Imagine a random walk that outputs a state only when visiting it for the first time. The observed output is therefore a repeat-censored version of the underlying walk, and consists of a permutation of the states or a prefix of it. We call this model initial-visit emitting random walk (INVITE). Prior work has shown that the random walks with such a repeat-censoring mechanism explain well human behavior in memory search tasks, which is of great interest in both the study of human cognition and various clinical applications. However, parameter estimation in INVITE is challenging, because naive likelihood computation by marginalizing over infinitely many hidden random walk trajectories is intractable. In this paper, we propose the first efficient maximum likelihood estimate (MLE) for INVITE by decomposing the censored output into a series of absorbing random walks. We also prove theoretical properties of the MLE including identifiability and consistency. We show that INVITE outperforms several existing methods on real-world human response data from memory search tasks.

Youngkin, joined by Virginia Attorney General Jason Miyares and other state attorneys general, compared human trafficking enforcement to addressing transnational gangs. "We must have multi-state and federal support in order to dismantle the networks, not just arrest an individual, we've got to unpack the networks," Youngkin told a crowd of a few hundred. The Trump administration has been a boon to human trafficking enforcement efforts, Youngkin said, noting he met with top Justice Department officials at the White House after the inauguration to discuss the matter and found them receptive. Virginia law enforcement has since been coordinating with the federal government to take down foreign gang operations, which Youngkin said overlaps with the human trafficking space. Youngkin used the example of gang crime inside correctional centers, which he said was the first "thread" his team pulled.

Perplexity AI said it has made a 34.5bn unsolicited all-cash offer for Alphabet's Google Chrome browser. The deal, if Alphabet agreed to it, would also require financing above the startup's most recently reported valuation of 18bn. The nearly three-year-old startup's purchase of Chrome, if approved, would give the company access to its more than three billion users as regulatory pressure weighs on Google's control over the tech industry. Perplexity did not disclose on Tuesday how it plans to fund the offer, but has raised 1bn in funding from investors including SoftBank and the semiconductor chip giant Nvidia. Several funds have said they would finance the deal in full if Alphabet accepts, the Reuters news agency reported citing unnamed sources familiar with the matter.

Elon Musk has threatened legal action against Apple on behalf of his artificial intelligence startup xAI, accusing the iPhone maker of favoring OpenAI and breaching antitrust regulations in managing the rankings in its App Store. The posts elicited snide responses from Sam Altman, the OpenAI CEO, and began a spat between the two former business partners on X. "Apple is behaving in a manner that makes it impossible for any AI company besides OpenAI to reach #1 in the App Store, which is an unequivocal antitrust violation. In a post earlier that day, he wrote: "Hey @Apple App Store, why do you refuse to put either X or Grok in your'Must Have' section when X is the #1 news app in the world and Grok is #5 among all apps? OpenAI's ChatGPT currently holds the top spot in the App Store's "Top Free Apps" section in the US, while xAI's Grok ranks fifth. Apple has a partnership with OpenAI that integrates ChatGPT into iPhones, iPads and Macs.

As a federal antitrust investigation into Google's Chrome browser wraps up, rivals are striking: Perplexity has launched an unsolicited bid to buy Chrome for a whopping 34.5 billion, according to reports. Bloomberg reported the proposed deal, confirmed by a Perplexity representative, as did The Wall Street Journal. But there's a hitch: Perplexity doesn't have 34.5 billion to fund the deal with. In fact, the WSJ estimates its own valuation at just 18 billion. This means Perplexity would have to come up with another source of cash, and it appears that it has done just that.

The feud between Musk and Altman has, over time, encompassed a slew of lawsuits, email dumps and social media digs. Their rivalry can be traced back a decade, with Musk's now public belief that OpenAI, under Altman's leadership, abandoned the principles he and others used to found it in 2015. The firm was created with the intention of building artificial general intelligence (AGI) - AI that can perform any task that a human being is capable of - but by making its technology open-source and promising to "benefit humanity". OpenAI was also set up as a not-for-profit company, meaning it would not aim to make money, but in 2019 it established a for-profit arm which Musk felt was antithetical to its original mission. Musk argued in his March 2024 lawsuit that the firm had instead been focusing on "maximising profits" for its major investor Microsoft.

Gone are the days when the web was dominated by humans posting social media updates or exchanging memes. Earlier this year, for the first time since the data has been tracked, web-browsing bots, rather than humans, accounted for the bulk of web traffic. Well over half of that bot traffic is from malicious bots, hoovering up personal data left unprotected online, for instance. But an increasing proportion comes from bots sent out by artificial intelligence companies to gather data for their models or respond to user prompts. Indeed, ChatGPT-User, a bot powering OpenAI's ChatGPT, is now responsible for 6 per cent of all web traffic, while ClaudeBot, an automated system developed by AI company Anthropic, accounts for 13 per cent.

HMRC has confirmed it uses artificial intelligence (AI) to monitor social media posts as part of criminal investigations into suspected tax cheats. It said the tech would not replace "human decision-making" and was subject to legal oversight. "Greater use of AI will enable our staff to spend less time on admin and more time helping taxpayers, as well as better target fraud and evasion to bring in more money for public services," it said in a statement. However, experts warn there are risks with using AI in this way.

The propensity for AI systems to make mistakes that humans miss has been on full display in the US legal system as of late. The follies began when lawyers submitted documents citing cases that didn't exist. Similar mistakes soon spread to other roles in the courts. Last December, a Stanford professor submitted sworn testimony containing hallucinations and errors in a case about deepfakes, despite being an expert on AI and misinformation himself. Now, judges are experimenting with generative AI too. Some believe that with the right precautions, the technology can expedite legal research, summarize cases, draft routine orders, and overall help speed up the court system, which is badly backlogged in many parts of the US.

Apple's AI Ambitions Leave Big Questions Over Its Climate Goals Halfway to its 2030 net-zero goal, Apple faces slow and hold-out suppliers, a tariffs scramble, and an AI race that could profoundly impact eco-friendly ambitions. Here's a simple question: Is the current top iPhone better for the environment than the top iPhone was five years ago? Let's take the iPhone Pro series. If we're looking at recycled and renewable materials, it's an easy yes. Compare the iPhone 11 Pro, released in September 2019, with the iPhone 16 Pro, released in September 2024, and there has been good progress--from a few smaller components and packaging to now at more than 25 percent of the whole phone.