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## Efficient Algorithm for Finding Roots of Error-Locator Polynomials

A novel method for finding roots of polynomials over finite fields has been proposed.

This method is based on the cyclotomic discrete Fourier transform algorithm.

The improvement is achieved by using the normalized cyclic convolutions,

which have a small complexity and allow matrix decomposition,

as well as methods of adapting the truncated normalized cyclic convolutions calculation.

For small values of degree of the error-locator polynomial the novel method has not only the smallest multiplicative complexity, but the full computational complexity of this method is also less than with other methods.

Thus, the multiplicative complexity of the novel method in comparison to the method of affine decomposition (the Fedorenko-Trifonov method) is up to ten times less,

although the additive complexity is approximately 10-15\% more.

The novel method has matrix representation convenient for implementation.

Fast algorithms for decoding of linear block codes.

Приведено доказательство теоремы об обратном циклотомическом DFT над конечным полем.

Separating codes have been used in many areas as diverse as automata synthesis, technical diagnosis and traitor tracing schemes. In this paper, we study a weak version of separating codes called almost separating codes. More precisely, we derive lower bounds on the rate of almost separating codes. From the main result it is seen that the lower bounds on the rate for almost separating codes are greater than the currently known lower bounds for ordinary separating codes. Moreover, we also show how almost separating codes can be used to construct a family of fingerprinting codes.

This volume contains a selection of contributions from the "First International Conference in Network Analysis," held at the University of Florida, Gainesville, on December 14-16, 2011. The remarkable diversity of fields that take advantage of Network Analysis makes the endeavor of gathering up-to-date material in a single compilation a useful, yet very difficult, task. The purpose of this volume is to overcome this difficulty by collecting the major results found by the participants and combining them in one easily accessible compilation.

The paper describes the method of finite element simulation of shape rolling process based on 2,5D techniques which is due to the number of simplifications, allows to increase the rate of calculation considerably (by comparison with 3D modeling). To verify this technique the comparison of model results with data obtained at the metallurgical plant Trinecke Zelezarny within the special industrial testing was performed. The comparison confirmed the adequacy and effectiveness of the proposed models and computer system developed on their basis.

The asymptotic theory is developed for polynomial sequences that are generated by the three-term higher-order recurrence. Our results generalize known results for p=1, that is, for orthogonal polynomial sequences on the real line that belong to the Blumenthal–Nevai class. As is known, for p≥2, the role of the interval is replaced by a starlike set S of p+1 rays emanating from the origin on which the Q n satisfy a multiple orthogonality condition involving p measures. Here we obtain strong asymptotics for the Q n in the complex plane outside the common support of these measures as well as on the (finite) open rays of their support. In so doing, we obtain an extension of Weyl’s famous theorem dealing with compact perturbations of bounded self-adjoint operators. Furthermore, we derive generalizations of the classical Szegő functions, and we show that there is an underlying Nikishin system hierarchy for the orthogonality measures that is related to the Weyl functions. Our results also have application to Hermite–Padé approximants as well as to vector continued fractions.

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.

Event logs collected by modern information and technical systems usually contain enough data for automated process models discovery. A variety of algorithms was developed for process models discovery, conformance checking, log to model alignment, comparison of process models, etc., nevertheless a quick analysis of ad-hoc selected parts of a journal still have not get a full-fledged implementation. This paper describes an ROLAP-based method of multidimensional event logs storage for process mining. The result of the analysis of the journal is visualized as directed graph representing the union of all possible event sequences, ranked by their occurrence probability. Our implementation allows the analyst to discover process models for sublogs defined by ad-hoc selection of criteria and value of occurrence probability

Existing approaches suggest that IT strategy should be a reflection of business strategy. However, actually organisations do not often follow business strategy even if it is formally declared. In these conditions, IT strategy can be viewed not as a plan, but as an organisational shared view on the role of information systems. This approach generally reflects only a top-down perspective of IT strategy. So, it can be supplemented by a strategic behaviour pattern (i.e., more or less standard response to a changes that is formed as result of previous experience) to implement bottom-up approach. Two components that can help to establish effective reaction regarding new initiatives in IT are proposed here: model of IT-related decision making, and efficiency measurement metric to estimate maturity of business processes and appropriate IT. Usage of proposed tools is demonstrated in practical cases.