The usual goal of modeling natural and artificial perception involves determining how a system can extract the object that it perceives from an image that is noisy. The "inverse" of this problem is one of modeling how even a clear image can be perceived to be blurred in certain contexts. To our knowledge, there is no solution to this in the literature other than for an oversimplified model in which the true image is garbled with noise by the perceiver himself. In this paper, we propose a chaotic model of pattern recognition (PR) for the theory of "blurring." This paper, which is an extension to a companion paper demonstrates how one can model blurring from the view point of a chaotic PR system. Unlike the companion paper in which a chaotic PR system extracts the pattern from the input, in this case, we show that even without the inclusion of additional noise, perception of an object can be "blurred" if the dynamics of the chaotic system are modified. We thus propose a formal model and present an analysis using the Lyapunov exponents and the Routh-Hurwitz criterion. We also demonstrate experimentally the validity of our model by using a numeral data set. A byproduct of this model is the theoretical possibility of desynchronization of the periodic behavior of the brain (as a chaotic system), rendering us the possibility of predicting, controlling, and annulling epileptic behavior.

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We consider the well known geometric problem of determining shortest paths between pairs of points on a polyhedral surface P , where P consists of triangular faces with positive weights assigned to them. The cost of a path in P is defined to be the weighted sum of Euclidean lengths of the sub-paths within each face of P .We present query algorithms that compute approximate distances and/or approximate shortest paths on P . Our all-pairs query algorithms take as input an approximation parameter ε ∈ (0, 1) and a query time parameter q, in a certain range, and builds a data structure APQ(P, ε; q), which is then used for answering ε-approximate distance queries in O(q) time. As a building block of the APQ(P, ε; q) data structure, we develop a single source query data structure SSQ(a; P, ε) that can answer ε-approximate distance queries from a fixed point a to any query point on P in logarithmic time. Our algorithms answer shortest path queries in weighted surfaces, which is an important extension, both theoretically and practically, to the extensively studied Euclidean distance case. In addition, our algorithms improve upon previously known query algorithms for shortest paths on surfaces. The algorithms are based on a novel graph separator algorithm introduced and analyzed here, which extends and generalizes previously known separator algorithms.

The longest increasing circular subsequence (LICS) of a list is considered. A Monte-Carlo algorithm to compute it is given which has worst case execution time O(n 3/2 log n) and storage requirement O(n). It is proved that the expected length µ(n) of the LICS satisfies limn→∞ µ(n) 2 √ n = 1. Numerical experiments with the algorithm suggest that |µ(n) − 2 √ n| = O(n 1/6 ).

A bipartite graph G = (A, B, E) is convex on B if there exists an ordering of the vertices of B such that for any vertex v ∈ A, vertices adjacent to v are consecutive in B. A complete bipartite subgraph of a graph G is called a biclique of G. Motivated by an application to analyzing DNA microarray data, we study the problem of finding maximum edge bicliques in convex bipartite graphs. Given a bipartite graph G = (A, B, E) which is convex on B, we present a new algorithm that computes a maximum edge biclique of G in O(n log 3 n log log n) time and O(n) space, where n = |A|. This improves the current O(n 2 ) time bound available for the problem. We also show that for two special subclasses of convex bipartite graphs, namely 312 Algorithmica (2012) 64:311-325 for biconvex graphs and bipartite permutation graphs, a maximum edge biclique can be computed in O(nα(n)) and O(n) time, respectively, where n = min(|A|, |B|) and α(n) is the slowly growing inverse of the Ackermann function.