On the forced matching numbers of bipartite graphs

Let G be a graph that admits a perfect matching. A forcing set for a perfect matching M of G is a subset S of M, such that S is contained in no other perfect matching of G. This notion has arisen in the study of finding resonance structures of a given molecule in chemistry. Similar concepts have been studied for block designs and graph colorings under the name defining set, and for Latin squares under the name critical set. There is some study of forcing sets of hexagonal systems in the context of chemistry, but only a few other classes of graphs have been considered. For the hypercubes Q(n), it turns out to be a very interesting notion which includes many challenging problems. In this paper we study the computational complexity of finding the forcing number of graphs, and we give some results on the possible values of forcing number for different matchings of the hypercube Q(n). Also we show an application to critical sets in back circulant Latin rectangles. (C) 2003 Elsevier B.V. All rights reserved.

A matching pursuit-based signal complexity measure for the analysis of newborn EEG

This paper presents a new relative measure of signal complexity, referred to here as relative structural complexity, which is based on the matching pursuit (MP) decomposition. By relative, we refer to the fact that this new measure is highly dependent on the decomposition dictionary used by MP. The structural part of the definition points to the fact that this new measure is related to the structure, or composition, of the signal under analysis. After a formal definition, the proposed relative structural complexity measure is used in the analysis of newborn EEG. To do this, firstly, a time-frequency (TF) decomposition dictionary is specifically designed to compactly represent the newborn EEG seizure state using MP. We then show, through the analysis of synthetic and real newborn EEG data, that the relative structural complexity measure can indicate changes in EEG structure as it transitions between the two EEG states; namely seizure and background (non-seizure).

Patient matching in treatment for alcohol dependence: is the null hypothesis still alive and well?

In the light of Project MATCH, is it reasonable to accept the null hypothesis that there are no clinically signi® cant matching effects between patient characteristics and cognitive± behaviour therapy (CBT), motivational enhancement therapy (MET) and Twelve-Step facilitation therapy (TSF)? The Project MATCH investigators considered the null hypothesis but preferred the alternative hypothesis that further analysis may reveal combinations of patient and therapist characteristics that show more substantial matching effects than any of the variables that they have examined to date.1

Matching occupation and self: Does matching theory adequately model children's thinking?

The present exploratory-descriptive cross-national study focused on the career development of 11- to 14-yr.-old children, in particular whether they can match their personal characteristics with their occupational aspirations. Further, the study explored whether their matching may be explained in terms of a fit between person and environment using Holland's theory as an example. Participants included 511 South African and 372 Australian children. Findings relate to two items of the Revised Career Awareness Survey that require children to relate personal-social knowledge to their favorite occupation. Data were analyzed in three stages using descriptive statistics, i.e., mean scores, frequencies, and percentage agreement. The study indicated that children perceived their personal characteristics to be related to their occupational aspirations. However, how this matching takes place is not adequately accounted for in terms of a career theory such as that of Holland.

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.

Matching prescription claims with medication data for nursing home residents: Implications for prescriber feedback, drug utilisation studies and selection of prescription claims database

Medication data retrieved from Australian Repatriation Pharmaceutical Benefits Scheme (RPBS) claims for 44 veterans residing in nursing homes and Pharmaceutical Benefits Scheme (PBS) claims for 898 nursing home residents were compared with medication data from nursing home records to determine the optimal time interval for retrieving claims data and its validity. Optimal matching was achieved using 12 weeks of RPBS claims data, with 60% of medications in the RPBS claims located in nursing home administration records, and 78% of medications administered to nursing home residents identified in RPBS claims. In comparison, 48% of medications administered to nursing home residents could be found in 12 weeks of PBS data, and 56% of medications present in PBS claims could be matched with nursing home administration records. RPBS claims data was superior to PBS, due to the larger number of scheduled items available to veterans and the veteran's file number, which acts as a unique identifier. These findings should be taken into account when using prescription claims data for medication histories, prescriber feedback, drug utilisation, intervention or epidemiological studies. (C) 2001 Elsevier Science Inc. All rights reserved.

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.