Characterization of rat behavior in the elevated plus-maze using a directed graph

The elevated plus-maze is a device widely used to assess rodent anxiety under the effect of several treatments, including pharmacological agents. The animal is placed at the center of the apparatus, which consists of two open arms and two arms enclosed by walls, and the number of entries and duration of stay in each arm are measured for a 5-min exposure period. The effect of an anxiolytic drug is to increase the percentage of time spent and number of entries into the open arms. In this work, we propose a new measure of anxiety levels in the rat submitted to the elevated plus-maze. We represented the spatial structure of the elevated plus-maze in terms of a directed graph and studied the statistics of the rat`s transitions between the nodes of the graph. By counting the number of times each transition is made and ordering them in descending frequency we represented the rat`s behavior in a rank-frequency plot. Our results suggest that the curves obtained under different pharmacological conditions can be well fitted by a power law with an exponent sensitive to both the drug type and the dose used. (C) 2009 Elsevier B.V. All rights reserved.

Star factorizations of graph products

A k-star is the graph K-1,K-k. We prove a general theorem about k-star factorizations of Cayley graphs. This is used to give necessary and sufficient conditions for the existence of k-star factorizations of any power (K-q)(S) of a complete graph with prime power order q, products C-r1 x C-r2 x ... x C-rk of k cycles of arbitrary lengths, and any power (C-r)(S) of a cycle of arbitrary length. (C) 2001 John Wiley & Sons, Inc.

R-matrices and the tensor product graph method

A systematic method for constructing trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of any two affinizable representations of a quantum algebra or superalgebra has been developed by the Brisbane group and its collaborators. This method has been referred to as the Tensor Product Graph Method. Here we describe applications of this method to untwisted and twisted quantum affine superalgebras.

Factorizations of the complete graph into C-5-factors and 1-factors

In this paper, we show that K-10n can be factored into alpha C-5-factors and beta 1-factors for all non-negative integers alpha and beta satisfying 2alpha + beta = 10(n) - 1.

Augmented LDPC Graph for Distributed Video Coding with Multiple Side Information

The advances made in channel-capacity codes, such as turbo codes and low-density parity-check (LDPC) codes, have played a major role in the emerging distributed source coding paradigm. LDPC codes can be easily adapted to new source coding strategies due to their natural representation as bipartite graphs and the use of quasi-optimal decoding algorithms, such as belief propagation. This paper tackles a relevant scenario in distributedvideo coding: lossy source coding when multiple side information (SI) hypotheses are available at the decoder, each one correlated with the source according to different correlation noise channels. Thus, it is proposed to exploit multiple SI hypotheses through an efficient joint decoding technique withmultiple LDPC syndrome decoders that exchange information to obtain coding efficiency improvements. At the decoder side, the multiple SI hypotheses are created with motion compensated frame interpolation and fused together in a novel iterative LDPC based Slepian-Wolf decoding algorithm. With the creation of multiple SI hypotheses and the proposed decoding algorithm, bitrate savings up to 8.0% are obtained for similar decoded quality.

An integer programming framework for sequencing cutting patterns based on interval graph completion

We derived a framework in integer programming, based on the properties of a linear ordering of the vertices in interval graphs, that acts as an edge completion model for obtaining interval graphs. This model can be applied to problems of sequencing cutting patterns, namely the minimization of open stacks problem (MOSP). By making small modifications in the objective function and using only some of the inequalities, the MOSP model is applied to another pattern sequencing problem that aims to minimize, not only the number of stacks, but also the order spread (the minimization of the stack occupation problem), and the model is tested.

An integer programming model for the minimum interval graph completion problem

The minimum interval graph completion problem consists of, given a graph G = ( V, E ), finding a supergraph H = ( V, E ∪ F ) that is an interval graph, while adding the least number of edges |F| . We present an integer programming formulation for solving the minimum interval graph completion problem recurring to a characteri- zation of interval graphs that produces a linear ordering of the maximal cliques of the solution graph.

Sequencing cutting patterns with colored interval graphs

The problem addressed here originates in the industry of flat glass cutting and wood panel sawing, where smaller items are cut from larger items accordingly to predefined cutting patterns. In this type of industry the smaller pieces that are cut from the patterns are piled around the machine in stacks according to the size of the pieces, which are moved to the warehouse only when all items of the same size have been cut. If the cutting machine can process only one pattern at a time, and the workspace is limited, it is desirable to set the sequence in which the cutting patterns are processed in a way to minimize the maximum number of open stacks around the machine. This problem is known in literature as the minimization of open stacks (MOSP). To find the best sequence of the cutting patterns, we propose an integer programming model, based on interval graphs, that searches for an appropriate edge completion of the given graph of the problem, while defining a suitable coloring of its vertices.

A Fractional Perspective to the Bond Graph Modelling of World Economies

Inspired in dynamic systems theory and Brewer’s contributions to apply it to economics, this paper establishes a bond graph model. Two main variables, a set of inter-connectivities based on nodes and links (bonds) and a fractional order dynamical perspective, prove to be a good macro-economic representation of countries’ potential performance in nowadays globalization. The estimations based on time series for 50 countries throughout the last 50 decades confirm the accuracy of the model and the importance of scale for economic performance.