arXiv research

We extend the definition of algebraic entropy to endomorphisms of affine varieties. We calculate algebraic entropy of the action of elements of mapping class groups on various character varieties, and show that it is equal to a quantity we call the spectral radius, a generalization of the dilatation of a Pseudo-Anosov …

Entropy-minimal measure calculated for a stochastic volatility model.

We numerically calculate Perelman's entropy for a variety of canonical metrics on $\mathbb{CP}^{1}$-bundles over products of Fano Kähler-Einstein manifolds. The metrics investigated are Einstein metrics, Kähler-Ricci solitons and quasi-Einstein metrics. The calculation of the entropy allows a rough picture of how the R…

Study uses holography to analyze entanglement entropy in deformed CFTs.

When a spacetime has boundaries, the entangling surface does not have to be necessarily compact and it may have boundaries as well. Then there appear a new, boundary, contribution to the entanglement entropy due to the intersection of the entangling surface with the boundary of the spacetime. We study the boundary cont…

We calculate the volume entropy of local Hermitian symmetric spaces of noncompact type in terms of its invariant $r$, $a$, $b$.

The study evaluates different probability models for uncertainty visualization using entropy calculations.

Researchers calculate Shannon entropy rates of hidden Markov processes efficiently.

Deep learning speeds up protein mapping entropy calculation.

We show that the entropy of a finitely generated pseudogroup (resp., of a foliation of a compact Riemannian manifold) can be calculated by suitable counting separated pseudo-orbits (resp., pseudoleaves).

The well known maximum-entropy principle due to Jaynes, which states that given mean parameters, the maximum entropy distribution matching them is in an exponential family, has been very popular in machine learning due to its "Occam's razor" interpretation. Unfortunately, calculating the potentials in the maximum-entro…

We generalize an entropy calculation of Perelman to the case of domains evolving inside a Ricciflow solution. In the case of Euclidean space as ambient manifold an interesting relation with Harnack inequalities emerges.

Study complexity in financial market using Shannon entropy.

The ability of many powerful machine learning algorithms to deal with large data sets without compromise is often hampered by computationally expensive linear algebra tasks, of which calculating the log determinant is a canonical example. In this paper we demonstrate the optimality of Maximum Entropy methods in approxi…

The aim of this paper is to provide new theoretical and computational understanding on two loss regularizations employed in deep learning, known as local entropy and heat regularization. For both regularized losses we introduce variational characterizations that naturally suggest a two-step scheme for their optimizatio…

In this report, we review the calculation of entropy-regularised Wasserstein loss introduced by Cuturi and document a practical implementation in PyTorch. Code is available at https://github.com/t-vi/pytorch-tvmisc/blob/master/wasserstein-distance/Pytorch_Wasserstein.ipynb

In this paper, we develop the notion of entropy for uniform hypergraphs via tensor theory. We employ the probability distribution of the generalized singular values, calculated from the higher-order singular value decomposition of the Laplacian tensors, to fit into the Shannon entropy formula. We show that this tensor …

In this article we prove two formulas for the topological entropy of an F-optical Hamiltonian flow induced by a C^{\infty} Hamiltonian, where F is a Lagrangian distribution. In these formulas, we calculate the topological entropy as the exponential growth rate of the average of the determinant of the differential of th…

Theoretical analysis of entropy approximation for Gaussian mixtures.

We translate the problem of calculating the entropy of a set of binary configurations/signals into a sequence of supervised classification tasks. Subsequently, one can use virtually any machine learning classification algorithm for computing entropy. This procedure can be used to compute entropy, and consequently the f…

The paper calculates bounds for risk metrics and entropies under partial information constraints.

The study calculates Weyl entropy in spacetime regions and shows its monotonic behavior.

News novelty predicts negative stock market returns.

This is full length article (draft version) where problem number of topics in Topic Modeling is discussed. We proposed idea that Renyi and Tsallis entropy can be used for identification of optimal number in large textual collections. We also report results of numerical experiments of Semantic stability for 4 topic mode…

Topological entropy measures the number of distinguishable orbits in a dynamical system, thereby quantifying the complexity of chaotic dynamics. One approach to computing topological entropy in a two-dimensional space is to analyze the collective motion of an ensemble of system trajectories taking into account how traj…

We use the conformal invariance and the holographic correspondence to fully specify the dependence of entanglement entropy on the extrinsic geometry of the 2d surface $Σ$ that separates two subsystems of quantum strongly coupled ${\mathcal{N}}=4$ SU(N) superconformal gauge theory. We extend this result and calculate en…

Novel kernelized Renyi's entropy improves deep learning generalization bounds.

The entropy models have been recently adopted in many studies to evaluate the distribution of the shear stress in circular channels. However, the uncertainty in their predictions and their reliability remains an open question. We present a novel method to evaluate the uncertainty of four popular entropy models, includi…

New method uses SVD entropy to price artworks.

The problem of determining the joint probability distributions for correlated random variables with pre-specified marginals is considered. When the joint distribution satisfying all the required conditions is not unique, the "most unbiased" choice corresponds to the distribution of maximum entropy. The calculation of t…

In this work a new way to calculate the multivariate joint entropy is presented. This measure is the basis for a fast information-theoretic based evaluation of gene relevance in a Microarray Gene Expression data context. Its low complexity is based on the reuse of previous computations to calculate current feature rele…

Paper compares two entropy concepts for finite presentation groups.

Calculates local Granger causality for Gaussian and nonlinear systems.

New MC-Tree method combines Monte Carlo and binomial tree for option pricing and CVA.

This article proposes a method to quantify the structure of a bipartite graph using a network entropy per link. The network entropy of a bipartite graph with random links is calculated both numerically and theoretically. As an application of the proposed method to analyze collective behavior, the affairs in which parti…

The economy globalization measure problem is discussed. Four macroeconomic indices of twenty among the "richest" countries are examined. Four types of "distances" are calculated.Two types of networks are next constructed for each distance measure definition. It is shown that the globalization process can be best charac…

Optimized fuzzy entropy framework improves feature selection and classification performance.

Constructs QFT on curved surfaces, proving axioms and calculating entropy.

Information transfer between time series is calculated by using the asymmetric information-theoretic measure known as transfer entropy. Geweke's autoregressive formulation of Granger causality is used to find linear transfer entropy, and Schreiber's general, non-parametric, information-theoretic formulation is used to …

Researchers calculate entropy of heat kernel on manifolds for very small times.

In recent years, deep reinforcement learning has been shown to be adept at solving sequential decision processes with high-dimensional state spaces such as in the Atari games. Many reinforcement learning problems, however, involve high-dimensional discrete action spaces as well as high-dimensional state spaces. This pa…

The change in Holographic entanglement entropy (HEE) for small fluctuations about pure anti De Sitter (AdS) is obtained by a perturbative expansion of the area functional in terms of the change in the bulk metric and the embedded extremal surface. However, it is known that change in the embedding appears in second orde…

LES optimizes designs by sampling descent sequences, achieving strong sample efficiency.

High entropy alloys (HEAs) have been increasingly attractive as promising next-generation materials due to their various excellent properties. It's necessary to essentially characterize the degree of chemical ordering and identify order-disorder transitions through efficient simulation and modeling of thermodynamics. I…

The paper develops a decision support system for hierarchical text classification of conference proceedings.

Study gauged supergravity, M5-branes, and class R theories, constraining supergravity coefficients and calculating partition functions.

Earlier studies have shown that stock market distributions can be well described by distributions derived from Tsallis entropy, which is a generalization of Shannon entropy to non-extensive systems. In this paper, Tsallis relative entropy (TRE), which is the generalization of Kullback-Leibler relative entropy (KLRE) to…

We investigate the position of the Buchen-Kelly density in a family of entropy maximising densities which all match European call option prices for a given maturity observed in the market. Using the Legendre transform which links the entropy function and the cumulant generating function, we show that it is both the uni…