Related papers: Statistical Geometry and Information Dynamics on H…
In dimension 2 and above, the Burgers dynamics, the so-called "adhesion model" in cosmology, can actually give rise to several dynamics in the inviscid limit. We investigate here the statistical properties of the density field when it is…
$\mathtt{d}$-dimensional hyperspherical quantum dot with either Dirichlet or Neumann boundary conditions (BCs) allows analytic solution of the Schr\"{o}dinger equation in position space and the Fourier transform of the corresponding wave…
We analyze the propagation properties of the numerical versions of one and two-dimensional wave equations, semi-discretized in space by finite difference schemes. We focus on high-frequency solutions whose propagation can be described, both…
Non-Gaussianities of dynamical origin are disentangled from primordial ones using the formalism of large deviation statistics with spherical collapse dynamics. This is achieved by relying on accurate analytical predictions for the one-point…
Motivated by recent studies of population coding in theoretical neuroscience, we examine the optimality of a recently described form of stochastic resonance known as suprathreshold stochastic resonance, which occurs in populations of noisy…
Understanding generalization in deep learning has been one of the major challenges in statistical learning theory over the last decade. While recent work has illustrated that the dataset and the training algorithm must be taken into account…
We consider the problems of clustering, classification, and visualization of high-dimensional data when no straightforward Euclidean representation exists. Typically, these tasks are performed by first reducing the high-dimensional data to…
Geometry of hypersurfaces defined by the relation which generalizes classical formula for free energy in terms of microstates is studied. Induced metric, Riemann curvature tensor, Gauss-Kronecker curvature and associated entropy are…
Despite the remarkable empirical success of score-based diffusion models, their statistical guarantees remain underdeveloped. Existing analyses often provide pessimistic convergence rates that do not reflect the intrinsic low-dimensional…
A novel information-geometric approach to chaotic dynamics on curved statistical manifolds based on Entropic Dynamics (ED) is suggested. Furthermore, an information-geometric analogue of the Zurek-Paz quantum chaos criterion is proposed. It…
A new information-geometric approach to chaotic dynamics on curved statistical manifolds based on Entropic Dynamics (ED) is proposed. It is shown that the hyperbolicity of a non-maximally symmetric 6N-dimensional statistical manifold M_{s}…
New geometric and computational analyses of power-weighted shortest-path distances (PWSPDs) are presented. By illuminating the way these metrics balance density and geometry in the underlying data, we clarify their key parameters and…
How does one generalize differential geometric constructs such as curvature of a manifold to the discrete world of graphs and other combinatorial structures? This problem carries significant importance for analyzing models of discrete…
The infinite-dimensional Hilbert sphere $S^\infty$ has been widely employed to model density functions and shapes, extending the finite-dimensional counterpart. We consider the Fr\'echet mean as an intrinsic summary of the central tendency…
The unavoidable interaction between a quantum system and the external noisy environment can be mimicked by a sequence of stochastic measurements whose outcomes are neglected. Here we investigate how this stochasticity is reflected in the…
We introduce a notion of "effective dimension" of a statistical model based on the number of cubes of size $1/\sqrt{n}$ needed to cover the model space when endowed with the Fisher Information Matrix as metric, $n$ being the number of…
This work addresses a modification of the random geometric graph (RGG) model by considering a set of points uniformly and independently distributed on the surface of a $(d-1)$-sphere with radius $r$ in a $d-$dimensional Euclidean space,…
We study the two-dimensional topology of the galactic distribution when projected onto two-dimensional spherical shells. Using the latest Horizon Run 4 simulation data, we construct the genus of the two-dimensional field and consider how…
We investigate the thermodynamic geometry of classical and quantum ideal gases in the relativistic regime, with particular emphasis on the effects of particle mass and spatial dimensionality. Relativistic kinematics is incorporated through…
We investigate the connection between the time-evolution of averages of stochastic quantities and the Fisher information and its induced statistical length. As a consequence of the Cramer-Rao bound, we find that the rate of change of the…