Scheduling in network flow shops

We consider the general problem of static scheduling of a set of jobs in a network flow shop. In network flow shops, the scheduler not only has to sequence and schedule but also must concurrently determine the process routing of the jobs through the shop. In this paper, we establish the computational complexity of this new class of scheduling problem and propose a general purpose heuristic procedure. The performance of the heuristic is analyzed when makespan, cycle time and average flow time are the desired objectives.This research has been supported by the UCLA Academic Senate Grant #95.     

The network approach to calculation of characteristic time constants of the flat two-layer superconducting cable

The matrix method was used to investigate the process of current decay in the samples of flat two-layer superconducting cables. The discrete spectrum of eigen-frequencies has been obtained. Each of these frequencies determines the rate of decay of the correspondent eigen-current. Despite of the increasing of the number of eigen-frequencies with the enlargement of the sample dimensions the spectrum remains finite, as the maximum and minimum frequencies tend to finite limits. An analysis made for the lowest eigen-frequencies showed the corresponding eigen-currents to be slowly decaying long current loops. Within the range of high frequencies the sinusoidal distribution of eigen-currents in the rows of the cable was observed.     

Detecting embedded pure network structures in LP problems

Recently, linear programming problems with special structures have assumed growing importance in mathematical programming. It is well known that exploiting network structures within linear programs can lead to considerable improvement of the computational solution of large-scale linear programming problems. A linear program is said to contain an embedded network structure provided that some subset of its constraints can be interpreted as specifying conservation of flow. If a column of the constraint matrix has at most two non-zeros, then it leads to embedded generalized network structure and if these non-zeros are unit elements and of opposite signs, then it leads to embedded pure network structure. In this paper, we are concerned with algorithms for detecting embedded pure network structures within linear programs. The network extraction methods are presented in two groups. The first group covers deletion and addition based algorithms and the second group covers GUB based algorithms. We have extended the GUB based algorithm appearing in the second group by introducing Markowitz merit count approach for exploiting matrix non zeros. A set of well known test problems has been used to carry out computational experiments which show that our extensions to the GUB based algorithms give better results than the algorithms reported earlier.     

Computational aspects of two-segment separable programming

Recursive separable programming algorithms based on local, two-segment approximations are described for the solution of separable convex programs. Details are also given for the computation of lower bounds on the optimal value by both a primal and a dual approach, and these approaches are compared. Computational comparisons of the methods are provided for a variety of test problems, including a water supply application (with more than 600 constraints and more than 900 variables) and an econometric modelling problem (with more than 200 variables). Research supported by National Science Foundation Grants MCS74-20584 A02 and MCS-7901066.     

Integral decomposition in polyhedra

We say that a polyhedronP satisfies weak integral decomposition if whenever an integral vector is the sum ofk vectors inP it is also the sum ofk integral vectors inP. This property is related to rounding results for packing and covering problems. We study the property and two related properties, and give results concerning integral polymatroids, totally unimodular matrices and network flows, pairs of strongly-base-orderable matroids, and branchings in directed graphs.     

Spinal effects of acupuncture stimulation assessed by proton density-weighted functional magnetic resonance imaging at 0.2 T

Signal changes can be detected by proton density-weighted functional imaging in both the brain and the spinal cord. These are attributed to changes in extravascular water proton (signal enhancement by extravascular protons) density during neuronal activation. In this study, we used this technique to detect correlations between acupoint stimulation and neural activity in the spinal cord. Stimulation of acupoints associated with treatment of sensorimotor deficits (LI4 and LI11) was performed on 11 volunteers. During stimulation, 8 of the 11 subjects had consistent functional activations in C6/C7. A bilateral activation pattern was common. Our findings show that acupoint stimulation modulates activity in the spinal cord.     

Moderate Deviations for the overlap parameter in the Hopfield model

We derive moderate deviation principles for the overlap parameter in the Hopfield model of spin glasses and neural networks. If the inverse temperature is different from the critical inverse temperature _c=1 and the number of patterns M(N) satisfies M(N)/N 0, the overlap parameter multiplied by N, 1/2 < < 1, obeys a moderate deviation principle with speed N^1–2 and a quadratic rate function (i.e. the Gaussian limit for = 1/2 remains visible on the moderate deviation scale). At the critical temperature we need to multiply the overlap parameter by N, 1/4 < < 1. If then M(N) satisfies (M(N)⁶ log N M(N)²N⁴ log N)/N 0, the rescaled overlap parameter obeys a moderate deviation principle with speed N^1–4 and a rate function that is basically a fourth power. The random term occurring in the Central Limit theorem for the overlap at _c = 1 is no longer present on a moderate deviation scale. If the scaling is even closer to N^1/4, e.g. if we multiply the overlap parameter by N^1/4 log log N the moderate deviation principle breaks down. The case of variable temperature converging to one is also considered. If _N converges to _c fast enough, i.e. faster than the non-Gaussian rate function persists, whereas for _N converging to one slower than the moderate deviations principle is given by the Gaussian rate. At the borderline the moderate deviation rate function is the one at criticality plus an additional Gaussian term.Research supported by the Volkswagen-Stiftung (RiP-program at Oberwolfach, Germany).Mathematics Subject Classification (2000): 60F10 (primary), 60K35, 82B44, 82D30 (secondary)     

Efficient Hopfield pattern recognition on a scale-free neural network

Neural networks are supposed to recognise blurred images (or patterns) of N pixels (bits) each. Application of the network to an initial blurred version of one of P pre-assigned patterns should converge to the correct pattern. In the “standard" Hopfield model, the N “neurons” are connected to each other via N² bonds which contain the information on the stored patterns. Thus computer time and memory in general grow with N². The Hebb rule assigns synaptic coupling strengths proportional to the overlap of the stored patterns at the two coupled neurons. Here we simulate the Hopfield model on the Barabási-Albert scale-free network, in which each newly added neuron is connected to only m other neurons, and at the end the number of neurons with q neighbours decays as 1/q ³. Although the quality of retrieval decreases for small m, we find good associative memory for 1 ≪ m ≪ N. Hence, these networks gain a factor N/m ≫ 1 in the computer memory and time. Received 12 January 2003 Published online 11 April 2003 RID="a" ID="a"e-mail: stauffer@thp.uni-koeln.de     

Network formed by traces of random walks

We propose a model of time evolving networks in which a kind of transport between vertices generates new edges in the graph. We call the model “Network formed by traces of random walks”, because the transports are represented abstractly by random walks. Our numerical calculations yield several important properties observed commonly in complex networks, although the graph at initial time is only a one-dimensional lattice. For example, the distribution of vertex degree exhibits various behaviors such as exponential, power law like, and bi-modal distribution according to change of probability of extinction of edges. Another property such as strong clustering structure and small mean vertex–vertex distance can also be found. The transports represented by random walks in a framework of strong links between regular lattice is a new mechanisms which yields biased acquisition of links for vertices.