“Sat Chatterjee has waged a campaign of misinformation against me and Azalia for over two years now,” Ms. Goldie said in a written statement.

She said the work had been peer-reviewed by Nature, one of the most prestigious scientific publications. And she added that Google had used their methods to build new chips and that these chips were currently used in Google’s computer data centers.

Laurie M. Burgess, Dr. Chatterjee’s lawyer, said it was disappointing that “certain authors of the Nature paper are trying to shut down scientific discussion by defaming and attacking Dr. Chatterjee for simply seeking scientific transparency.” Ms. Burgess also questioned the leadership of Dr. Dean, who was one of 20 co-authors of the Nature paper.

“Jeff Dean’s actions to repress the release of all relevant experimental data, not just data that supports his favored hypothesis, should be deeply troubling both to the scientific community and the broader community that consumes Google services and products,” Ms. Burgess said.

Dr. Dean did not respond to a request for comment.

After the rebuttal paper was shared with academics and other experts outside Google, the controversy spread throughout the global community of researchers who specialize in chip design.

The chip maker Nvidia says it has used methods for chip design that are similar to Google’s, but some experts are unsure what Google’s research means for the larger tech industry.

“If this is really working well, it would be a really great thing,” said Jens Lienig, a professor at the Dresden University of Technology in Germany, referring to the A.I. technology described in Google’s paper. “But it is not clear if it is working.”

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F.T.C. Sues to Block Nvidia’s Takeover of Arm

WASHINGTON — The Federal Trade Commission on Thursday sued to block Nvidia’s $40 billion acquisition of a fellow chip company, Arm, halting what would be the biggest semiconductor industry deal in history, as federal regulators push to rein in corporate consolidation.

The F.T.C. said the deal between Nvidia, which makes chips, and Arm, which licenses chip technology, would stifle competition and harm consumers. The proposed deal would give Nvidia control over computing technology and designs that rival firms rely on to develop competing chips.

“Tomorrow’s technologies depend on preserving today’s competitive, cutting-edge chip markets,” said Holly Vedova, the director of the F.T.C.’s competition bureau. “This proposed deal would distort Arm’s incentives in chip markets and allow the combined firm to unfairly undermine Nvidia’s rivals.”

Federal antitrust regulators have promised greater scrutiny of mergers and a clamp down on monopolies in a push to reinvigorate competition in the economy. The action against the deal is the first major merger decision by the Federal Trade Commission under the leadership of Lina Khan, a critic of big corporate mergers and monopolies in technology. Ms. Khan is among a slew of top antitrust officials picked by President Biden to rein in the power of Silicon Valley giants.

promised to break open gas, telecom and pharmaceutical markets to bring down consumer prices at the gas pump and for home internet and prescriptions. Last month, the Justice Department sued to stop Penguin Random House, the largest publisher in the United States, from acquiring its rival Simon & Schuster.

In a statement, Nvidia said it would contest the F.T.C. lawsuit. “We will continue to work to demonstrate that this transaction will benefit the industry and promote competition.”

The F.T.C. suit, if successful, would not have much immediate financial impact on Nvidia or Arm. Shares in Nvidia rose slightly in aftermarket trading.

But a successful suit would be a blow to Nvidia’s ambitions to play a more central role in shaping the direction of the computer industry — particularly in the field of artificial intelligence.

Arm, a British company that the Japanese conglomerate SoftBank bought in 2016, licenses designs for microprocessors and other technology that other companies use in their semiconductors. Its technology has been wildly successful, providing the calculating functions in essentially all smartphones and many other devices. Arm recently estimated its technology is used in about 25 billion chips per year.

Nvidia, based in California, is a dominant provider of chips used to render graphics in video games, technology it has adapted in recent years to also power artificial-intelligence applications used by cloud companies and self-driving cars.

Jensen Huang, the company’s chief executive, has been pushing the company to become a broader, “full-stack” provider of computing technology. In April, for example, Nvidia said it was building an Arm-based microprocessor for servers used in data centers.

In announcing the deal in September 2020 to buy Arm, Mr. Huang said the combination would create a premier company for advancing A.I. technology. He also promised to operate Arm without any change to its business model, acting independently and treating all chip customers fairly.

Mr. Huang said at the time that artificial intelligence would set off a new wave of computing and that “our combination will create a company fabulously positioned for the age of A.I.”

But the deal was controversial from the start, with some of Arm’s big customers, like Qualcomm, worried about the heightened competition from Nvidia and the possibility of a rival gaining access to their confidential information. Mr. Huang took a dig at Qualcomm’s new chief executive, Cristiano Amon, at an annual dinner hosted by the Semiconductor Industry Association last month in Silicon Valley, asking, “How is it possible that Cristiano knew every regulator on the planet?”

The deal had already attracted close scrutiny from regulators in Europe, particularly in the United Kingdom, where Arm’s headquarters in Cambridge is a major employer. Britain’s Competition and Markets Authority launched an in-depth inquiry into the transaction in November, citing both competition and national-security concerns.

The F.T.C. said the merger would give Nvidia access to sensitive information about its rivals, who license technology and designs from Arm.

“Licensees rely on Arm for support in developing, designing, testing, debugging, troubleshooting, maintaining and improving their products,” the F.T.C. said in a statement. “Arm licensees share their competitively sensitive information with Arm because Arm is a neutral partner, not a rival chip maker. The acquisition is likely to result in a critical loss of trust in Arm and its ecosystem.”

The vote to block the merger was unanimous among the F.T.C.’s commissioners. The full complaint filed by the agency is not expected to be released for a few days. An administrative trial for the lawsuit is scheduled for May 10.

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Apple’s Compromises in China: 5 Takeaways

Apple has created an internal bureaucracy that rejects or removes apps the company believes could run afoul of Chinese rules. Apple trains its app reviewers and uses special software to inspect apps for any mention of topics Apple has deemed off limits in China, including Tiananmen Square, the Chinese spiritual movement Falun Gong, the Dalai Lama, and independence for Tibet and Taiwan.

Apple said it removes apps in China to comply with local laws.

In 2018, China’s internet regulators ordered Apple to reject an app from Guo Wengui, a Chinese billionaire who had broadcast claims of corruption inside the Communist Party. Top Apple executives then decided to add Mr. Guo to Apple’s “China sensitivities list,” which meant software would scan apps for mention of him and app reviewers would be trained to reject his apps, according to court documents.

When an app by Mr. Guo later slipped by Apple’s defenses and was published to the App Store, Chinese officials contacted Apple wanting answers. Apple’s app review chief then sent colleagues an email at 2:32 a.m. that said, “This app and any Guo Wengui app cannot be on the China store.” Apple investigated the incident and later fired the app reviewer who had approved the app.

Apple said that it had fired the app reviewer for poor performance and that it had removed Mr. Guo’s app in China because it had determined it was illegal there.

Since 2017, roughly 55,000 active apps have disappeared from Apple’s App Store in China, with most remaining available in other countries, according to a Times analysis.

More than 35,000 of those apps were games, which in China must get approval from regulators. The remaining 20,000 cut across a wide range of categories, including foreign news outlets, gay dating services and encrypted messaging apps. Apple also blocked tools for organizing pro-democracy protests and skirting internet restrictions, as well as apps about the Dalai Lama.

Apple disputed The Times’s figures, saying that some developers removed their own apps from China.

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Amazon’s profits soar 220 percent as pandemic drives shopping online.

With the pandemic shifting sales online and consumers flush with stimulus checks, Amazon on Thursday reported $108.5 billion in sales in the first three months of the year, up 44 percent from a year earlier. It also posted $8.1 billion in profit, an increase of 220 percent from the same period last year.

The first-quarter results surpassed Wall Street’s expectations. Shares were up as much as 5 percent in aftermarket trading.

The most profitable parts of Amazon’s retail business boomed. Revenue from merchants listing items on its website and using its warehouses was up 64 percent, to $23.7 billion. Its “other” business segment, which is largely its lucrative advertising business, increased 77 percent, to almost $7 billion.

Amazon previously disclosed that 200 million people pay for Prime memberships, and subscription revenue for that service and others reached almost $7.6 billion in the quarter. In addition to paying Amazon $119 a year or $12.99 a month for free shipping and other perks, households with Prime memberships typically spend $3,000 a year on Amazon, more than twice what households without the membership spend, according to Morgan Stanley.

step down as chief executive later this year and transition into the role of executive chairman.

Amazon’s total work force dipped slightly between December and the end of March, falling by 27,000 to 1,271,000 employees globally. That was still 51 percent more workers than the same period last year. On Wednesday, Amazon announced it would increase pay for half a million workers and was hiring “tens of thousands” more.

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Apple to Increase Spending in U.S. by 20%

Apple said on Monday that it would increase its spending in the United States by 20 percent, or $80 billion, over the next five years and that it planned to build a new office in North Carolina.

The company said it would invest more than $1 billion in North Carolina, with a new office in the Raleigh-Durham area and at least 3,000 new jobs there. Many of those jobs will be in high-tech fields like machine learning and artificial intelligence.

The overall spending includes its operations at its Cupertino, Calif., headquarters and on data centers across the country, as well as the U.S. taxes it pays. But Apple also announced a number of new investments.

Apple said it was expanding in San Diego, Boston, Seattle and Boulder, Colo. The company also announced a $100 million investment with a supplier named XPO Logistics to create an advanced distribution center in Clayton, Ind., a small town outside Indianapolis.

spend $350 billion in the country over the following five years. That figure included a one-time $38 billion tax payment as it moved billions of dollars it was holding overseas under the new tax law signed by former President Donald J. Trump. Apple saved an estimated $43 billion under the law, more than any other company.

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