Related papers: Mathematical aspects of degressive proportionality
We study the distributional behavior of additive arithmetic functions evaluated at integers drawn from the harmonic distribution. Our main result shows that a broad family of such functions converges in law to conditioned Dickman-type…
We explore the asymptotic distributions of sequences of integer-valued additive functions defined on the symmetric group endowed with the Ewens probability measure as the order of the group increases. Applying the method of factorial…
Sigmoid functions play an important role in many areas of applied mathematics, including machine learning, population dynamics and probability. We place the study of sigmoid functions in the context of the derivative sub-group of the group…
We consider overdetermined problems related to the fractional capacity. In particular we study $s$-harmonic functions defined in unbounded exterior sets or in bounded annular sets, and having a level set parallel to the boundary. We first…
Proportional apportionment is the problem of assigning seats to parties according to their relative share of votes. Divisor methods are the de-facto standard solution, used in many countries. In recent literature, there are two algorithms…
An analytical approach to convolution of functions, which appear in perturbative calculations, is discussed. An extended list of integrals is presented.
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…
An unconditional inequality of the totient function is contributed to the literature. This result is associated with various problems about the distribution of prime numbers.
A classical inequality, which is known for families of monotone functions, is generalized to a larger class of families of measurable functions. Moreover we characterize all the families of functions for which the equality holds. We apply…
Seven mathematicians and one political scientist met at the Cambridge Apportionment Meeting in January 2011. They agreed a unanimous recommendation to the European Parliament for its future apportionments between the EU Member States. This…
Suppose we are given a family of choice functions on pairs from a given finite set (with at least three elements) closed under permutations of the given set. The set is considered the set of alternatives (say candidates for an office). The…
We present projective descriptions of classical spaces of functions and distributions. More precisely, we provide descriptions of these spaces by semi-norms which are defined by a combination of classical norms and multiplication or…
Functions that are piecewise defined are a common sight in mathematics while convexity is a property especially desired in optimization. Suppose now a piecewise-defined function is convex on each of its defining components - when can we…
We apply the topology of convergence on compact sets to define unpredictable functions [5, 6]. The topology is metrizable and easy for applications with integral operators. To demonstrate the effectiveness of the approach, the existence and…
We study the statistical complexity of estimating partition functions given sample access to a proposal distribution and an unnormalized density ratio for a target distribution. While partition function estimation is a classical problem,…
We consider a voting model, where a number of candidates need to be selected subject to certain feasibility constraints. The model generalises committee elections (where there is a single constraint on the number of candidates that need to…
This is a survey paper concerning some theorems on stochastic convex ordering and their applications to functional inequalities for convex functions. We present the recent results on those subjects
When given a class of functions and a finite collection of sets, one might be interested whether the class in question contains any function whose domain is a subset of the union of the sets of the given collection and whose restrictions to…
This paper focuses on stochastic orders and its applications : policy limits and deductibles. Further, many applications and some examples are given : comparison of two families of copulas, individual and collective risk model, reinsurance…
Submodularity is a fundamental phenomenon in combinatorial optimization. Submodular functions occur in a variety of combinatorial settings such as coverage problems, cut problems, welfare maximization, and many more. Therefore, a lot of…