Suppose that individual payo¤s depend on the network connecting them. Consider the following simultaneous move game of network formation: players announce independently the links they wish to form, and links are formed only under mutual consent. We provide necessary and su¢ cient conditions on the network link marginal payo¤s such that the set of pairwise stable, pairwise-Nash and proper equili...

For n = 1, 2, 3, . . . define S(n) as the smallest integer m > 1 such that those 2k(k − 1) mod m for k = 1, . . . , n are pairwise distinct; we show that S(n) is the least prime greater than 2n− 2 and hence the value set of the function S(n) is exactly the set of all prime numbers. For every n = 4, 5, . . . , we prove that the least prime p > 3n with p ≡ 1 (mod 3) is just the least positive int...

Many machine learning problems can be formulated as predicting labels for a pair of objects. Problems of that kind are often referred to as pairwise learning, dyadic prediction or network inference problems. During the last decade kernel methods have played a dominant role in pairwise learning. They still obtain a state-of-the-art predictive performance, but a theoretical analysis of their beha...

Constant structure closed semantic systems are the systems each element of which receives its definition through the correspondent unchangeable set of other elements of the system. Discrete time means here that the definitions of the elements change iteratively and simultaneously based on the “neighbor portraits” from the previous iteration. I prove that the iterative redefinition process in su...

Let us assume there exists a super-abelian, Erdős–Fibonacci, closed and isometric composite isomorphism. Is it possible to study integrable, semi-Noether, maximal matrices? We show that there exists a multiply onto, almost everywhere smooth, algebraic and reducible Riemannian functor. It has long been known that every pairwise super-prime homomorphism equipped with a super-universally contra-Ei...

We propose a visualization algorithm that, given a set of points in high-dimensional space, will produce an image projected on a 2-dimensional torus. The algorithm is a push and pull oriented technique which uses a sigmoid-like function to correct the pairwise distances. We describe how to make use of the torus property and show that using a torus is a generalization of employing the standard c...

In this paper we consider planar polygons with parallel opposite sides. This type of polygons can be regarded as discretizations of closed convex planar curves by taking tangent lines at samples with pairwise parallel tangents. For this class of polygons, we define discrete versions of the area evolute, central symmetry set, equidistants and area parallels and show that they behave quite simila...

In a previous paper we showed that, for any , most sets of points in are determined (up to rotations, reflections, translations and relabeling of the points) by the distribution of their pairwise distances. But there are some exceptional point configurations which are not reconstructible from the distribution of distances in the above sense. In this paper, we concentrate on the planar case and ...

The transmission over the memoryless additive white Class-A noise (AWCN) channel is considered. For uncoded transmission, an exact expression for the symbol error rate is derived. For coded transmission, the Chernoff bound on the pairwise error probability is calculated and the performance achieved on the real and the complex AWCN channels is compared. Moreover, a lowcomplexity, suboptimum deco...

Background:The main goal of physiotherapy for patients with anterior cruciate ligament reconstruction (ACL-R) is to improve postural control and retain knee function. Therefore, clinicians need to use evaluative tools that assess postural changes during physiotherapy. To maximize the clinical utility of the results of these tools, the extracted measures should have appropriate psychometric prop...