Related papers: A new bound of concurrence
For a class of competition-diffusion nonlinear systems involving fractional powers of the Laplacian, including as a special case the fractional Gross-Pitaevskii system, we prove that uniform boundedness implies H\"older boundedness for…
In the context of auctions for digital goods, an interesting random sampling auction has been proposed by Goldberg, Hartline, and Wright [2001]. This auction has been analyzed by Feige, Flaxman, Hartline, and Kleinberg [2005], who have…
We study scenarios where multiple sellers of a homogeneous good compete on prices, where each seller can only sell to some subset of the buyers. Crucially, sellers cannot price-discriminate between buyers. We model the structure of the…
In the quest for market mechanisms that are easy to implement, yet close to optimal, few seem as viable as posted pricing. Despite the growing body of impressive results, the performance of most posted price mechanisms however, rely…
We propose new results for the existence and uniqueness of a general nonparametric and nonseparable competitive equilibrium with substitutes. These results ensure the invertibility of a general competitive system. The existing literature…
Theory of $n$-complements with applications is presented.
For an input graph $G$, an additive spanner is a sparse subgraph $H$ whose shortest paths match those of $G$ up to small additive error. We prove two new lower bounds in the area of additive spanners: 1) We construct $n$-node graphs $G$ for…
We give a new asymptotic upper bound on the size of a code in the Grassmannian space. The bound is better than the upper bounds known previously in the entire range of distances except very large values.
We consider a simple model of rational agents competing in a single product market described by simple linear demand curve. Contrary to accepted economic theory, the agents' production levels synchronise in the absence of conscious…
In this paper, a new upper bound for the Multiple Knapsack Problem (MKP) is proposed, based on the idea of relaxing MKP to a {\em Bounded Sequential Multiple Knapsack Problem}, i.e., a multiple knapsack problem in which item sizes are…
Deep neural networks have been widely deployed in various machine learning tasks. However, recent works have demonstrated that they are vulnerable to adversarial examples: carefully crafted small perturbations to cause misclassification by…
I show that firms price almost competitively and consumers can infer product quality from prices in markets where firms differ in quality and production cost, and learning prices is costly. Bankruptcy risk or regulation links higher quality…
We construct an infinite order loose cork.
We construct a machine that knows its own code, at the price of not knowing its own factivity.
We present novel bounds on the capacity of the independent and identically distributed binary deletion channel. Four upper bounds are obtained by providing the transmitter and the receiver with genie-aided information on suitably-defined…
A seller with one unit of a good faces N\geq3 buyers and a single competitor who sells one other identical unit in a second-price auction with a reserve price. Buyers who do not get the seller's good will compete in the competitor's…
We show some estimations for the Coffee Shop Problem with a modification respect the original statement: there is a rival competing against us. We present different results based on how fast the rival is able to grow. As main tool, we use a…
Does a high dispersal rate provide a competitive advantage when risking competitive exclusion? To this day, the theoretical literature cannot answer this question in full generality. The present paper focuses on the simplest mathematical…
We establish a relation between the Schwarz inequality and the generalized concurrence of an arbitrary, pure, bipartite or tripartite state. This relation places concurrence in a geometrical and functional-analytical setting.
We give an upper-bound for the $X$-rank of points with respect to a non-degenerate irreducible variety $X$ in the case that sub-generic $X$-rank points generate a hypersurface. We give examples where this bound is sharp and it improves the…