A Kenyan court on Friday prohibited the deployment of 1,000 Kenyan police officers to Haiti, jeopardizing a multinational security force charged with stabilizing the chaos-hit Caribbean island nation before it even got off the ground.

The force, which is backed by the United Nations and financed by the United States, had been stalled since October, when Kenyan opponents of the mission challenged it in court, calling it unconstitutional. The High Court upheld those arguments on Friday, throwing into doubt the latest international effort to rescue an impoverished country that is spiraling ever deeper into violence and instability.

“An order is hereby issued prohibiting the deployment of police officers to Haiti or any other country,” Justice Chacha Mwita said at the conclusion of a judgment that took over 40 minutes to read.

The international force was meant to help break the grip of the armed gangs that control most of Haiti’s capital, Port-au-Prince, and that have turned Haiti into one of the world’s most dangerous nations. Haiti’s government has pleaded for foreign military forces to be sent in to restore order, but the United States and Canada have been unwilling to commit their own troops.

Kenya agreed last summer to lead the mission, with backing from Washington, which pledged $200 million. The force was intended to eventually increase to 3,000 security officers.

But just a handful of Caribbean nations have stepped forward to contribute troops, and the court order on Friday threw the mission even further into doubt. The Kenyan government is expected to appeal the decision.

The daunting task facing any mission to Haiti was highlighted by the latest violent eruption in the capital last week.

Flaming barricades sprang up across Port-au-Prince as police officers clashed with armed gangs, sending the city into lockdown as residents retreated into their homes, seeking shelter. About 24 people were killed — not an unusual toll in a country of fewer than 12 million people where about 5,000 people died violently last year, twice as many as in 2022, and about 2,500 were kidnapped, the United Nations said this week.

Haiti’s political system is teetering on the verge of collapse. Calls have been growing for the resignation of the interim prime minister, Ariel Henry, who has been in charge since the assassination in 2021 of President Jovenal Moïse.

In advance of Friday’s ruling, a spokesman for Kenya’s police declined to answer questions about the composition of the force. But Western officials briefed on the force said it was intended to initially comprise up to 400 officers drawn mostly from Kenya’s Border Police Unit and the paramilitary General Service Unit — officers whose work normally involves fighting Islamist militants, border smugglers and cattle rustlers.

All of that is now in doubt, even though the Kenyan Parliament approved the mission in November.

The ruling represents yet another sharp rebuke to Kenya’s president, William Ruto, by the country’s courts, which have blocked or stalled several major policy initiatives in the past six months.

Those decisions have visibly angered Mr. Ruto, who publicly hin ted in recent months that he might defy the courts, stoking worries about a wider clash between Kenya’s government and its fiercely independent higher judiciary.

In his ruling on Friday, the judge said that Kenya’s National Security Council lacked the authority to deploy a police mission to Haiti. Under the law, it could only take place if a “reciprocal arrangement” was in place with the Haitian government, he said.

The prohibition is also a major challenge for Mr. Ruto’s relationship with the United States, which is almost entirely funding the proposed mission to Haiti.

In September, soon after Kenya agreed to lead the international mission to Haiti, the U.S. ambassador to Kenya, Meg Whitman, accompanied Mr. Ruto on a tour of major Silicon Valley firms like Apple, Google and Intel, hoping to attract investment in Kenya. (Ms. Whitman was previously the chief executive officer of eBay and Hewlett-Packard).

For the Biden administration, calming the waters in Haiti has advantages in an election year, especially when the wave of migrants seeking asylum has become a political and humanitarian crisis. The number of Haitians immigrating to the United States has more than doubled in the past two years, with more than 160,000 people arriving in 2023, according to U.S. data.

In recent months, United Nations and American officials have been coordinating closely with Kenyan police leaders at training centers near the capital, Nairobi, as they prepared for the expected deployment to Haiti.

Still, many Kenyans had questioned the merits of a dangerous mission in a distant country. Although Kenya forces have participated in several U.N. and regional peacekeeping missions, the public is highly sensitive to casualties.

The deaths of Kenyan soldiers deployed to neighboring Somalia to fight Al Shabab militants often stirs vocal public opprobrium. Any further deaths from a Haiti mission could stoke criticism of Mr. Ruto’s government, which is already grappling with a severe economic downturn.

Financial problems were also a worry. The $200 million in American support, about half from the Defense Department, would pay for equipment, advisers and medical support to the Kenyans, as well as help with planning, logistics and communications, a State Department spokeswoman said.

But Kenyan officials said that much more was needed. Addressing the U.N. Security Council on Thursday, Kenya’s ambassador, Martin Kimani, appealed for other nations to bridge the mission’s “substantial resource gap” with contributions of money, equipment and logistical support.

There was no immediate reaction to the court ruling in Haiti, where it was early morning when the decision was announced.

Haitians have long been wary of international interventions. In 2010, a United Nations peacekeeping force brought cholera to the country as poor sanitation at a base camp sent sewage downriver, leading to over 9,000 deaths. Sexual exploitation by peacekeepers and aid workers has been documented repeatedly, and researchers say it resulted in the births of hundreds of children.

Still, Haiti’s increasingly desperate security crisis has left many Haitians open to another international intervention. Armed gangs regularly abduct passengers from buses, to be held for ransom. Six nuns were released on Wednesday, six days after they were kidnapped.

At a waiting room in a health clinic in Port-au-Prince on Wednesday, patients said that they would support the effort if the Kenyans were willing to try. None of the patients agreed to be named, saying they feared they would be killed for speaking out.

But several predicted that an international force could succeed only if it were backed by a heavily armed pro-government militia, and not the discredited national police that the Kenyans were expected to be working alongside.

Some communities banded together last year to form vigilante groups that fought back against gangs, sometimes committing atrocities of their own. That movement largely fizzled out.

Jeff Frazier, a former United States paratrooper who runs a nonprofit in Haiti and has been lobbying Washington for a stronger intervention, said that a Kenyan-led mission was the best option in dire times.

“Are there alternatives? Sure, but they’re a mess,” said Mr. Frazier, who spent 43 days in captivity last year after being kidnapped by a gang. The Kenyans’ focus, he said, should be to rescue desperate Haitians from “vicious gangs that kidnap women and send torture videos of them with bloodied faces and cigarette-burned backs to their loved ones.”

As a motivation for undertaking such a dangerous mission, Kenyan officials have cited their country’s longstanding ties with the Caribbean, going back to Kenya’s founding father Jomo Kenyatta. Financial considerations may play a role too: Many developing nations have viewed United Nations peacekeeping missions, often in Africa, as a way to subsidize or reward their security forces.

Andre Paulte contributed reporting from Port-au-Prince, Haiti.

King Charles III has been admitted to a London hospital for a procedure to treat an enlarged prostate, Buckingham Palace confirmed on Friday.

News images showed Charles arriving around 9 a.m. at the London Clinic, a private hospital, where his daughter-in-law Catherine, Princess of Wales, is recovering from abdominal surgery.

The palace announced the king’s pending treatment last week shortly after the news that Catherine, Prince William’s wife, had undergone surgery in London. Her office in Kensington Palace said she would remain in the hospital for 10 to 14 days to recover.

The king’s recovery is expected to be much swifter, though the palace did not say how long he was expected to stay in the hospital. By announcing his elective prostate procedure in advance, the palace said, Charles, 75, hoped to encourage other men with similar symptoms to get checked.

“The king was this morning admitted to a London hospital for scheduled treatment,” the palace said in a statement. “His Majesty would like to thank all those who sent their good wishes over the past week, and is delighted to learn the diagnosis is having a positive impact on public health awareness.”

Benign prostate enlargement is common in men over age 50, according to Britain’s National Health Service. It can be found in up to 90 percent of men over 70. Symptoms include difficulty urinating and urgency to urinate. It is not cancerous and it does not usually pose a serious health threat.

Treatment includes medication and changes to diet and lifestyle, as well as surgical procedures in more severe cases to remove excess tissue from the prostate gland. Buckingham Palace did not describe the procedure that Charles would undergo.

Medical experts said that the most common treatment was a transurethral resection of the prostate, in which a surgeon scrapes out the inside of the prostate gland, giving the urethra more space.

Charles’s planned treatment follows a period of troubling health news for the British royal family. In addition to Catherine, Sarah Ferguson, Duchess of York and ex-wife of the king’s younger brother, Prince Andrew, said on Monday that she had been diagnosed with melanoma, a serious type of skin cancer.

It was her second cancer diagnosis within a year. Ms. Ferguson, 64, had spoken publicly about her decision to undergo a mastectomy and reconstructive surgery last year after a breast cancer diagnosis in the summer.

The London Clinic, an elite private institution in the Marylebone neighborhood of London, has treated other members of the royal family, as well as celebrities like the actress Elizabeth Taylor and foreign leaders like the Chilean dictator Augusto Pinochet. John F. Kennedy, the future president, was told by doctors he had Addison’s disease while a patient at the hospital in 1947.

Fake, sexually explicit images of Taylor Swift likely generated by artificial intelligence spread rapidly across social media platforms this week, disturbing fans who saw them and reigniting calls from lawmakers to protect women and crack down on the platforms and technology that spread such images.

One image shared by a user on X, formerly Twitter, was viewed 47 million times before the account was suspended on Thursday. X suspended several accounts that posted the faked images of Ms. Swift, but the images were shared on other social media platforms and continued to spread despite those companies’ efforts to remove them.

While X said it was working to remove the images, fans of the pop superstar flooded the platform in protest. They posted related keywords, along with the sentence “Protect Taylor Swift,” in an effort to drown out the explicit images and make them more difficult to find.

Reality Defender, a cybersecurity company focused on detecting A.I., determined with 90 percent confidence that the images were created using a diffusion model, an A.I.-driven technology accessible through more than 100,000 apps and publicly available models, said Ben Colman, the company’s co-founder and chief executive.

As the A.I. industry has boomed, companies have raced to release tools that enable users to create images, videos, text and audio recordings with simple prompts. The A.I. tools are wildly popular but have made it easier and cheaper than ever to create so-called deepfakes, which portray people doing or saying things they have never done.

Researchers now fear that deepfakes are becoming a powerful disinformation force, enabling everyday internet users to create nonconsensual nude images or embarrassing portrayals of political candidates. Artificial intelligence was used to create fake robocalls of President Biden during the New Hampshire primary, and Ms. Swift was featured this month in deepfake ads hawking cookware.

“It’s always been a dark undercurrent of the internet, nonconsensual pornography of various sorts,” said Oren Etzioni, a computer science professor at the University of Washington who works on deepfake detection. “Now it’s a new strain of it that’s particularly noxious.”

“We are going to see a tsunami of these A.I.-generated explicit images. The people who generated this see this as a success,” Mr. Etzioni said.

X said it had a zero-tolerance policy toward the content. “Our teams are actively removing all identified images and taking appropriate actions against the accounts responsible for posting them,” a representative said in a statement. “We’re closely monitoring the situation to ensure that any further violations are immediately addressed, and the content is removed.”

X has seen an increase in problematic content including harassment, disinformation and hate speech since Elon Musk bought the service in 2022. He has loosened the website’s content rules and fired, laid off or accepted the resignations of staff members who worked to remove such content. The platform also reinstated accounts that had been previously banned for violating rules.

Although many of the companies that produce generative A.I. tools ban their users from creating explicit imagery, people find ways to break the rules. “It’s an arms race, and it seems that whenever somebody comes up with a guardrail, someone else figures out how to jailbreak,” Mr. Etzioni said.

The images originated in a channel on the messaging app Telegram that is dedicated to producing such images, according to 404 Media, a technology news site. But the deepfakes garnered broad attention after being posted on X and other social media services, where they spread rapidly.

Some states have restricted pornographic and political deepfakes. But the restrictions have not had a strong impact, and there are no federal regulations of such deepfakes, Mr. Colman said. Platforms have tried to address deepfakes by asking users to report them, but that method has not worked, he added. By the time they are flagged, millions of users have already seen them.

“The toothpaste is already out of the tube,” he said.

Ms. Swift’s publicist, Tree Paine, did not immediately respond to requests for comment late Thursday.

The deepfakes of Ms. Swift prompted renewed calls for action from lawmakers. Representative Joe Morelle, a Democrat from New York who introduced a bill last year that would make sharing such images a federal crime, said on X that the spread of the images was “appalling,” adding: “It’s happening to women everywhere, every day.”

“I’ve repeatedly warned that AI could be used to generate non-consensual intimate imagery,” Senator Mark Warner, a Democrat from Virginia and chairman of the Senate Intelligence Committee, said of the images on X. “This is a deplorable situation.”

Representative Yvette D. Clarke, a Democrat from New York, said that advancements in artificial intelligence had made creating deepfakes easier and cheaper.

“What’s happened to Taylor Swift is nothing new,” she said.

There’s a shift underway in Asia that’s reverberating through global financial markets.

Japan’s stock market, overlooked by investors for decades, is making a furious comeback. The benchmark Nikkei 225 index is edging closer to the record it set on Dec. 29, 1989, which effectively marked the peak of Japan’s economic ascendancy before a collapse that led to decades of low growth.

China, long an impossible-to-ignore market, has been spiraling downward. Stocks in China recently touched lows not seen since a rout in 2015, and Hong Kong’s Hang Seng Index was the worst-performing major market in the world last year. Stocks stemmed their slide only when Beijing recently signaled its intention to intervene but remain far below previous highs.

This year was set to be a tumultuous one for global markets, with unpredictable swings as economic fortunes diverge and voters in more than 50 countries go to the polls. But there’s one unforeseen reversal already underway: a change in perception among investors about China and Japan.

Seizing on this shift, Japan’s prime minister, Fumio Kishida, addressed more than 3,000 global financiers gathered in Hong Kong this week for a conference sponsored by Goldman Sachs. It was the first time a Japanese prime minister had given a keynote address at the event.

“Now Japan has a golden opportunity to completely overcome low economic growth and a deflationary environment that have persisted for a quarter of a century,” Mr. Kishida said in a video recording. His government, he said, would “demonstrate to all of you Japan’s transition to a new economic stage by mobilizing all the policy tools.”

It’s the kind of message that Japan has been honing for a decade, and now investors want to hear more of it. Foreign investors pumped $2.6 billion into the Japanese stock market last week, adding to $6.5 billion the week before, according to data from Japan Exchange Group. That is a stark shift from the roughly $3.6 billion that was yanked out in December.

All that money has sent Tokyo’s Nikkei 225 surging about 8 percent this month. The market is up over 30 percent over the past 12 months. This week, Toyota rose to a record market value for a Japanese company, about $330 billion, surpassing the mark set in 1987 by the telecom conglomerate NTT.

A combination of factors has contributed to Japan’s recent success. A weak yen has made stocks look cheap to foreign investors, and it has been a boon to exporters and multinationals based in Japan that make their profits overseas. Important reforms to the corporate sector have given shareholders more rights, enabling them to call for changes in strategy and management. Unlike inflation in other parts of the world, rising inflation in Japan has been a sign that things are headed in the right direction, after decades of falling prices and sluggish economic growth dampened appetite among consumers and companies to spend.

And there is one additional factor: geopolitics. The longer-term prospects for Japan, the third-largest economy, are looking good when parts of the world are souring on the second-largest economy, China.

“One of the best things to happen to Japan is China,” said Seth Fischer, the founder and chief investment officer at Oasis Management, a hedge fund based in Hong Kong.

“Japan has for 10 years been working on creating a more productive corporate environment and a better place to be an equity investor through consistently trying to improve value,” Mr. Fischer said. “People don’t believe the same about China.”

In a recent survey of global fund managers by Bank of America, selling Chinese stocks and buying Japanese stocks were two of the three most popular trade ideas. (The other was to load up on high-flying U.S. tech stocks.)

China’s ruling Communist Party has sought to insert itself into the business sector in recent years, leaving investors worried that politics often trumps the bottom line for many of China’s corporate titans. The blurring of politics and business has also raised concerns in Washington and in European capitals, leading to regulations that have prevented foreign investments into certain sectors and companies.

China has not struggled for economic growth like Japan, but a protracted property market collapse has shredded consumer and investor confidence. Lingering issues with China’s economy have exacerbated weakness in the country’s currency, the yuan.

Much of the negative sentiment has played out in Hong Kong, an open market where global investors traditionally place their bets on China and its companies. The market was pummeled last year, and it slipped further over the first three weeks of this year.

Beijing intervened this week to try to reverse the sell-off. On Monday, the country’s No. 2 official, Premier Li Qiang, called on the authorities to be more “forceful” and take more measures to “improve market confidence.” His speech lifted stocks, as did a report from Bloomberg, citing unnamed officials, that the authorities were contemplating a $278 billion market rescue.

Then on Wednesday, the central bank, the People’s Bank of China, freed commercial banks to do more lending, essentially pumping $139 billion into the market by lowering the amount of money banks are required to keep in reserve. Regulators also loosened rules for how indebted property developers could pay back loans.

The words and actions propelled the market higher this week, with the Hang Seng Index posting three of its best days this year. China’s Shanghai and Shenzhen markets also bounced, though not by as much.

But many investors say the measures have failed to address a much bigger problem: China’s economic trajectory. They remain disappointed with China’s response to its broader economic slump and its perceived reluctance to pull off a showstopping stimulus, as it did in previous periods of economic stress.

“We hope it will still happen,” said Daniel Morris, an analyst at BNP Paribas, referring to a more substantial effort to prop up markets. “But we don’t have confidence that it will. I honestly would have thought that at the end of last year all the bad news had to be priced in, and yet we have fallen further again this year.”

Economists, financiers and corporate executives around the world looked to China last year for an economic rebound after its government scrapped its “zero Covid” policy, punishing lockdowns that at times put the country into an economic freeze. But Chinese consumers didn’t participate in the kind of “revenge spending” seen elsewhere after reopenings, and a property crisis has weighed on families, many of whom have nearly three-quarters of their savings tied up in real estate.

“There is not much confidence domestically, and then you have a government that isn’t very interested in supporting the economy,” said Louis Kuijs, chief Asia economist at S&P Global Ratings. “Markets somehow had expected much more and are becoming increasingly disappointed and disillusioned.”

And the ranks of the disillusioned include some Chinese investors, who have been moving money into exchange-traded funds that track Japanese stocks. At times these funds’ prices have traded far above the value of their underlying assets, a sign of investors’ enthusiasm to invest.

Alabama carried out on Thursday the first execution using nitrogen gas in the United States, an untested method that was the subject of debate before it was used. The inmate, Kenneth Smith, was pronounced dead at 8:25 p.m. Central time at the William C. Holman Correctional Facility in Atmore, Ala., after the U.S. Supreme Court denied an appeal to stay the execution.

Here are a few things to know about the case.

Who was Kenneth Smith, and what was his crime?

Kenneth Eugene Smith, 58, was one of three men convicted in the stabbing murder of Elizabeth Dorlene Sennett, 45, whose husband, a pastor, had recruited them to kill her in March 1988 in Colbert County, Ala.

According to court documents, Ms. Sennett, a mother of two, was stabbed 10 times in the attack by Mr. Smith and another man. Charles Sennett Sr., Ms. Sennett’s husband, had recruited a man to handle her killing, who in turn recruited Mr. Smith and another man.

Mr. Sennett arranged the murder in part to collect on an insurance policy that he had taken out on his wife, according to court records. He had promised the men $1,000 each for the killing.

What were the circumstances around his death sentence?

Mr. Smith was convicted in 1996. At his sentencing, 11 out of 12 jurors voted to spare his life and to sentence him to life in prison, but the judge in the case, N. Pride Tompkins, decided to overrule their decision and condemned him to death.

In 2017, Alabama stopped allowing judges to overrule death penalty juries in such a way, and such rulings are no longer allowed anywhere in the United States.

Mr. Smith, who was 22 years old at the time of the crime, had said that he did not believe that it was just for the judge to override the jury’s sentence in his case.

In a statement, Gov. Kay Ivey of Alabama previously said that while Alabama had made a “necessary” change to ban judges from overruling jurors’ recommendations, lawmakers had chosen not to make the law retroactive in order to honor sentences that had already been handed down and the victims’ relatives who were relying on them for justice.

What happened to Ms. Sennett’s husband and the others?

Mr. Sennett killed himself shortly after the murder of his wife.

One of the other men involved in the murder, John Forrest Parker, was executed by lethal injection in 2010, and another, Billy Gray Williams, was sentenced to life in prison and died behind bars in 2020.

The state tried to execute Mr. Smith before. What happened?

In November 2022, the state tried to execute Mr. Smith using lethal injection. But that night, a team of correctional facility workers tried and repeatedly failed to insert an intravenous line into Mr. Smith’s arms and hands and, eventually, a vein near his heart.

Finally, after multiple attempts, prison officials decided that they did not have the time to carry out the execution before the death warrant expired at midnight.

What is known about this method using nitrogen?

The method, known as nitrogen hypoxia, has been used in assisted suicides in Europe. Mr. Smith was fitted with a mask and administered a flow of nitrogen gas, effectively depriving him of oxygen until he dies.

Lawyers for the state argued that death by nitrogen hypoxia is painless, with unconsciousness occurring in a matter of seconds, followed by stoppage of the heart.

They also noted that Mr. Smith and his lawyers themselves identified the method as preferable to the troubled practice of lethal injection in the state.

But before the execution, Mr. Smith’s lawyers argued that Alabama was not adequately prepared to carry out the execution, and that a mask — rather than a bag or other enclosure — could allow in enough oxygen to prolong the process and cause suffering.

On Thursday, Alabama officials said the process had proved to be effective and humane.

Mr. Smith appeared conscious for several minutes after the nitrogen gas began entering his mask, according to a report from Alabama journalists who witnessed the execution. He then “shook and writhed” before breathing heavily for several minutes. Eventually, his breathing slowed, then stopped.

What was the stance of the victim’s family?

“Some of these people out there say, ‘Well, he doesn’t need to suffer like that,’” Charles Sennett Jr., one of Ms. Sennett’s sons, told the local station WAAY31 this month. “Well, he didn’t ask Mama how to suffer. They just did it. They stabbed her multiple times.”

Another son, Michael Sennett, told NBC News in December that he was frustrated that the state had taken so long to carry out an execution that the judge ordered decades ago.

“It doesn’t matter to me how he goes out, so long as he goes,” he said, noting that Mr. Smith had been in prison “twice as long as I knew my mom.”

Alabama is set to carry out the first American execution using nitrogen gas on Thursday evening, potentially opening a new frontier in how states execute death row prisoners despite concerns from death penalty opponents about the untested method.

The U.S. Supreme Court on Thursday evening allowed the execution of the condemned prisoner, Kenneth Smith, to move forward in a 6-to-3 vote, with the court’s three liberal members dissenting.

Prison officials said they were moving forward with the execution. Mr. Smith, 58, is one of three men convicted in the 1988 murder of a woman whose husband, a pastor, had recruited them to kill her.

The protocol released by prison officials calls for strapping Mr. Smith to a gurney in the state’s execution chamber in Atmore, Ala., after which a mask will be placed on his head and a flow of nitrogen will be released into it, depriving him of oxygen. Mr. Smith’s lawyers say it would be the first nitrogen execution in the world. It would be the second time Alabama has tried to kill Mr. Smith, after a failed lethal injection in November 2022 in which executioners could not find a suitable vein before his death warrant expired.

Nitrogen hypoxia has been used in some assisted suicides in Europe and elsewhere, though the precise method Alabama is using differs from common practice. Lawyers for the state have argued that death by nitrogen hypoxia, as it is known, is painless, with unconsciousness occurring in a matter of seconds, followed by stoppage of the heart. They also note that Mr. Smith and his lawyers have themselves identified the method as preferable to the troubled practice of lethal injection in the state.

Mr. Smith’s lawyers contend that Alabama is not adequately prepared to carry out the execution, that a mask — rather than a bag or other enclosure — could allow in enough oxygen to prolong the process and cause Mr. Smith to suffer, and that Mr. Smith, who has lately experienced frequent nausea, could choke under the mask if he vomits.

A federal appeals court on Wednesday night voted 2-1 to allow the execution to go forward.

On Thursday morning, Mr. Smith’s lawyers had filed their last-ditch emergency petition with the Supreme Court, , asking the justices to halt the execution in order to consider the latest arguments.

In their petition, Mr. Smith’s lawyers argued that Alabama’s plan for his execution, including what they describe as a “one-size-fits-all mask,” would create a substantial risk that he would “be left in a persistent vegetative state, experience a stroke, or asphyxiate on his own vomit.” They identified alternative methods that they said would reduce the risk, including nitrogen hypoxia using a hood or closed chamber, as well as a firing squad.

Before declining to hear that appeal, the Supreme Court had already declined to intervene in the lawyers’ appeal of a separate case, in which the lawyers had argued that trying to execute Mr. Smith a second time amounted to unconstitutional cruel and unusual punishment, in part because of how harrowing the failed 2022 execution attempt had been.

Mr. Smith’s case is unique in part because the jury that convicted him of murder also voted 11 to 1 to sentence him to life in prison, rather than death, but the judge overruled their decision. Alabama has since made it illegal for judges to overrule juries that have recommended a life sentence — a prohibition that now exists in every state — but the new law did not apply to previous cases.

Mr. Smith’s spiritual adviser, the Rev. Jeff Hood, who will be in the room during the execution, said Mr. Smith had spent the morning meeting with family members, one of his lawyers, and Mr. Hood. Mr. Smith and his mother had their heads close for much of the visit, he said, and there were “a lot of tears.”

He also said Mr. Smith had eaten his last meal on Thursday morning: a T-bone steak, hash browns and eggs, all from Waffle House and slathered with steak sauce.

Prison officials have said that, in an effort to reduce the likelihood of Mr. Smith vomiting during the execution, they would not allow him to eat after 10 a.m.

Mr. Hood said that when he met with Mr. Smith on Wednesday, he had frequently been throwing up in a trash can at the prison and fearing that his nausea could complicate the execution.

“We feel like we’re walking into some sick, twisted house of horrors,” said Mr. Hood, who met with prison officials on Wednesday in the execution chamber to discuss the protocols. “It feels like the more that this goes along, the less we know.”

“Kenny is terrified,” he added. “He’s terrified that this thing is going to completely torture him.”

The execution is taking place in a rural stretch of southern Alabama about an hour’s drive northeast of Mobile, near the state’s border with the Florida panhandle. Police officers blocked off the road to the William C. Holman prison, where the execution was to take place, and it was shrouded by trees, out of view from the highway nearby.

A handful of anti-death penalty protesters gathered for a time at a designated protest zone nearby, but the dirt road was quickly pockmarked with muddy puddles after a stretch of strong rain.

A White House spokeswoman on Thursday declined to comment on the execution.

“This is a state-level case and I won’t speak to the details of this particular case,” said the spokeswoman, Olivia Dalton, adding that President Biden has broad concerns about how the death penalty “is implemented and whether or not it’s consistent with our values of fairness and justice.”

Mr. Biden campaigned on ending the federal death penalty after it was resurrected by former President Donald J. Trump. Under Mr. Biden, the Justice Department has instituted a moratorium on federal executions, but the department also said this month that it would seek the death penalty against the white gunman who fatally shot 10 Black people in a racist attack at a Buffalo grocery store.

If Thursday’s execution goes forward without visible problems, it is likely the method would also be examined by other states facing mounting problems obtaining lethal injection drugs from drug companies because of pressure from medical groups, activists and lawyers. Mississippi and Oklahoma have authorized their prisons to carry out executions by nitrogen hypoxia if they cannot use lethal injection, though they have never tried to do so.

Nitrogen makes up about 78 percent of the air on Earth and is normally harmless; oxygen, which makes up about 21 percent, is essential to human life. But when nitrogen is pumped into an enclosure, or a mask, it can quickly push out the oxygen and lead to rapid unconsciousness and death.

Dr. Philip Nitschke, a pioneer in assisted suicide who estimated that he has witnessed roughly 50 deaths by nitrogen, has said that Alabama’s use of a mask could lead to problems if there is a leak that allows in too much oxygen, prolonging Mr. Smith’s suffering. He said he could imagine a range of potential scenarios, from a quick death to one involving substantial distress and pain.

Alabama’s first attempt at the method comes after several botched or difficult executions in which executioners struggled to find veins on the men they were trying to put to death.

In 2022, executioners tried for hours to access the veins of Joe Nathan James, ultimately slicing into one of his arms in what is known as a “cutdown” in order to administer the fatal drugs, according to a private autopsy. Since 2018, three death row prisoners in the state, including Mr. Smith, have survived execution attempts because of difficulty inserting intravenous lines.

Four days after failing to execute Mr. Smith in 2022, the state’s governor, Kay Ivey, a Republican, halted all executions in the state and asked the prison system, the Alabama Department of Corrections, to review its procedures. The state resumed executing people in 2023, killing two men by lethal injection.

In addition to Mr. Smith’s spiritual adviser, other witnesses to the execution include Mr. Smith’s family members and lawyers, prison officials and five Alabama-based reporters. Some family members of the woman who was killed in the 1988 stabbing, Elizabeth Sennett, have also indicated that they plan to attend. Two of her sons have publicly said they support the execution and view it as long overdue.

Ms. Sennett was stabbed 10 times in the attack by Mr. Smith and another man, according to court documents. Her husband, Charles Sennett Sr., had recruited a man to handle her killing, who in turn recruited Mr. Smith and a third man. Mr. Sennett arranged the murder in part to collect on an insurance policy that he had taken out on his wife, according to court records. He had promised the men $1,000 each for the killing.

Mr. Sennett later killed himself; one of the other men involved in the murder was executed by lethal injection in 2010, and the third was sentenced to life in prison and died in 2020.

Katie Rogers and Abbie VanSickle contributed reporting.

Peter Navarro, a trade adviser to former President Donald J. Trump who helped lay plans to keep Mr. Trump in office after the 2020 election, was sentenced on Thursday to four months in prison for defying a subpoena from the House committee investigating the Jan. 6, 2021, attack on the Capitol.

Mr. Navarro, 74, was found guilty in September of two misdemeanor counts of criminal contempt of Congress, making him the second Trump aide to face penalties related to one of the chief investigations into the Capitol riot. The judge overseeing the case, Amit P. Mehta, had rejected Mr. Navarro’s primary defense: that Mr. Trump had personally directed him not to cooperate with the subpoena, and that he believed he was shielded by executive privilege.

“The words ‘executive privilege’ are not magical incantations,” Judge Mehta said in handing down the sentence after a tense two-and-a-half-hour hearing in which he repeatedly took issue with Mr. Navarro’s claim of executive privilege.

“It’s not a get-out-of-jail-free card,” he said.

Mr. Navarro was also ordered to pay a $9,500 fine. He will stay out of jail for now, at least until Judge Mehta decides whether he can remain free while he appeals his conviction.

In a testy exchange with Mr. Navarro’s lawyers beforehand, the judge singled out Mr. Navarro’s decision to flout the subpoena even as other aides to Mr. Trump negotiated whether to comply. “I have a great deal of respect for your client and what he’s achieved professionally, I do,” he said. “Which makes it all the more disappointing the way he behaved.”

Appearing taken aback by Judge Mehta’s responses to one of his lawyers Mr. Navarro at one point stood up to speak for himself, against what he said was his lawyers’ advice.

Recounting his thought process when he received the subpoena, Mr. Navarro said that he was torn about whether to cooperate and that he had hoped his case would become a blueprint for White House aides subpoenaed by Congress.

“All they have to do is read the transcript of you here today and they’ll know what to do, sir,” he said. “I didn’t know what to do.”

Outside Federal District Court in Washington, Mr. Navarro, surrounded by reporters and cameras on an unseasonably warm day, was immediately drowned out by hecklers blowing whistles and jostling with his lawyers for space behind him to brandish signs.

Over the din, Mr. Navarro defiantly solicited donations for his legal defense, adding that he was “not expecting or hoping for” a pardon from Mr. Trump should he be re-elected to the presidency.

Mr. Navarro, a Harvard-trained economist and a vocal critic of China, served as a trade adviser to Mr. Trump before turning his focus to the pandemic response. After the 2020 election, however, he increasingly explored ways to subvert the outcome of the race and keep Mr. Trump in power.

Along with Stephen K. Bannon, a longtime adviser to Mr. Trump, Mr. Navarro devised a plan known as the Green Bay Sweep. Under the strategy, they would try to delay certification of the election by persuading Republican lawmakers to repeatedly challenge the results in various swing states and apply pressure on former Vice President Mike Pence to discredit the outcome. He also cast doubt on the results of the race, compiling instances of purported irregularities and issuing a three-part report claiming election fraud as part of what he described as an “immaculate deception.”

For weeks, Mr. Navarro openly celebrated his strategizing, sharing details of the plan in his 2021 memoir and in an interview with Rolling Stone magazine.

Those efforts ultimately elicited the attention of the House committee, which sought documents and testimony from Mr. Navarro.

When the committee reached out to Mr. Navarro, he immediately replied by email, stating only “executive privilege” and never cooperating with the panel.

After voting to hold Mr. Navarro in contempt, the House referred the matter to the Justice Department, which obtained a grand jury indictment.

Judge Mehta noted the disconnect between Mr. Navarro’s public appearances and his response to Congress.

“You’re more than happy to talk to the press about what you did, write it in your book but not go up to the Hill and talk to Congress, which was investigating what happened and the causes of that day,” he said.

Mr. Navarro’s lawyers had asked for six months’ probation and a minimal fine. His dismissal of the House committee was essentially a misunderstanding, they contended, adding that Mr. Navarro had genuinely believed that Mr. Trump had invoked executive privilege.

In asking for a more lenient sentence, his lawyers said the case had hinged on murky and unsettled legal questions about executive privilege and the complex separation of powers between Congress and the White House — questions that Judge Mehta had struggled to untangle over months of litigation before the trial.

“We’re but a pit stop in our journey to understanding what executive privilege means and how it should be invoked,” Stanley Woodward Jr., a lawyer for Mr. Navarro, said on Thursday.

“This case is far from over,” he added.

Judge Mehta bristled at the suggestion, noting that others in Mr. Trump’s orbit had complied with the House committee’s subpoenas.

“Any lawyer worth his salt,” he replied angrily, would have advised Mr. Navarro “to engage with Congress and figure out what is covered and what isn’t covered.”

Judge Mehta also questioned Mr. Woodward’s assertion that Mr. Navarro had accepted responsibility for his actions and was merely trying to clarify the law surrounding executive privilege.

Judge Mehta cited fund-raising emails and news conferences outside the courtroom in which Mr. Navarro denounced the Jan. 6 committee as “domestic terrorists” and a “kangaroo court.”

“It’s those type of statements from someone who should know better that contributes to why our politics are so corrosive,” Judge Mehta said.

Mr. Bannon, who left the White House in 2017, was convicted on nearly identical contempt charges in 2022 and sentenced to four months in prison. He, too, remains free as his appeal moves forward.

When Joel Adler decided it was time to downsize from his six-bedroom house in Parkland, Fla., where he had lived for more than 20 years, he was disappointed with the lack of options.

“There weren’t a lot of homes to look at,” said Mr. Adler, a 76-year-old retired teacher, who had been searching for a year and a half.

Eventually, he turned to Valencia Sound, a gated community in Boynton Beach, Fla., that opened in 2019, joining the growing ranks of home buyers who opted for a newly built house instead of an existing one, a rare bright spot in an otherwise gloomy market.

The housing market has been mired for much of the past year, bogged down by high prices, soaring mortgage rates and a dearth of inventory, pushing many would-be buyers to the sidelines.

Existing homes typically account for about 90 percent of sales, but homeowners who have locked in low-rate mortgages have been reluctant to sell, resulting in limited choices and sky-high prices for prospective buyers. Last year, existing-home sales fell to the lowest level in nearly 30 years, while the median price hit a record high, according to a recent report by the National Association of Realtors.

That spurred a rise in construction, as developers rushed to meet demand and dangled incentives to entice buyers. Sales of new homes jumped 4.2 percent last year from 2022, the Census Bureau reported on Thursday.

“The new-home market has been a bright spot, bucking the trend a little bit,” said Odeta Kushi, the deputy chief economist at First American Financial Corporation, a title insurance company. The inventory of new homes now makes up 30 percent of the overall market, she noted, up from 11 percent.

The expanding choices of new homes appealed to Steve Hawthorne, a co-owner of Vertical Runner, a shoe store in Hudson, Ohio. After owning older homes for most of his life, he said, he was burned out by maintenance costs.

“This is a big headache,” Mr. Hawthorne, 49, said. “When the prospect of buying another house came about, I thought this time, I’m going to buy a new home.” Plotting a move west, he bought a two-bedroom house in Summerlin, a planned community outside Las Vegas developed by Howard Hughes Holdings.

Buyers like Mr. Hawthorne are providing a jolt to the economy; residential investment, which includes the construction and purchase of new homes, jumped in the second half of last year, rising at a 6.7 percent annual pace in the third quarter and 1.1 percent in the fourth, the Commerce Department reported on Thursday.

That is a boon for developers like Howard Hughes, which in its most recent earnings report said it sold twice as many new homes in the third quarter as it had the year before. “Our job is to make sure we have enough houses to meet that buyer demand,” said David R. O’Reilly, the company’s chief executive.

Since March 2022, the Federal Reserve has increased interest rates 11 times in an effort to tamp down inflation. That led to higher mortgage rates: After falling below 3 percent during the pandemic, the average rate for a 30-year fixed-rate mortgage jumped above 7 percent last summer, and has recently hovered around 6.7 percent, according to Freddie Mac.

“The consensus is mortgage rates are going to stay at these levels for a while,” said Jeff Ostrowski, an analyst at Bankrate, a consumer financial services company. His firm has forecast that mortgage rates will fall below 6 percent by the end of 2024, as the Fed has signaled it will begin cutting rates this year.

It will take time for the housing market to adjust, as the supply of homes — new and existing — rises and puts downward pressure on prices. “There is a real shortage of inventory,” Mr. Ostrowski said. “I got a phone call from somebody this morning asking if I want to sell my house.”

Home prices nationwide inched up 0.4 percent in December from the month before, the third straight month of slower growth and the smallest increase since June, according to a report from Redfin, a real estate services company.

New homes are typically more expensive than existing ones, and builders are reconfiguring floor plans and shrinking room sizes in an effort to appeal to budget-conscious buyers.

Sellers of new homes are also offering incentives like discounts on mortgage rates and upgraded features like new appliances and countertops, said Ms. Kushi, the First American economist.

“It’s an affordability question,” she said. “How do you get people in the door? As a builder, you don’t want to lower prices.”

Mr. Hawthorne, the buyer in Nevada, said he was able to negotiate a new washer and dryer and epoxy flooring in his garage. “In the grand scheme of things, they were not big-money items, but they were nice amenities,” he said.

And by opting to buy a new home when he did, Mr. Hawthorne said, he encountered less jockeying from rival buyers.

“When money was cheap, competition was immense,” he said. “When I closed at the beginning of September, there was hardly anyone looking.”

The trial of Jennifer Crumbley, whose son carried out the worst school shooting in Michigan history, began on Thursday with dueling portraits: of a negligent mother whose indifference caused a tragedy, and of a good, even “hypervigilant” mother who was in the dark about her son’s troubles until after that tragedy unfolded.

Lawyers for the prosecution and defense sketched out those starkly different images before jurors in a courtroom in Pontiac, Mich., about 20 miles south of Oxford High School, where the mass shooting took place on Nov. 30, 2021.

The shooter, Ethan Crumbley, who was 15 at the time, killed four students and injured seven others. He pleaded guilty to 24 charges, including first-degree murder, and was sentenced last month to life in prison without the possibility of parole.

The case against Ms. Crumbley and her husband is at the leading edge of a push by some prosecutors to hold parents accountable when they are suspected of enabling deadly violence by their children. Just in the last few months, parents whose children carried out gun violence in other states have pleaded guilty to charges of reckless conduct or neglect.

In the Michigan trial, Ms. Crumbley, 45, faces more serious charges: four counts of involuntary manslaughter. Prosecutors say that despite glaring signals of Ethan’s violent intentions, his mother’s failures to take “just ordinary care” to act on what she knew made her criminally liable for the carnage at Oxford High School.

Her husband, James Crumbley, 47, has also been charged and will be tried separately in March. Unable to post a combined $1 million bail, both parents are being held in the Oakland County Jail.

In his opening statement on Thursday, Marc Keast, an Oakland County prosecutor, emphasized that Ms. Crumbley was not charged with murder, nor was she simply accused of being a bad parent. But, he said, because of her “willful disregard for the danger that she knew,” she was a cause of the mass shooting that Ethan carried out.

“Jennifer Crumbley didn’t pull the trigger that day,” Mr. Keast said. “But she is responsible for those deaths.”

Mr. Keast spent much of his opening statement describing the litany of troubling signals leading up the shooting — information that he said the Crumbleys knew but did not share with the school — while suggesting that prosecutors would also highlight Ms. Crumbley’s actions in the aftermath. After Ethan’s arrest, the Crumbleys fled the area, and the police later found them in the basement of a Detroit art studio.

“Her first instinct was to lie,” Mr. Keast said. “Her second was to run.”

Shannon Smith, a lawyer representing Ms. Crumbley, said the prosecution was trying to lay blame for a heinous attack on a woman who “did the best she could” in raising her son.

Ms. Smith said Ms. Crumbley learned only after the shooting about many of the alarming signs, such as Ethan’s text exchanges with friends, that the prosecution would point out as evidence of Ethan’s mental descent. Ms. Smith said that Ethan hid these signs from her and that school officials had never told her about some of the more troubling instances of Ethan’s behavior.

“He did something she could have never anticipated or fathomed or predicted,” Ms. Smith said.

A long record of motions, rulings and other filings leading up to the trial portrays a chaotic home in which, prosecutors say, Ethan’s mental breakdown was ignored and his pleas for help went unheeded.

The week before the shooting, Mr. Crumbley took Ethan to buy a 9 millimeter SIG Sauer handgun, and Ms. Crumbley took him for target practice. On the morning of Nov. 30, both parents were called to the school because Ethan had drawn violent images of a shooting on some class work. Against the suggestion of a school counselor, they did not take their son out of school to get immediate medical help, and they were unaware that he had taken the gun to school in his backpack that day.

Within hours of that meeting, Ethan began shooting.

Ms. Smith said that Mr. Crumbley was responsible for storing the gun. She also said that her client never even considered Ethan a risk for committing violence against others, even after she was alerted that a mass shooting had taken place at the high school. Until authorities explicitly told her what had happened, Ms. Smith said, “it still has not crossed her mind that he would ever shoot another person.”

She also insisted that the Crumbleys went to Detroit after the shooting because they were facing death threats and that they had planned to turn themselves in after learning they were facing charges.

Ms. Crumbley’s lawyers had planned to call Ethan to testify at the trial, along with three of doctors who had spoken with him. But lawyers representing Ethan told the court in a letter that they advised him to “invoke his right to remain silent,” and to assert protections when it comes to confidential information, including conversations with treatment providers.

Ms. Crumbley’s lawyers responded by asking the judge to compel Ethan and the doctors to testify. The judge hasn’t ruled on the question.

After the opening statements on Thursday, Molly Darnell, a teacher at Oxford at the time of the shooting, took the stand as the first witness. She described that day: the commotion, the loud pops, the announcement of a lockdown and the terrifying moment when she went to close her door and locked eyes with Ethan. He shot her in the arm.

Ms. Darnell, recalling that moment, broke down in tears. “I couldn’t wrap my head around what was happening,” she said.

If what goes up must come down, then the urgent question on the minds of many in Europe is when will interest rates begin dropping? For months, rates have been set at the highest in the European Central Bank’s history.

Investors have been betting that the central bank will cut rates quite soon — possibly in April. Traders figure rates must come down because inflation has slowed notably — it’s been below 3 percent since October — and the region’s economy is weak. By the end of year, the central bank will have cut rates by more than 1 percentage point, or between five and six quarter-point cuts, trading in financial markets implied.

Policymakers, however, are trying to pull market opinion in the other direction and delay the expectations of rate cuts. Many of the central bank’s Governing Council are wary of declaring victory over inflation too soon, lest it settle above the bank’s target of 2 percent.

On Thursday, the European Central Bank stuck to this outlook. It held interest rates steady, leaving the deposit rate at 4 percent, where it has been since September.

Rates are at levels that, “maintained for a sufficiently long duration, will make a substantial contribution” toward returning inflation to 2 percent in a “timely manner,” Christine Lagarde, the president of the bank, said on Thursday.

The region needs to be “further along” in the disinflation process before the bank can be confident that inflation will stay at target, she added.

Not now, but probably in the summer

There has been a shift at the central bank recently. In December, Ms. Lagarde said rate cuts hadn’t been discussed and emphasized the need to be vigilant against inflation. But the new year brought a slight change of tune. And last week, Ms. Lagarde said in an interview with Bloomberg News that it was likely that rates could come down in the summer.

Asked about this again at a news conference in Frankfurt on Thursday, Ms. Lagarde said the 26-member Governing Council still agreed that it was “premature to discuss rate cuts.” Policymakers would make their decisions based on incoming economic data, not by following a calendar, she said, seemingly in an effort to keep bets on rate cuts at bay.

Still, she said, “I typically stand by my comments.”

It’s a comment traders have seized on, and they are now firmly expecting a rate cut at the bank’s June meeting, while bets for April have increased.

Central banks have to choose their words carefully to guide markets because it matters what investors think. If traders begin to anticipate lower interest rates, they can move the markets in that direction and ease financial conditions sooner than the central bank would like. That could potentially undermine efforts to restrain the economy and slow inflation. This started to happen in earnest late last year, after the Federal Reserve signaled it would cut rates this year, which caused markets to move in the United States and internationally.

Delaying expectations

Policymakers have tried to delay expectations of rate cuts until at least the summer, arguing they won’t have the data they need, particularly on wage growth, until their meeting in June.

“The E.C.B. will err on the side of caution,” said Oliver Rakau, chief German economist at Oxford Economics, because they are nervous about being wrong again on inflation, after previously underestimating its strength.

Meanwhile, those who say inflation will keep slowing are relying on the economy not enduring any more major shocks. Attacks on commercial ships in the Red Sea has caused shipping prices to spike and analysts are warning that it could lead to a resurgence in inflation if the disruption goes on for a long time and those cost increases are passed to consumers.

Sooner rather than later?

On the other hand, data shows inflation has been easing faster than the central bank predicted. Headline inflation ticked up in December as some government support measures ended, but could fall below 2 percent by the autumn, according to economists at Berenberg bank.

The region’s economy is also weak, not overheating. Germany, the largest economy in the bloc, is sluggish, after data showed it contracted 0.3 percent last year. Separate data published this week showed that demand for loans from businesses and households across the eurozone was continuing to decline.

But its possible to look at this situation somewhat positively, according to Frederik Ducrozet, head of macroeconomic research at Pictet Wealth Management. “It could have been much, much worse,” he said. For example, the recession in Germany could have been significantly deeper, he added. “Inflation was a disaster,” he said. “It’s not under control but is going in the right direction.”

He expects the central bank to start lowering rates in June and cut them by a full percentage point in aggregate by the end of the year. Other economists, including those at Goldman Sachs and Deutsche Bank, predict rate cuts to begin in April.

While there is a debate over how soon and how fast rates will go down, most economists agree that the ultralow rates are a thing of the past.

“The very low rates we had seen prepandemic are unlikely to return, said Mr. Rakau of Oxford Economics, because there is a much greater need to borrow money to invest, particularly in renewable energy and new technologies.