Combinatorial optimization model for railway engine assignment problem

This paper presents an experimental study for the Hungarian State Railway Company (M\'AV). The engine assignment problem was solved at M\'AV by their experts without using any explicit operations research tool. Furthermore, the operations research model was not known at the company. The goal of our project was to introduce and solve an operations research model for the engine assignment problem on real data sets. For the engine assignment problem we are using a combinatorial optimization model. At this stage of research the single type train that is pulled by a single type engine is modeled and solved for real data. There are two regions in Hungary where the methodology described in this paper can be used and M\'AV started to use it regularly. There is a need to generalize the model for multiple type trains and multiple type engines

On the stable degree of graphs

We define the stable degree s(G) of a graph G by s(G)∈=∈ min max d (v), where the minimum is taken over all maximal independent sets U of G. For this new parameter we prove the following. Deciding whether a graph has stable degree at most k is NP-complete for every fixed k∈≥∈3; and the stable degree is hard to approximate. For asteroidal triple-free graphs and graphs of bounded asteroidal number the stable degree can be computed in polynomial time. For graphs in these classes the treewidth is bounded from below and above in terms of the stable degree

Density of critical points for a Gaussian random function

Critical points of a scalar quantitiy are either extremal points or saddle points. The character of the critical points is determined by the sign distribution of the eigenvalues of the Hessian matrix. For a two-dimensional homogeneous and isotropic random function topological arguments are sufficient to show that all possible sign combinations are equidistributed or with other words, the density of the saddle points and extrema agree. This argument breaks down in three dimensions. All ratios of the densities of saddle points and extrema larger than one are possible. For a homogeneous Gaussian random field one finds no longer an equidistribution of signs, saddle points are slightly more frequent.Comment: 11 pages 1 figure, changes in list of references, corrected typo

Solving order constraints in logarithmic space.

We combine methods of order theory, finite model theory, and universal algebra to study, within the constraint satisfaction framework, the complexity of some well-known combinatorial problems connected with a finite poset. We identify some conditions on a poset which guarantee solvability of the problems in (deterministic, symmetric, or non-deterministic) logarithmic space. On the example of order constraints we study how a certain algebraic invariance property is related to solvability of a constraint satisfaction problem in non-deterministic logarithmic space

Molecular dynamics approach: from chaotic to statistical properties of compound nuclei

Statistical aspects of the dynamics of chaotic scattering in the classical model of $\alpha$-cluster nuclei are studied. It is found that the dynamics governed by hyperbolic instabilities which results in an exponential decay of the survival probability evolves to a limiting energy distribution whose density develops the Boltzmann form. The angular distribution of the corresponding decay products shows symmetry with respect to $\pi/2$ angle. Time estimated for the compound nucleus formation ranges within the order of $10^{-21}$s.Comment: 11 pages, LaTeX, non

Linking Dynamical and Thermal Models of Ultrarelativistic Nuclear Scattering

To analyse ultrarelativistic nuclear interactions, usually either dynamical models like the string model are employed, or a thermal treatment based on hadrons or quarks is applied. String models encounter problems due to high string densities, thermal approaches are too simplistic considering only average distributions, ignoring fluctuations. We propose a completely new approach, providing a link between the two treatments, and avoiding their main shortcomings: based on the string model, connected regions of high energy density are identified for single events, such regions referred to as quark matter droplets. Each individual droplet hadronizes instantaneously according to the available n-body phase space. Due to the huge number of possible hadron configurations, special Monte Carlo techniques have been developed to calculate this disintegration.Comment: Complete paper enclosed as postscript file (uuencoded

Microcanonical Treatment of Hadronizing the Quark-Gluon Plasma

We recently introduced a completely new way to study ultrarelativistic nuclear scattering by providing a link between the string model approach and a statistical description. A key issue is the microcanonical treatment of hadronizing individual quark matter droplets. In this paper we describe in detail the hadronization of these droplets according to n-body phase space, by using methods of statistical physics, i.e. constructing Markov chains of hadron configurations.Comment: Complete paper enclosed as postscript file (uuencoded

Tropically convex constraint satisfaction

A semilinear relation S is max-closed if it is preserved by taking the componentwise maximum. The constraint satisfaction problem for max-closed semilinear constraints is at least as hard as determining the winner in Mean Payoff Games, a notorious problem of open computational complexity. Mean Payoff Games are known to be in the intersection of NP and co-NP, which is not known for max-closed semilinear constraints. Semilinear relations that are max-closed and additionally closed under translations have been called tropically convex in the literature. One of our main results is a new duality for open tropically convex relations, which puts the CSP for tropically convex semilinaer constraints in general into NP intersected co-NP. This extends the corresponding complexity result for scheduling under and-or precedence constraints, or equivalently the max-atoms problem. To this end, we present a characterization of max-closed semilinear relations in terms of syntactically restricted first-order logic, and another characterization in terms of a finite set of relations L that allow primitive positive definitions of all other relations in the class. We also present a subclass of max-closed constraints where the CSP is in P; this class generalizes the class of max-closed constraints over finite domains, and the feasibility problem for max-closed linear inequalities. Finally, we show that the class of max-closed semilinear constraints is maximal in the sense that as soon as a single relation that is not max-closed is added to L, the CSP becomes NP-hard.Comment: 29 pages, 2 figure

Baryon stopping and hyperon enhancement in the improved dual parton model

We present an improved version of the dual parton model which contains a new realization of the diquark breaking mechanism of baryon stopping. We reproduce in this way the net baryon yield in nuclear collisions. The model, which also considers strings originating from diquark-antidiquark pairs in the nucleon sea, reproduces the observed yields of p and Lambda and their antiparticles and underestimates cascades by less than 50 %. However, Omega's are underestimated by a factor five. Agreement with data is restored by final state interaction, with an averaged cross-section as small as 0.14 mb. Hyperon yields increase significantly faster than antihyperons, in agreement with experiment.Comment: 40 pages, 18 postscript figure