autoimmunity] like the blind men feeling around the elephant, where every person is seeing different things, and they’re not able to connect these to the whole.” Seeing the entire immunological picture will require more studies on different types of biomolecular dynamics, and that research will have to be done in large populations of people. Such an approach could amount to “millions of data points,” Miller says. €œWe need to embrace the complexity.”Struggles with mental ill-health are the world’s leading cause of disability.

Beset by the erectile dysfunction cialis, underresourced mental health systems have strained to keep up. But access to care is limited by three major obstacles. A dearth of professional care providers, embedded stigma surrounding mental health problems and a distrust of institutions.

The scenario is by no means uniformly dire. Both the public and private sectors have demonstrated a willingness to promote change. Innovative programs show promise for improving efficient access to care, whether a community’s financial resources are large or small.

They combine the latest science with digital delivery of information and services and collaborative efforts among people with mental health challenges, professionals and the community at large. Digital care options through teletherapy and all manner of new apps have seen explosive growth during the cialis. Online services reach the most remote regions and circumvent fears of stigma for making the decision to seek treatment.

They can effectively extend the capacity of health and social services. But they cannot overcome the scarcity of professional therapists. The dearth of providers who coordinate care means that even app-based teletherapy confronts challenges in reaching people in need.

One solution is to bolster peer and community support to extend the effectiveness and reach of in-person and online mental health care. A major development has seen people with mental illnesses help others by providing peer support to show that they are not alone in their struggles with mental health. People confronting mental health issues assist recovery by building trust among their peers with similar experiences.

Care teams made up of peers lead group discussions and serve as coaches for others experiencing mental challenges. Training and support for community health workers also help. Community health workers are lay members of a community tasked with providing basic health care, including prevention, health promotion and rehabilitation services, thereby extending care to more people in need worldwide.

Research has begun to show the effectiveness of these approaches even when delivered online. Public and private sectors in several countries have developed programs combining these approaches. Online mental health support and services such as Togetherall, ReachOut, 7 Cups and UCLA STAND, often co-designed and advised by community peers, have become trusted sources of help and referral for young people, their families and others in distress and coping with mental ill-health.

A public-private partnership, Strong 365’s NYWell is a digital outreach pilot project to assist young people facing the onset of serious mental illness. NYWell’s search engine and social media ads link to a Web site that provides assistance ranging from self-education and online peer support to more intensive professional care. The site has attracted thousands of visitors from the time of its launch in New York State in November 2020.

About half of visitors take a self-administered mental health screening test. One in 10 connect online with a peer or therapist, and one in five of those are referred to care in the community. The program is expanding, and a randomized controlled trial has begun to measure its effectiveness.

Early findings indicate that youth facing serious mental illness are willing to engage in what is called tiered online care, ranging from peer interactions to sessions with professional therapists. Continued progress will require collaboration among people with mental illness, community workers, mental health and technology professionals, public and private sector leaders, and others. The programs show promise, however, of furnishing a breakthrough in care for people wherever they are.

This is an opinion and analysis article, and the views expressed by the author or authors are not necessarily those of Scientific American.On a crisp fall New England day during my junior year of college, I was walking past a subway entrance when a math problem caught my eye. A man was standing near a few brainteasers he had scribbled on the wall, one of which asked for the construction, with an imaginary straightedge and compass, of a cube with a volume twice that of a different, given cube. This stopped me in my tracks.

I had seen this problem before. In fact, the challenge is more than two millennia old, attributed to Plato by way of Plutarch. A straightedge can be used to extend a line segment in any direction, and a compass can be used to draw a circle with any radius from the chosen center.

The catch for this particular puzzle is that any points or lengths appearing in the final drawing must have been either present at the start or constructable from previously provided information. To double a cube’s volume, you start with its side length. Here that value might as well be 1 because it is the only unit of measurement given.

To construct the larger cube, you have to figure out a way to draw one of its sides with the new required length, which is ∛2 (the cube root of two), using just the straightedge and compass as tools. It is a tough problem. For more than 2,000 years no one managed to solve it.

Finally, in 1837, Pierre Laurent Wantzel explained why no one had succeeded by proving that it was impossible. His proof used cutting-edge mathematics of the time, the foundations of which were laid by his French contemporary Évariste Galois, who died at 20 in a duel that may have involved an unhappy love affair. At the ripe old age of 20 myself, I had achieved considerably less impressive mathematical accomplishments, but I at least understood Wantzel’s proof.

Here is the idea. Given a point as the origin and a length of distance 1, it is relatively straightforward to use the straightedge and compass to construct all points on a number line whose coordinates are rational numbers (ignoring, as mathematicians tend to do, the impossibility of actually plotting infinitely many points in only a finite amount of time). Wantzel showed that if one uses only these tools, each newly constructed point must be a solution to a quadratic polynomial equation ax2+ bx + c = 0 whose coefficients a, b and c are among the previously constructed points.

In contrast, the point ∛2 is a solution to the cubic polynomial x3 2 = 0, and Galois’s theory of “field extensions” proves decisively that you can never get the solution to an irreducible cubic polynomial by solving quadratic equations, essentially because no power of 2 evenly divides the number 3. Credit. Matteo Farinella Armed with these facts, I could not restrain myself from engaging with the man on the street.

Predictably, my attempt to explain how I knew his problem could not be solved did not really go anywhere. Instead he claimed that my education had left me closed-minded and unable to “think outside the box.” Eventually my girlfriend managed to extricate me from the argument, and we continued on our way. But an interesting question remains.

How was I, a still-wet-behind-the-ears undergraduate in my third year of university study, able to learn to comfortably manipulate abstract number systems such as Galois’s fields in just a few short weeks?. This material came at the end of a course filled with symmetry groups, polynomial rings and related treasures that would have blown the minds of mathematical giants such as Isaac Newton, Gottfried Leibniz, Leonhard Euler and Carl Friedrich Gauss. How is it that mathematicians can quickly teach every new generation of undergraduates discoveries that astonished the previous generation’s experts?.

Credit. Matteo Farinella Part of the answer has to do with recent developments in mathematics that provide a “birds-eye view” of the field through ever increasing levels of abstraction. Category theory is a branch of mathematics that explains how distinct mathematical objects can be considered “the same.” Its fundamental theorem tells us that any mathematical object, no matter how complex, is entirely determined by its relationships to similar objects.

Through category theory, we teach young mathematicians the latest ideas by using general rules that apply broadly to categories across mathematics rather than drilling down to individual laws that apply only in a single area. As mathematics continues to evolve, mathematicians’ sense of when two things are “the same” has expanded. In the past few decades many other researchers and I have been working on an extension of category theory to make sense of this new expanded notion of uniqueness.

These new categories, called infinity categories (∞-categories), broaden category theory to infinite dimensions. The language of ∞-categories gives mathematicians powerful tools to study problems in which relations between objects are too nuanced to be defined in traditional categories. The perspective of “zooming out to infinity” offers a novel way to think about old concepts and a path toward the discovery of new ones.

Categories Like many other mathematicians I know, I was drawn into the subject partly because of my poor memory. This confounds many people who remember high school mathematics as rife with formulas to memorize—the trigonometric identities come to mind. But I took comfort in the fact that the most commonly used formulas could be rederived from sin2θ + cos2θ = 1, which itself has an elegant geometric explanation.

It is an application of the Pythagorean theorem to a right triangle with a hypotenuse of length 1 and an acute angle of θ degrees. This utopian vision of mathematics where everything just “makes sense” and nothing needs to be memorized falls apart to some extent at the university level. At that point students get to know the zoo of mathematical objects that have been conjured into existence in the past few centuries.

€œGroups,” “rings” and “fields” belong to an area of mathematics known as algebra, a word derived from a ninth-century book by Persian mathematician and astronomer Muhammad ibn Musa al-Khwarizmi, the title of which is sometimes translated as The Science of Restoring and Balancing. Over the next millennium, algebra evolved from the study of the nature of solutions to polynomial equations to the study of abstract number systems. Because no real number x satisfies the equation x2+ 1 = 0, mathematicians built a new number system—now known as the complex numbers—by adding an imaginary number i and imposing the stipulation that i2 + 1= 0.

Algebra is only one of the subjects in a mathematics undergraduate’s curriculum. Other cornerstones include topology—the abstract study of space—and analysis, which begins with a rigorous treatment of the calculus of real functions before branching into the more exotic terrains of probability spaces and random variables and complex manifolds and holomorphic functions. How is a student supposed to make sense of it all?.

Credit. Matteo Farinella A paradoxical idea in mathematics is that of simplification through abstraction. As Eugenia Cheng puts it in The Art of Logic in an Illogical World, “a powerful aspect of abstraction is that many different situations become the same when you forget some details.” Modern algebra was created in the early 20th century when mathematicians decided to unify their studies of the many examples of algebraic structure that arose in the consideration of solutions to polynomial equations or of configurations of figures in the plane.

To connect investigations of these structures, researchers identified “axioms” that describe their common properties. Groups, rings and fields were introduced to the mathematical universe, along with the idea that a mathematical object could be described in terms of the properties it has and explored “abstractly,” independently of the scaffolding of particular examples or constructions. John Horton Conway famously pondered the curious ontology of mathematical things.

€œThere’s no doubt that they do exist but you can’t poke and prod them except by thinking about them. It’s quite astonishing and I still don’t understand it, despite having been a mathematician all my life. How can things be there without actually being there?.

€ But this world of mathematical objects that can exist without actually being there created a problem. Such a world is vastly too large for any person to comprehend. Even within algebra, there are just too many mathematical things to study for there to be time to make sense of them all.

Around the turn of the 20th century, mathematicians began to investigate so-called universal algebra, referring to a “set,” which could be a collection of symmetries, of numbers in some system or something else entirely, together with various operations—for instance, addition and multiplication—satisfying a list of relevant axioms such as associativity, commutativity or distributivity. By making different choices—Is an operation partially or totally defined?. Is it invertible?.

€”one arrives at the standard algebraic structures. The groups, rings and fields. But the subject is not constrained by these choices, which represent a vanishingly small portion of an infinite array of possibilities.

Credit. Matteo Farinella The proliferation of new abstract mathematical objects brings its own complexity. One way to simplify is to introduce a further level of abstraction where, astonishingly, we can prove theorems about a wide variety of mathematical objects simultaneously without specifying exactly what kinds of objects we are talking about.

Category theory, which was created in the 1940s by Samuel Eilenberg and Saunders Mac Lane, does just this. Although it was originally introduced to give a rigorous definition of the colloquial term “natural equivalence,” it also offers a way to think universally about universal algebra and other areas of mathematics as well. With Eilenberg and Mac Lane’s language, we can now understand that every variety of mathematical object belongs to its own category, which is a specified collection of objects together with a set of transformations depicted as arrows between the objects.

For example, in linear algebra one studies abstract vector spaces such as three-dimensional Euclidean space. The corresponding transformations in this case are called linear transformations, and each must have a specified source and target vector space indicating which kinds of vectors arise as inputs and outputs. Like functions, the transformations in a category can be “composed,” meaning you can apply one transformation to the results of another transformation.

For any pair of transformations f. A → B (read as “f is a transformation from A to B”) and g. B → C, the category specifies a unique composite transformation, written as g ∘f.

A → C (read as “g composed f is a transformation from A to C”). Finally, this composition law is associative, meaning h ∘(g ∘f) = (h ∘g) ∘f. It is also unital.

Each object B has an “identity transformation” commonly denoted by 1Bwith the property that g ∘1B= g and 1B∘f = f for any transformations g and f whose source and target, respectively, equal B. How do categories help the hapless undergraduate confronted with too many mathematical objects and not enough time to learn about them all?. Any class of structures you can define in universal algebra may be distinct from all others, but the categories these objects inhabit are very similar in ways that can be expressed precisely through categorical language.

With sufficient experience, mathematicians can know what to expect when they encounter a new type of algebraic structure. This idea is reflected in modern textbooks on the subject that develop the theories of groups, rings and vector spaces in series, essentially because the theories are parallel. There are other, looser analogies among these categories and the ones students encounter in topology or analysis courses, and these similarities enable them to absorb the new material more quickly.

Such patterns allow students to spend more time exploring the special topics that distinguish individual mathematical subdisciplines—although research advances in mathematics are often inspired by new and surprising analogies between previously unconnected areas. Symmetries The cascading levels of abstraction, from concrete mathematical structures to axiomatic systems and then beyond to the general objects that belong to categories, present a new challenge. It is no longer very clear what it means to say that one thing is “the same” as another thing.

Consider, for instance, a group, which in math is an abstract collection of symmetries whose elements Amie Wilkinson of the University of Chicago likes to describe as “moves” that flip or rotate an object before settling it into something like the original position. For example, we might explore the symmetries of a T-shirt. One symmetry can be thought of as the “identity move,” where a person simply wears the T-shirt as it is usually worn.

Another symmetry corresponds to a move where the wearer takes their arms out of the arm holes and, with the T-shirt still around their neck, rotates the shirt 180 degrees to put their arms in the opposite holes. The T-shirt remains right-side out but is now being worn backward. Another symmetry corresponds to a move where the T-shirt is removed entirely, flipped inside out and put back on in such a way that each arm goes through the hole it was originally in.

The T-shirt is now inside out and backward. A final symmetry combines these two moves. Atypically for groups, these moves can be performed in any order without changing the end result.

Each of these four moves counts as a “symmetry” because they result in the shirt being worn in essentially the same way as when you started. Credit. Matteo Farinella Another group is the “mattress-flipping group,” which describes the symmetries of a mattress.

In addition to the identity move, which applies when the mattress is left in its original position, a person can move the mattress by rotating it top to bottom, flipping back to front or performing both moves in sequence. (Mattresses typically are not square, but if they were, there would be more symmetries than described here.) Although a T-shirt does not have much to do with a mattress, there is a sense in which the two symmetry groups have the same “shape.” First, both groups of symmetries have the same number of moves (in this case, four), and, crucially, you can pair each move in the T-shirt group with a move in the mattress-flipping group such that the compositions of corresponding moves also correspond. In other words, you can match up moves from the two groups (match the identity with the identity, the flip with the flip, the rotation with the rotation, and so on).

Second, if you take two moves from one group and perform them in sequence, the final position will match with the end result of performing the corresponding moves from the other group in sequence. In technical terms, these groups are connected by an “isomorphism,” a term whose etymology—from the Greek isos, meaning “equal,” and morphe, meaning “form”—indicates its meaning. We can define the notion of isomorphism in any category, which allows us to transport this concept between mathematical contexts.

An isomorphism between two objects A and B in a category is given by a pair of transformations, f. A → B and g. B → A, with the property that the composites g ∘f and f ∘g equal the respective identities 1Aand 1B.

In the category of topological spaces, the categorical notion of isomorphism is represented by an inverse pair of continuous functions. For instance, there is a continuous deformation that would allow you to convert an unbaked doughnut into a shape like a coffee mug. The doughnut hole becomes the handle, and the cup is formed by a depression you make with your thumb.

(For the deformation to be continuous, you must do this without tearing the dough, which is why the doughnut should not be baked before the experiment is attempted.) This example inspired the joke that a topologist cannot tell the difference between a coffee mug and a doughnut. As abstract spaces, these objects are the same. In practice, many topologists are arguably much less observant than this because it is common to adopt a more flexible convention concerning situations when two spaces are “the same,” identifying any two spaces that are merely “homotopy-equivalent.” This term refers to the notion of isomorphism in the more exotic homotopy category of spaces.

A homotopy equivalence is another type of continuous deformation, but in this case, you can identify distinct points. For instance, imagine starting with a pair of pants and then shrinking the lengths of the legs until you are left with a G-string, another “space” with the same fundamental topological structure—there are still two holes for legs—even though the original two-dimensional garment has been shrunk down to a one-dimensional bit of string. Credit.

Matteo Farinella Another homotopy equivalence collapses the infinite expanse of three-dimensional Euclidean space down to a single point via a “reverse big bang” in which each point flies back to its origin, with the speed of this motion increasing with the distance from the location of the initial big bang. The intuition that we can substitute isomorphic things for one another without fundamentally changing the nature of a construction or an argument is so strong that in fact category theorists have redefined the word “the” to mean something closer to “a” in colloquial English. For example, there is a concept known as the disjoint union of two sets A and B.

Like the ordinary union, the disjoint union A ⨆ B has a copy of every element of A and a copy of every element of B. Unlike in the ordinary union, however, if A and B have an element in common, then the disjoint union A ⨆ B has two copies of that element, one of which somehow remembers that it came from A, and the other somehow remembers it came from B. There are many different ways to construct the disjoint union using the axioms of set theory, which will not produce exactly the same set but will, necessarily, produce isomorphic ones.

Rather than wasting time arguing about which construction is the most canonical, it is more convenient to just sweep this ambiguity under the rug and refer to “the” disjoint union when one means to consider any particular set that satisfies the desired universal property. In another example, mathematicians refer to both the T-shirt symmetry group and the mattress-flipping group as “the Klein four-group.” Infinite-Dimensional Categories An oft-told story about the origin of the fundamental theorem of category theory is that a young mathematician named Nobuo Yoneda described a “lemma,” or helper theorem, to Mac Lane at the Gare du Nord train station in Paris in 1954. Yoneda began explaining the lemma on the platform and continued it on the train before it departed the station.

The consequence of this lemma is that any object in any category is entirely determined by its relation to the other objects in the category as encoded by the transformations to or from this object. So we can characterize a topological space X by probing it with continuous functions f. T → X mapping out other spaces T.

For instance, the points of the space X correspond to continuous functions x. * → X, whose domain is a space with a single point. We can answer the question of whether the space X is connected or disconnected by considering mappings p.

I → X, whose domain is an interval I = [0,1]. Each such mapping defines a parameterized “path” in the space X from the point p(0) to the point p(1), which can be thought of as a possible trajectory an ant might take when walking around the space X. We can use the points and paths of a space to translate problems of topology into problems of algebra.

Each topological space X has an associated category π1X called the “fundamental groupoid” of X. The objects of this category are the points of the space, and the transformations are paths. If one path can be deformed into another in the space while its end points remain fixed, the two paths define the same transformation.

These deformations, which are technically called homotopies, are necessary for the composition of paths to define an associative operation, as is required by a category. Credit. Matteo Farinella A key advantage of the fundamental groupoid construction is that it is “functorial,” meaning that a continuous function f.

X → Y between topological spaces gives rise to a corresponding transformation π1f. π1X → π1Y between the fundamental groupoids. This assignment respects composition and identities, meaning π1(g f) = π1g π1f and π1(1X) = 1π1X, respectively.

These two properties, which collectively go by the name “functoriality,” suggest that the fundamental group captures some essential information about topological spaces. In particular, if two spaces are not homotopy-equivalent, then their fundamental groupoids are necessarily inequivalent. The fundamental groupoid is not a complete invariant, however.

It can easily distinguish between a circle and the solid disk that circle bounds. In the fundamental groupoid of the circle, the different wiggling versions of a path between two points can be labeled by integers that record the number of times the trajectory winds around the circle and a + or sign indicating, respectively, a clockwise or counterclockwise direction of transit. In contrast, in the fundamental groupoid of the disk, there is only one path up to homotopy between any pair of points.

The fundamental groupoid of the space formed by the inflatable exterior of a beach ball, a sphere in topological terms, also has this description. There is a unique path up to homotopy between any two points. Credit.

Matteo Farinella The big problem with the fundamental groupoid is that points and paths do not detect the higher-dimensional structure of a space, because the point and interval are themselves zero- and one-dimensional, respectively. A solution is to also consider continuous functions from the two-dimensional disk, called homotopies, and “higher homotopies,” defined by continuous functions from the solid three-dimensional ball and similarly for other balls in 4, 5, 6 or more dimensions. It is natural to ask what kind of algebraic structure the points, paths, homotopies and higher homotopies in a space X form.

This structure π ∞ X (“pi infinity X”), referred to as the fundamental ∞-groupoid of X, defines an example of an -category, an infinite-dimensional analogue of the categories first introduced by Eilenberg and Mac Lane. Like an ordinary category, an ∞-category has objects and transformations visualized as one-dimensional arrows, but it also contains “higher transformations” depicted by two-dimensional arrows, three-dimensional arrows, and so on. For example, in π ∞ X the objects and arrows are the points and the paths—no longer considered up to wiggling—while the higher-dimensional transformations encode the higher homotopies.

Like in an ordinary category, the arrows in any fixed dimension can be composed. If you have two arrows f. X Y and g.

Y Z, there must also be an arrow g f. X Z. But there is a catch.

In attempts to capture natural examples such as the fundamental ∞-groupoid of a space, the composition law must be weakened. For any composable pair of arrows, there must exist a composite arrow, but there is no longer a unique specified composite arrow. Credit.

Matteo Farinella This failure of uniqueness makes it challenging to define ∞-categories in the classical set-based foundations of mathematics because we can no longer think of composition as an operation resembling those appearing in universal algebra. Although ∞-categories are increasingly central to modern research in many areas of mathematics, from quantum field theory to algebraic geometry to algebraic topology, they are often considered “too hard” for all but specialists and are not featured regularly in curricula, even at the graduate level. Nevertheless, many others and I see ∞-categories as a revolutionary new direction that can enable mathematicians to dream of new connections that would otherwise have been impossible to rigorously state and prove.

A Quick Guide to Modern Math Terminology Category. A specified collection of objects and transformations between them, with a composition rule Composition. To apply one transformation to the results of another Identity.

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Above-average temperatures, coupled with a low-pressure system that helped drive warm air over southern Greenland, caused two back-to-back melting events across the ice sheet in the second half of July. Scientists estimated that 12.5 billion tons of ice melted and ran off the ice sheet in a single day, on July 28. That’s the third largest one-day melting event generic cialis online for sale in recorded history, topped only by similar events in 2019 and 2012. Another strong melting event struck the ice sheet in mid-August.

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Melt rates were highest in 2012. But the total amount of ice loss was higher in 2019, likely because snowfall was unusually low that year. Scientists estimate that the ice generic cialis online for sale sheet lost about 532 billion tons of ice in 2019. Scientists project that strong melting events will become more common on the Greenland ice sheet as the Arctic climate continues to warm.

That’s a concern for coastal communities all over the world. As ice melts and runs into the ocean, it raises global sea levels generic cialis online for sale. The snowfall from Larry, while unusual, is a welcome addition to the Greenland ice sheet’s mass balance after such strong melting earlier this summer. €œGood news for the ice sheet where no significant melt or rainfall is forecasted,” tweeted Xavier Fettweis, a climate scientist at the University of Liège, as the storm approached Greenland over the weekend.

€œOnly snow! generic cialis online for sale. € Reprinted from E&E News with permission from POLITICO, LLC. Copyright 2021. E&E News provides essential news for energy and environment professionals.When Decio Eizirik began treating patients with type 1 diabetes in the 1980s, he was pretty sure about what was behind the disease generic cialis online for sale.

An immune system gone haywire. People with the illness lacked insulin, a crucial hormone, because beta cells in the pancreas—the body’s insulin factories—were being attacked and destroyed by immune system cells. €œAt that time, the idea was that if you could control the generic cialis online for sale immune system, perhaps you could prevent diabetes” says the endocrinologist, who now has research appointments at the Indiana Biosciences Research Institute and at the Free University of Brussels in Belgium. (He no longer sees patients.) This was the classic model of an autoimmune disorder.

Protector cells that turn on their bodily kin. Although treatments with extra insulin could keep people with diabetes alive, the immune assault on innocent beta cells was the root generic cialis online for sale of the problem. €œPeople saw beta cells as being like the corpse at a funeral. It’s the focus of a lot of attention, but it’s doing nothing,” Eizirik recalls.

Now, however, those beta cells are not looking quite as innocent, and the immune system is looking like it generic cialis online for sale has gotten an unfair share of blame. Over the course of several decades Eizirik—and a number of other researchers—has become convinced that beta cells can actually trigger the disease. The way beta cells do this began to emerge in the late 1990s, when Eizirik measured levels of chemical signals from the cells in the pancreas. Those experiments showed that generic cialis online for sale in certain circumstances the cells produce their own inflammatory chemicals, which act as flares that draw the attention, and ire, of immune system cells.

Exactly what sets off these flares is still not clear—it could be a viral or some kind of damaging stress—but this work and more recent experiments by several other scientists strongly suggest that beta cells play an active role. €œIt all starts at the target tissue,” says Sonia Sharma, an immunologist at the La Jolla Institute for Immunology in California. €œWhat we know now is that the target tissue is not merely a bystander generic cialis online for sale. It’s an active participant in the damaging inflammation.” Type 1 diabetes is just one autoimmune disease, but now evidence is starting to suggest that other cellular targets in other ailments also can bring about their own demise.

Recent genetic studies indicate that cells afflicted in rheumatoid arthritis and multiple sclerosis have overactive genes that code for disease-related proteins, and immune cells home in on such targets. Sharma says there could be generic cialis online for sale 10 steps between an initiating event and the ultimate attack on a target tissue by immune system cells. €œWe’ve been looking at step 10, whereas we should be looking at steps one, two and three,” she says. €œIt’s almost like we’ve been working backwards.” If researchers could understand those early steps, she says, that could lead to better treatments, cures or even measures to prevent disease.

It is hard to fault researchers for concentrating initially on generic cialis online for sale the immune system end. Autoimmune diseases seem like betrayals by an exquisitely sophisticated defense system that evolved not only to protect us from invading pathogens but also to monitor cells that threaten to turn cancerous and to clean up the cellular aftermath of an injury. It is the sentinel in our bodies that stands between us and chaos. And clearly, key parts of the immune generic cialis online for sale system, particularly B cells and T cells, are critical players in autoimmune diseases.

Treatments, Eizirik says, will require “a two-hit approach” aimed at these cells and at their targets. €œThe immune system is persistent, and it has an elephant’s memory,” he says. Once T cells have learned to recognize molecules on these target cells, he says, “they will keep coming.” Agents of Self-Destruction Much research of the past 50 years generic cialis online for sale has focused on a classic hallmark of autoimmune disease. Autoantibodies.

Antibodies are tiny proteins produced by B cells in the immune system, and they bind to proteins called antigens on foreign invaders such as bacteria and cialises. When attached in this way, the antibodies mark such invaders for generic cialis online for sale destruction. Auto-antibodies, however, bind to so-called self-antigens on the surface of our own cells. There they act as homing beacons for specialized assassins called cytotoxic, or killer, T-cells.

These cells generic cialis online for sale are the actual agents of destruction, so scientists investigating autoimmunity look for these T cell–autoantibody pairs. What scientists have recently learned is that although the killer T cells and autoantibodies are signs of an autoimmune problem, their location seems more important than the mere fact of their existence. Healthy people can have these T cells in their blood, for example, without becoming ill. In 2018 immunologist Roberto Mallone of INSERM in France and his colleagues published a study that compared people with type 1 diabetes, others with the type 2 generic cialis online for sale version of the disease (a nonautoimmune disorder in which insulin is produced but works badly), and people without either disease.

The levels of killer T cells in the bloodstream were remarkably similar across all three groups, including the nondiabetic people. Everyone had them. By this measure, Mallone says, “we are all generic cialis online for sale autoimmune.” But it was a different story in the pancreas. There, Mallone and his colleagues found, autoreactive T cells were present at much higher levels in people with the type 1 version of the disease.

Mallone, like Eizirik before him, suspects that they are there not coincidentally but because of a problem with the target tissue, the beta cells. Another reason researchers are considering target cells as major players in autoimmune diseases comes from genetic studies, which have shown that genes influencing these diseases are generic cialis online for sale expressed not just by immune cells but also by target cells. Starting in the early 2000s, the complete sequencing of the human genome made it possible to do genome-wide association studies (GWAS), which revealed many genes that, when mutated, were linked to higher risk of autoimmune disorders. And those genes turned up not just in Bcells or T cells but also in cells that were not part of the immune system, Sharma says.

For example, nonimmune cells have genes that allow them to release cytokines generic cialis online for sale and chemokines, chemical messengers that summon an immune response. This activity is quite important for cellular health. All cells are susceptible to transformation into cancers, for instance, or to . When such harmful changes happen to cells, Sharma explains, they need to be able to tell the generic cialis online for sale immune system that they are in trouble.

But mutations in those genes may create apparent distress signals when the cells are not really damaged. The immune system will react as if they are and swoop in. Credit generic cialis online for sale. David Cheney.

Source. €œNew Insights into the Role of Autoreactive CD8 T Cells and Cytokines in Human Type 1 Diabetes,” by Christine Bender, Sakthi Rajendran and generic cialis online for sale Matthias G.von Herrat, in Frontiers in Endocrinology, Vol. 11. 2021 (reference) Signs of Vulnerability A study by Eizirik and his colleagues published this past January in Science Advances provides examples of misleading target cells in multiple autoimmune diseases.

The scientists examined published genome association research and found that more than 80 percent of identified genetic variants were expressed by target cells in generic cialis online for sale type 1 diabetes and three other autoimmune diseases. Multiple sclerosis, lupus and rheumatoid arthritis. The study showed not only that target cells contain disease-related genes but also that in people with disease, they make more of those proteins than in healthy people. Eizirik and his generic cialis online for sale colleagues mined genetic databases created from biopsies of affected tissues from people with autoimmune disease.

Pancreas cells of people with diabetes, joint tissue from people with rheumatoid arthritis, kidney cells from those with lupus and even autopsy samples from the brains of people with multiple sclerosis. Their analysis showed that many candidate genes were exceptionally active in the targeted tissues, and many of these active bits of DNA appeared in multiple diseases, pointing to common threads. Among the top genes showing extra activity were those related to interferons, a class of proinflammatory cytokines that cells release to flag down immune cells when there is generic cialis online for sale a problem such as a viral . Many of the target cells in autoimmune disease also share nongenetic features that make them exceptionally vulnerable to assault.

€œThese cells have at least three intrinsic weaknesses,” Mallone says. First, many of them reside in glands such as the thyroid and pancreas, where “they are hormone factories, pumping out hormones at high rates, which creates a lot of stress.” Because they are already under a lot of strain, a little additional generic cialis online for sale cellular stress could flip the balance toward malfunction and pathology, alerting an immune system cleanup crew. Second, the cells secrete hormones and other peptides directly into the bloodstream. Such molecules travel throughout the body, which means that, as signatures of these cells, they “can sensitize the immune system from a distance,” Mallone says.

A third weakness for target cells is that they are penetrated by lots of blood vessels, making generic cialis online for sale them easily accessible. €œThis means that once the immune cells are sensitized, they have an easy job to get to [the targets],” he concludes. On top of those vulnerabilities, target cells may react to an outside threat—damage from a cialis, for example—in ways that bring on a strong immune response. Some cells self-destruct when infected by generic cialis online for sale a cialis, taking themselves out before the harm can spread and before immune system intervention is needed.

But certain cells afflicted in autoimmune diseases, such as neurons and beta cells, are in limited supply. Simply dying off after a viral is not an option for them, Eizirik says. €œIf too many cells die, we’re cooked,” he says generic cialis online for sale. Instead they stick around, and the immune system starts interpreting the molecules they release as signs that all cells of that class are in trouble.

Then an autoimmune attack ensues. One striking example of a weakness in target cells that leads to an immune response comes from generic cialis online for sale the blood vessel disease vasculitis. The disorder is not a classic autoimmune disease, because it does not rely on autoantibodies. Rather it is an example of an autoinflammatory disease in which a cell class known as myeloid immune cells goes after other cells that form arteries, veins and capillaries.

A rare, aggressive form in children results from a mutation generic cialis online for sale in a gene for a metabolic enzyme called adenosine deaminase 2. The enzyme regulates activity in both the attacking cells and the attacked ones, according to a 2020 study led by Sharma and published in Science Advances. €œWhen they lose this enzyme, the whole system becomes deregulated,” Sharma says. €œThe end result is that generic cialis online for sale the target cells start producing cytokines, and this has a bystander effect to activate the myeloid cells.

What we’re talking about is the target cell causing its own problem.” Outside Triggers But even cells with inherent weaknesses do not get into autoimmune trouble all by themselves. Remember that in nondiabetic people, Mallone found T cells that could have assaulted beta cells, but they held their fire. Something tips the balance, initiating events in target tissues that seem to start immune system generic cialis online for sale interference. Many scientists think that thing is often a passing viral or perhaps exposure to toxic chemicals, and it may occur years before an autoimmune disorder becomes obvious enough to be detected.

One long-suspected culprit in type 1 diabetes is the Coxsackie cialis, a common pathogen. It usually causes a mild illness that shows up as passing skin rashes and generic cialis online for sale mouth sores. But Coxsackie can attack the pancreas under the right circumstances, Mallone says. €œThese cialises can infect beta cells, so they can kill some if there’s enough of a viral load.” That could lead to inflammation that draws more immune cells to the place where beta cells are dying.

In their death throes, the betas could release signature self-antigens generic cialis online for sale that sensitize nearby immune cells, causing them to go after other beta cells, because such cells have similar antigen signatures. That multipart mix is crucial, Mallone says. €œBasically, you need three ingredients. Self-antigen, an inflammatory environment generic cialis online for sale and autoimmune predisposition,” he says.

€œAnd these ingredients have to meet at the same place and the same time. This is probably one reason it’s so difficult to identify environmental triggers. Because we’re all exposed, but it depends on specific conditions.” This view is generic cialis online for sale replacing an older idea. That cialises trigger autoimmune reactions when the viral proteins look, molecularly, a lot like self-antigens, leading immune cells to get confused by the similarity and attack the self.

Support for this idea, called viral mimicry, began to crumble as researchers amassed evidence that such molecular doppelgängers are fairly common but very rarely cause disease. There are a number of molecules in human bodies and infectious agents that look like one another, and they are called cross-reactive generic cialis online for sale. €œCross-reactivity is extremely abundant. You can find it everywhere,” says DeLisa Fairweather, an immunologist at the Mayo Clinic in Jacksonville, Fla.

If cross-reactivity led to illness, generic cialis online for sale she says, “we should see diseases at higher levels. It’s not the answer.” Thus, the idea has gained currency that a cialis kills some target cells and creates some inflammation, and in the middle of all this, some immune cells become sensitized to the dying cells’ proteins. A Rising Count Other irritants from outside the body, such as drugs and other chemicals, can create these inflammatory conditions, providing more occasions for encounters with immune system sentinels to go wrong. Some scientists think encounters generic cialis online for sale with such substances can explain a spike in autoimmune disease frequency over the past few decades.

In 2020 rheumatologist Frederick Miller of the National Institute of Environmental Health Sciences and his colleagues published an analysis that tracked the prevalence of antinuclear antibodies, a subset of autoantibodies that go after proteins in a cell’s nucleus. The study followed more than 14,000 participants in the U.S. Over a generic cialis online for sale 25-year period. Between 1988 and 1991, 11 percent of those tested carried the antibodies.

That number stayed roughly stable through 2004, with a small rise toward the end of that period. But by 2012 the data showed a big generic cialis online for sale jump in the number of people carrying the antibodies, to nearly 16 percent of participants. The rise was particularly striking in adolescents, Miller says, “which to me was the scariest thing.” That could indicate a coming wave of autoimmune diseases. What has changed to cause the increase?.

“We don’t know yet,” Miller generic cialis online for sale says. He can, however, rattle off a number of possible environmental and behavioral factors. During the time span of his study, approximately 80,000 to 90,000 new chemicals have been approved for use, he says. €œWe have generic cialis online for sale a completely different diet,” he continues.

€œOur use of electronics, while handy and useful, has also meant we’re not getting enough sleep.” People have also encountered increases in air, water and food pollution. €œThere are hundreds of differences in our lifestyle and exposure in the past 30 years,” Miller says. Another, somewhat paradoxical idea is that our immune systems now get too generic cialis online for sale little exposure to the outside world and consequently overreact when they encounter relatively benign molecular representatives from it. The theory is related to a notion called the hygiene hypothesis, put forth in the early 2000s, which was based on changes to sanitary conditions.

This iteration is more closely tied to changes in our intestinal bacteria, our gut microbiome, that come with the habits of modern society. A quirk of geopolitics has presented a unique generic cialis online for sale opportunity to study this effect. After World War II, a region in northeastern Europe called Karelia was split into Finnish and Russian territories. The populations are genetically similar, but Finnish Karelia rapidly modernized after the war, whereas living conditions in rural Russian Karelia remained similar to those of 60 years ago.

You might think an improvement in living conditions would reduce generic cialis online for sale the burden of disease, but that has not happened with autoimmune illnesses. In fact, the reverse effect has been observed. The incidence of type 1 diabetes in Finland is the highest in the world and about six times that in Russian Karelia. Rates of other autoimmune diseases such generic cialis online for sale as celiac disease are also six to 10 times higher in Finland compared with Russia.

Mikael Knip of the University of Helsinki and his colleagues think these changes in disease prevalence can be tied to changes in the microbiome in the Karelian populations. Our internal ecosystem of gut bacteria becomes established during infancy and is heavily influenced by our surroundings. For a 2016 study published in Cell, Knip’s team collected stool samples from infants on both sides of the Finnish-Russian border for the generic cialis online for sale first three years of their lives. €œWhen we analyzed the data, we did see a clear difference between the infants in Finnish and Russian Karelia,” he says.

The microbes in Russian children were dominated by a nonpathogenic form of Escherichia coli. Finnish children, in contrast, were home to high levels of generic cialis online for sale a bacterial genus called Bacteroides, which typically does not prompt a strong immune reaction. €œExposure to various microbes in the environment has an effect on training the immune system, particularly in the first year of life,” Knip says, and it looks as if the Finnish systems did not get very rigorous training. The Finnish microbiomes also lacked the variety seen among the Russians.

Although Knip emphasizes that it generic cialis online for sale is too soon to cement a cause-effect relation between any drop in microbiome diversity on the Finnish side and the rise in autoimmune problems, he does think there is a connection. €œI’d say we need to rename the hygiene hypothesis to the biodiversity hypothesis,” Knip says. Sharma agrees that gut biodiversity is important, and exposure to variety—for example, by eating nonprocessed foods or at least much less heavily processed versions—is key for training the immune system. €œThat makes generic cialis online for sale our gut flora more abundant and more diverse,” she says.

And it gives our immune system a chance to get used to molecules that are not inherently dangerous so that it does not overreact when it encounters them. Ultimately a better understanding of the causes of autoimmune diseases—and improved treatments for them—will come from an approach that is quite different from narrow studies of immune cells or target tissues or the microbiome, Miller says. It will generic cialis online for sale come from a more holistic view. Much like in the old Indian parable, he says, “everyone’s looking [at autoimmunity] like the blind men feeling around the elephant, where every person is seeing different things, and they’re not able to connect these to the whole.” Seeing the entire immunological picture will require more studies on different types of biomolecular dynamics, and that research will have to be done in large populations of people.

Such an approach could amount to “millions of data points,” Miller says. €œWe need to embrace the complexity.”Struggles with mental ill-health are generic cialis online for sale the world’s leading cause of disability. Beset by the erectile dysfunction cialis, underresourced mental health systems have strained to keep up. But access to care is limited by three major obstacles.

A dearth of professional care providers, embedded stigma surrounding generic cialis online for sale mental health problems and a distrust of institutions. The scenario is by no means uniformly dire. Both the public and private sectors have demonstrated a willingness to promote change. Innovative programs show promise for improving efficient access to care, whether a community’s financial resources are large or generic cialis online for sale small.

They combine the latest science with digital delivery of information and services and collaborative efforts among people with mental health challenges, professionals and the community at large. Digital care options through teletherapy and all manner of new apps have seen explosive growth during the cialis. Online services generic cialis online for sale reach the most remote regions and circumvent fears of stigma for making the decision to seek treatment. They can effectively extend the capacity of health and social services.

But they cannot overcome the scarcity of professional therapists. The dearth of providers who generic cialis online for sale coordinate care means that even app-based teletherapy confronts challenges in reaching people in need. One solution is to bolster peer and community support to extend the effectiveness and reach of in-person and online mental health care. A major development has seen people with mental illnesses help others by providing peer support to show that they are not alone in their struggles with mental health.

People confronting mental health issues assist recovery by building trust generic cialis online for sale among their peers with similar experiences. Care teams made up of peers lead group discussions and serve as coaches for others experiencing mental challenges. Training and support for community health workers also help. Community health workers are generic cialis online for sale lay members of a community tasked with providing basic health care, including prevention, health promotion and rehabilitation services, thereby extending care to more people in need worldwide.

Research has begun to show the effectiveness of these approaches even when delivered online. Public and private sectors in several countries have developed programs combining these approaches. Online mental health support and services such as Togetherall, ReachOut, generic cialis online for sale 7 Cups and UCLA STAND, often co-designed and advised by community peers, have become trusted sources of help and referral for young people, their families and others in distress and coping with mental ill-health. A public-private partnership, Strong 365’s NYWell is a digital outreach pilot project to assist young people facing the onset of serious mental illness.

NYWell’s search engine and social media ads link to a Web site that provides assistance ranging from self-education and online peer support to more intensive professional care. The site has attracted thousands of visitors from the time of its launch in New York State in November generic cialis online for sale 2020. About half of visitors take a self-administered mental health screening test. One in 10 connect online with a peer or therapist, and one in five of those are referred to care in the community.

The program is expanding, and a randomized controlled trial has begun to measure its generic cialis online for sale effectiveness. Early findings indicate that youth facing serious mental illness are willing to engage in what is called tiered online care, ranging from peer interactions to sessions with professional therapists. Continued progress will require collaboration among people with mental illness, community workers, mental health and technology professionals, public and private sector leaders, and others. The programs show promise, however, of furnishing a breakthrough generic cialis online for sale in care for people wherever they are.

This is an opinion and analysis article, and the views expressed by the author or authors are not necessarily those of Scientific American.On a crisp fall New England day during my junior year of college, I was walking past a subway entrance when a math problem caught my eye. A man was standing near a few brainteasers he had scribbled on the wall, one of which asked for the construction, with an imaginary straightedge and compass, of a cube with a volume twice that of a different, given cube. This stopped me generic cialis online for sale in my tracks. I had seen this problem before.

In fact, the challenge is more than two millennia old, attributed to Plato by way of Plutarch. A straightedge can be used to extend a line segment in any direction, and a compass can be used to draw a circle with generic cialis online for sale any radius from the chosen center. The catch for this particular puzzle is that any points or lengths appearing in the final drawing must have been either present at the start or constructable from previously provided information. To double a cube’s volume, you start with its side length.

Here that value might as well be 1 because generic cialis online for sale it is the only unit of measurement given. To construct the larger cube, you have to figure out a way to draw one of its sides with the new required length, which is ∛2 (the cube root of two), using just the straightedge and compass as tools. It is a tough problem. For more than 2,000 years no generic cialis online for sale one managed to solve it.

Finally, in 1837, Pierre Laurent Wantzel explained why no one had succeeded by proving that it was impossible. His proof used cutting-edge mathematics of the time, the foundations of which were laid by his French contemporary Évariste Galois, who died at 20 in a duel that may have involved an unhappy love affair. At the ripe old age of 20 myself, I had achieved considerably less generic cialis online for sale impressive mathematical accomplishments, but I at least understood Wantzel’s proof. Here is the idea.

Given a point as the origin and a length of distance 1, it is relatively straightforward to use the straightedge and compass to construct all points on a number line whose coordinates are rational numbers (ignoring, as mathematicians tend to do, the impossibility of actually plotting infinitely many points in only a finite amount of time). Wantzel showed that if one uses only these tools, each newly constructed point must be a solution to a quadratic polynomial equation ax2+ bx + c = 0 whose coefficients a, b and c generic cialis online for sale are among the previously constructed points. In contrast, the point ∛2 is a solution to the cubic polynomial x3 2 = 0, and Galois’s theory of “field extensions” proves decisively that you can never get the solution to an irreducible cubic polynomial by solving quadratic equations, essentially because no power of 2 evenly divides the number 3. Credit.

Matteo Farinella Armed with these facts, generic cialis online for sale I could not restrain myself from engaging with the man on the street. Predictably, my attempt to explain how I knew his problem could not be solved did not really go anywhere. Instead he claimed that my education had left me closed-minded and unable to “think outside the box.” Eventually my girlfriend managed to extricate me from the argument, and we continued on our way. But an interesting question generic cialis online for sale remains.

How was I, a still-wet-behind-the-ears undergraduate in my third year of university study, able to learn to comfortably manipulate abstract number systems such as Galois’s fields in just a few short weeks?. This material came at the end of a course filled with symmetry groups, polynomial rings and related treasures that would have blown the minds of mathematical giants such as Isaac Newton, Gottfried Leibniz, Leonhard Euler and Carl Friedrich Gauss. How is it that mathematicians can quickly teach every new generation of undergraduates discoveries generic cialis online for sale that astonished the previous generation’s experts?. Credit.

Matteo Farinella Part of the answer has to do with recent developments in mathematics that provide a “birds-eye view” of the field through ever increasing levels of abstraction. Category theory is a branch of mathematics that explains how distinct mathematical objects can be considered “the same.” Its fundamental theorem generic cialis online for sale tells us that any mathematical object, no matter how complex, is entirely determined by its relationships to similar objects. Through category theory, we teach young mathematicians the latest ideas by using general rules that apply broadly to categories across mathematics rather than drilling down to individual laws that apply only in a single area. As mathematics continues to evolve, mathematicians’ sense of when two things are “the same” has expanded.

In the past few decades generic cialis online for sale many other researchers and I have been working on an extension of category theory to make sense of this new expanded notion of uniqueness. These new categories, called infinity categories (∞-categories), broaden category theory to infinite dimensions. The language of ∞-categories gives mathematicians powerful tools to study problems in which relations between objects are too nuanced to be defined in traditional categories. The perspective of “zooming out generic cialis online for sale to infinity” offers a novel way to think about old concepts and a path toward the discovery of new ones.

Categories Like many other mathematicians I know, I was drawn into the subject partly because of my poor memory. This confounds many people who remember high school mathematics as rife with formulas to memorize—the trigonometric identities come to mind. But I took comfort in the fact that the most commonly used formulas could be rederived from sin2θ + cos2θ = 1, which itself has an elegant geometric generic cialis online for sale explanation. It is an application of the Pythagorean theorem to a right triangle with a hypotenuse of length 1 and an acute angle of θ degrees.

This utopian vision of mathematics where everything just “makes sense” and nothing needs to be memorized falls apart to some extent at the university level. At that point students get to know the zoo of generic cialis online for sale mathematical objects that have been conjured into existence in the past few centuries. €œGroups,” “rings” and “fields” belong to an area of mathematics known as algebra, a word derived from a ninth-century book by Persian mathematician and astronomer Muhammad ibn Musa al-Khwarizmi, the title of which is sometimes translated as The Science of Restoring and Balancing. Over the next millennium, algebra evolved from the study of the nature of solutions to polynomial equations to the study of abstract number systems.

Because no real number x satisfies the equation x2+ 1 = 0, mathematicians built a new number system—now known as the complex numbers—by adding an imaginary number i and imposing the stipulation that i2 + 1= generic cialis online for sale 0. Algebra is only one of the subjects in a mathematics undergraduate’s curriculum. Other cornerstones include topology—the abstract study of space—and analysis, which begins with a rigorous treatment of the calculus of real functions before branching into the more exotic terrains of probability spaces and random variables and complex manifolds and holomorphic functions. How is a student generic cialis online for sale supposed to make sense of it all?.

Credit. Matteo Farinella A paradoxical idea in mathematics is that of simplification through abstraction. As Eugenia Cheng puts it in The Art of Logic in an Illogical World, “a powerful aspect of abstraction is that many different situations become the same when you forget some details.” Modern algebra was created in the early 20th generic cialis online for sale century when mathematicians decided to unify their studies of the many examples of algebraic structure that arose in the consideration of solutions to polynomial equations or of configurations of figures in the plane. To connect investigations of these structures, researchers identified “axioms” that describe their common properties.

Groups, rings and fields were introduced to the mathematical universe, along with the idea that a mathematical object could be described in terms of the properties it has and explored “abstractly,” independently of the scaffolding of particular examples or constructions. John Horton Conway famously pondered generic cialis online for sale the curious ontology of mathematical things. €œThere’s no doubt that they do exist but you can’t poke and prod them except by thinking about them. It’s quite astonishing and I still don’t understand it, despite having been a mathematician all my life.

How can generic cialis online for sale things be there without actually being there?. € But this world of mathematical objects that can exist without actually being there created a problem. Such a world is vastly too large for any person to comprehend. Even within algebra, there are just too many mathematical things to study for generic cialis online for sale there to be time to make sense of them all.

Around the turn of the 20th century, mathematicians began to investigate so-called universal algebra, referring to a “set,” which could be a collection of symmetries, of numbers in some system or something else entirely, together with various operations—for instance, addition and multiplication—satisfying a list of relevant axioms such as associativity, commutativity or distributivity. By making different choices—Is an operation partially or totally defined?. Is generic cialis online for sale it invertible?. €”one arrives at the standard algebraic structures.

The groups, rings and fields. But the subject generic cialis online for sale is not constrained by these choices, which represent a vanishingly small portion of an infinite array of possibilities. Credit. Matteo Farinella The proliferation of new abstract mathematical objects brings its own complexity.

One way to simplify is to introduce a further level of abstraction where, astonishingly, we can prove theorems about a wide variety of mathematical objects simultaneously without specifying exactly generic cialis online for sale what kinds of objects we are talking about. Category theory, which was created in the 1940s by Samuel Eilenberg and Saunders Mac Lane, does just this. Although it was originally introduced to give a rigorous definition of the colloquial term “natural equivalence,” it also offers a way to think universally about universal algebra and other areas of mathematics as well. With Eilenberg and Mac Lane’s language, we can now understand that every variety of mathematical object belongs to its own category, which is a specified collection of objects together with a set of transformations depicted as arrows between the objects generic cialis online for sale.

For example, in linear algebra one studies abstract vector spaces such as three-dimensional Euclidean space. The corresponding transformations in this case are called linear transformations, and each must have a specified source and target vector space indicating which kinds of vectors arise as inputs and outputs. Like functions, the transformations in a generic cialis online for sale category can be “composed,” meaning you can apply one transformation to the results of another transformation. For any pair of transformations f.

A → B (read as “f is a transformation from A to B”) and g. B → C, the category specifies a unique composite transformation, written as g ∘f generic cialis online for sale. A → C (read as “g composed f is a transformation from A to C”). Finally, this composition law is associative, meaning h ∘(g ∘f) = (h ∘g) ∘f.

It is also unital generic cialis online for sale. Each object B has an “identity transformation” commonly denoted by 1Bwith the property that g ∘1B= g and 1B∘f = f for any transformations g and f whose source and target, respectively, equal B. How do categories help the hapless undergraduate confronted with too many mathematical objects and not enough time to learn about them all?. Any class of structures you generic cialis online for sale can define in universal algebra may be distinct from all others, but the categories these objects inhabit are very similar in ways that can be expressed precisely through categorical language.

With sufficient experience, mathematicians can know what to expect when they encounter a new type of algebraic structure. This idea is reflected in modern textbooks on the subject that develop the theories of groups, rings and vector spaces in series, essentially because the theories are parallel. There are other, looser analogies among these categories and the ones students encounter in topology or analysis generic cialis online for sale courses, and these similarities enable them to absorb the new material more quickly. Such patterns allow students to spend more time exploring the special topics that distinguish individual mathematical subdisciplines—although research advances in mathematics are often inspired by new and surprising analogies between previously unconnected areas.

Symmetries The cascading levels of abstraction, from concrete mathematical structures to axiomatic systems and then beyond to the general objects that belong to categories, present a new challenge. It is no longer very clear what it means to say that one thing is “the same” as another thing generic cialis online for sale. Consider, for instance, a group, which in math is an abstract collection of symmetries whose elements Amie Wilkinson of the University of Chicago likes to describe as “moves” that flip or rotate an object before settling it into something like the original position. For example, we might explore the symmetries of a T-shirt.

One symmetry can be thought of as the “identity move,” where a person simply wears generic cialis online for sale the T-shirt as it is usually worn. Another symmetry corresponds to a move where the wearer takes their arms out of the arm holes and, with the T-shirt still around their neck, rotates the shirt 180 degrees to put their arms in the opposite holes. The T-shirt remains right-side out but is now being worn backward. Another symmetry corresponds to a move where the T-shirt is removed entirely, generic cialis online for sale flipped inside out and put back on in such a way that each arm goes through the hole it was originally in.

The T-shirt is now inside out and backward. A final symmetry combines these two moves. Atypically for groups, these moves can be performed generic cialis online for sale in any order without changing the end result. Each of these four moves counts as a “symmetry” because they result in the shirt being worn in essentially the same way as when you started.

Credit. Matteo Farinella Another generic cialis online for sale group is the “mattress-flipping group,” which describes the symmetries of a mattress. In addition to the identity move, which applies when the mattress is left in its original position, a person can move the mattress by rotating it top to bottom, flipping back to front or performing both moves in sequence. (Mattresses typically are not square, but if they were, there would be more symmetries than described here.) Although a T-shirt does not have much to do with a mattress, there is a sense in which the two symmetry groups have the same “shape.” First, both groups of symmetries have the same number of moves (in this case, four), and, crucially, you can pair each move in the T-shirt group with a move in the mattress-flipping group such that the compositions of corresponding moves also correspond.

In other words, you can match up moves from the two groups (match the identity with the identity, the flip with the flip, the rotation with the generic cialis online for sale rotation, and so on). Second, if you take two moves from one group and perform them in sequence, the final position will match with the end result of performing the corresponding moves from the other group in sequence. In technical terms, these groups are connected by an “isomorphism,” a term whose etymology—from the Greek isos, meaning “equal,” and morphe, meaning “form”—indicates its meaning. We can define the notion of generic cialis online for sale isomorphism in any category, which allows us to transport this concept between mathematical contexts.

An isomorphism between two objects A and B in a category is given by a pair of transformations, f. A → B and g. B → A, with the property that the composites generic cialis online for sale g ∘f and f ∘g equal the respective identities 1Aand 1B. In the category of topological spaces, the categorical notion of isomorphism is represented by an inverse pair of continuous functions.

For instance, there is a continuous deformation that would allow you to convert an unbaked doughnut into a shape like a coffee mug. The doughnut hole becomes the handle, and the cup is formed by a generic cialis online for sale depression you make with your thumb. (For the deformation to be continuous, you must do this without tearing the dough, which is why the doughnut should not be baked before the experiment is attempted.) This example inspired the joke that a topologist cannot tell the difference between a coffee mug and a doughnut. As abstract spaces, these objects are the same.

In practice, many topologists are arguably much less observant than this because it is common to adopt a more flexible convention concerning situations when two spaces are “the same,” identifying any two spaces that are merely “homotopy-equivalent.” This term refers to the notion of isomorphism in the more exotic homotopy category of generic cialis online for sale spaces. A homotopy equivalence is another type of continuous deformation, but in this case, you can identify distinct points. For instance, imagine starting with a pair of pants and then shrinking the lengths of the legs until you are left with a G-string, another “space” with the same fundamental topological structure—there are still two holes for legs—even though the original two-dimensional garment has been shrunk down to a one-dimensional bit of string. Credit generic cialis online for sale.

Matteo Farinella Another homotopy equivalence collapses the infinite expanse of three-dimensional Euclidean space down to a single point via a “reverse big bang” in which each point flies back to its origin, with the speed of this motion increasing with the distance from the location of the initial big bang. The intuition that we can substitute isomorphic things for one another without fundamentally changing the nature of a construction or an argument is so strong that in fact category theorists have redefined the word “the” to mean something closer to “a” in colloquial English. For example, there is a concept known as the disjoint union of two sets generic cialis online for sale A and B. Like the ordinary union, the disjoint union A ⨆ B has a copy of every element of A and a copy of every element of B.

Unlike in the ordinary union, however, if A and B have an element in common, then the disjoint union A ⨆ B has two copies of that element, one of which somehow remembers that it came from A, and the other somehow remembers it came from B. There are many different ways generic cialis online for sale to construct the disjoint union using the axioms of set theory, which will not produce exactly the same set but will, necessarily, produce isomorphic ones. Rather than wasting time arguing about which construction is the most canonical, it is more convenient to just sweep this ambiguity under the rug and refer to “the” disjoint union when one means to consider any particular set that satisfies the desired universal property. In another example, mathematicians refer to both the T-shirt symmetry group and the mattress-flipping group as “the Klein four-group.” Infinite-Dimensional Categories An oft-told story about the origin of the fundamental theorem of category theory is that a young mathematician named Nobuo Yoneda described a “lemma,” or helper theorem, to Mac Lane at the Gare du Nord train station in Paris in 1954.

Yoneda began explaining the lemma on the platform and continued it on the train before it departed generic cialis online for sale the station. The consequence of this lemma is that any object in any category is entirely determined by its relation to the other objects in the category as encoded by the transformations to or from this object. So we can characterize a topological space X by probing it with continuous functions f. T → generic cialis online for sale X mapping out other spaces T.

For instance, the points of the space X correspond to continuous functions x. * → X, whose domain is a space with a single point. We can answer generic cialis online for sale the question of whether the space X is connected or disconnected by considering mappings p. I → X, whose domain is an interval I = [0,1].

Each such mapping defines a parameterized “path” in the space X from the point p(0) to the point p(1), which can be thought of as a possible trajectory an ant might take when walking around the space X. We can use the generic cialis online for sale points and paths of a space to translate problems of topology into problems of algebra. Each topological space X has an associated category π1X called the “fundamental groupoid” of X. The objects of this category are the points of the space, and the transformations are paths.

If one path can be deformed into another in the space while its end points remain fixed, the two generic cialis online for sale paths define the same transformation. These deformations, which are technically called homotopies, are necessary for the composition of paths to define an associative operation, as is required by a category. Credit. Matteo Farinella A key advantage generic cialis online for sale of the fundamental groupoid construction is that it is “functorial,” meaning that a continuous function f.

X → Y between topological spaces gives rise to a corresponding transformation π1f. π1X → π1Y between the fundamental groupoids. This assignment respects composition and identities, meaning π1(g f) = π1g π1f and generic cialis online for sale π1(1X) = 1π1X, respectively. These two properties, which collectively go by the name “functoriality,” suggest that the fundamental group captures some essential information about topological spaces.

In particular, if two spaces are not homotopy-equivalent, then their fundamental groupoids are necessarily inequivalent. The fundamental groupoid is not a complete invariant, however generic cialis online for sale. It can easily distinguish between a circle and the solid disk that circle bounds. In the fundamental groupoid of the circle, the different wiggling versions of a path between two points can be labeled by integers that record the number of times the trajectory winds around the circle and a + or sign indicating, respectively, a clockwise or counterclockwise direction of transit.

In contrast, in the fundamental groupoid of the disk, there is only one path up to homotopy generic cialis online for sale between any pair of points. The fundamental groupoid of the space formed by the inflatable exterior of a beach ball, a sphere in topological terms, also has this description. There is a unique path up to homotopy between any two points. Credit.

Matteo Farinella The big problem with the fundamental groupoid is that points and paths do not detect the higher-dimensional structure of a space, because the point and interval are themselves zero- and one-dimensional, respectively. A solution is to also consider continuous functions from the two-dimensional disk, called homotopies, and “higher homotopies,” defined by continuous functions from the solid three-dimensional ball and similarly for other balls in 4, 5, 6 or more dimensions. It is natural to ask what kind of algebraic structure the points, paths, homotopies and higher homotopies in a space X form. This structure π ∞ X (“pi infinity X”), referred to as the fundamental ∞-groupoid of X, defines an example of an -category, an infinite-dimensional analogue of the categories first introduced by Eilenberg and Mac Lane.

Like an ordinary category, an ∞-category has objects and transformations visualized as one-dimensional arrows, but it also contains “higher transformations” depicted by two-dimensional arrows, three-dimensional arrows, and so on. For example, in π ∞ X the objects and arrows are the points and the paths—no longer considered up to wiggling—while the higher-dimensional transformations encode the higher homotopies. Like in an ordinary category, the arrows in any fixed dimension can be composed. If you have two arrows f.

X Y and g. Y Z, there must also be an arrow g f. X Z. But there is a catch.

In attempts to capture natural examples such as the fundamental ∞-groupoid of a space, the composition law must be weakened. For any composable pair of arrows, there must exist a composite arrow, but there is no longer a unique specified composite arrow.

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