Related papers: Information geometry for Fermi-Dirac and Bose-Eins…
Many machine learning methods assume that the training and test data follow the same distribution. However, in the real world, this assumption is very often violated. In particular, the phenomenon that the marginal distribution of the data…
We extend our earlier study about the fractional exclusion statistics to higher dimensions in full physical range and in the non-relativistic and ultra-relativistic limits. Also, two other fractional statistics, namely Gentile and…
We define a local Riemannian metric tensor in the manifold of Gaussian channels and the distance that it induces. We adopt an information-geometric approach and define a metric derived from the Bures-Fisher metric for quantum states. The…
Is the geometry of space a macroscopic manifestation of an underlying microscopic statistical structure? Is geometrodynamics - the theory of gravity - derivable from general principles of inductive inference? Tentative answers are suggested…
This thesis is a compilation of research in relativistic quantum information theory, and research in quantum reference frames. The research in the former category provides a fundamental construction of quantum information theory of…
We present exact and explicit results for the thermodynamic properties (isochores, isotherms, isobars, response functions, velocity of sound) of a quantum gas in dimensions D>=1 and with fractional exclusion statistics 0<=g<=1 connecting…
In this paper, we introduce \emph{$\ell^p$-information geometry}, an infinite dimensional framework that shares key features with the geometry of the space of probability densities \( \mathrm{Dens}(M) \) on a closed manifold, while also…
This report concerns the problem of dimensionality reduction through information geometric methods on statistical manifolds. While there has been considerable work recently presented regarding dimensionality reduction for the purposes of…
In this paper, we introduce \emph{$\ell^p$-information geometry}, an infinite-dimensional framework that shares key features with the geometry of the space of probability densities \( \mathrm{Dens}(M) \) on a closed manifold, while also…
In this paper a class of dynamical systems describing expectation variables exactly derived from continuous-time master equations is introduced and studied from the viewpoint of differential geometry, where such master equations consist of…
The method of maximum entropy is used to model curved physical space in terms of points defined with a finite resolution. Such a blurred space is automatically endowed with a metric given by information geometry. The corresponding…
In the application of Bayesian methods to metrology, pre-data probabilities play a critical role in the estimation of the model uncertainty. Following the observation that distributions form Riemann's manifolds, methods of differential…
We propose a unified theoretical framework for quantifying spatio-temporal interactions in a stochastic dynamical system based on information geometry. In the proposed framework, the degree of interactions is quantified by the divergence…
A generalized entropy arising in the context of superstatistics is obtained for an ideal gas. The curvature scalar associated to the thermodynamic space generated by this modified entropy is calculated using two formalisms of the geometric…
Fisher Information (FI) is a quantity ubiquitously measured in such varied areas like metrology, machine learning, and biological complexity. Mathematically, it represents a lower bound in the variance of unknown parameters that are related…
We study how information geometry is described by bulk geometry in the gauge/gravity correspondence. We consider a quantum information metric that measures the distance between the ground states of a CFT and a theory obtained by perturbing…
The quantum corrections related to the ideal gas model that are often considered are those which are related to the particles nature: bosons or fermions. These corrections lead respectively to the Bose-Einstein and Fermi-Dirac statistics.…
We illustrate how quantum information theory and free (i.e. noncommutative) semialgebraic geometry often study similar objects from different perspectives. We give examples in the context of positivity and separability, quantum magic…
Numerical modelling of quantum effects caused by bosonic or fermionic character of secondaries produced in high energy collisions of different sorts is at the moment still far from being established. In what follows we propose novel…
Shock waves in gas dynamics feature jump discontinuities that hinder numerical simulations. Viscous regularizations are prone to excessive dissipation of fine-scale structures. In this work, we propose the first inviscid regularization of…