### Working paper

## Two-Station Single-Track Railway Scheduling Problem With Trains of Equal Speed

We investigate regular realizability (RR) problems, which are the prob- lems of verifying whether intersection of a regular language – the input of the problem – and fixed language called filter is non-empty. In this pa- per we focus on the case of context-free filters. Algorithmic complexity of the RR problem is a very coarse measure of context-free languages com- plexity. This characteristic is compatible with rational dominance. We present examples of P-complete RR problems as well as examples of RR problems in the class NL. Also we discuss RR problems with context- free filters that might have intermediate complexity. Possible candidates are the languages with polynomially bounded rational indices.

At the particular article we provide a methodological approach to selection of companies for horizontal cooperation in procurement logistics. In context of modern logistics (globalization, high customer expectations, high transportation costs), and changes regarding Russia’s plans to join WTO, this topic is highly relevant from a practical point of view. The purpose of this article is to provide single methodological approach to selection of companies for horizontal cooperation.

The purpose of the conference is to bring together academics and professionals from all over the world to discuss the themes of the conference

This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.

This book constitutes the thoroughly refereed post-conference proceedings of the 8th International Conference on Learning and Optimization, LION 8, which was held in Gainesville, FL, USA, in February 2014. The 33 contributions presented were carefully reviewed and selected for inclusion in this book. A large variety of topics are covered, such as algorithm configuration; multiobjective optimization; metaheuristics; graphs and networks; logistics and transportation; and biomedical applications.

The book deals with the models and methods of combined rail-road transportation development.

Modern concepts of combined tramsport and their implementation in European and North-American regions are analyzed. Scientific researh results in this sphere are studied as well as the principle business decisions in combined transport. Mathematical models are developed in order to identify the parameters of the combined transport systems. Prerequisites and possible directions of combined transportation technologies in Russia are discussed.

We study the following computational problem: for which values of k, the majority of n bits MAJn can be computed with a depth two formula whose each gate computes a majority function of at most k bits? The corresponding computational model is denoted by MAJk o MAJk. We observe that the minimum value of k for which there exists a MAJk o MAJk circuit that has high correlation with the majority of n bits is equal to Θ(n1/2). We then show that for a randomized MAJk o MAJk circuit computing the majority of n input bits with high probability for every input, the minimum value of k is equal to n2/3+o(1). We show a worst case lower bound: if a MAJk o MAJk circuit computes the majority of n bits correctly on all inputs, then k ≥ n13/19+o(1). This lower bound exceeds the optimal value for randomized circuits and thus is unreachable for pure randomized techniques. For depth 3 circuits we show that a circuit with k = O(n2/3) can compute MAJn correctly on all inputs.

The preemptive single machine scheduling problem of minimizing the total weighted completion time with equal processing times and arbitrary release dates is one of the four single machine scheduling problems with an open computational complexity status. In this paper we present lower and upper bounds for the exact solution of this problem based on the assignment problem. We also investigate properties of these bounds and worst-case behavior.

A form for an unbiased estimate of the coefficient of determination of a linear regression model is obtained. It is calculated by using a sample from a multivariate normal distribution. This estimate is proposed as an alternative criterion for a choice of regression factors.