相关论文: Information geometric complexity of a trivariate G…

We present an extension of the ergodic, mixing, and Bernoulli levels of the ergodic hierarchy for statistical models on curved manifolds, making use of elements of the information geometry. This extension focuses on the notion of…

We formulate the problem of determining the volume of the set of Gaussian physical states in the framework of information geometry. That is, by considering phase space probability distributions parametrized by the covariances and supplying…

Experimental design is crucial for inference where limitations in the data collection procedure are present due to cost or other restrictions. Optimal experimental designs determine parameters that in some appropriate sense make the data…

We formulate meta learning using information theoretic concepts; namely, mutual information and the information bottleneck. The idea is to learn a stochastic representation or encoding of the task description, given by a training set, that…

During a spontaneous change, a macroscopic physical system will evolve towards a macro-state with more realizations. This observation is at the basis of the Statistical Mechanical version of the Second Law of Thermodynamics, and it provides…

We introduce an information theoretic measure of statistical structure, called 'binding information', for sets of random variables, and compare it with several previously proposed measures including excess entropy, Bialek et al.'s…

A central issue of the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate to a -…

Motivated by the possible applications that a better understanding of consciousness might bring, we follow Tononi's idea and calculate analytically a complexity index for two systems of Ising spins with parallel update dynamics, the…

Industrial dynamical systems often exhibit multi-scale response due to material heterogeneities, operation conditions and complex environmental loadings. In such problems, it is the case that the smallest length-scale of the systems…

Observations of gravitational waves emitted by merging compact binaries have provided tantalising hints about stellar astrophysics, cosmology, and fundamental physics. However, the physical parameters describing the systems, (mass, spin,…

Non-Gaussian bosonic states are ubiquitous in interacting light--matter systems, many-body platforms, and relativistic quantum field settings, but their quantitative characterization is hindered by the infinite-dimensional Hilbert space and…

We analytically and numerically characterize the structure of hard-sphere fluids in order to review various geometrical frustration scenarios of the glass transition. We find generalized polytetrahedral order to be correlated with…

The Hubbard model with geometrical frustration is investigated in a metallic phase close to half-filling. We calculate the single particle spectral function for the triangular lattice within dynamical cluster approximation, which is further…

This paper presents a heuristic framework for analyzing the Goldbach Conjecture (GC) from the perspective of the physics of information. Through empirical analysis, we propose an Informational Economy Principle (IEP), which posits that…

Geometric frustration arises when lattice structure prevents simultaneous minimization of local interactions. It leads to highly degenerate ground states and, subsequently, complex phases of matter such as water ice, spin ice and frustrated…

Most problems within and beyond the scientific domain can be framed into one of the following three levels of complexity of function approximation. Type 1: Approximate an unknown function given input/output data. Type 2: Consider a…

Topological frustration arises when boundary conditions impose geometric frustration in a quantum system, creating delocalized defects in the ground states and profoundly altering the low-energy properties. While previous studies have been…

Quantum information scrambling (QIS), from the perspective of quantum information theory, is generally understood as local non-retrievability of information evolved through some dynamical process, and is often quantified via entropic…

We show that recent results on randomized dimension reduction schemes that exploit structural properties of data can be applied in the context of persistent homology. In the spirit of compressed sensing, the dimension reduction is…

Group formation is important in many economic contexts. The current literature on group formation assumes that individuals may join any existing group. In this paper, I consider the implications of social, geographic, and informational…