Results 51 to 60 of about 1,647 (169)

Information-Geometric Models in Data Analysis and Physics

Mathematics
Information geometry provides a data-informed geometric lens for understanding data or physical systems, treating data or physical states as points on statistical manifolds endowed with information metrics, such as the Fisher information.
D. Bernal-Casas, José M. Oller
doaj   +1 more source

Arti4D: Statistical Analysis and Modelling of the Spatio‐temporal Variability in Articulated 4D Shapes

Computer Graphics Forum, EarlyView.
Abstract We propose a novel framework for the statistical modeling and analysis of the spatio‐temporal shape variability in articulated 4D (i.e., 3D + time) shapes such as human bodies and animals. We treat articulated 3D shapes, represented using parametric models such as SMPL or its variants, as elements of the product space of shape and pose ...
Z. Li, A. Amrani, S. Rai, H. Laga
wiley   +1 more source

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

Local solvability of degenerate Monge-Ampere equations and applications to geometry

Electronic Journal of Differential Equations, 2007
We consider two natural problems arising in geometry which are equivalent to the local solvability of specific equations of Monge-Ampere type. These are: the problem of locally prescribed Gaussian curvature for surfaces in $mathbb{R}^{3}$, and the local
Marcus A. Khuri
doaj  

Geometry of State-Update Processes and Wave Function Collapse

Quantum Reports
We develop an information-geometric framework for describing quantum state-update processes associated with measurement and statistical distinguishability.
Angelo Plastino
doaj   +1 more source

On the Design of Model Predictive Setpoint Controllers for Nonholonomic Multibody Systems

Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 4, December 2026.
ABSTRACT Systems subject to constraints that are not integrable to position‐level constraints pose significant challenges for setpoint control. In particular, conventional linearization techniques may fail to yield controllable approximations, since certain directions of motion are only accessible through higher‐order interactions of the control inputs.
Mario Rosenfelder, Henrik Ebel, Peter Eberhard   +2 more
wiley   +1 more source

A Spike‐Based Graph Surrogate for Modeling Finite Element Structures

Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 4, December 2026.
ABSTRACT The use of Artificial Intelligence (AI) in structural mechanics has grown substantially in the recent years, with diverse applications ranging from constitutive laws and Gauss‐point‐level enhancements to the complete replacement of classical Finite Element Methods (FEM) with surrogate models.
Vaishnav Bhaskaran, Rutwik Gulakala, Marcus Stoffel   +2 more
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

Hearing the Serre Invariant of a Compact p‐Adic Analytic Manifold

Mathematische Nachrichten, Volume 299, Issue 10, Page 3126-3138, October 2026.
ABSTRACT Using a previous novel way of defining kernel functions for Laplacian integral operators on a compact p$p$‐adic analytic manifold X$X$, one such operator Δ0s$\Delta _0^s$ with s∈R$s\in \mathbb {R}$ is applied to hearing the Serre invariant i(X)$i(X)$ by showing that a wavelet eigenvalue (with the wavelet having small support) is always ...
Patrick Erik Bradley, Ángel Morán Ledezma   +1 more
wiley   +1 more source

Local non-injectivity of the exponential map at critical points in sub-Riemannian geometry

Nonlinear Analysis
We prove that the sub-Riemannian exponential map is not injective in any neighbourhood of certain critical points. Namely that it does not behave like the injective map of reals given by $f(x) = x^3$ near its critical point $x = 0$. As a consequence, we characterise conjugate points in ideal sub-Riemannian manifolds in terms of the metric structure of ...
Borza, Samuël, Klingenberg, Wilhelm
openaire   +2 more sources