No abstract

No abstract

We show that the problem of minimizing a concave quadratic function with one concave direction is NP-hard. This result can be interpreted as an attempt to understand exactly what makes nonconvex quadratic programming problems hard. Sahni in 1974 [8] showed that quadratic programming with a negative definite quadratic term (n negative eigenvalues) is NP-hard, whereas Kozlov, Tarasov and Hacijan [2] showed in 1979 that the ellipsoid algorithm solves the convex quadratic problem (no negative eigenvalues) in polynomial time. This report shows that even one negative eigenvalue makes the problem NP-hard.

Identifying and quantifying dissimilarities among graphs is a fundamental and challenging problem of practical importance in many fields of science. Current methods of network comparison are limited to extract only partial information or are computationally very demanding. Here we propose an efficient and precise measure for network comparison, which is based on quantifying differences among distance probability distributions extracted from the networks. Extensive experiments on synthetic and real-world networks show that this measure returns non-zero values only when the graphs are non-isomorphic. Most importantly, the measure proposed here can identify and quantify structural topological differences that have a practical impact on the information flow through the network, such as the presence or absence of critical links that connect or disconnect connected components.

No abstract

Current epileptic seizure "prediction" algorithms are generally based on the knowledge of seizure occurring time and analyze the electroencephalogram (EEG) recordings retrospectively. It is then obvious that, although these analyses provide evidence of brain activity changes prior to epileptic seizures, they cannot be applied to develop implantable devices for diagnostic and therapeutic purposes. In this paper, we describe an adaptive procedure to prospectively analyze continuous, long-term EEG recordings when only the occurring time of the first seizure is known. The algorithm is based on the convergence and divergence of short-term maximum Lyapunov exponents (STLmax) among critical electrode sites selected adaptively. A warning of an impending seizure is then issued. Global optimization techniques are applied for selecting the critical groups of electrode sites. The adaptive seizure prediction algorithm (ASPA) was tested in continuous 0.76 to 5.84 days intracranial EEG recordings from a group of five patients with refractory temporal lobe epilepsy. A fixed parameter setting applied to all cases predicted 82% of seizures with a false prediction rate of 0.16/h. Seizure warnings occurred an average of 71.7 min before ictal onset. Similar results were produced by dividing the available EEG recordings into half training and testing portions. Optimizing the parameters for individual patients improved sensitivity (84% overall) and reduced false prediction rate (0.12/h overall). These results indicate that ASPA can be applied to implantable devices for diagnostic and therapeutic purposes.

No abstract

This paper aims at describing the state of the art on quadratic assignment problems (QAPs). It discusses the most important developments in all aspects of the QAP such as linearizations, QAP polyhedra, algorithms to solve the problem to optimality, heuristics, polynomially solvable special cases, and asymptotic behavior. Moreover, it also considers problems related to the QAP, e.g. the biquadratic assignment problem, and discusses the relationship between the QAP and other well known combinatorial optimization problems, e.g. the traveling salesman problem, the graph partitioning problem, etc. The paper will appear in the Handbook of Combinatorial Optimization to be published by Kluwer Academic Publishers, P. Pardalos and D.-Z. Du, eds.