相关论文: Three Applications of Entropy to Gerrymandering
This paper presents entropy maps, an approach to describing and visualising uncertainty among alternative potential movement intentions in pedestrian simulation models. In particular, entropy maps show the instantaneous level of randomness…
In statistical physics, useful notions of entropy are defined with respect to some coarse graining procedure over a microscopic model. Here we consider some special problems that arise when the microscopic model is taken to be relativistic…
Geographical considerations such as contiguity and compactness are necessary elements of political districting in practice. Yet an analysis of the problem without such constraints yields mathematical insights that can inform real-world…
Deciding whether a political districting plan was distorted by a hidden agenda, or whether it dilutes the voting power of some group, requires a neutral baseline for comparison. Remarkably, all nine U.S. Supreme Court justices have now…
The Shannon entropy, and related quantities such as mutual information, can be used to quantify uncertainty and relevance. However, in practice, it can be difficult to compute these quantities for arbitrary probability distributions,…
We develop algorithms for sampling from a probability distribution on a submanifold embedded in Rn. Applications are given to the evaluation of algorithms in 'Topological Statistics'; to goodness of fit tests in exponential families and to…
Given entropy's central role in multiple areas of physics and science, one important task is to develop a systematic and unifying approach to defining entropy. Games of chance become a natural candidate for characterising the uncertainty of…
Entropy is a measure of self-information which is used to quantify losses. Entropy was developed in thermodynamics, but is also used to compare probabilities based on their deviating information content. Corresponding model uncertainty is…
We argue that traditional formulations of the reduction thesis that tie it to privileged relational operations do not suffice for Peirce's justification of the categories, and invite the charge of gerrymandering to make it come out as true.…
The recently discussed notion of geometric entropy is shown to be related to earlier calculations of thermal effects in Rindler space. The evaluation is extended to de Sitter space and to a two-dimensional black hole.
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 -…
Entropy is the measure of uncertainty in any data and is adopted for maximisation of mutual information in many remote sensing operations. The availability of wide entropy variations motivated us for an investigation over the suitability…
Partisan gerrymandering, i.e., manipulation of electoral district boundaries for political advantage, is one of the major challenges to election integrity in modern day democracies. Yet most of the existing methods for detecting partisan…
The geometric Brownian motion (GBM) is widely employed for modeling stochastic processes, yet its solutions are characterized by the log-normal distribution. This comprises predictive capabilities of GBM mainly in terms of forecasting…
To assess the presence of gerrymandering, one can consider the shapes of districts or the distribution of votes. The "efficiency gap," which does the latter, plays a central role in a 2016 federal court case on the constitutionality of…
We survey some recent applications of machine learning to problems in geometry and theoretical physics. Pure mathematical data has been compiled over the last few decades by the community and experiments in supervised, semi-supervised and…
The notion of entropy appears in many fields and this paper is a survey about entropies in several branches of Mathematics. We are mainly concerned with the topological and the algebraic entropy in the context of continuous endomorphisms of…
Problems of probabilistic inference and decision making under uncertainty commonly involve continuous random variables. Often these are discretized to a few points, to simplify assessments and computations. An alternative approximation is…
Entropy Estimation is an important problem with many applications in cryptography, statistic,machine learning. Although the estimators optimal with respect to the sample complexity have beenrecently developed, there are still some…
The policy gradient theorem is defined based on an objective with respect to the initial distribution over states. In the discounted case, this results in policies that are optimal for one distribution over initial states, but may not be…