Related papers: Three Applications of Entropy to Gerrymandering

Physics concepts have often been borrowed and independently developed by other fields of science. In this perspective a significant example is that of entropy in Information Theory. The aim of this paper is to provide a short and…

This work explores entropy analysis as a tool for probing information distribution within Transformer-based architectures. By quantifying token-level uncertainty and examining entropy patterns across different stages of processing, we aim…

The transfer matrix is a powerful technique that can be applied to statistical mechanics systems as, for example, in the calculus of the entropy of the ice model. One interesting way to study such systems is to map it onto a 3-color…

This past decade has seen a noticeable uptick in asymmetric election results along with the inevitable claims of gerrymandering and litigation. Research, too, has followed, giving rise to intense scrutiny of elections, where the goal is to…

The outcome of elections is strongly dependent on the districting choices, making thus possible (and frequent) the gerrymandering phenomenon, i.e.\ politicians suitably changing the shape of electoral districts in order to win the…

Entropy is arguably one of the most powerful concepts to understand the world, from the behavior of molecules to the expansion of the universe, from how life emerges to how hybrid complex systems like cities come into being and continue…

This book brings new mathematical rigour to the ongoing vigorous debate on how to quantify biological diversity. The question "what is diversity?" has surprising mathematical depth, and breadth too: this book involves parts of mathematics…

We construct a space which is useful in order to study the entropy of meromorphic maps by using projective limits. We deduce a variational principle for meromorphic maps.

Entropy numbers and covering numbers of sets and operators are well known geometric notions, which found many applications in various fields of mathematics, statistics, and computer science. Their values for finite-dimensional embeddings…

The microscopic explanation of entropy has been challenged from both experimental and theoretical point of view. The expression of entropy is derived from the first law of thermodynamics indicating that entropy or the second law of…

Citizens' assemblies are a form of democratic innovation in which a randomly selected panel of constituents deliberates on questions of public interest. We study a novel goal for the selection of panel members: maximizing the entropy of the…

A definition of entropy via the Kolmogorov algorithmic complexity is discussed. As examples, we show how the meanfield theory for the Ising model, and the entropy of a perfect gas can be recovered. The connection with computations are…

This paper is to obtain a simple dividing-diagram of the congressional districts, where the only limit is that each district should contain the same population if possibly. In order to solve this problem, we introduce three different…

While manipulative attacks on elections have been well-studied, only recently has attention turned to attacks that account for geographic information, which are extremely common in the real world. The most well known in the media is…

The category of metric spaces is a subcategory of quasi-metric spaces. In this paper the notion of entropy for the continuous maps of a quasi-metric space is extended via spanning and separated sets. Moreover, two metric spaces that are…

Classification is a machine learning method used in many practical applications: text mining, handwritten character recognition, face recognition, pattern classification, scene labeling, computer vision, natural langage processing. A…

Inverse optimization has received much attention in recent years, but little literature exists for solving generalized mixed integer inverse optimization. We propose a new approach for solving generalized mixed-integer inverse optimization…

We commonly encounter the problem of identifying an optimally weight adjusted version of the empirical distribution of observed data, adhering to predefined constraints on the weights. Such constraints often manifest as restrictions on the…

This paper examines an area of Game Theory called Voting Power Theory. With the adoption of a measure theoretic framework it argues that the many different indices and tools currently used for measuring voting power can be replaced by just…

Various properties of relative entropy have led to its widespread use in information theory. These properties suggest that relative entropy has a role to play in systems that attempt to perform inference in terms of probability…