Related papers: Compact majority-minority districts almost never e…
We develop a theory of multidimensional randomization in Lebesgue spaces $L^p$ with the aid of Kahane-Khintchine-Marcus-Pisier inequalities. More precisely, we obtain a result in the spirit of Maurey-Pisier's theorem which involves random…
We show that min-max minimal hypersurfaces can be localized. As a consequence, we obtain the sharp generalization to complete manifolds of the famous Almgren-Pitts min-max theorem in closed manifolds. We use this result to prove the…
In recent years, statistical characterization of the discrete conservative dynamical systems (more precisely, paradigmatic examples of area-preserving maps such as the standard and the web maps) has been analyzed extensively and shown that,…
Assessing equity in treatment of a subpopulation often involves assigning numerical "scores" to all individuals in the full population such that similar individuals get similar scores; matching via propensity scores or appropriate…
Finding outlying elements in probability distributions can be a hard problem. Taking a real example from Voting Rights Act enforcement, we consider the problem of maximizing the number of simultaneous majority-minority districts in a…
We study random dynamical systems generated by volume-preserving piecewise $C^{1}$ maps. For this class of systems, we establish an invariance principle stating that if all Lyapunov exponents vanish, then there exists a measurable family of…
We consider two classes of piecewise expanding maps $T$ of $[0,1]$: a class of uniformly expanding maps for which the Perron-Frobenius operator has a spectral gap in the space of bounded variation functions, and a class of expanding maps…
Given a computable probability measure P over natural numbers or infinite binary sequences, there is no computable, randomized method that can produce an arbitrarily large sample such that none of its members are outliers of P.
While modern large-scale datasets often consist of heterogeneous subpopulations -- for example, multiple demographic groups or multiple text corpora -- the standard practice of minimizing average loss fails to guarantee uniformly low losses…
This paper develops a general inferential framework for discrete copulas on finite supports in any dimension. The copula of a multivariate discrete distribution is defined as Csiszar's I-projection (i.e., the minimum-Kullback-Leibler…
Comparing the differences in outcomes (that is, in "dependent variables") between two subpopulations is often most informative when comparing outcomes only for individuals from the subpopulations who are similar according to "independent…
We propose a method for redistricting, decomposing a geographical area into subareas, called districts, so that the populations of the districts are as close as possible and the districts are compact and contiguous. Each district is the…
Stable distributions are of fundamental importance in probability theory, yet their absolute continuity makes them unsuitable for modeling count data. A discrete analog of strict stability has been previously proposed by replacing scaling…
This paper gives the definition of the Conley index for a piecewise continuous map, which is only well defined on compatible isolating neighborhoods with Wazewski property slightly weaker than continuous situation.
In the process of redistricting, one important metric is the number of competitive districts, that is, districts where both parties have a reasonable chance of winning a majority of votes. Competitive districts are important for achieving…
It was proved that whenever $\mathbb{N}$ is partitioned into finitely many cells, one cell must contain arbitrary length arithmetic and geometric progression nicely intertwined, so that one cell must be rich in the sense of containing…
Manipulation, bribery, and control are well-studied ways of changing the outcome of an election. Many voting rules are, in the general case, computationally resistant to some of these manipulative actions. However when restricted to…
In this paper we prove that for any definable subset $X\subset \mathbb{R}^{n}$ in a polynomially bounded o-minimal structure, with $dim(X)<n$, there is a finite set of regular projections (in the sense of Mostowski ). We give also a weak…
We study algebraic properties on a group G such that if the discrete group G has these properties then every locally compact shift continuous topology on G with adjoined zero is either compact, or discrete. We introduce electorally flexible…
Dense crowd counting is a challenging task that demands millions of head annotations for training models. Though existing self-supervised approaches could learn good representations, they require some labeled data to map these features to…