相关论文: Piercing Numbers in Approval Voting

We study the a.s. convergence of a sequence of random embeddings of a fixed manifold into Euclidean spaces of increasing dimensions. We show that the limit is deterministic. As a consequence, we show that many intrinsic functionals of the…

Several measures of partisan bias are reviewed for single member districts with two dominant parties. These include variants of the simple bias that considers only deviation of seats from 50% at statewide 50% vote. Also included are…

Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…

Statistical Shape Modeling (SSM) is a quantitative method for analyzing morphological variations in anatomical structures. These analyses often necessitate building models on targeted anatomical regions of interest to focus on specific…

An ordinal preference domain is a subset of preference orders that the voters are allowed to cast in an election. We introduce and study the notion of outer diversity of a domain and evaluate its value for a number of well-known structured…

In this paper we discuss about properties of lattices and its application in theoretical and algorithmic number theory. This result of Minkowski regarding the lattices initiated the subject of Geometry of Numbers, which uses geometry to…

Motivated by the increasing interest of the control community towards social sciences and the study of opinion formation and belief systems, in this paper we address the problem of exploiting voting data for inferring the underlying…

In this note, I describe a formalism for treating knots as geometric spaces, and make an application to a simple statistical mechanics computation. The motivation for this study is the natural visual symmetry of the knot, and I describe how…

Coalitional manipulation in voting is considered to be any scenario in which a group of voters decide to misrepresent their vote in order to secure an outcome they all prefer to the first outcome of the election when they vote honestly. The…

Let $G$ be a digraph where every node has preferences over its incoming edges. The preferences of a node extend naturally to preferences over branchings, i.e., directed forests; a branching $B$ is popular if $B$ does not lose a head-to-head…

We consider ruled surfaces with finite multiplicity. We study behaviors of the striction curves and the singularities of the ruled surfaces. We also give geometric meanings of invariants related to the ruled surfaces.

This paper presents an algorithm for enumerating biases in word embeddings. The algorithm exposes a large number of offensive associations related to sensitive features such as race and gender on publicly available embeddings, including a…

Utilizing recently developed abstract notions of sectional curvature, we introduce a method for constructing a curvature-based geometric profile of discrete metric spaces. The curvature concept that we use here captures the metric relations…

Referring to a standard context of voting theory, and to the classic notion of voting situation, here we show that it is possible to observe any arbitrary set of elections' outcomes, no matter how paradoxical it may appear. On this purpose…

A method is given for quantitatively rating the social acceptance of different options which are the matter of a preferential vote. In contrast to a previous article, here the individual votes are allowed to be incomplete, that is, they…

Voting rules based on evaluation inputs rather than preference orders have been recently proposed, like majority judgement, range voting or approval voting. Traditionally, probabilistic analysis of voting rules supposes the use of…

We study a system of interacting reinforced random walks defined on polygons. At each stage, each particle chooses an edge to traverse which is incident to its position. We allow the probability of choosing a given edge to depend on the sum…

Trimming is a core technique in geometric modeling. Unfortunately, the resulting objects do not take the requirements of numerical simulations into account and yield various problems. This paper outlines principal issues of trimmed models…

In the context of modern sampling methods for redistricting, we define a natural measurement of the clustering of a political party, and we study how clustering affects the expected election outcome. We first prove general results and then…

The problem of searching for a model-based scene interpretation is analyzed within a probabilistic framework. Object models are formulated as generative models for range data of the scene. A new statistical criterion, the truncated object…