A graph G is 1-extendable or almost 1-extendable if every edge is contained in a perfect or almost perfect matching of G, respectively. Let d ≥ 3 be an integer, and let G be a graph of order n with exactly one odd component such that the degree of each vertex is either d or d + 1. If G is not almost 1-extendable, then we prove that n ≥ 2d + 5. In the special case that d ≥ 4 is even and G is a d...

Our goal in this paper is to study the market impact in a market in which order flow is autocorrelated. We build a model which explains qualitatively and quantitatively the empirical facts observed so far concerning market impact. We define different notions of market impact, and show how they lead to the different price paths observed in the literature. For each one, under the assumption of pe...

It is known that necessary and sufficient conditions for the existence of a 2-perfect 6-cycle system of order n are that n = 1 or 9 mod 12 and n > 9 (Lindner, Phelps and Rodger [2]). Hence the smallest possible order of such a system is 13. The existence of a 2-perfect 6-cycle system of order 13 is shown by example in [2]. The example is cyclic. It is obvious that for large n the construction o...

Vehicular Ad hoc Networks (VANETs) are a subset of the Internet Things (IoT) that used in smart traffic applications. Due to their high speed, mobility, and exposure environment, security requirements for VANETs result conflicting design goals protecting member privacy while also ensuring non-repudiation. Group signature schemes can fulfill these requirements, but often at cost expensive biline...

A linear (qd, q, t)-perfect hash family of size s in a vector space V of order qd over a field F of order q consists of a set φ1, . . . , φs of linear functionals from V to F with the following property: for all t subsets X ⊆ V there exists i ∈ {1, . . . , s} such that φi is injective when restricted to F . A linear (qd, q, t)-perfect hash family of minimal size d(t− 1) is said to be optimal. I...

The study of probabilistic secret sharing schemes using arbitrary probability spaces and possibly infinite number of participants lets us investigate abstract properties of such schemes. It highlights important properties, explains why certain definitions work better than others, connects this topic to other branches of mathematics, and might yield new design paradigms. A probabilistic secret s...