We here establish an a priori Hölder estimate of Krylov and Safonov type for the viscosity solutions of a degenerate quasilinear elliptic PDE of non-divergence form. The diffusion matrix may degenerate when the norm of the gradient of the solution is small: the exhibited Hölder exponent and Hölder constant only depend on the growth of the source term and on the bounds of the spectrum of the dif...

Percolation theory has become a useful tool for the analysis of large scale wireless networks. We investigate the fundamental problem of characterizing the critical density λc for Poisson random geometric graphs in continuum percolation theory. In two-dimensional space with the Euclidean norm, simulation studies show λc ≈ 1.44, while the best theoretical bounds obtained thus far are 0.696 < λc ...

In this article, we introduce a general concept of fuzzy operators. These operators are then used to generalize the possibilistic conditioning formulation proposed by Nguyen [1]. This generalization depends on the relation which exists between this conditioning and the probabilistic t-norm. By using other t-norms, other conditionings are obtained, and their properties are studied. One applicati...

We give sufficient conditions for a non-zero sum discounted stochastic game with compact and convex action spaces and with norm-continuous transition probabilities, but with possibly unbounded state space, to have a Nash equilibrium in homogeneous Markov strategies that depends in a Lipschitz continuous manner on the current state. If the underlying state space is compact this yields the existe...

Variational methods provide a tractable approximation to the intractable task of computing inference in probabilistic graphical models. Much of the literature in this field concerns the convexity of the variational objective, since convexity guarantees convergence to a global optimum. However, less attention has focused on the strength of the convexity. By this we mean the following. Definition...

Let O be a maximal order in a definite quaternion algebra over Q of prime discriminant p, and ` a small prime. We describe a probabilistic algorithm, which for a given left O-ideal, computes a representative in its left ideal class of `-power norm. In practice the algorithm is efficient, and subject to heuristics on expected distributions of primes, runs in expected polynomial time. This breaks...

The relationship between body size and the probability of maturing, often referred to as the probabilistic maturation reaction norm (PMRN), has been increasingly used to infer genetic variation in maturation schedule. Despite this trend, few studies have directly evaluated plasticity in the PMRN. A transplant experiment using white-spotted charr demonstrated that the PMRN for precocious males e...

Marouf (1993) presented definitions for asymptotically equivalent sequences and asymptotic regular matrices. Patterson (2003), extended those concepts by presenting an asymptotically statistical equivalent analog of these definitions and natural regularity conditions for non-negative sum ability matrices. In Patterson and Savas (2006) extended the definitions presented in (Patterson, 2003) to l...

In this lecture, we show two results dealing with lower bounds in communication complexity. The first lower bound is an Ω(n) lower bound on the distributional complexity of Disjointness due to [3, 8]. Here we will present the simplified proof presented in [8]. In the second part, we will show how to obtain lower bounds on the unbounded error probabilistic communication complexity by Forster’s m...

In this paper, we investigate the Max-Cut problem and propose a probabilistic heuristic to address its classic and weighted version. Our approach is based on the Estimation of Distribution Algorithm (EDA) that creates a population of individuals capable of evolving at each generation towards the global solution. We have applied the MaxCut problem for image segmentation and defined the edges’ we...