drought in Taiwan and a cold snap in Texas that temporarily shut down factories operated by Samsung Electronics, NXP Semiconductors and Infineon.

“It’s hell on earth right now,” said Frank McKay, chief procurement officer at Jabil, which buys billions of dollars’ worth of chips each year to assemble products for customers that include Apple, Amazon, Cisco Systems and Tesla.

On any given day, he said, his company is facing shortages of 100 or so components and has to use all its negotiating power to get them — successfully so far. “But it’s a roller-coaster ride every day,” Mr. McKay said.

Fixing other issues is likely to stretch into 2022. Mr. Gelsinger said Intel was talking to auto industry suppliers about shifting some production of their chips to older Intel factories, possibly starting in six to nine months. But adding new production tools to an existing chip plant can take a year. Building a new one takes three years.

“This is going to be a long healing,” said Thomas Caulfield, chief executive of GlobalFoundries, a big U.S. chip manufacturer that is doubling capital spending this year so it can meet demand.

For now, chip delivery schedules have stretched from around 12 weeks to more than a year in some cases, chip buyers and brokers said. That is bad news for companies like the webcam start-up Wyze Labs.

“We’re going to be straight up with you about some bad news we got this week,” the company wrote in a note to customers in January. “Some of our key suppliers informed us they would only be able to supply about one-third of the chips we need to make Wyze Cams.”

The company, which is based in Kirkland, Wash., predicted problems stocking the third version of its flagship webcam. The company website says it is sold out, with more inventory expected in one to two weeks. Wyze did not respond to requests for additional comment.

Supply problems can be a touchy topic, said Zach Supalla, chief executive of Particle, a San Francisco company that buys chips to make communication and computing equipment. It sells its devices to thousands of companies that make products like hot tubs, air-conditioners and industrial and medical equipment.

Particle has so far has secured enough chips to keep making its products, he said. But the company is asking customers to order further and further in advance to ensure it can meet demand, Mr. Supalla said.

When chips can be found, price markups can be stark. One particularly unglamorous widget, a type of ceramic capacitor that ordinarily sells for around 3 cents each, became hard to find when a Covid-19 outbreak temporarily closed a factory in China.

The capacitor shortage hurt production of a popular cellular modem. That modem, which normally sells for $10 to $20, spiraled to $200 on the spot market, Mr. Supalla said. Customers like car companies may be willing to pay such sums to keep producing $40,000 cars, Mr. Supalla said. But not all can.

Some buyers suspect profiteering. Jens Gamperl, chief executive of an online components exchange called Sourcengine, recounted a call from an executive who fumed that a chip normally priced at $1 each was listed for sale by the exchange at $32. Mr. Gamperl had to explain that his own company had been forced to pay $28 for the component.

“That is the kind of craziness that we see left and right now,” he said.

Besides the direct effect on hardware makers, chip shortages can reduce shipments and raise the cost of servers and networking equipment to offer services like streaming entertainment, remote learning and medicine. They can also affect software makers.

Tripp, a Los Angeles start-up that makes a kind of meditation app that exploits virtual-reality headsets from Sony and others, was banking on the new PlayStation 5 to lift software demand, said Nanea Reeves, Tripp’s chief executive. But chip shortages helped to hobble that console launch.

“We were expecting a bigger bump from the PS5,” she said. The company is hoping more consoles arrive in the second quarter.

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Carlton Tavern Was Reduced to Rubble. They Fought to Bring It Back.

LONDON — “Your local pub, it’s a bit like your favorite pair of shoes or jeans, something you just completely take for granted,” Rob Cope said, sitting outside the Carlton Tavern in North London on Monday.

With the glow of the afternoon sun easing the bite of the chilly April air, he gazed at the building’s brick facade and explained, “You don’t really understand that it’s there until it’s gone.”

The Carlton Tavern joined thousands of other pubs on Monday in reopening with outdoor spaces as lockdown restrictions in England eased after months of closures. But its story still stood out in that shared national moment, as its closure was counted not in months but in years.

Its story began when developers tore it down.

Six years ago, people watched in dismay as the Carlton Tavern, built in the 1920s and nestled against a park on the edge of the affluent Maida Vale neighborhood, was reduced to rubble. The building’s overseas owners had skirted local laws and abruptly demolished it to make way for luxury apartments.

Outraged, a group of neighborhood campaigners and local lawmakers fought for years to have the building restored. Eventually, the developers were ordered to rebuild it.

So when glasses were raised and meals shared outside the red brick building on Monday, the patrons were toasting a pub that was simultaneously brand-new and 100 years old as well as celebrating the reclamation of a piece of their community, and, in some cases, a piece of themselves.

Polly Robertson, one of the campaigners at the heart of the fight, laughed and chatted on Monday over fish and chips at the pub with her mother-in-law and sister-in-law, flitting among groups of campaigners, the pub’s new owners and neighbors. The generations of families seated around her were why she fought so hard for the place, she said.

“It’s wonderful coming in, just seeing people we haven’t seen in a long, long time,” she said, “not just because of Covid but because we had no location to meet up.”

Before the pub was demolished in 2015, the preservation society English Heritage surveyed the Carlton Tavern as it was being considered for historical status. The society recorded the layout of the pub’s rooms and took molds of its distinctive architectural features, so when it was time to rebuild, there was something to work with.

“It’s identical,” Ms. Robertson said.

From the ocher red letters spelling out “Charrington Sparkling Ales and Famous Stout” on its brick and tile facade to the swooping brass door handles to the elaborate plasterwork inside, the pub’s original charm and character has been recreated.

For some, the reopening was like welcoming back a long-lost friend. Neighbors likened the space to a communal living room where lives had played out and overlapped. They recalled decades of christenings, birthdays, first communions and wakes held within the tavern’s walls by local people who mostly lived in modest flats.

Martin Shannon has lived in London since 1965, and raised a family in the area. He came to the reopening of the pub with his wife, son and daughter-in-law on Monday. They paused to pose for photos at the sign out front and laughed as they shared a cherished memory of celebrating their son’s 30th birthday there more than a decade ago.

“These are the things the system walks over, average people’s ideas and norms all the time,” he said, growing reflective as he talked about the temporary loss of the pub. “It should survive anyway, and not be rolled over and knocked down.”

To many there, the building’s demolition had felt like a personal affront. Mr. Cope said it had amounted to someone coming in and stealing your favorite pair of shoes.

“It’s like someone saying: ‘You don’t matter. And your values don’t matter. Your memories don’t matter,’” Mr. Cope said, pausing to adjust his glasses. “It feels very deeply personal.”

Behind the pub’s reopening are Tom Rees and Ben Martin, business partners who have a connection to the area and a background running pubs. They hope to see the Carlton Tavern once again at the heart of the community.

“There have been people wandering past, wanting to talk to us, telling us great stories about how they used to work here, they used to drink here, how their parents used to drink here,” Mr. Rees said. “It’s amazing really.”

The middle of a pandemic may seem like a strange time to embark on a venture reviving a pub, especially with so many businesses struggling to survive, but Mr. Rees believes the prolonged lockdown brought a new appreciation for local spaces like this one. Their business, aptly named Homegrown Pubs, is focused on local beers as much as it is on the local people the proprietors hope to see return.

“I think the pandemic has forced people to re-evaluate their local area and their relationships to it, and all those great memories they had in these places,” Mr. Rees said.

It seemed fitting to its new owners that the pub’s rebirth would begin 100 years after its founding. The Carlton Tavern first opened its doors in 1921, and was one of the few buildings on the street to survive bombing during World War II.

Its location at the border of Kilburn and Maida Vale is also a junction of two London worlds. On one adjacent street, rows of glass and brick luxury apartment blocks face off against pockets of subsidized housing.

On Saturday, two days before the pub welcomed back visitors, the new owners and an army of workers and volunteers, including Ms. Robertson, were putting the finishing touches on the building. Outside, workers shook the dust from their hands as they heaved the last bits of construction waste into a dumpster, while others tidied inside to ready the Carlton Tavern for its big debut.

As Ms. Robertson flitted between wiping down the wooden bar counter — salvaged from the original tavern — and preparing fresh juice for the other workers, she reflected on the changes she had seen since moving to the area in the 1980s.

For much of the latter half of the last century, the neighborhood was home to waves of immigrants, first from Ireland, then the Caribbean, the Middle East and Asia. Then came the developers and with them steep housing costs that pushed many from the once diverse, largely working-class area. But despite that, the community has remained close knit.

Ms. Robertson’s husband grew up in the area, and they raised two children there alongside generations of family. Seeing the Carlton Tavern restored and reopened will mean a lot, she said, particularly for older residents who built decades of memories within its red brick walls.

The whole aim was to save a space where people felt they belonged, in a city that has grown increasingly unfamiliar around them.

“The city can be a very lonely place,” Ms. Robertson said as she wiped a dusty film from a mirror behind the bar. “And this, it’s a familiar place. This is their place as much as anything.”

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Their London Pub Was Reduced to Rubble. They Fought to Bring It Back.

LONDON — “Your local pub, it’s a bit like your favorite pair of shoes or jeans, something you just completely take for granted,” Rob Cope said, sitting outside the Carlton Tavern in North London on Monday.

With the glow of the afternoon sun easing the bite of the chilly April air, he gazed at the building’s brick facade and explained, “You don’t really understand that it’s there until it’s gone.”

The Carlton Tavern joined thousands of other pubs on Monday in reopening with outdoor spaces as lockdown restrictions in England eased after months of closures. But its story still stood out in that shared national moment, as its closure was counted not in months but in years.

Its story began when developers tore it down.

Six years ago, people watched in dismay as the Carlton Tavern, built in the 1920s and nestled against a park on the edge of the affluent Maida Vale neighborhood, was reduced to rubble. The building’s overseas owners had skirted local laws and abruptly demolished it to make way for luxury apartments.

Outraged, a group of neighborhood campaigners and local lawmakers fought for years to have the building restored. Eventually, the developers were ordered to rebuild it.

So when glasses were raised and meals shared outside the red brick building on Monday, the patrons were toasting a pub that was simultaneously brand-new and 100 years old as well as celebrating the reclamation of a piece of their community, and, in some cases, a piece of themselves.

Polly Robertson, one of the campaigners at the heart of the fight, laughed and chatted on Monday over fish and chips at the pub with her mother-in-law and sister-in-law, flitting among groups of campaigners, the pub’s new owners and neighbors. The generations of families seated around her were why she fought so hard for the place, she said.

“It’s wonderful coming in, just seeing people we haven’t seen in a long, long time,” she said, “not just because of Covid but because we had no location to meet up.”

Before the pub was demolished in 2015, the preservation society English Heritage surveyed the Carlton Tavern as it was being considered for historical status. The society recorded the layout of the pub’s rooms and took molds of its distinctive architectural features, so when it was time to rebuild, there was something to work with.

“It’s identical,” Ms. Robertson said.

From the ocher red letters spelling out “Charrington Sparkling Ales and Famous Stout” on its brick and tile facade to the swooping brass door handles to the elaborate plasterwork inside, the pub’s original charm and character has been recreated.

For some, the reopening was like welcoming back a long-lost friend. Neighbors likened the space to a communal living room where lives had played out and overlapped. They recalled decades of christenings, birthdays, first communions and wakes held within the tavern’s walls by local people who mostly lived in modest flats.

Martin Shannon has lived in London since 1965, and raised a family in the area. He came to the reopening of the pub with his wife, son and daughter-in-law on Monday. They paused to pose for photos at the sign out front and laughed as they shared a cherished memory of celebrating their son’s 30th birthday there more than a decade ago.

“These are the things the system walks over, average people’s ideas and norms all the time,” he said, growing reflective as he talked about the temporary loss of the pub. “It should survive anyway, and not be rolled over and knocked down.”

To many there, the building’s demolition had felt like a personal affront. Mr. Cope said it had amounted to someone coming in and stealing your favorite pair of shoes.

“It’s like someone saying: ‘You don’t matter. And your values don’t matter. Your memories don’t matter,’” Mr. Cope said, pausing to adjust his glasses. “It feels very deeply personal.”

Behind the pub’s reopening are Tom Rees and Ben Martin, business partners who have a connection to the area and a background running pubs. They hope to see the Carlton Tavern once again at the heart of the community.

“There have been people wandering past, wanting to talk to us, telling us great stories about how they used to work here, they used to drink here, how their parents used to drink here,” Mr. Rees said. “It’s amazing really.”

The middle of a pandemic may seem like a strange time to embark on a venture reviving a pub, especially with so many businesses struggling to survive, but Mr. Rees believes the prolonged lockdown brought a new appreciation for local spaces like this one. Their business, aptly named Homegrown Pubs, is focused on local beers as much as it is on the local people the proprietors hope to see return.

“I think the pandemic has forced people to re-evaluate their local area and their relationships to it, and all those great memories they had in these places,” Mr. Rees said.

It seemed fitting to its new owners that the pub’s rebirth would begin 100 years after its founding. The Carlton Tavern first opened its doors in 1921, and was one of the few buildings on the street to survive bombing during World War II.

Its location at the border of Kilburn and Maida Vale is also a junction of two London worlds. On one adjacent street, rows of glass and brick luxury apartment blocks face off against pockets of subsidized housing.

On Saturday, two days before the pub welcomed back visitors, the new owners and an army of workers and volunteers, including Ms. Robertson, were putting the finishing touches on the building. Outside, workers shook the dust from their hands as they heaved the last bits of construction waste into a dumpster, while others tidied inside to ready the Carlton Tavern for its big debut.

As Ms. Robertson flitted between wiping down the wooden bar counter — salvaged from the original tavern — and preparing fresh juice for the other workers, she reflected on the changes she had seen since moving to the area in the 1980s.

For much of the latter half of the last century, the neighborhood was home to waves of immigrants, first from Ireland, then the Caribbean, the Middle East and Asia. Then came the developers and with them steep housing costs that pushed many from the once diverse, largely working-class area. But despite that, the community has remained close knit.

Ms. Robertson’s husband grew up in the area, and they raised two children there alongside generations of family. Seeing the Carlton Tavern restored and reopened will mean a lot, she said, particularly for older residents who built decades of memories within its red brick walls.

The whole aim was to save a space where people felt they belonged, in a city that has grown increasingly unfamiliar around them.

“The city can be a very lonely place,” Ms. Robertson said as she wiped a dusty film from a mirror behind the bar. “And this, it’s a familiar place. This is their place as much as anything.”

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Some Children With Covid-Related Syndrome Develop Neurological Symptoms

Reports about the mysterious Covid-related inflammatory syndrome that afflicts some children and teenagers have mostly focused on physical symptoms: rash, abdominal pain, red eyes and, most seriously, heart problems like low blood pressure, shock and difficulty pumping.

Now, a new report shows that a significant number of young people with the syndrome also develop neurological symptoms, including hallucinations, confusion, speech impairments and problems with balance and coordination. The study of 46 children treated at one hospital in London found that just over half — 24 — experienced such neurological symptoms, which they had never had before.

Those patients were about twice as likely as those without neurological symptoms to need ventilators because they were “very unwell with systemic shock as part of their hyperinflammatory state,” said an author of the study, Dr. Omar Abdel-Mannan, a clinical research fellow at University College London’s Institute of Neurology. Patients with neurological symptoms were also about twice as likely to require medication to improve the heart’s ability to squeeze, he said.

The condition, called Multisystem Inflammatory Syndrome in Children (MIS-C), typically emerges two to six weeks after a Covid infection, often one that produces only mild symptoms or none at all. The syndrome is rare, but can be very serious. The latest data from the Centers for Disease Control and Prevention reports 3,165 cases in 48 states, Puerto Rico and the District of Columbia, including 36 deaths.

study published last month in JAMA Neurology, 126 of 616 young people with the syndrome admitted to 61 U.S. hospitals last year had neurological issues, including 20 with what the researchers described as “life-threatening” problems like strokes or “severe encephalopathy.”

The new report, presented as preliminary research on Tuesday as part of an annual conference of the American Academy of Neurology, evaluated children under 18 who were admitted to Great Ormond Street Hospital (GOSH) between April and September of last year with the syndrome (it has a different name and acronym, PIMS-TS, in Britain). The data is also included in a preprint of a larger study that has not yet been peer-reviewed.

As was the case with other studies of the syndrome, including in the United States, the researchers said a majority of those afflicted were “nonwhite,” a pattern that public health experts believe reflects the disproportionate way the pandemic has affected communities of color. Nearly two-thirds of the patients were male, and the median age was 10.

All 24 of the patients with neurological symptoms had headaches and 14 had encephalopathy, a general term that can involve confusion, problems with memory or attention and other types of altered mental function. Six of the children were experiencing hallucinations, including “describing people in the room that were not there or seeing cartoons or animals moving on the walls,” Dr. Abdel-Mannan said. He said some experienced auditory hallucinations involving “hearing voices of people not present.”

Six of the children had weakness or difficulty controlling muscles used in speech. Four had balance or coordination problems. One child had seizures and three children had peripheral nerve abnormalities including weakness in facial or shoulder muscles. One patient’s peripheral nerve damage led to a foot-drop problem that required the use of crutches and a recommendation for a nerve transplant, said Dr. Abdel-Mannan, who is also a senior resident in pediatric neurology at GOSH.

Some of the patients underwent brain scans, nerve conduction tests or electroencephalograms (EEGs), including 14 who showed slower electrical activity in their brains, the study reported.

Thirteen of the 24 with neurological symptoms needed to be placed on ventilators and 15 needed medication to improve their heart contractions, Dr. Abdel-Mannan said. By contrast, only three of the 22 children without neurological issues needed ventilators and seven needed such heart medication, he said. None of the children with hallucinations needed psychotropic medications.

Three children had to be hospitalized again after their initial stay, one for another episode of encephalopathy and two for infectious complications, Dr. Abdel-Mannan said, but he added that there were no deaths and “almost all children made a complete functional recovery.”

Dr. Abdel-Mannan said a team led by the study’s senior author, Dr. Yael Hacohen, will be following patients who had the syndrome — both those who had neurological symptoms and those who did not. They will conduct brain scans and cognitive assessments to see if the children experience any long-term cognitive or psychological effects.

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Prince Philip’s Life in Pictures

Prince Philip, the husband of Queen Elizabeth II and the longest-serving consort in British history, was born into Greek royalty in the 1920s, served on a battleship in World War II, toured the world on royal missions for decades and sought for most of his life to defend the interests of Britain’s monarchy.

His life spanned almost a century of upheaval and change for Britain: As a child, he lived with a granddaughter of Queen Victoria, and he died nearly 100 years old, survived by eight great grandchildren who will grow up in an era of smartphones and the internet.

Philip came to England after his father, Prince Andrew of Greece, was banished by a revolutionary Greek junta. He was educated at the Cheam School, an institution bent on toughening privileged children, and then went to Gordonstoun School in Scotland, which promoted a regimen of grueling work, cold showers and hard beds.

He met Princess Elizabeth when she was about 13 or 14. She was instantly smitten, telling her father, King George VI, that she could love no other man but him. They married on Nov. 20, 1947, when he was 26 and she was 21.

warning about greenhouse gases and lending his time to causes like protecting endangered wildlife.

But he grew to hate the relentless tabloid coverage of palace affairs. The public often perceived him as a remote if occasionally loose-lipped figure who made remarks that were called oblivious, insensitive or worse.

He was pained by the headlines that followed the tumultuous marriage and divorce of his eldest son, Prince Charles, and Lady Diana Spencer. He became known as a stern and even imperious figure in the royal family who belittled Charles, and he and the family were castigated by the public for their response to the death of Diana.

Philip died as Buckingham Palace was embroiled in turmoil over Oprah Winfrey’s televised interview last month with his grandson Prince Harry and Harry’s wife, Meghan.

Here is his life in pictures:

Philip on his ninth birthday, in Greek dress.

Philip, second from left, at the MacJannet American School in St. Cloud, France.

Philip and Elizabeth, then a princess, after their wedding ceremony on Nov. 20, 1947.

The couple in the grounds of Broadlands in Hampshire, where they spent their honeymoon, in 1947.

Elizabeth and Philip with their children, Prince Charles and Princess Anne, at Clarence House, in 1951.

The queen and prince in Boston in 1975.

Philip flying a Blackburn military transport plane a few minutes before a fire extinguisher burst in 1956. He landed the plane 10 minutes later.

Throwing a javelin during a visit to the Outward Bound Sea School, in Wales, in 1949.

Feeding a colony of penguins during a visit to the Antarctic.

Philip, an avid horseman and polo player, taking part in a bicycle polo game at Windsor.

Philip at a group therapy session at the National Addiction and Research Institute in London, in 1969.

A photo of the royal family in July 1969 shows Philip and the queen with their children: Charles, 21; Anne,18; Prince Andrew, 9; and Prince Edward, 5.

Philip in 1980 driving a team of horses through a water obstacle in the World Carriage Driving Championships at Windsor Great Park.

Speaking in 1986 at a banquet held by the Japanese Equestrian Federation in Tokyo, as the chairman of the International Equestrian Federation.

Philip and the queen ride in an open carriage down the course at the Royal Ascot in 1986. He regularly accompanied Elizabeth on royal visits and often stood in for her.

Philip and Elizabeth looking at tributes that had been left outside Buckingham Palace in memory of Princess Diana, who was killed in a car crash on Aug. 31, 1997.

Philip visiting the Richmond Adult Community College in June 2015 in London.

Elizabeth and Philip in Westminster, during the state opening of Parliament in 2012.

Philip, as colonel in chief of the Royal Canadian Regiment, inspecting members of a battalion at Queen’s Park.

Attending a garden party at Buckingham Palace in 2017.

Feeding an elephant named Donna after opening the new Centre for Elephant Care in Whipsnade, north of London, in 2017.

Philip and Elizabeth walking in Romsey, in southern England, in 2007.

Philip at a garden party held at Buckingham Palace in June 2014, when he was 93.

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Covid-19 Live Updates: U.K. to Offer Alternatives to AstraZeneza Vaccine to Adults Under 30

finally over rare, but sometimes fatal, blood clots reported in some recipients.

Those concerns led several European countries to first restrict the use of AstraZeneca in older age groups, then suspend it over reports of blood clots, only to roll it out again last month after the European Medicines Agency issued a preliminary opinion that the benefits of the vaccine outweighed the risks.

As doctors reported a higher incidence of serious blood clots in younger people, some countries decided to stop administering the shot to anyone younger than 55.

Europe’s concerns over the vaccine’s side effects are also likely to threaten global inoculation efforts, with much of the developing world depending on the AstraZeneca vaccine to tackle the pandemic. The shot is the cornerstone of Covax, a program designed to make vaccine access more equitable worldwide.

The vaccine appeared to be causing an immune reaction in which antibodies bind to platelets, activating them, German doctors and the European Medicines Agency have said. Those platelets, in turn, were causing the formation of dangerous clots in certain parts of the body, including in veins that drain blood from the brain, leading in some cases to a rare type of stroke.

Why the antibodies develop in these people is not known, doctors have said. Some component of the vaccine, or excessive immune reaction — or both — could be the cause, they said.

No pre-existing conditions are known to make patients more vulnerable to this clotting disorder after a vaccination, European regulators said.

A mass vaccination event for teachers in Carteret, N.J., this month. About eight million school employees had received at least one vaccine dose by the end of March.
Credit…Bryan Anselm for The New York Times

Nearly 80 percent of school staff and child care workers in the United States have received at least one dose of the coronavirus vaccine, the Centers for Disease Control and Prevention said on Tuesday.

The announcement comes as the Biden administration has made an ambitious push to reopen schools and return to in-person instruction by the president’s 100th day in office. That goal has been tempered by dangerous virus variants, protests from teachers’ unions, and the fears and frustrations of students and parents.

The push to reopen schools has gathered momentum as evidence mounted that proper safety measures limited virus transmission in schools and coronavirus cases fell sharply from their January peak. Education officials and experts have cited the urgency of getting students back in classrooms before the academic year ends.

About eight million teachers, school staff and child care workers received their first vaccine dose by the end of March, according to the C.D.C., with about two million receiving their shot through the Federal Retail Pharmacy Program.

President Biden announced the program in March, urging nationwide access to vaccines for school employees and child care workers. But a hodgepodge of eligibility guidelines followed, as some states chose not to deviate from their rollout plans. By the end of March, however, K-12 educators in all states had become eligible to receive the vaccine.

While the acceleration of vaccinations among educators and staff has reduced the resistance from teachers’ unions to reopening classrooms, school systems with powerful unions, especially on the West Coast, have been slower to revert to in-person instruction.

Union resistance has led a bipartisan group of governors in several states to prod, and sometimes force, school districts to open. The result has been a major increase in the number of students who now have the option of attending school in-person, or will soon.

According to a school reopening tracker created by the American Enterprise Institute, 7 percent of the more than 8,000 districts being tracked were fully remote on March 22, the lowest percentage since the tracker was started in November. Forty-one percent of districts were offering full-time in-person instruction, the highest percentage in that time. Those findings have been echoed by other surveys.

In February, the C.D.C. issued guidelines that said K-12 schools could reopen safely as long as they followed basic health protocols like masking or distancing.

More recently, it said that elementary students and some middle and high schoolers could be spaced three feet apart in classrooms, instead of six feet, as long as everyone was wearing a mask. Unions had used the six-foot guidance to oppose bringing children back for normal schedules.

“Our push to ensure that teachers, school staff, and child care workers were vaccinated during March has paid off and paved the way for safer in-person learning,” Dr. Rochelle Walensky, the center’s director, said in a statement released on Tuesday.

Mr. Biden touted the C.D.C.’s newly released benchmark while visiting a vaccination site in Alexandra, Va., on Tuesday.

“That is great progress protecting our educators and our essential workers,” Mr. Biden said of the new estimate. “And because our vaccine program is in overdrive, we are making it easier to get a vaccination shot.”

The American Federation of Teachers, the nation’s second-largest teacher’s union, on Tuesday released a survey that reported over 80 percent of association members had been vaccinated or had made a vaccine appointment. About 85 percent of members said their school was “operating on at least a part-time basis,” according to the survey.

Randi Weingarten, the federation’s president, said in a statement on Tuesday that “A.F.T. members have embraced vaccines as vital to getting back in the classroom.”

“They want to return, the road map to reopening is robust, and if we instill trust and meet fear with facts we can finally end this national nightmare,” Ms. Weingarten said.

A guest showed her “Excelsior Pass,” with proof of vaccination, on a phone outside the The Shed, a performing and visual arts venue in New York.
Credit…Angela Weiss/Agence France-Presse — Getty Images

Around the United States, businesses, schools and politicians are considering “vaccine passports” — digital proof of vaccination against the coronavirus — as a path to reviving the economy and getting Americans back to work and play.

New York has rolled out “Excelsior Pass,” billed by the state as “a free, fast and secure way to present digital proof of Covid-19 vaccination” in case reopening sports and entertainment venues require proof of attendees’ status.

Walmart is offering electronic verification apps to patients vaccinated in its stores so they “can easily access their vaccine status as needed,” the company said.

But the idea is raising charged legal and ethical questions: Can businesses require employees or customers to provide proof of vaccination against the coronavirus when the vaccine is ostensibly voluntary?

Can schools require that students prove they have been injected with what is still officially an experimental prophylaxis the same way they require long-approved vaccines for measles and polio? And finally, can governments mandate vaccinations — or stand in the way of businesses or educational institutions that demand proof?

Legal experts say the answer to all of these questions is generally yes, though in a society so divided, politicians are girding for a fight. Government entities like school boards and the Army can require vaccinations for entry, service and travel — practices that flow from a 1905 Supreme Court ruling that said states could require residents to be vaccinated against smallpox or pay a fine.

Backers of digital vaccination cards are pressing the Biden administration to become involved, at least by setting standards for privacy and for verifying the accuracy of the records.

The White House is clearly skittish.

“The government is not now nor will we be supporting a system that requires Americans to carry a credential,” Jen Psaki, the White House press secretary, said on Tuesday.

Republican critics say vaccine passports raise the specter of centralized databases of vaccinated people, which they view as a government intrusion on privacy.

“A vaccine passport — a unified, centralized system for providing or denying access to everyday activities like shopping and dining — would be a nightmare for civil liberties and privacy,” Justin Amash, a former Republican congressman who is now a libertarian, wrote on Twitter last week.

But, in fact, every state already has a database, or an “immunization registry.” And under “data use agreements,” the states are required to share their registries with the C.D.C., though the agency de-identifies the information and not all states have agreed to provide it.

global roundup

A vaccination center in Kathmandu, Nepal, last month.
Credit…Niranjan Shrestha/Associated Press

Three weeks after suspending its vaccination campaign, Nepal has started administering shots again thanks to a gift of doses from China.

Nepal, a poor Himalayan nation, had been depending on vaccines manufactured in neighboring India, but last month India began cutting vaccine exports as the country experienced a surge in coronavirus cases. Nepal’s vaccination effort ground to a halt, even as infections began to rise again.

Last week, Nepal’s other giant neighbor, China, stepped in with a donation of 800,000 doses of the vaccine developed by Sinopharm, a state-owned company.

The vaccines will be administered to essential workers, Nepali students preparing to travel to China to study and those living in districts along the Nepal-China border, health officials said. Taranath Pokhrel, a senior official in Nepal’s health department, said that the Chinese government asked Nepal to give priority to the students and to people involved in cross-border trade, presumably to reduce the risk of infected people crossing into China.

Thousands of Nepali students study at Chinese universities under Chinese government scholarships. China, to increase the appeal of its vaccines, has said that foreigners who are inoculated with Chinese-made vaccines may face fewer bureaucratic hurdles entering the country.

Nepal, a nation of 30 million people, has vaccinated more than 1.7 million and slowly begun reopening to visitors, including to a few hundred climbers attempting to scale Mount Everest. The country reported very few infections in January, but new cases have surpassed 300 in recent days, part of a worrying resurgence in new cases across South Asia. India, which shares a porous border with Nepal, recorded more than 115,000 new infections on Wednesday, by far its highest daily total since the pandemic began.

The future of Nepal’s vaccination campaign remains uncertain because the Chinese donation falls short of the two million vaccine doses Nepal was due to receive under an agreement with the Indian manufacturer, the Serum Institute of India. Nepal officials said that they had paid the company 80 percent of the contract price but received only half of the doses. Serum’s chief executive said this week that he hoped to restart exports by June if new infections in India subsided.

“Our entire diplomatic channels are mobilized to get vaccines, but none has assured us of providing vaccines when we tried to procure them,” Dr. Pokhrel said.

In other news from around the world:

With only months left in office, Chancellor Angela Merkel of Germany has struggled to rally support for a national lockdown.
Credit…Hannibal Hanschke/Agence France-Presse — Getty Images

Chancellor Angela Merkel of Germany has called for a short and strict nationwide lockdown to bring down the number of new coronavirus infections in the country, according to her spokeswoman, but will meet with local officials next week to discuss potential regulations.

A year after the first lockdown was successful in tamping down cases, the country’s 16 governors are finding it harder than ever to agree on a unified plan to stem new infections. And with only months left in office, Ms. Merkel has found it increasingly difficult to rally support for a national lockdown as fatigue from prolonged restrictions looms large even as cases rise.

The governors and Ms. Merkel are scheduled to meet on Monday to hammer out new regulations.

While Armin Laschet, the governor of the country’s most populous state and a potential successor to Ms. Merkel, has made similar calls for a two- to three-week hard lockdown to bring down infections, other governors are pushing back. The governor of one small state even began a pilot program on Tuesday to reopen theaters, gyms and restaurant patios.

“A common nationwide approach would also be important here,” Ulrike Demmer, the deputy government spokeswoman, said during a daily news conference, referring to the confusing and often contradictory rules set by state governors. Ms. Demmer also pointed to the rising number of coronavirus patients in intensive care wards as a cause for concern.

According to Ms. Demmer, the goal is to get the infection rate below 100 new cases per 100,000 before the authorities should consider easing restrictions.

On Tuesday, the German health authorities recorded an average of 110 infections per 100,000 people over the previous 7 days, but warned that because fewer people were tested over the Easter holiday weekend, the number was likely to be much higher.

According to a New York Times database, Germany is averaging 15,562 new infections daily and since the pandemic began. More than 77,000 have died with the disease in the country since the pandemic began.

People accused of breaking coronavirus rules were made to exercise as punishment in Manila last month.
Credit…Lisa Marie David/Reuters

A 28-year-old man has died in the Philippines after the police forced him to do 300 squats as punishment after he was caught violating coronavirus lockdown rules.

The man, Darren Manaog Peñaredondo, was detained on Thursday in General Trias city, a Manila suburb, over a curfew violation. Officials have struggled to contain infections in the southeast Asian nation and have increasingly resorted to harsh tactics to enforce restrictions, rights groups say.

He was released the following day, but first was forced to complete 300 squats, his relatives said.

It is not the first time that the authorities have been accused of using aggressive tactics against civilians during the pandemic. President Rodrigo Duterte told the police last year not to be afraid to shoot anyone who “causes commotion,” after 20 people protesting restrictions were arrested. Last year, a former soldier suffering from mental health issues was gunned down by the police as he tried to cross a coronavirus checkpoint.

Mr. Peñaredondo’s partner, Reichelyn Balce, said that when he returned home on Friday after being detained, he had shown signs of fatigue.

“He told me that he fell when doing the exercises,” she said. “He struggled to walk when he got home. When he went to relieve himself, he turned blue and convulsed.”

She said that Mr. Peñaredondo was revived but he later died.

Two police officers who imposed the harsh punishment have been suspended pending the results of an investigation into their actions, said Brig. Gen. Ildebrandi Usana, a national police spokesman.

The local police had initially denied the events, but two men who were detained with Mr. Peñaredondo signed a sworn statement about the ordeal.

Cristina Palabay, who leads a local rights group called Karapatan, said that the police punishment amounted to “a form of torture that is cruel and inhuman” and signaled that the local police had adopted a “strongman approach.”

Ms. Palabay’s group aids families of the thousands of citizens killed in the president’s aggressive war on drugs.

The country’s Commission on Human Rights was critical of what it called an “overreach of the enforcement of quarantine rules and regulations,” according to the body’s spokeswoman, Jacqueline Ann de Guia.

Ms. de Guia said that curfew violations called for community service or a fine, rather than harsh physical punishment.

Near Cora, Wyo., in March. In the throes of a pandemic that has made the indoors inherently dangerous, tens of thousands more Americans than usual have flocked outdoors.
Credit…Max Whittaker for The New York Times

Kenna Tanner and her team can list the cases from memory: There was the woman who got tired and did not feel like finishing her hike; the campers, in shorts during a blizzard; the base jumper, misjudging his leap from a treacherous granite cliff face; the ill-equipped snowmobiler, buried up to his neck in an avalanche.

All of them were pulled by Ms. Tanner and the Tip Top Search and Rescue crew from the rugged Wind River mountain range — the Winds, as the range is known locally — in the past year in a sprawling, remote pocket of western Wyoming. And all of them, their rescuers said, were wildly unprepared for the brutal backcountry in which they were traveling.

“It is super frustrating,” said Ms. Tanner, Tip Top’s director. “We just wish that people respected the risk.”

In the throes of a pandemic that has made the indoors inherently dangerous, tens of thousands more Americans than usual have flocked outdoors, fleeing crowded cities for national parks and the public lands around them. But as these hordes of inexperienced adventurers explore the treacherous terrain of the backcountry, many inevitably call for help. It has strained the patchwork, volunteer-based search-and-rescue system in America’s West.

Where places like Canada or Switzerland have professional, full-time teams that manage everything from lost tourists to fatal mountaineering accidents, most operations in the United States are handled by a loose network of volunteer organizations like Tip Top, which are overseen by local sheriffs.

For much of the country’s history, this patchwork system met demand. But that trend has shifted in the past decade — and rapidly, over the past year — as less experienced recreationalists push further into treacherous places.

No one expects the eventual end of the pandemic to stem the flood of newcomers to the Winds, which people grudgingly admit have been discovered. Property values continue to soar in Sublette County, and even this winter, locals say out-of-state plates were more common than Wyoming plates in trailhead parking lots.

“You can’t stop it,” said Chris Hayes, who works at an outdoor retailer in Pinedale and also runs a fishing guide service. “There’s no secret place anymore. They’re all gone.”

Credit…Moritz Wienert

Before the pandemic, I found comfort in the routine of my life and the rhythms of my family — what Nora Ephron once called the “peanut-butter-and-jellyness” of days with children. I liked the morning thunderdome of getting the children dressed and fed, dropping them at school and taking the 20-minute walk to the subway.

At this point my commute is the five feet from my bed to my desk, and I am somehow both tired and agitated when I start work each day. My kids never leave the house, except when we go to the same three parks in our neighborhood. Sometimes when I go running outside, I fantasize about just … not stopping, my eyes thirsty for some new horizon.

In other words, I’m so freaking bored.

Here’s how one boredom researcher — yes, there are boredom researchers — has defined the emotion. “‘Feeling unchallenged’ and perceiving one’s ‘activities as meaningless’ is central to boredom,” concluded a study by Wijnand Van Tilburg, an experimental social psychologist at the University of Essex in England.

Even in normal times, boredom is a very common emotion — a study of almost 4,000 American adults found that 63 percent felt bored at least once in a 10-day sampling period. The causes of boredom are multifaceted, but a lack of control over your situation is a common one. He added, “There’s research that shows when you’re limited in your control over the situation — that intensifies boredom.”

Knowing that many of us may not be able to have much control over our movements for at least the next few months, how do we try to alleviate our boredom? First, the researchers I spoke to said it’s important to acknowledge there’s no easy fix for our doldrums — so much of what is happening right now is beyond our control, and the vaccines are just beginning to be tested in children under 12, so we may not be able to make big moves just yet.

This weekend, we saw relatives I adore for an outdoor Easter egg hunt. Just 90 minutes of warm interaction with these beloved adults made me feel so happy and alive that I was smiling for the rest of the day.

As the weather gets warmer and more of my peers are inoculated, I am planning more get-togethers. Whenever I drop back into the doldrums, I will think about all the walks and dinners and hugs on the horizon.

Kate Whelley McCabe, a co-founder of Vermont Evaporator Company, which saw customer demand double during the pandemic, tapping trees in a neighbor’s yard near Montpelier, Vt.
Credit…Jay Ericson

Stress-baking and panic shopping. Vegetable regrowing and crafting. Now we can add another hobby to a year of quarantine trends: backyard maple sugaring.

Among the many indicators that it’s on the rise: a run on at-home evaporators and other syrup-making accouterments. A surge in traffic and subscriptions to syrup-making websites and trade publications. And, of course, lots of documentation on social media. (The Facebook group Backyard Maple Syrup Makers added some 5,000 members, almost doubling the its community, in the past year.)

Tapping maple trees and boiling the sap into syrup — known as sugaring — isn’t a new hobby. What’s unique about this year is the influx of suburban and urban backyard adventurers fueling these maple sugaring highs.

Claire and Thomas Gallagher, for example, tapped a tree behind their home in New Rochelle, N.Y., for the first time three weeks ago.

“It’s such a fun thing to do with the kids, it gets us outside, it’s educational,” Ms. Gallagher, 37, said. And with everyone at home all winter and probably the spring as well, the Gallaghers decided there would never be a better year to try it.

Because sugaring is a sticky business — and boiling sap indoors can mean resin all over the walls — many backyard amateurs turn to small-scale, hobby-size evaporators like the ones sold by Vermont Evaporator Company in Montpelier, Vt.

“When we started our company five years ago, our customers used to look just like us: rural homeowners with five to 10 acres of land,” said Kate Whelley McCabe, the chief executive. “Now we sell to people all over the country and to a growing number of suburban and urban customers.”

The governor of New Hampshire, Chris Sununu, is a dedicated sugarer. His 8-year old son, Leo, is his tree tapping assistant, and his two teenagers, Edie and Calvin, “do the heavy lifting.”

Governor Sununu said that when the tree sap begins to flow, it’s the official signal that spring has arrived. “It’s been a long winter and a long year. The sun is coming up, the days are getting warmer, and when the sap ran this year, we knew we were really coming out of winter with a lot of optimism,” he said in an interview.

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Imagining the Timeless Childhood of Beverly Cleary’s Portland

Fifteen months ago I traveled to Portland, Ore., to visit the childhood haunts and homes of Beverly Cleary, the beloved and award-winning author of more than 40 books for children and young adults. I was accompanied by my husband and our daughter, all three of us aficionados of Ramona Quimby, us parents having read all the books as children, before rereading them aloud to our kid.

With an overseas move on the horizon, we had decided to visit the city that plays its own subtle but essential role in the author’s most popular novels: Portland, with its moody rain and splashy puddles, its streets named after regional Native American tribes, its welcoming libraries and worm-filled parks. The Oregon of Ms. Cleary’s childhood clearly inspired her imagination — among her books, close to half of them are set in Portland.

So in the last days of December 2019, we took a trip to the City of Roses, visiting the northeastern Grant Park and Hollywood neighborhoods of Ms. Cleary’s childhood. I didn’t know then that it would be our last family vacation before the coronavirus pandemic — and I couldn’t have imagined how often I would return to those memories during the months of our confinement.

Credit…Alamy

When Ms. Cleary died on March 25 at the age of 104, my sorrow at the loss of an adored author who was declared a “Living Legend” by the Library of Congress in 2000 was coupled with memories of our journey. Scrolling through the photos of our trip, the simple scenes of Craftsman homes, verdant parks, and crowded children’s libraries evoked a lost innocence.

As a child, I loved Ms. Cleary’s books because they didn’t condescend. Her characters are ordinary kids succumbing to ordinary temptations, such as squeezing an entire tube of toothpaste into the sink, or taking the first, juicy bite out of every apple in the crate.

As an adult, rereading the books aloud to my daughter, I was struck by their sense of timelessness — sisters struggling with sibling rivalry, parents grappling with financial worries and job loss. The author’s own father lost his Yamhill farm when she was 6, moving the family of three about 40 miles northeast to Portland — the “city of regular paychecks, concrete sidewalks instead of boardwalks, parks with lawns and flower beds, streetcars instead of a hack from the livery stable, a library with a children’s room that seemed as big as a Masonic hall,” she wrote in her 1988 memoir, “A Girl From Yamhill.”

I thought of that when I saw one of Ms. Cleary’s cherished childhood homes, a modest, bungalow near Grant Park, on a block lined with closely set houses. She romped with a gang of “children the right age to play with,” and their escapades made her yearn for stories about the neighborhood kids. “I longed for books about the children of Hancock Street,” she wrote in “A Girl from Yamhill.” In her stories, she changed Hancock Street to Klickitat Street “because I had always liked the sound of the name when I had lived nearby.”

We found the Klickitat Street of the books nearby, along with Tillamook Street, both named after Native American tribes of the Pacific Northwest. As my 6-year-old daughter raced along, searching for vintage hitching rings, I pictured Ramona — or even a young Beverly — on these same sidewalks, stumping on stilts made from two-pound coffee cans and twine, or perching on the curb to watch the Rose Festival parade.

Over the next few days, we found the author’s former elementary school, a brick building now named the Beverly Cleary School, Fernwood Campus. We stopped by the Multnomah County Central Library, a stately brick structure downtown where she did summer “practice work” as a student librarian (and where the children’s section also bears her name). We ate doughnuts and pizza. We visited Grant Park, where the local artist Lee Hunt created a trio of bronze sculptures depicting three of Ms. Cleary’s cherished characters: Henry Huggins, his dog, Ribsy, and Ramona, posed, as if in motion.

Credit…Ann Mah

Though it was a typical Portland winter day — wet — nothing could dampen my daughter’s joy when she saw her favorite characters rendered slightly larger than life. She ran to hold Ramona’s hand, beaming, and the picture I snapped will be forever burned on my heart.

For my daughter, the best part of the trip was our visit to the Willamette Valley town of Yamhill, where we glimpsed the turreted Victorian house in which Ms. Cleary spent the first six years of her life. We spent the night in a vintage trailer park nearby, sleeping in a 1963 Airstream Overlander, as I imagined the author might have done with her own young family. For dinner, we roasted hot dogs and marshmallows, a meal that my daughter still describes as one of the best of her life.

These are the memories I’ve turned to over the past year as the pandemic has stolen away life’s simple pleasures. A wet afternoon at the park. Warming up at the library story hour. A cup of hot chocolate sipped at a crowded cafe. The rain beating on the metal roof of our camper van, reminding me of the creative inspiration that Ms. Cleary described in “A Girl From Yamhill”: “Whenever it rains, I feel the urge to write. Most of my books are written in winter.”

Before our trip, I had wondered if my daughter was too young for a literary pilgrimage — and perhaps she was, for there were moments when searching for yet another filament of the author’s girlhood tried her patience. And yet, though it was only a few days, our trip has captured her memory. She speaks of it now with crystalline precision, reminiscing of the last days before the strangest year of our lives began.

Our last morning in Portland found us a weary group of travelers as we waited to board our pre-dawn flight. We queued at the airport coffee counter for muffins and hot drinks — but when I tried to pay, the cashier told me that an anonymous stranger had bought us breakfast.

“Mama! It’s just like in the book!” exclaimed my daughter. It took me a few minutes to realize she was talking about a scene from “Ramona Quimby, Age 8,” when the Quimby family — worn down by financial worries, family squabbles and dreary weather — try to cheer themselves up with a hamburger dinner they can barely afford, only to have a kindly gentleman anonymously pick up their check.

That moment seems like a dream now, disconnected as we are from one another, all of us existing in our bubbles. But one day soon we will meet again and touch each other’s lives, not just as friends and family, but also as strangers. In the meantime, we have Beverly Cleary’s books to remind us.


Ann Mah, the author of the novel, The Lost Vintage, lives in Hanoi, Vietnam.

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Why We Romanticize the Past

Then there’s the simple fact that most of us prefer reminiscing about positive experiences, which gives us “preferential access” to those memories, Dr. Schacter explained. In other words, aspects of the past that we enjoy thinking about tend to stick with us over time, while elements we don’t think about fade away. Researchers call this retrieval-induced forgetting. “This may contribute to a positive memory bias because we tend not to rehearse, rehash and retrieve negative experiences,” Dr. Schacter added. Traumatic memories, which are often intrusive and persistent, are the notable exception.

Our general tendency to recall positive memories over negative ones is especially pronounced when we feel discomfort in the present. That’s because the process of recalling the past is always dictated by “the perspective that we’re coming in with and the questions we’re asking about the past,” Dr. Wilson said. She called this our “current lens.”

Your current lens acts as a kind of filter, determining what details you dredge up and what you make of them. Living amid a deadly pandemic and the worst economic crisis since the Great Depression, we’re all primed with some degree of collective nostalgia as a baseline. “If we start out with the hypothesis that things were better in the past, then we’ll pull out memories to confirm that,” Dr. Wilson said.

Part of this has to do with what researchers call “mood repair” — doing what we can to lift ourselves up when we’re feeling down. “Memory isn’t just there to help us remember where the car is parked,” Dr. de Brigard said. “It also plays other roles, and one of them is to help us feel better.”

None of this is incidental — autobiographical memory has evolved this way for good reason.

In her research, Dr. Wilson found that we manipulate our personal memories to create a coherent identity and favorable sense of self over time.

This may mean embellishing our memories with imaginative elements, or omitting details we’d rather not dwell on. “We know that memory and imagination interact enormously,” Dr. de Brigard said. “We often imagine ways in which the past could’ve happened. Then our imagination penetrates the original memory and modifies the content.”

While the malleable quality of our memory makes it vulnerable to manipulation, and error, it’s also a real adaptation of the human mind. “Recalling past positive events is an adaptive way to regulate emotion in the present and enhance optimism about the future,” Dr. Schacter said.

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