Related papers: Computational information geometry: theory and pra…
Mathematical information is essential for technical work, but its creation, interpretation, and search are challenging. To help address these challenges, researchers have developed multimodal search engines and mathematical question…
This monograph presents a geometric modeling method nonlinear dynamical systems from experimental data . basis method is a qualitative approach to the analysis of linear models and construction of the symmetry groups of attractors of…
We expose (without proofs) a unified computational approach to integrable structures (including recursion, Hamiltonian, and symplectic operators) based on geometrical theory of partial differential equations. We adopt a coordinate based…
Volunteered geographic information (VGI), one of the most important types of user-generated web content, has been emerging as a new phenomenon. VGI is contributed by numerous volunteers and supported by web 2.0 technologies. This chapter…
Physical systems behave according to their underlying dynamical equations which, in turn, can be identified from experimental data. Explaining data requires selecting mathematical models that best capture the data regularities. Identifying…
Complex models in physics, biology, economics, and engineering are often sloppy, meaning that the model parameters are not well determined by the model predictions for collective behavior. Many parameter combinations can vary over decades…
The information geometry of the 2-manifold of gamma probability density functions provides a framework in which pseudorandom number generators may be evaluated using a neighbourhood of the curve of exponential density functions. The process…
To what extent can we distinguish one probability distribution from another? Are there quantitative measures of distinguishability? The goal of this tutorial is to approach such questions by introducing the notion of the "distance" between…
Geometrical methods in quantum information are very promising for both providing technical tools and intuition into difficult control or optimization problems. Moreover, they are of fundamental importance in connecting pure geometrical…
Using the mathematical framework of information geometry, we introduce a novel method which allows one to efficiently determine the exact shape of simultaneous confidence regions for non-linearly parametrised models. Furthermore, we show…
Author developed a uniform model for different spaces where distance and angle measure kinds are parameters. This model is calculus centric, but can also be used in theoretical research. It is useful in the following domains: deduction of…
In this paper, we examine a ciphertext on the basis of using geometrical objects. Each symbol normative alphabet is determined as a point on the plane. We consider possible ways for presentation of these points.
Partial Information Decomposition (PID) has become one of the most prominent information-theoretic frameworks for describing the structure and quality of information in complex systems. Despite its widespread utility, there exists no unique…
Motivated by the presence of deep connections among dynamical equations, experimental data, physical systems, and statistical modeling, we report on a series of findings uncovered by the Authors and collaborators during the last decade…
Circular and non-flat data distributions are prevalent across diverse domains of data science, yet their specific geometric structures often remain underutilized in machine learning frameworks. A principled approach to accounting for the…
Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…
We introduce diffusion geometry as a new framework for geometric and topological data analysis. Diffusion geometry uses the Bakry-Emery $\Gamma$-calculus of Markov diffusion operators to define objects from Riemannian geometry on a wide…
We describe a method for modeling the geometry of porous materials. The approach enables the independent selection of crucial parameters, including porosity, pore size distribution, pore shape, and connectivity. Consequently, it can…
In this paper, we show how information geometry, the natural geometry of discrete probability distributions, can be used to derive the quantum formalism. The derivation rests upon three elementary features of quantum phenomena, namely…
Dependency networks (Heckerman et al., 2000) provide a flexible framework for modeling complex systems with many variables by combining independently learned local conditional distributions through pseudo-Gibbs sampling. Despite their…