Related papers: Information Graph Flow: a geometric approximation …
A number of recent proposals for a quantum theory of gravity are based on the idea that spacetime geometry and gravity are derivative concepts and only apply at an approximate level. There are two fundamental challenges to any such…
We present approximation algorithms for several network design problems in the model of Flexible Graph Connectivity (Adjiashvili, Hommelsheim and M\"uhlenthaler, "Flexible Graph Connectivity", Math. Program. pp. 1-33 (2021), and IPCO 2020:…
Information geometry provides a tool to systematically investigate parameter sensitivity of the state of a system. If a physical system is described by a linear combination of eigenstates of a complex (that is, non-Hermitian) Hamiltonian,…
In this paper we describe a triple correspondence between graph limits, information theory and group theory. We put forward a new graph limit concept called log-convergence that is closely connected to dense graph limits but its main…
The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…
Although the notion of entropy lies at the core of statistical mechanics, it is not often used in statistical mechanical models to characterize phase transitions, a role more usually played by quantities such as various order parameters,…
Graph compression is a data analysis technique that consists in the replacement of parts of a graph by more general structural patterns in order to reduce its description length. It notably provides interesting exploration tools for the…
Information geometry is a study of statistical manifolds, that is, spaces of probability distributions from a geometric perspective. Its classical information-theoretic applications relate to statistical concepts such as Fisher information,…
This article elaborates on entanglement entropy and quantum information theory of geometric flows of (relativistic) Lagrange--Hamilton mechanical systems. A set of basic geometric and quantum mechanics and probability concepts together with…
In this paper, we leverage the properties of non-Euclidean Geometry to define the Geodesic distance (GD) on the space of statistical manifolds. The Geodesic distance is a real and intuitive similarity measure that is a good alternative to…
An important problem in geometric reasoning is to find the configuration of a collection of geometric bodies so as to satisfy a set of given constraints. Recently, it has been suggested that this problem can be solved efficiently by…
Using the generalized entropies which depend on two parameters we propose a set of quantitative characteristics derived from the Information Geometry based on these entropies. Our aim, at this stage, is modest, as we are first constructing…
A distance-approximation algorithm for a graph property $\mathcal{P}$ in the adjacency-matrix model is given an approximation parameter $\epsilon \in (0,1)$ and query access to the adjacency matrix of a graph $G=(V,E)$. It is required to…
Geometric quantum mechanics, through its differential-geometric underpinning, provides additional tools of analysis and interpretation that bring quantum mechanics closer to classical mechanics: state spaces in both are equipped with…
Boxicity of a graph $G(V,$ $E)$, denoted by $box(G)$, is the minimum integer $k$ such that $G$ can be represented as the intersection graph of axis parallel boxes in $\mathbb{R}^k$. The problem of computing boxicity is inapproximable even…
This thesis explores important concepts in the area of quantum information geometry and their relationships. We highlight the unique characteristics of these concepts that arise from their quantum mechanical foundations and emphasize the…
In this paper, we propose a new geometric approach for knowledge graph completion via low rank tensor approximation. We augment a pretrained and well-established Euclidean model based on a Tucker tensor decomposition with a novel hyperbolic…
On the background of the Born-Oppenheimer (adiabatic) approximation, we investigate the geometrical and topological structure in the theory of quantum gravity by using the path integral method and halfclassical approximation. As we know,…
A geometric approach to some quantum statistical systems (including the harmonic oscillator) is presented. We regard the (N+1)-dimensional Euclidean {\it coordinate} system (X$^i$,$\tau$) as the quantum statistical system of N quantum…
Effective information analysis generally boils down to properly identifying the structure or geometry of the data, which is often represented by a graph. In some applications, this structure may be partly determined by design constraints or…