On lattice point counting in Δ\Delta-modular polyhedra

Let a polyhedron $P$ be defined by one of the following ways: (i) $P = \{x \in R^n \colon A x \leq b\}$, where $A \in Z^{(n+k) \times n}$, $b \in Z^{(n+k)}$ and $rank\, A = n$; (ii) $P = \{x \in R_+^n \colon A x = b\}$, where $A \in Z^{k \times n}$, $b \in Z^{k}$ and $rank\, A = k$. And let all rank order minors of $A$ be bounded by $\Delta$ in absolute values. We show that the short rational generating function for the power series $$\sum\limits_{m \in P \cap Z^n} x^m$$ can be computed with the arithmetic complexity $O\left(T_{SNF}(d) \cdot d^{k} \cdot d^{\log_2 \Delta}\right),$ where $k$ and $\Delta$ are fixed, $d = \dim P$, and $T_{SNF}(m)$ is the complexity to compute the Smith Normal Form for $m \times m$ integer matrix. In particular, $d = n$ for the case (i) and $d = n-k$ for the case (ii). The simplest examples of polyhedra that meet conditions (i) or (ii) are the simplicies, the subset sum polytope and the knapsack or multidimensional knapsack polytopes. We apply these results to parametric polytopes, and show that the step polynomial representation of the function $c_P(y) = |P_{y} \cap Z^n|$, where $P_{y}$ is parametric polytope, can be computed by a polynomial time even in varying dimension if $P_{y}$ has a close structure to the cases (i) or (ii). As another consequence, we show that the coefficients $e_i(P,m)$ of the Ehrhart quasi-polynomial $$\left| mP \cap Z^n\right| = \sum\limits_{j = 0}^n e_i(P,m)m^j$$ can be computed by a polynomial time algorithm for fixed $k$ and $\Delta$

On the number of two-dimensional threshold functions

A two-dimensional threshold function of k-valued logic can be viewed as coloring of the points of a k x k square lattice into two colors such that there exists a straight line separating points of different colors. For the number of such functions only asymptotic bounds are known. We give an exact formula for the number of two-dimensional threshold functions and derive more accurate asymptotics.Comment: 17 pages, 2 figure

Psychological and Pedagogical Facilitation of the Higher School Students Personal and Professional Formation

The paper reveals the system of psychological and pedagogical facilitation of higher school students personal and professional formation. The role of socio-psychological centers in organizing and implementing the system is being proved.В статье представлена система психолого-педагогического сопровождения профессионально-личностного становления студентов вуза. Обоснована роль социально-психологического центра вуза в организации и реализации названной системы

Conceptual Design of Experimental Facility for Large-Diameter NTD-Si at the IRT-T Reactor

The IRT-T reactor has been conducting research in the field of irradiation of ingots of single-crystal semiconductor materials since 1987. The article describes the existing silicon doping facility. The results of studies on the possibility of creating an additional irradiation channel for neutron-transmutation doping of silicon are presented. It is shown that the use of a graphite reflector and a thermal neutron filter based on boron makes it possible to achieve non-uniformity of irradiation up to 5 %. The principal possibility of irradiating single-crystal silicon ingots with a diameter of up to 203 mm and a length of up to 500 mm is shown. The questions of optimizing the configuration of the core and the regime of reactors operation for increasing the neutron flux in the irradiation channels are discussed. In addition, applying the facility to produce base materials for neutron dosimeter in neutron capture therapy studies is proposed

PROBABILITY DISTRIBUTION OVER THE SET OF CLASSES IN ARABIC DIALECT CLASSIFICATION TASK

Subject of Research.We propose an approach for solving machine learning classification problem that uses the information about the probability distribution on the training data class label set. The algorithm is illustrated on a complex natural language processing task - classification of Arabic dialects. Method. Each object in the training set is associated with a probability distribution over the class label set instead of a particular class label. The proposed approach solves the classification problem taking into account the probability distribution over the class label set to improve the quality of the built classifier. Main Results. The suggested approach is illustrated on the automatic Arabic dialects classification example. Mined from the Twitter social network, the analyzed data contain word-marks and belong to the following six Arabic dialects: Saudi, Levantine, Algerian, Egyptian, Iraq, Jordan, and to the modern standard Arabic (MSA). The paper results demonstrate an increase of the quality of the built classifier achieved by taking into account probability distributions over the set of classes. Experiments carried out show that even relatively naive accounting of the probability distributions improves the precision of the classifier from 44% to 67%. Practical Relevance. Our approach and corresponding algorithm could be effectively used in situations when a manual annotation process performed by experts is connected with significant financial and time resources, but it is possible to create a system of heuristic rules. The implementation of the proposed algorithm enables to decrease significantly the data preparation expenses without substantial losses in the precision of the classification

The basic principles of pedagogical diagnostics in an assessment of the educational achievements of learners

The problem of pedagogical diagnostics which remains actual in modern pedagogical science and practice is considered in the article. Considering a state, properties and characteristics of learners, conditions in which the process of education and training is carried out, and also features of activity and professional and personal qualities of the teacher, the basic principles of pedagogical control at an assessment of educational achievements of students are defined in this scientific research. Module-rating assessment of educational achievements of students contributes to the quality of education in the University, because the educational process is carried out timely diagnosis, timely and objective, facilitating the timely introduction of changes in the educational process, the correct statement of teaching goals and the correct selection of pedagogical tools.Рассматривается проблема педагогической диагностики, которая остается актуальной и в современной педагогической науке и практике. Показано, что модульно-рейтинговая технология оценки учебных достижений студентов способствует повышению качества образования в вузе, так как в образовательном процессе осуществляется своевременная диагностика, оперативная и объективная, способствующая своевременному внесению изменений в учебный процесс, правильной постановке педагогических целей и корректному отбору педагогических средств