Results 51 to 60 of about 752 (172)

Difference and the Liberation of Sufficient Reason

European Journal of Philosophy, EarlyView.
Abstract The Principle of Sufficient Reason (PSR) holds that every event and entity can be explained by a sufficient reason or cause. Philosophers have long struggled with the question of the PSR's compatibility with freedom, for if what occurs or exists follows necessarily from its sufficient reason then it seems it could not have been otherwise ...
Louis Matheou
wiley   +1 more source

Stochastic Gradient Descent in High Dimensions for Multi‐Spiked Tensor PCA

Communications on Pure and Applied Mathematics, Volume 79, Issue 10, Page 2291-2369, October 2026.
ABSTRACT We study the high‐dimensional dynamics of online stochastic gradient descent (SGD) for the multi‐spiked tensor model. This multi‐index model arises from the tensor principal component analysis (PCA) problem with multiple spikes, where the goal is to estimate the unknown signal vectors within the N$N$‐dimensional unit sphere through maximum ...
Gérard Ben Arous, Cédric Gerbelot, Vanessa Piccolo   +2 more
wiley   +1 more source

Free semigroups of large critical exponent

Journal of Topology, Volume 19, Issue 3, September 2026.
Abstract For a convergence group equipped with an expanding coarse‐cocycle, we construct finitely generated free subsemigroups, which we call Bishop−−Jonessemigroups$\textit{Bishop--Jones semigroups}$, of critical exponent arbitrarily close to but strictly less than the critical exponent of the ambient group.
Aleksander Skenderi
wiley   +1 more source

Corrections to: ``Sub-Riemannian geometry''

Journal of Differential Geometry, 1989
An error in the proof of Corollary 6.2 of [1] has been pointed out by Gerard Ben-Arous. The computation of M(x,λ) in the case λo = 0 on p. 243 is incorrect, because M(x,λ) = 0 when λ0 = 0 and λjg (x) = 0 for all k. (There is also a factor of \ missing in the formula as stated for λ0 φ 0, but this is not significant.) Thus when applying the Pontryagin ...
openaire   +2 more sources

Invariant Measure and Universality of the 2D Yang–Mills Langevin Dynamic

Communications on Pure and Applied Mathematics, Volume 79, Issue 8, Page 1973-2102, August 2026.
ABSTRACT We prove that the Yang–Mills (YM) measure for the trivial principal bundle over the two‐dimensional torus, with any connected, compact structure group, is invariant for the associated renormalised Langevin dynamic. Our argument relies on a combination of regularity structures, lattice gauge‐fixing and Bourgain's method for invariant measures ...
Ilya Chevyrev, Hao Shen
wiley   +1 more source

Subdifferentials and minimizing Sard conjecture in sub-Riemannian geometry

Journal de l’École polytechnique — Mathématiques, 2023
We use techniques from nonsmooth analysis and geometric measure theory to provide new examples of complete sub-Riemannian structures satisfying the Minimizing Sard conjecture. In particular, we show that complete sub-Riemannian structures associated with distributions of co-rank 2
openaire   +3 more sources

A sub-Riemannian model of the motor cortex with Wasserstein distance

Frontiers in Computational Neuroscience
This study aims to better understand the functional geometry of the motor cortex, starting from different sources of experimental evidence. Recent studies have proved that cells of the primary motor cortex (M1) are sensitive to short hand trajectories ...
Jawad Ali, Giovanna Citti, Alessandro Sarti   +2 more
doaj   +1 more source

Kuga–Satake Construction on Families of K3 Surfaces of Picard Rank 14

Mathematische Nachrichten, Volume 299, Issue 8, Page 1894-1916, August 2026.
ABSTRACT The isometry between the type IV6 and the type II4 hermitian symmetric domains suggests a possible relation between suitable moduli spaces of K3 surfaces of Picard rank 14 and of polarized abelian 8‐folds with totally definite quaternion multiplication. We show how this isometry induces a geometrically meaningful map between such moduli spaces
Flora Poon
wiley   +1 more source

Boundary‐Only Weak Deflection by Regular Black Holes, Black‐Bounces, Wormholes, and Static Quadrupolar Spacetimes

Fortschritte der Physik, Volume 74, Issue 8, August 2026.
ABSTRACT We apply the boundary‐only isothermal formulation of finite‐distance weak gravitational deflection to regular black holes, black‐bounces, traversable wormholes, non‐asymptotically flat backgrounds, and static quadrupolar spacetimes. The methodological advance is not a new value for a known bending angle.
Reggie C. Pantig, Ali Övgün
wiley   +1 more source

A connection theoretic approach to sub-Riemannian geometry [PDF]

Journal of Geometry and Physics, 2003
We use the notion of generalized connection over a bundle map in order to present an alternative approach to sub-Riemannian geometry. Known concepts, such as normal and abnormal extremals, will be studied in terms of this new formalism. In particular, some necessary and sufficient conditions for the existence of abnormal extremals will be derived.
openaire   +2 more sources