Sergej Znamenskij

• Doctor of Philosophy
• Principal Investigator at Aylamazyan University of Pereslavl http://site.u.pereslavl.ru

C-convexity of the closure, interiors and their lineal convexity are considered for C-convex sets under additional conditions of boundedness and nonempty interiors. The following questions on closure and the interior of C-convex sets were tackled 1. The closure of a bounded C-convex domain may not be lineally-convex. 2. The closure of a non-empty i...

This is the Russian version of paper submitted in English to the special issue of the SFU journal. The abstract is the following: For C-convex sets, also under additional conditions of boundedness and nonempty interiors, C-convexity of the closure and interiors and their lineal convexity are investigated. The following answers were obtained to the...

Выбор средств поиска скрытой общности в данных новой природы требует устойчивых и воспроизводимых сравнительных оценок качества абстрактных алгоритмов близости символьных строк. Обычные оценка на основе искусственно сгенерированных или вручную размеченных тестов существенно разнятся, надёжнее оценивая метод этой искусственной генерации по отношению...

The choice of search tools for hidden commonality in the data of a new nature requires stable and reproducible comparative assessments of the quality of abstract algorithms for the proximity of symbol strings. Conventional estimates based on artificially generated or manually labeled tests vary significantly, rather evaluating the method of this ar...

The paper contains a comparison of the accuracy of the restoration of elementary functions by the values in the nodes for algorithms of low-degree piecewise-polynomial interpolation. The test results demonstrate in graphical form the advantages and disadvantages of the widely used cubic interpolation splines. The comparison revealed that, contrary...

Сравнение точности восстановления элементарных функций по значениям в узлах проведено для алгоритмов интерполяции низкой степени. Результаты тестирования представлены в графическом виде, наглядно демонстрирующем преимущества и недостатки широко используемых кубических интерполяционных сплайнов. Сравнение выявило, что вопреки распространённому мнени...

How to normalise similarity metric to a metric space for a clusterization? A new system of axioms describes the known generalizations of distance metrics and similarity metrics, the Pearson correlation coefficient and the cosine metrics. Equivalent definitions of order-preserving transformations of metrics (both monotonic and pivot-monotonic) are g...

This numeric evaluation of string metric accuracy is based on the following idea: taking the paragraph of text in one language sort all paragraphs of the document in other language by similarity with given paragraph string and consider place of the right translation as the value of the evaluation score. Such a search of proper translation provides...

This numeric evaluation of string metric sensibility is based on the following idea: taking the paragraph of text in one language sort all paragraphs of the document in other language by similarity with given paragraph string and consider place of the right translation as the value of the evaluation score. Such a search of proper translation provid...

This numeric evaluation of string metric sensibility is based on the following idea: taking the paragraph of text in one language sort all paragraphs of the document in other language by similarity with given paragraph string and consider place of the right translation as the value of the evaluation score. Such a search of proper translation provid...

How to normalise similarity metric to a metric space for a clusterization? A new system of axioms describes the known generalizations of distance metrics and similarity metrics, the Pearson correlation coefficient and the cosine metrics. Equivalent definitions of order-preserving transformations of metrics (both monotonic and pivot-monotonic) are g...

Modern applications usually combine different similarity metrics taking into account the algorithms complexity, the peculiarities of human perception, data resources and samples. The optimization requires a unified formal description of the basic similarity metrics. The system of the similarity metric axioms is enchanced and its universal model is...

Expressive examples show that either the normalization of the similarity measure or its replacement by metrics may lead to errors of clustering and ranking by similarity. For applications of alignment based similarity, an analog OCS of the longest common subsequence (LCS) is described. A proposed model responds the needs of the basic LCS applicatio...

The expected value E of the longest common subsequence of letters in two random words is considered as a function of the α = |A| of alphabet and of words lengths m and n. It is assumed that each letter independently appears at any position with equal probability. A simple expression for E(α, m, n) and its empirical proof are presented for fixed α a...

The maximal length of longest common subsequence (LCS) for a couple of random finite sequences over an alphabet of 4 characters was considered as a random function of the sequences lengths m and n. Exact probability distributions tables are presented for all couples of length in a range 2 < m+n < 19. The graphs of expected value and standard deviat...

The ROUGE-W algorithm to calculate the similarity of texts is referred in more than 500 scientific publications since 2004. The power of the algorithm depends on the weight function choice. An optimal selection of the weight function is studied. The weight functions used previously are far from optimality. An example of incorrect output of the algo...

This paper discovers the major shortcomings of the Levenshtein Distance method, the longest common subsequence (LCS) method, and other general approaches to finding common parts, including the unjustified fragmentation of selected parts, the lack of sensitivity to transposition of large blocks, and no mechanisms to prevent accidental matches. The b...

The change detection problem is aimed at identifying common and different strings and usually has non-unique solutions. The identification of the best alignment is canonically based on finding a longest common subsequence (LCS) and is widely used for various purposes. However, many recent version control systems prefer alternative heuristic algorit...

A new approach is proposed to evolutionary information system engineering. The approach aims to provide high-quality support for large and complex socio-technical systems. The main idea is to replace usual developer framework of formal restrictions and tasks with the developer framework of local transparency and high motivation to increase total sy...

The notion of structural dimension of ℂ-convex sets is introduced. The spiral connectedness of sections and projections of these sets, as well as of the complements of these sections and projections is established. Examples refining L. A. Aizenberg’s well-known conjecture about the approximation of strongly linearly convex sets are presented.

Let H(ℂ n ) be, as usual, the Fréchet space of entire functions of n complex variables. Linear functionals on H(ℂ n ) are called analytical functionals. Since H(ℂ n ) is a closed subspace in the space C(ℂ n ) of complex-valued continuous functions, it follows that each analytical functional T is continued to an element of the space C ' (ℂ n ) dual...