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We study scenarios where multiple sellers of a homogeneous good compete on prices, where each seller can only sell to some subset of the buyers. Crucially, sellers cannot price-discriminate between buyers. We model the structure of the…

Computer Science and Game Theory · Computer Science 2013-11-12 Moshe Babaioff , Brendan Lucier , Noam Nisan

Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground. However, a much broader class of discrete-event processes operates in continuous-time. Here, we provide…

Statistical Mechanics · Physics 2020-05-11 S. E. Marzen , J. P. Crutchfield

Entropy has emerged as a dynamic, interdisciplinary, and widely accepted quantitative measure of uncertainty across different disciplines. A unified understanding of entropy measures, supported by a detailed review of their theoretical…

Probability · Mathematics 2025-03-21 Naveen Kumar , Ambesh Dixit , Vivek Vijay

The worldwide trade network has been widely studied through different data sets and network representations with a view to better understanding interactions among countries and products. Here we investigate international trade through the…

Physics and Society · Physics 2018-12-12 Luiz G. A. Alves , Giuseppe Mangioni , Francisco A. Rodrigues , Pietro Panzarasa , Yamir Moreno

Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…

Statistics Theory · Mathematics 2019-11-12 Linda Altieri , Daniela Cocchi , Giulia Roli

A framework for numerical evaluation of entropy-conservative volume fluxes in gas flows with internal energies is developed, for use with high-order discretization methods. The novelty of the approach lies in the ability to use arbitrary…

Fluid Dynamics · Physics 2024-10-18 Georgii Oblapenko , Manuel Torrilhon

We develop an entropic framework to model the dynamics of stocks and European Options. Entropic inference is an inductive inference framework equipped with proper tools to handle situations where incomplete information is available. The…

Pricing of Securities · Quantitative Finance 2019-08-20 Mohammad Abedi , Daniel Bartolomeo

Using known entropic and information inequalities new inequalities for some classical polynomials are obtained. Examples of Jacobi and Legendre polynomials are considered.

Mathematical Physics · Physics 2014-06-30 V. I. Man'ko , L. A. Markovich

We introduce uncertainty into a pure exchange economy and establish a connection between Shannon's differential entropy and uniqueness of price equilibria. The following conjecture is proposed under the assumption of a uniform probability…

Theoretical Economics · Economics 2021-02-22 Andrea Loi , Stefano Matta

Currently, knowledge discovery in databases is an essential step to identify valid, novel and useful patterns for decision making. There are many real-world scenarios, such as bankruptcy prediction, option pricing or medical diagnosis,…

Artificial Intelligence · Computer Science 2018-11-20 José-Ramón Cano , Pedro Antonio Gutiérrez , Bartosz Krawczyk , Michał Woźniak , Salvador García

This chapter presents key concepts and theoretical results for analyzing estimation and inference in high-dimensional models. High-dimensional models are characterized by having a number of unknown parameters that is not vanishingly small…

Statistics Theory · Mathematics 2018-06-12 Alexandre Belloni , Victor Chernozhukov , Denis Chetverikov , Christian Hansen , Kengo Kato

In the traditional art pricing models, the variables that capture the painting's content are often missing. Recent research starts to apply the computer graphic techniques to extract the information from the painting content. Most of the…

General Finance · Quantitative Finance 2020-11-19 Lan Ju , Zhiyong Tu , Changyong Xue

Neural networks have dramatically increased our capacity to learn from large, high-dimensional datasets across innumerable disciplines. However, their decisions are not easily interpretable, their computational costs are high, and building…

Computer Vision and Pattern Recognition · Computer Science 2024-07-08 Mackenzie J. Meni , Ryan T. White , Michael Mayo , Kevin Pilkiewicz

We consider the following classification problem: Given a population of individuals characterized by a set of attributes represented as a vector in ${\mathbb R}^N$, the goal is to find a hyperplane in ${\mathbb R}^N$ that separates two sets…

Machine Learning · Computer Science 2025-07-04 Argimiro Arratia , Mahmoud El Daou , Henryk Gzyl

The method of maximum entropy has been very successful but there are cases where it has either failed or led to paradoxes that have cast doubt on its general legitimacy. My more optimistic assessment is that such failures and paradoxes…

Data Analysis, Statistics and Probability · Physics 2015-06-12 Ariel Caticha

We study a market mechanism that sets edge prices to incentivize strategic agents to efficiently share limited network capacity. In this market, agents form coalitions, with each coalition sharing a unit capacity of a selected route and…

Computer Science and Game Theory · Computer Science 2025-11-19 Saurabh Amin , Patrick Jaillet , Haripriya Pulyassary , Manxi Wu

It is not obvious how to extend Shannon's original information entropy to higher dimensions, and many different approaches have been tried. We replace the English text symbol sequence originally used to illustrate the theory by a discrete,…

Information Theory · Computer Science 2016-09-06 Kieran G. Larkin

Maximum Entropy is a powerful concept that entails a sharp separation between relevant and irrelevant variables. It is typically invoked in inference, once an assumption is made on what the relevant variables are, in order to estimate a…

Statistical Mechanics · Physics 2018-01-09 Luigi Gresele , Matteo Marsili

Modelling a complex system is almost invariably a challenging task. The incorporation of experimental observations can be used to improve the quality of a model, and thus to obtain better predictions about the behavior of the corresponding…

Computational Physics · Physics 2015-11-24 Massimiliano Bonomi , Carlo Camilloni , Andrea Cavalli , Michele Vendruscolo

Organizations generate vast amounts of interconnected content across various platforms. While language models enable sophisticated reasoning for use in business applications, retrieving and contextualizing information from organizational…

Information Retrieval · Computer Science 2025-04-11 Adam McCabe , Matthew H. Chequers