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Perfect divisibility and perfect-Pollyanna in bull-free graphs

arXiv:2603.21538v2 Announce Type: replace-cross Abstract: A graph $G$ is {\em perfectly divisible} if, for each induced subgraph $H$ of $G$, $V(H)$ can be partitioned into $A$ and $B$ such that $H[A]$ is perfect and $\omega(H[B])<\omega(H)$. A {\em bull} is a graph consisting of a triangle with two disjoint pendant edges. Ho\`ang [Discrete Math. 349 (2026) 114809] proposed four conjectures: 1.

arXiv CS 1d ago

Big 12 preview: Despite the drama, Texas Tech stil...

Back when the NIL era was in its nascent stages, with a new Big 12 and a 12-team College Football Playoff on the way, I wondered if there was room for the emergence of a Clemson-style dynasty from a conference known primarily for the endless number of close games. If some team could craft a recruiting boost from both solid spending and sustained success, perhaps they could ride that to a series of conference titles and, perhaps, even playoff runs? I admittedly didn't have a specific team in...

ESPN 6h ago

Revisiting $O(n \log \log n)$ chaining for anchored edit distance

arXiv:2606.03929v1 Announce Type: new Abstract: Colinear chaining is a classical heuristic for sequence alignment: it enables scalable genome comparison and is a main component of many state-of-the-art read mappers based on seed-chain-extend. The earliest $O(n \log \log n)$ time algorithms by Eppstein et al. (J. ACM, 1992) chained $n$ fragments between two sequences $T$ and $Q$ while minimizing a gap cost based on the diagonal distance $\Delta_{\text{diag}}$ between consecutive fragments.

arXiv CS 7d ago

Planar Perfect Matching Counting is as Hard as Determinants

Announce Type: new Abstract: In the 1960s, Fisher, Kasteleyn and Temperley designed an ingenious algorithm for computing the partition function of the dimer model, or equivalently, for counting perfect matchings in edge-weighted planar graphs (Philos. Mag. 1961; J. Mathematical Phys. 1963). This FKT algorithm later became the foundation for Valiant's holographic algorithms (FOCS 2004; SIAM J. Comput. 2008), which motivated the study of counting problems under the Holant framework. Combined...

arXiv CS 7d ago

Molecular glue degraders of HuR suppress BRAF-mutant colorectal cancer

Abstract BRAF gain-of-function mutations, particularly BRAF(V600E), affect roughly 10% of all patients with colorectal cancer (CRC), and portend poor prognosis with limited therapeutic interventions. BRAF inhibitors such as encorafenib are ineffective due to MAPK pathway reactivation driven by BRAF dimerization. Combined inhibition of BRAF and EGFR, although approved therapies, results in short survival benefits and frequent treatment resistance and relapse1,2,3.

Nature 20h ago

Improved quantum processor logical error rates via correction and detection

Abstract Performing quantum algorithms for critical problems in physics and chemistry requires substantially lower error rates than the physical error rates of present quantum computers. Achieving such low logical error rates requires quantum error correction1,2 and physical error rates below a critical threshold value3,4,5,6,7,8. We experimentally demonstrate on a trapped-ion quantum charge-coupled device (QCCD)9,10 improvements in logical error rates ranging from 11× to 800× compared with...

Nature 20h ago

Jim Cramer says look to buy these 5 stocks outside the AI trade for diversification

CNBC's Jim Cramer on Tuesday provided investors a handful of beaten-down stocks that he believes could outperform if the artificial intelligence trade begins to cool. "These are the stocks that will start going higher if tech retreats," the "Mad Money" host said. "You'll wish you had some of these when the time comes and the momentum tech stocks run out of, well, momentum."

CNBC 7d ago

How Trials turned traumatic childhood into triumphant solo album

How Trials grew up, got sober and confronted his past on debut solo album Hendle Sun 31 May 2026 at 6:30am Aboriginal and Torres Strait Islander readers are advised that this article contains the names of people who have died. For 25 years, Trials has been making music with or for others. But now, he's doing it for himself.

ABC Australia 11d ago

Variable-preconditioned transformed primal-dual method for generalized Wasserstein Gradient Flows

arXiv:2509.15385v3 Announce Type: replace Abstract: We propose a Variable-Preconditioned Transformed Primal-Dual (VPTPD) method for solving generalized Wasserstein gradient flows based on the structure-preserving JKO scheme. This is a nontrivial extension of the TPD method [Chen et al. incorporating proximal splitting techniques to address the challenges arising from the nonsmoothness of the objective function.

arXiv CS 8d ago

Dirty soda drinks are everywhere, but doctors warn of health risks: 'Metabolic disaster'

The latest beverage trend is far from clean – and it’s raising red flags with doctors. Known as a "dirty soda," it’s a soft drink that also includes a combination of added ingredients, such as flavored syrups, creamers, fruit juices and other garnishes. The result is a sweet beverage that’s a combination of a soda, mocktail and dessert.

Fox News 9h ago