Having its origin in theoretical computer science, the Kannan-Lovász-Simonovits (KLS) conjecture is one of major open problems asymptotic convex geometry and high-dimensional probability theory today. In this work, we establish a connection between study large moderate deviations for isotropic log-concave random vectors. We then Euclidean norm orthogonally projected vectors an ℓpn–ball. This le...

We perform importance sampling for a randomized matrix multiplication algorithm by Drineas, Kannan, and Mahoney and derive probabilities that minimize the expected value (with regard to the distributions of the matrix elements) of the variance. We compare these optimized probabilities with uniform probabilities and derive conditions under which the actual variance of the optimized probabilities...

We generalize, extend, and improve some recent fixed point results in conemetric spaces including the results of H. Guang and Z. Xian 2007 ; P. Vetro 2007 ; M. Abbas and G. Jungck 2008 ; Sh. Rezapour and R. Hamlbarani 2008 . In all our results, the normality assumption, which is a characteristic of most of the previous results, is dispensed. Consequently, the results generalize several fixed re...

Recently, Samet et al [24] introduced the concept of α-ψ contractive mappings and studied the existence of fixed points for such mappings. In this article, we prove three fixed point theorems for this class of operators in complete metric spaces. Our results extend the results in [24] and well known fixed point theorems due to Banach, Kannan, Chatterjea, Zamfirescu, Berinde, Suzuki, Ćirić, Niet...

We present symmetric and asymmetric similarity measures for labeled directed rooted graphs that are inspired by the simulation and bisimulation relations on labeled transition systems. Computation of the similarity measures has close connections to discounted Markov decision processes in the asymmetric case and to perfect-information stochastic games in the symmetric case. For the symmetric cas...