“The paper details the properties of each of the twelve infinite families of examples, describing their ideals and quotients, subalgebras and idempotents in all characteristics. It also describes all exceptional isomorphisms between them.”

“Triangulation provides a falsifiable standard for mechanistic claims that filters spurious circuits passing single-environment tests but failing cross-lingual invariance.”

“The paper discovers three new families of periodic orbits and proves the existence of stable periodic orbits for restitution coefficients larger than previously known.”

“The paper proves that any ancient, asymptotically cylindrical flow is non-collapsed, convex, rotationally symmetric, and belongs to one of three canonical families: ancient ovals, the bowl soliton, or the flying wing translating solitons.”

“The construction makes it possible to design infinite families of graphs on which exact and stable completion is possible for every fixed rank matrix through the sum-of-squares hierarchy.”

“Necessary and sufficient conditions for complete positivity and trace preservation are derived and the canonical decomposition describing DU-covariant superchannels is provided.”

“The framework yields UNSAT certificates for a collection of anchored subfamilies. We also report pronounced runtime variability across configurations, including heavy-tailed behavior that currently dominates the computational effort and motivates further encoding refinements.”

“GCA losses are $H$-consistent for any hypothesis set that is bounded or complete, with $H$-consistency bounds that scale more favorably as $1/\sqrt{\mathsf p_{\min}}$, offering significantly stronger theoretical guarantees in imbalanced settings.”

“The paper introduces the term Hoffman-London to refer to graphs that are minimal in this sense (minimizing H-colorings with paths).”

“Ensembles of heterogeneous model families achieve better performance scaling than those formed within a single model family, indicating that model diversity is a primary driver of collaboration gains.”

“The paper introduces a new class of integrable 3D lattice models, possessing continuous families of commuting layer-to-layer transfer matrices.”

“PI-MFM consistently outperforms purely data-driven counterparts, especially with sparse labeled spatiotemporal points, partially observed time domains, or few labeled function pairs.”

“The paper reports on the presence of families of exact solutions for a complex scalar field that behaves according to the rules of discrete $Z_N$ symmetry.”

“The paper establishes bounds, presents realizability results, determines exact values for some graph families, and demonstrates an equivalence between the weighted Roman domination number and the differential of a weighted graph.”

“The paper establishes a correspondence between the auxiliary field model of Russo and Townsend and the Ivanov--Zupnik formalism in four-dimensional electrodynamics.”

“Evaluations with a PRM reveal that hybrid reasoning chains often preserve, and in some cases even improve, final accuracy and logical structure.”

“Hoping that this company, born from helping countless families trapped in the mire of illness, can forge a unique path of development that combines commercial and social value in a track surrounded by giants.”

“OpenAI is considering placing ads in ChatGPT.”

“"C-end companies must clearly judge who the product is to be sold to in product design,"”

“The article uses the Jones polynomial to prove infinite families of knots satisfy the Cosmetic Surgery Conjecture.”

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“The research focuses on hash-based malware clustering using K-Means.”

“The article does not contain a direct quote.”

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“The article likely explores how distant supervision, which uses readily available data (e.g., from the web) to label sentiment, can be applied effectively across multiple languages, including those with limited labeled data.”

“We’re rolling out parental controls and a new parent resource page to help families guide how ChatGPT works in their homes.”

“I've had an idea for a long time to generate a cute coloring book based on family photos, send it to a printing service, and then deliver it to people.”

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“The film examines the lives of three families as they try to survive the continued assault on Gaza.”

“Large language models generate functional protein sequences across families”

“Libby Watson explains how many states are able to seize the estates of Medicaid users after their deaths.”

“Orit's work focuses on understanding the behavior of disordered living systems, by merging tools from physics, biology, engineering, and computer science.”

“We explore David’s thoughts about the progression towards larger models, the focus on parameters and how it ties to the architecture of these models, and how we should assess how attention works in these models.”