The expected value of L n , the length of the longest increasing subsequence of a random permutation of f1; : : : ; ng, has been studied extensively. This paper presents the results of both Monte Carlo and exact computations that explore the ner structure of the distribution of L n. The results suggested that several of the conjectures that had been made about L n were incorrect, and led to new...

Let the random variable Zn,k denote the number of increasing subsequences of length k in a random permutation from Sn, the symmetric group of permutations of {1, ..., n}. In a recent paper [4] we showed that the weak law of large numbers holds for Zn,kn if kn = o(n 2 5 ); that is, lim n→∞ Zn,kn EZn,kn = 1, in probability. The method of proof employed there used the second moment method and demo...

In recent work of Baik, Deift and Rains convergence of moments was established for the limiting joint distribution of the lengths of the first k rows in random Young tableaux. The main difficulty was obtaining a good estimate for the “tail” of the distribution and this was accomplished through a highly nontrival Riemann-Hilbert analysis. Here we give a simpler derivation. A conjecture is stated...

This paper presents a novel scheme coined AIR (Agent for Image Recognition), acting as an agent, to oversee the image matching and retrieval processes. Firstly, neighboring keypoints within close spatial proximity are examined and used to hypothesize true keypoint matches. While this approach is robust to noise (e.g. a tree) since spatial relation is considered, missing (undetected) keypoints i...

Given a string S = {a1, a2, a3, · · · , an}, the longest increasing subsequence (LIS) problem is to find a subsequence of the given string such that the subsequence is increasing and its length is maximal. In a previous result, to find the longest increasing subsequences of each sliding windows with a fixed size w of a given string can be solved in O(w log log n + OUTPUT ) time, where O(w log l...

purpose: to evaluate the effect of vertical prism induced stress on binocular visual evoked potentials. methods: using checkerboard stimulus patterns in two spatial frequencies (sfs) of 0.48 cpd as a low sf and 2.18 cpd as a moderate sf reversing with temporal frequency of 4 hz, the effect of increasing visual stress using vertical prisms of 0, 1, 2 and 3 prism diopters on binocular visual evok...

‎In this essay we introduce and study the notion of dimension for observers via Caratheodory structures and relative probability measures‎. ‎We show that the dimension as a three variables function is an increasing function on observers‎, ‎and decreasing function on the cuts of an observer‎. ‎We find observers with arbitrary non-negative dimensions‎. ‎We show that Caratheodory dimension for obs...