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Eliminating Switching Components in Binary Matrices by 0-1 Flips and Column Permutations

100%

Hantos N. , Balázs P.

Fundamenta Informaticae

2015

tom Vol. 141, nr 2/3

135--150

Analysis of patterns in binary matrices plays a vital role in numerous applications of computer science. One of the most essential patterns of such matrices are the so called switching components, where the number and location of the components gives valuable information about the binary matrix. One way to measure the effect of switching components in a binary matrix is counting the number of 0-s which have to be replaced with 1-s in order to eliminate the switching components. However, finding the minimal number of 0-1 flips is generally an NP-complete problem. We present two novel-type heuristics for the above problem and show via experiments that they outperform the formerly proposed ones, both in optimality and in running time. We also show how to use those heuristics for determining the so-called nestedness level of a matrix, and how to use the flips for binary image compression.

Ecological interaction networks: prospects and pitfalls

67%

Ulrich W.

Ecological Questions

2009

tom 11

Interaction networks are a tool to visualize and to study the relationships between interacting species across and within trophic levels. Recent research uncovered many properties of such networks that remained undetected in previous food web studies. These patterns could be related to evolutionary and ecological processes. The study of interaction networks promises therefore progress in the study of constraints that act on the coevolution of interacting species and on food webs. However, there are still many pitfalls associated with the statistical analysis, the properties of the metrics involved and the appropriate null model choice. Here I review the mechanisms that shape interaction matrices, the possible internal structures and their ecological interpretation, and the analytical tools to identify matrix structure. Progress in the field needs critical meta-analytical and comparative studies that indentify the best suited null models (low type I and II error probabilities and high power to disentangle statistical from ecological processes) and clarify the interdependence of different concepts and metrics associated with network approaches. It is not improbable that many patterns recently associated with ecological and evolutionary processes might turn out to be simple side effects of the sampling from the underlying metacommunity distributions.