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Effective Constrained Scalar--Gauss--Bonnet Inflation Motivated by $f(R,\mathcal{G})$ Gravity

arXiv:2606.05212v1 Announce Type: new Abstract: We develop an effective framework for inflation in a constrained scalar--Gauss--Bonnet theory motivated by a restricted sector of $f(R,\mathcal{G})$ gravity. Using unified parametrizations of the Hubble expansion rate and the Gauss--Bonnet coupling function within a generalized slow-roll formalism, we derive analytical expressions for the scalar spectral index $n_s$ and tensor-to-scalar ratio $r$, and study their dependence on the model parameters.

arXiv Physics 5d ago

Sibley's Guard-Point Convexity Measure: A Perimeter Counterexample and a Dominance Bound

Announce Type: new Abstract: We study Sibley's guard-point convexity measure for simple polygons and compare it with the exterior and perimeter convexity measures. We prove the exterior inequality G(F) <= E(F) and disprove the pointwise perimeter inequality G(F)

arXiv CS 6d ago

A Kronecker algorithm for locally closed sets over a perfect field

arXiv:2512.14888v2 Announce Type: replace-cross Abstract: We develop a probabilistic algorithm of Kronecker type for computing a Kronecker representation of a zero-dimensional linear section of an algebraic variety $V$ defined over a perfect field $k$. The variety $V$ is the Zariski closure of the set of common zeros $\{F_1=0,\ldots,F_r=0,G\not=0\}$ of multivariate polynomials $F_1,\ldots,F_r\in k[X_1,\ldots,X_n]$ outside a prescribed hypersurface $\{G=0\}$. We assume that $F_1,\ldots,F_r$...

arXiv CS 1d ago

Transfer portal superlatives: Louisville, Duke, St...

We've passed every major mile marker of the men's college basketball offseason: The transfer portal opened and closed, the NBA draft withdrawal deadline has come and gone, and all of ESPN's top 100 transfers have committed. Now, Jeff Borzello and Myron Medcalf are here to make sense of all the player movement and what it means for the teams they joined. From contenders that improved title hopes the most to teams that should have done more, here are the biggest winners and losers.

ESPN 5h ago

The grid-minor theorem revisited

arXiv:2307.02816v2 Announce Type: replace-cross Abstract: We prove that for every planar graph $X$ of treedepth $h$, there exists a positive integer $c$ such that for every $X$-minor-free graph $G$, there exists a graph $H$ of treewidth at most $f(h)$ such that $G$ is isomorphic to a subgraph of $H\boxtimes K_c$. This is a qualitative strengthening of the Grid-Minor Theorem of Robertson and Seymour (JCTB 1986), and treedepth is the optimal parameter in such a result. As an example...

arXiv CS 8d ago

Multilevel randomized quasi-Monte Carlo estimator for nested integration

arXiv:2412.07723v5 Announce Type: replace Abstract: Nested integration problems arise in various scientific and engineering applications, including Bayesian experimental design, financial risk assessment, and uncertainty quantification. These nested integrals take the form $\int f\left(\int g(\boldsymbol{y},\boldsymbol{x})\mathrm{d}\boldsymbol{x}\right)\mathrm{d}\boldsymbol{y}$, for nonlinear $f$, making them computationally challenging, particularly in high-dimensional settings. Although...

arXiv CS 7d ago

Ordinals and recursively defined functions on the reals

arXiv:2311.17210v5 Announce Type: replace-cross Abstract: We determine sufficient conditions under which certain recursively defined functions are well defined for all real inputs. Given a function $f:\mathbb R\to\mathbb R$, call a decreasing sequence $x_1>x_2>x_3>\cdots$ "$f$-bad" if $f(x_1)>f(x_2)>f(x_3)>\cdots$, and call the function $f$ "ordinal decreasing" if there exist no infinite $f$-bad sequences. We prove the following result:

arXiv CS 1d ago

Follow live: USWNT take on Brazil in friendly

Brazil v USA 2026 Women's International Friendly Formations & Lineups Match Leaders 1 Ary Borges M 0 SOG, 0 G 1 -- None -- 1 Dudinha F 1 PASS 1 2 WesleyD 2 PASS 2 3 I. HaasD 1 TKLW, 1 DUELW 3 -- None -- -- None -- --

ESPN 17h ago

A 5.3-million-year-old deep-sea whale necropolis in the Diamantina Zone

Abstract Whale falls are biodiversity oases at seabeds1,2,3,4,5,6, yet their record from the oceans has remained sparse and fragmentary6,7. Here we report the discovery of a vast whale necropolis in the Diamantina Zone (4,616- to 7,001-m depth), extending about 1,200 km along the sea floor of the southeastern Indian Ocean. This area has a deep and extensive accumulation comprising five modern natural whale-fall communities and 476 fossil cetaceans recorded.

Nature 19h ago

A first-in-class pulsatile FXR agonist for bile-acid-related liver diseases

Abstract Nuclear receptors are central regulators of metabolism1, yet therapeutic strategies that enforce continuous receptor activation frequently lead to reduced efficacy and unacceptable toxicity. Here we report a first-principles drug design strategy that aligns pharmacokinetics with physiological signalling cycles. We developed linafexor, a potent non-bile-acid agonist of the farnesoid X receptor (FXR)2; it is engineered for rapid systemic clearance, which enables pulsatile receptor...

Nature 19h ago