A new method to handle problems of Information Retrieval (IR) and related applications is proposed. The method is based on Fuzzy Interval Numbers (FINs) introduced in fuzzy system applications. Definition, interpretation and a computation algorithm of FINs are presented. The frame of use FINs in IR is given. An experiment showing the anticipated importance of these techniques in Cross Language ...

Three results on the interval number of a graph on n vertices are presented. (1) The interval number of almost every graph is between n/4lg n and n/4 (this also holds for almost every bipartite graph). (2) There exist Km,+ -free bipartite graphs with interval number at least c(m)n’-*I( , m+lj/lg n which can be improved to &$4+0(&) for m = 2 and (n/2):/lg n for m = 3. (3) There exists a regular ...

This paper is concerned with the restriction of interval exchange transformations (IETs) to algebraic number fields, which leads to maps on lattices. We characterize renormalizability arithmetically, and study its relationships with a geometrical quantity that we call the drift vector. We exhibit some examples of renormalizable IETs with zero and non-zero drift vector and carry out some investi...

Article history: Received 11 April 2012 Received in revised form 5 May 2013 Accepted 4 September 2013 Communicated by J. Kratochvil

The interval number i(G) of a simple graph G is the smallest number such that to each vertex in G there can be assigned a collection of at most finite closed intervals on the real line so that there is an edge between vertices v and w in G if and only if some interval for v intersects some interval for w. The well known interval graphs are precisely those graphs G with i(G)=<I. We prove here th...

| We investigate large deviations performance of the interval algorithm for random number generation, especially for intrinsic randomness. First, we show that the length of output fair random bits per the length of input sequence approaches to the entropy of the source almost surely. Next, we consider to obtain the xed number of fair random bits from the input sequence with xed length. We show ...

The total interval number of an n-vertex graph with maximum degree ∆ is at most (∆+1/∆)n/2, with equality if and only if every component of the graph is K∆,∆. If the graph is also required to be connected, then the maximum is ∆n/2+1 when ∆ is even, but when ∆ is odd it exceeds [∆+1/(2.5∆+7.7)]n/2 for infinitely many n. c © 1997 John Wiley & Sons, Inc. J Graph Theory 25: 79–84, 1997

A random interval graph of order n is generated by picking 2n numbers X 1 : : : X 2n independently from the uniform distribution on 0; 1] and considering the collection of n intervals with extremities X 2i?1 and X 2i for i 2 f1;:::ng. The graph vertices correspond to intervals. Two vertices are connected if the corresponding intervals intersect. This paper characterizes the uctuations of the in...

Let G(V,E) be a simple, undirected graph where V is the set of vertices and E is the set of edges. A b-dimensional cube is a Cartesian product I1 × I2 × · · · × Ib, where each Ii is a closed interval of unit length on the real line. The cubicity of G, denoted by cub(G) is the minimum positive integer b such that the vertices in G can be mapped to axis parallel b-dimensional cubes in such a way ...

MOTIVATION Somatic copy number aberrations SCNAS: are frequent in cancer genomes, but many of these are random, passenger events. A common strategy to distinguish functional aberrations from passengers is to identify those aberrations that are recurrent across multiple samples. However, the extensive variability in the length and position of SCNA: s makes the problem of identifying recurrent ab...