Related papers: Nice Bounds for the Generalized Ballot Problem

For fixed weights w_1,...,w_n, and for d>0, we let B denote a collection of d*n balls, with d balls of weight w_i for each i=1,...,n. We consider the problem of assigning the balls to n bins with capacities C_1,...,C_n, in such a way that…

We consider a wide class of linear boundary-value problems for systems of $m$ ordinary differential equations of order $r$, known as general boundary-value problems. Their solutions $y:[a,b]\to \mathbb{C}^{m}$ belong to the Sobolev space…

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…

Suppose $B_i:= B(p,r_i)$ are nested balls of radius $r_i$ about a point $p$ in a dynamical system $(T,X,\mu)$. The question of whether $T^i x\in B_i$ infinitely often (i. o.) for $\mu$ a.e.\ $x$ is often called the shrinking target problem.…

We study a kind of generalized porous medium equation with fractional Laplacian and abstract pressure term. For a large class of equations corresponding to the form: $u_t+\nu \Lambda^{\beta}u=\nabla\cdot(u\nabla Pu)$, we get their local…

Concentration bounds are given for throwing balls into bins independently according to a distribution $p$. The probability of a $k$-loaded bin after $m$ balls is shown to be controlled on both sides by $\rho_{m,k} := m \|p\|_k / k$. This…

The generalization error of a learning algorithm refers to the discrepancy between the loss of a learning algorithm on training data and that on unseen testing data. Various information-theoretic bounds on the generalization error have been…

In this short paper, we give an upper bound for the number of different basic feasible solutions generated by the simplex method for linear programming problems having optimal solutions. The bound is polynomial of the number of constraints,…

We address the problem of producing a lower bound for the mean of a discrete probability distribution, with known support over a finite set of real numbers, from an iid sample of that distribution. Up to a constant, this is equivalent to…

In this paper, we consider sums of four generalized polygonal numbers whose parameters are restricted to integers with a bounded number of prime divisors. With some restriction on m modulo 30, we show that for n sufficiently large, it can…

We study computational problems for two popular parliamentary voting procedures: the amendment procedure and the successive procedure. While finding successful manipulations or agenda controls is tractable for both procedures, our…

We consider a real random variable X represented through a random pair of real random variables (R,T) and a deterministic function u as X=Ru(T). Under some additional assumptions, we prove a limit theorem for (R,T) given X>x, as x tends to…

We consider the problem of manipulating elections by cloning candidates. In our model, a manipulator can replace each candidate c by several clones, i.e., new candidates that are so similar to c that each voter simply replaces c in his vote…

We study the voting problem with two alternatives where voters' preferences depend on a not-directly-observable state variable. While equilibria in the one-round voting mechanisms lead to a good decision, they are usually hard to compute…

We study the problem of bribery in multiwinner elections, for the case where the voters cast approval ballots (i.e., sets of candidates they approve) and the bribery actions are limited to: adding an approval to a vote, deleting an approval…

We present an alternative voting system that aims at bridging the gap between proportional representative systems and majoritarian, single winner election systems. The system lets people vote for multiple parties, but then assigns each…

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…

We study a higher-dimensional 'balls-into-bins' problem. An infinite sequence of i.i.d. random vectors is revealed to us one vector at a time, and we are required to partition these vectors into a fixed number of bins in such a way as to…

In this paper, we present a generalized Bell inequality for mixed states. The distinct characteristic is that the inequality has variable bound depending on the decomposition of the density matrix. The inequality has been shown to be more…

Control and manipulation are two of the most studied types of attacks on elections. In this paper, we study the complexity of control attacks on elections in which there are manipulators. We study both the case where the "chair" who is…