Related papers: Parametric models and information geometry on W*-a…

We show that given a rigid C*-tensor category, there is an equivalence of categories between normalized irreducible Q-systems, also known as connected unitary Frobenius algebra objects, and compact connected W*-algebra objects. Although…

Spatial symmetries and invariances play an important role in the behaviour of materials and should be respected in the description and modelling of material properties. The focus here is the class of physically symmetric and positive…

We analyze isomonodromic deformations of rational connections on the Riemann sphere with Fuchsian and irregular singularities. The Fuchsian singularities are allowed to be of arbitrary resonant index; the irregular singularities are also…

Classical Fisher-information asymptotics describe the covariance of regular efficient estimators through the local quadratic approximation of the log-likelihood, and thus capture first-order geometry only. In curved models, including…

The notions of (metric) hypersurface data were introduced in [Mars,2013] as a tool to analyze, from an abstract viewpoint, hypersurfaces of arbitrary signature in pseudo-riemannian manifolds. In this paper, general geometric properties of…

We give the necessary and sufficient (local) conditions for a metric tensor to be a non conformally flat spherically symmetric solution. These conditions exclusively involve explicit concomitants of the Riemann tensor. As a direct…

This paper studies large-scale optimization problems on Riemannian manifolds whose objective function is a finite sum of negative log-probability losses. Such problems arise in various machine learning and signal processing applications. By…

This is a review of the ideas behind the Fisher--Rao metric on classical probability distributions, and how they generalize to metrics on density matrices. As is well known, the unique Fisher--Rao metric then becomes a large family of…

A pedagogical but concise overview of Riemannian geometry is provided, in the context of usage in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions,…

This document contains a description of physics entirely based on a geometric presentation: all of the theory is described giving only a pseudo-riemannian manifold (M, g) of dimension n > 5 for which the g tensor is, in studied domains,…

Information geometry is the application of differential geometry in statistics, where the Fisher-Rao metric serves as the Riemannian metric on the statistical manifold, providing an intrinsic property for parameter sensitivity. In this…

The family $\mathcal{N}$ of $n$-variate normal distributions is parameterized by the cone of positive definite symmetric $n\times n$-matrices and the $n$-dimensional real vector space. Equipped with the Fisher information metric,…

We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…

The general linear model is a universally accepted method to conduct and test multiple linear regression models. Using this model one has the ability to simultaneously regress covariates among different groups of data. Moreover, there are…

A class of pseudo-hermitian quantum system with an explicit form of the positive-definite metric in the Hilbert space is presented. The general method involves a realization of the basic canonical commutation relations defining the quantum…

An earlier scheme [arXiv:2404.03360], where torsion plays an essential part in a flat spacetime account of fermion spin, is extended to spacetimes with non-zero Riemann curvature. It is found that further essential features of the fermion,…

In this paper we express some simple random tensor models in a Givental-like fashion i.e. as differential operators acting on a product of generic 1-Hermitian matrix models. Finally we derive Hirota's equations for these tensor models. Our…

We characterize completely bounded normal Jordan $*$-homomorphisms acting on von Neumann algebras. We also characterize completely positive isometries acting on noncommutative $\mathrm{L}^p$-spaces.

Classical and quantum aspects of physical systems that can be described by Riemannian non degenerate superspaces are analyzed from the topological and geometrical points of view. For the N=1 case the simplest supermetric introduced in…

In this thesis manuscript we explore different facets of random tensor models. These models have been introduced to mimic the incredible successes of random matrix models in physics, mathematics and combinatorics. After giving a very short…