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A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme
arXiv:2509.17710v2 Announce Type: replace Abstract: We derive two forms of conditional a posteriori error estimates for a finite volume scheme approximating the parabolic-elliptic Keller-Segel system. The estimates control the error in the $L^\infty(0,T, L^2(\Omega))$- and $L^2(0,T;H^1(\Omega))$-norm and exhibit linear convergence in the mesh size, as observed in numerical experiments. Crucially, we show that, as long as the condition of the error estimate is satisfied, a weak solution exists.
Albuquerque uses weed tax to fund 'no-strings-attached' guaranteed income, sparking policy debate
Albuquerque city leaders are touting the results of a controversial taxpayer-funded guaranteed basic income (GBI) pilot program, asserting that direct, monthly cash injections have significantly stabilized struggling households. During a Friday press conference, Albuquerque City Councilor Nichole Rogers emphasized that the city is making history by operating one of the few GBI initiatives in the country funded directly via municipal tax dollars. Albuquerque Mayor Tim Keller noted that while...
He feared he couldn't compete with AI: Indian family dumps American Dream, leaves US after tragedy
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American soccer still has a global stigma: Can the USMNT at this World Cup change that?
Eric Wynalda had reached his breaking point. The year was 1992, and "everybody" at then-Bundesliga side FC Saarbrucken, including Wynalda's teammates, had regaled him with taunts of "scheiss Ami" or German for "s--- American." After six weeks of hearing this, he decided to take matters into his own hands.
A thalamus–brainstem attractor network drives history-biased decisions
Abstract Natural environments often change gradually, making it adaptive to bias decisions on the basis of the recent past — a phenomenon known as serial dependence1,2,3. Large-scale recordings during behaviour have identified that serial dependence is a common motif for decision-making, with neural representations of past experiences found throughout the brain4,5,6,7,8,9,10,11. However, it remains unclear whether this bias arises from dedicated neural circuits with history-specific...
Poch: U.S. can win WC despite no top 100 players
United States men's national team coach Mauricio Pochettino said his team can win the World Cup despite not having any players ranked among the top 100. "We are USA and competing against Belgium, Portugal," the U.S. coach said after a pair of March losses in friendlies. "I think for sure Belgium and Portugal have in the top 100 players few, or some players playing in that top 100.
The Global Story: The Fifa-Trump bromance
Fifa’s president, Gianni Infantino, is widely expected to award Donald Trump the inaugural FIFA Peace Prize on Friday, at the draw for the 2026 World Cup in Washington DC. The prize has led to scrutiny over Infantino’s close relationship with Trump, along with concerns that Trump might move matches from host cities and fears over visa delays or refusals for travelling fans and officials. We speak to Dan Roan, the BBC’s sports editor, about why Infantino is cozying up to Trump, and what it...
The Global Story: The AI model that’s ‘too powerful’ to be released to the public
Anthropic - one of Silicon Valley’s leading AI firms - recently announced that they have built a model which is too dangerous to be released to the public.Instead, they are only giving access to the model to a handful of big companies, to help them find security vulnerabilities.The company says the model has already found weak spots in “every major operating system and web browser”. Is this a genuine example of a company acting responsibly, or more of a carefully calibrated publicity move?...
The Global Story: How Canada's Mark Carney is taking on Trump
Canadian Prime Minister Mark Carney seemed to challenge Donald Trump in a speech at the World Economic Forum in Davos this week, declaring that “the old world order is not coming back” and urging fellow “middle powers” to come together. In response, Trump said Canada gets “a lot of freebies” from the United States and “they should be grateful”. After striking a major trade and tariff deal with China – the US’s rival superpower – is Carney emerging as the leader of a global resistance to Trump?
C++: The Programming Language back cover raises questions not answered by front
A little while ago, we considered how the cover of the book C++: The Programming Language raises questions not answered by the cover, since the cover illustration for a book putatively about the C++ programming language shows code written in JavaScript.¹ But there’s also a question raised by the back cover. According to the blurb for the book, The topics included in it are of utmost significance and are bound to provide incredible insights to students.