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We study a model of temporal voting where there is a fixed time horizon, and at each round the voters report their preferences over the available candidates and a single candidate is selected. Prior work has adapted popular notions of…
An optical flow variational model is proposed for a sequence of images defined on a domain in $\mathbb{R}^2$. We introduce a regularization term given by the $L^1$ norm of a fractional differential operator. To solve the minimization…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
In this PhD thesis we introduce a generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives, and study them using standard (indirect) and direct methods. In…
In this paper, Sturm-Liouville problem for difference equations is considered with potential function q(n). The representations of solutions are obtained by variation of parameters method. These solutions are proved, using summation by…
We prove variational forms of the Barban-Davenport-Halberstam Theorem and the large sieve inequality. We apply our result to prove an estimate for the sum of the squares of prime differences, averaged over arithmetic progressions.
We design a recursive measure of voting power based on partial as well as full voting efficacy. Classical measures, by contrast, incorporate solely full efficacy. We motivate our design by representing voting games using a division lattice…
Proportional representation plays a crucial role in electoral systems. In ordinal elections, where voters rank candidates based on their preferences, the Single Transferable Vote (STV) is the most widely used proportional voting method. STV…
In this communication, we propose a tentative to set the fundamental problem of measuring process done by a large structure on a microsopic one. We consider the example of voting when an entire society tries to measure globally opinions of…
The variance gamma model is a widely popular model for option pricing in both academia and industry. In this paper, we provide a new perspective for pricing European style options for the variance gamma model by deriving closed-form…
We consider elections where both voters and candidates can be associated with points in a metric space and voters prefer candidates that are closer to those that are farther away. It is often assumed that the optimal candidate is the one…
We generalize the method of Van Hove so as to deal with the case of non-ordinary statistical mechanics, that being phenomena with no time-scale separation. We show that in the case of ordinary statistical mechanics, even if the adoption of…
A method of representation of a solution as segments of the series in powers of the step of the independent variable is expanded for solving complex systems of ordinary differential equations (ODE): the Lorenz system and other systems. A…
Election rules are formal processes that aggregate voters preferences, typically to select a single candidate, called the winner. Most of the election rules studied in the literature require the voters to rank the candidates from the most…
The study of proportionality in multiwinner voting with approval ballots has received much attention in recent years. Typically, proportionality is captured by variants of the Justified Representation axiom, which say that cohesive groups…
The paper presents an alternative way to classical stereocorrelation. First, 2D image processing of random patterns is described. Sub-pixel displacements are determined using phase analysis. Then distortion evaluation is presented. The…
We study the complexity of deciding whether there is a tie in a given approval-based multiwinner election, as well as the complexity of counting tied winning committees. We consider a family of Thiele rules, their greedy variants,…
The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…
We prove some invariance principles for processes which generalize FARIMA processes, when the innovations are in the domain of attraction of a nonGaussian stable distribution. The limiting processes are extensions of the fractional L\'evy…
Plurality and approval voting are two well-known voting systems with different strengths and weaknesses. In this paper we consider a new voting system we call beta(k) which allows voters to select a single first-choice candidate and approve…