Abstract: We consider problems to classify data represented as discrete probability distributions. For the classification we propose the Voronoi partition technique with respect to -divergence, which is a statistically justified pseudo- distance on the space of probability distributions. In order to improve computational efficiency and performance of the classification, we introduce two nonlinear transformations respectively called the escort and projective transform, and weighted -centroids. Finally we demonstrate performances of the proposed tools via simple numerical examples.

Keywords: -divergence, -Voronoi partition, Escort transformation, Projective transformation

ACM Classification Keywords: I.3.5 Computational Geometry and Object Modeling

MSC: 53A15, 68T10

Link:

GEOMETRICAL TOOLS FOR ALPHA-VORONOI PARTITIONS

Atsumi Ohara and Yuya Nagatani

http://www.foibg.com/ibs_isc/ibs-25/ibs-25-p17.pdf

Abstract: Distance geometry consists of finding an embedding of a weighted undirected graph in Rn. Since some years, we are working on suitable discretizations for this problem. Because of the discretization, the search domain is reduced froma continuous to a discrete set which has the structure of a tree. Based on this combinatorial structure, we developed an efficient branch-and-prune (BP) algorithm for the solution of distance geometry problems. In this paper, we focus on two important aspects of the discretization: the identification of suitable vertex discretizing orderings and the analysis of the symmetries that can be found in BP trees.

Keywords: distance geometry, discretization, combinatorial optimization, discretizing orderings, symmetries.

ACMClassification Keywords: G.2.1 Combinatorics - Combinatorial algorithms; B.5.2 Design Aids -Optimization; J.3 Life andMedical Sciences - Biology and genetics;

MSC: 05C85, 90C27, 51K99.

Link:

ON THE DISCRETIZATION OF DISTANCE GEOMETRY PROBLEMS

Antonio Mucherino,Carlile Lavor,Leo Liberti,Nelson Maculan

http://www.foibg.com/ibs_isc/ibs-25/ibs-25-p16.pdf

Abstract: Functions defining a distance and a distinguish degree between objects described by predicate formulas are introduced. It is proved that the introduced function of distance satisfies all properties of a distance. The function of objects distinguish degree adequately reflects similarity of objects but does not define a distance because the triangle inequality is not fulfilled for it. The calculation of the introduced functions is based on the notion of partial deduction of a predicate formula.

Keywords: artificial intelligence, pattern recognition, distance between objects, predicate calculus.

ACM Classification Keywords: I.2.4 ARTIFICIAL INTELLIGENCE Knowledge Representation Formalisms and Methods – Predicate logic.

Link:

DISTANCE BETWEEN OBJECTS DESCRIBED BY PREDICATE FORMULAS

Tatiana Kosovskaya

http://www.foibg.com/ibs_isc/ibs-25/ibs-25-p15.pdf

Abstract: An antimatroid is an accessible set system (U,F) closed under union. Every antimatroid may be represented as a graph whose vertices are sets of F, where two vertices are adjacent if the corresponding sets are differ by one element. This graph is a partial cube. Hence an antimatroid with the ground set U of size n may be isometrically embedded into the hypercube {0, 1}n. Thus the distance on an antimatroid considered as a graph coincides with the Hamming distance. A poset antimatroid is an antimatroid, which is formed by the lower sets of a poset. We consider different definitions of the distance between elements of an antimatroid, and give a new characterization of poset antimatroids.

Keywords: antimatroid, partial cube, zigzag distance, Hamming distance.

ACM Classification Keywords: G.2

MSC: 05C12; 52B40

Link:

DISTANCES ON ANTIMATROIDS

Yulia Kempner, Vadim E. Levit

http://www.foibg.com/ibs_isc/ibs-25/ibs-25-p14.pdf

Abstract: Given two distances d and d′ defined on a finite set I, with d  d′, we characterise the set of all ultrametrics lying between d and d′ (if any), showing they are the union of finitely many intervals with a common top endpoint, the subdominant ultrametric of d′. We also provide an algorithm to compute the bottom of any interval, given by any upperminimal ultrametric of d less than d′. A series of approximations according to the supremum norm derive from this.

Keywords: ultrametric, subdominant ultrametric, upperminimal ultrametrics, approximation, supremum norm

MSC: G3: Statistics

Link:

INTERVALS AS ULTRAMETRIC APPROXIMATIONS ACCORDING TO THE SUPREMUM NORM

Bernard Fichet

http://www.foibg.com/ibs_isc/ibs-25/ibs-25-p13.pdf

Abstract: Purely geometric arguments are used to extract information from three-dimensional structures of oligomeric proteins, that are very common biological entities stably made of several polypeptidic chains. They are characterized by the presence of an interface between adjacent amino acid chains and can be investigated with the approach proposed here. We introduce a method, called symmetrization, that allows one to rank interface interactions on the basis of inter-atomic distances and of the local geometry. The lowest level of the ranking has been used previously with interesting results. Now, we need to complete this picture with a careful analysis of the higher ranks, that are for the first time introduced here, in a proper mathematical set up. The interface finds a very nice mathematical abstraction by the notion of weighted bipartite graph, where the inter-atomic distance provides the weight. Thus, our approach is partially inspired to graph theory decomposition methods but with an emphasis to “locality”, namely the idea that structures constructed by the symmetrization adapt to the local scales of the problem. This is an important issue as the known interfaces may present major differences in relation to their size, their composition and the local geometry. Thus, we looked for a local method, that can autonomously detect the local structure. The physical neighborhood is introduced by the concept of cluster of interactions. We discuss the biological applications of this ranking and our previous fruitful experience with the lowest symmetrized level. An example is given, using the prototypical cholera toxin.

Keywords: symmetrization, protein interfaces, oligomeric proteins, graphs, bonds ranking, interaction clusters.

ACM Classification Keywords: J.2 Physical sciences - Mathematics and statistics J.3 Life and medical sciences - Biology and genetics

Link:

SYMMETRIZATION: RANKING AND CLUSTERING IN PROTEIN INTERFACES

Giovanni Feverati, Claire Lesieur, Laurent Vuillon

http://www.foibg.com/ibs_isc/ibs-25/ibs-25-p12.pdf

Abstract: Universal Fechnerian Scaling (UFS) is a principled approach to computing “subjective” distances among objects (stimuli) from their pairwise discrimination probabilities. It is based on the concept of ‘dissimilarity function’ leading to a locally symmetrical quasimetric in the context of Dissimilarity Cumulation (DC) theory developed by Dzhafarov and Colonius. Here we show that, for finite sets of objects, the replacement of dissimilarity cumulation with a dissimilarity maximization procedure results in “subjective” distances satisfying the ultrametric inequality.

Keywords: Fechnerian scaling; dissimilarity function; quasimetric; ultrametric.

ACM Classification Keywords: G.2.3 Discrete Mathematics – Applications;

MSC: 54E05, 54E15, 54E35, 05C12

Link:

ULTRAMETRIC FECHNERIAN SCALING OF DISCRETE OBJECT SETS

Hans Colonius, Ehtibar N. Dzhafarov

http://www.foibg.com/ibs_isc/ibs-25/ibs-25-p11.pdf

Abstract: Maximum rank distance (MRD) codes have been used for the construction of space time block code (STBC) using a matrix method. Like orthogonal STBC’s in most popular cases, MRD-STBC’s can also achieve full diversity. Though an OSTBC is known to yield the best BER performance, a unique case is described where MRD- STBC performs better than Alamouti code (OSTBC). Moreover, the viability of Gabidulin’s decoding algorithm has been established by decoding complex symbols generated from MRD-STBC’s. Under this decoding scheme, MRD- STBC’s have been shown to be preferred candidate for higher antenna configuration as the decoding complexity of Gabidulin’s algorithm is far less than that of maximum likelihood (ML) decoding algorithm.

Keywords: Rank codes, Gaussian integers, space time block codes, orthogonal space time block codes.

MSC: 12E20

Link:

RANK CODES OVER GAUSSIAN INTEGERS AND SPACE TIME BLOCK CODES

Hafiz M.Asif, Ernst Gabidulin, Bahram Honary

http://www.foibg.com/ibs_isc/ibs-25/ibs-25-p10.pdf

Abstract: Information overload and an abundance of choices create situations where selecting one option becomes extremely difficult or even worse, a guessing game. Collaborative ranking systems address this problem by creating intelligent rankings of items based on user opinions aggregation. This paper presents a metric-based multi-criteria recommender system that can be used on non-rigid sets of criteria. These systems fare well with respect to accuracy, transparency and flexibility.

Keywords: Multi-dimensional recommender system, metric method.

ACM Classification Keywords: H.4: Information systems applications

MSC: 68N30: Mathematical aspects of software engineering

Link:

METRIC BASED RECOMMENDER SYSTEMS

Ali Akhtarzada, Cristian S. Calude, John Hosking

http://www.foibg.com/ibs_isc/ibs-25/ibs-25-p09.pdf

Abstract: A divergence function is a skew-symmetric distance like function on a manifold. In the geometric theory of statistical inference, such a divergence function is useful. In complex systems, Tsallis anomalous statistics is developing rapidly. A q-exponential family is an important statistical model in Tsallis statistics. For this q-exponential family, a divergence function is constructed from the viewpoint of affine differential geometry.

Keywords: information geometry, affine differential geometry, Tsallis statistics, divergence, q-exponential family

ACM Classification Keywords: G.0 General

MSC: 53A15, 62B10, 53A30

Link:

CONSTRUCTION OF GEOMETRIC DIVERGENCE ON q-EXPONENTIAL FAMILY

Hiroshi Matsuzoe

http://www.foibg.com/ibs_isc/ibs-25/ibs-25-p08.pdf

Abstract: Corresponding to each regular asymptotic polytope P in hyperbolic n-space Hn is an isomorphic figure °P in inversive (n1)-space In−1 having many related metric properties. A regular inversive polytope °P has a

Abstract: The main objects of Coding theory are metric vector or matrix spaces. Subsets of spaces are known as codes. The main problem is constructing codes of given pairwise distance and having maximal cardinality. Most known and most investigated spaces are Hamming spaces. Thousands papers and books are devoted to codes in the Hamming metric. We mention here only two books 1; 2 and will not consider this metric in details. Other metrics are investigated much less. In this paper, we give many examples of useful metrics. It is still non exhaustive review.

Keywords: metrics and norms, the uniform and non-uniform Hamming metrics, the Lee and Sharma-Kaushik? metrics, the city block (Manhattan) metric, the Varshamov metric, the burst metric, the 2-dimensional burst metric, the term rank metric, the rank metric, combinatorial metrics, projective metrics, graph metrics, the subspace metric.

ACM Classification Keywords: A.0 General Literature - Conference proceedings

MSC: 94B05, 94B20, 94B25

Link:

A BRIEF SURVEY OF METRICS IN CODING THEORY

Ernst Gabidulin

http://www.foibg.com/ibs_isc/ibs-25/ibs-25-p06.pdf

Abstract: The main purpose of this paper is to popularize Danzer’s power complex construction and establish some new results about covering maps between two power complexes. Power complexes are cube-like combinatorial structures that share many structural properties with higher-dimensional cubes and cubical tessellations on manifolds. Power complexes that are also abstract polytopes have repeatedly appeared somewhat unexpectedly in various contexts, although often under a different name. However, the non-polytope case is largely unexplored.

Keywords: cube; cubical tessellation; abstract polytope; incidence complex; covering.

MSC (2000): Primary: 51M20. Secondary: 52B15.

Link:

CUBE-LIKE POLYTOPES AND COMPLEXES

Andrew Duke, Egon Schulte

http://www.foibg.com/ibs_isc/ibs-25/ibs-25-p05.pdf

Abstract: We showthat the cone ofweighted n-point quasi-metricsWQMetn, the cone ofweighted quasi-hypermetrics WHypn and the cone of oriented cuts OCutn are projections along an extreme ray of the metric cone Metn+1, of the hypermetric cone Hypn+1 and of the cut cone Cutn+1, respectively. This projection is such that if one knows all faces of an original cone then one knows all faces of the projected cone.

Keywords: distance, metrics, hypermetrics, cutmetrics, quasi-metrics.

MSC: 52B12, 51F99, 90C57

Link:

CONES OF WEIGHTED QUASIMETRICS,WEIGHTED QUASIHYPERMETRICS AND OF ORIENTED CUTS

Michel Deza,Vyacheslav P.Grishukhin,Elena Deza

http://www.foibg.com/ibs_isc/ibs-25/ibs-25-p04.pdf

Abstract: The walk distances in graphs are defined as the result of appropriate transformations of the P1 k=0(tA)k proximity measures, where A is the weighted adjacency matrix of a graph and t is a sufficiently small positive parameter. The walk distances are graph-geodetic; moreover, they converge to the shortest path distance and to the so-called long walk distance as the parameter t approaches its limiting values. Furthermore, the logarithmic forest distances which are known to generalize the resistance distance and the shortest path distance are a specific subclass of walk distances. On the other hand, the long walk distance is equal to the resistance distance in a transformed graph.

Keywords: graph distances, walk distances, logarithmic forest distances, transitional measure, Laplacian matrix, resistance distance, network

ACM Classification Keywords: G.2.2 Graph Theory – Network problems; E.1 Data Structures – Graphs and networks; C.2.1 Network Architecture and Design – Network topology

Link:

LOGARITHMIC DISTANCES IN GRAPHS

Pavel Chebotarev

http://www.foibg.com/ibs_isc/ibs-25/ibs-25-p03.pdf

Abstract: Classifications of (v, k, 1) cyclic difference families (CDFs) by other authors are known for k = 3 and v  57, k = 4 and v  64, k = 5 and v  65, k = 6 and v = 91 and k = 7 and v = 91. In this work we construct all inequivalent (v, k, 1) CDFs (respectively all multiplier inequivalent cyclic 2-(v, k, 1) designs) with k  11 and some small v by a computer search and an algorithm similar to the one applied for the classification of optimal orthogonal codes in our previous works. We obtain the same number of inequivalent CDFs for all the parameters, for which previous classification results are known. The new parameters covered by our software for k  7 are (61, 3, 1), (73, 4, 1), (76, 4, 1), (81, 5, 1), and (85, 5, 1) CDFs.

Keywords: cyclic difference set, Steiner triple system, optical orthogonal code

ACM Classification Keywords: Algorithms

Link:

CLASSIFICATION RESULTS FOR (v, k, 1) CYCLIC DIFFERENCE FAMILIES WITH SMALL PARAMETERS

Tsonka Baicheva, Svetlana Topalova

http://www.foibg.com/ibs_isc/ibs-25/ibs-25-p02.pdf

Abstract: We study differential-geometrical structure of an information manifold equipped with a divergence function. A divergence function generates a Riemannian metric and furthermore it provides a symmetric third-order tensor, when the divergence is asymmetric. This induces a pair of affine connections dually coupled to each other with respect to the Riemannian metric. This is the arising emerged from information geometry. When a manifold is dually flat (it may be curved in the sense of the Levi-Civita? connection), we have a canonical divergence and a pair of convex functions from which the original dual geometry is reconstructed. The generalized Pythagorean theorem and projection theorem hold in such a manifold. This structure has lots of applications in information sciences including statistics, machine learning, optimization, computer vision and Tsallis statistical mechanics. The present article reviews the structure of information geometry and its relation to the divergence function. We further consider the conformal structure given rise to by the generalized statistical model in relation to the power law.

Keywords: divergence, information geometry, dual affine connection, Bregman divergence, generalized Pythagorean theorem

ACM Classification Keywords: G.3 PROBABILITY AND STATISTICS

Link:

DIFFERENTIAL GEOMETRY DERIVED FROM DIVERGENCE FUNCTIONS: INFORMATION GEOMETRY APPROACH

Shun-ichi Amari

http://www.foibg.com/ibs_isc/ibs-25/ibs-25-p01.pdf

Résumé: An approach for researching fingers' movement with an aim to create a formal notion of sign language fingerspelling units (dactyls) is considered. Then an informational parametric model of a human arm is suggested that describes possible movements during fingerspelling process. 10 fingerspelling alphabets are analyzed mutually compared for exact and partial similarity as well as notable distinctions. The example of a .Net-based software application is then provided that teaches proper Ukrainian fingerspelling.

Keywords: fingerspelling alphabet, specification, model of human movements.

ACM Classification Keywords: I.2.8 Problem Solving, Control Methods, and Search H.1.1 Systems and Information

Link:

INFORMATIONAL-PARAMETRIC MODEL OF SIGN LANGUAGE FINGERSPELLING UNITS

Iurii Krak, Bogdan Trotsenko, Julia Barchukova

http://foibg.com/ijitk/ijitk-vol05/ijitk05-4-p06.pdf

Abstract: Estimating of the Hurst exponent for experimental data plays a very important role in the research of processes which show properties of self-similarity. There are many methods for estimating the Hurst exponent using time series. The aim of this research is to carry out the comparative analysis of the statistical properties of the Hurst exponent estimators obtained by different methods using model stationary and nonstationary fractal time series. In this paper the most commonly used methods for estimating the Hurst exponents are examined. There are: /RS-analysis, variance-time analysis, detrended fluctuation analysis (DFA) and wavelet-based estimation. The fractal Brownian motion that is constructed using biorthogonal wavelets have been chosen as a model random process which exhibit fractal properties. In this paper, the results of a numerical experiment are represented where the fractal Brown motion was modelled for the specified values of the exponent H. The values of the Hurst exponent for the model realizations were varied within the whole interval of possible values 0 < H < 1.The lengths of the realizations were defined as 500, 1000, 2000 and 4000 values. For the nonstationary case model time series are presented by the sum of fractional noise and the trend component, which are a polynomial in varying degrees, irrational, transcendental and periodic functions. The estimates of H were calculated for each generated time series using the methods mentioned above. Samples of the exponent H estimates were obtained for each value of H and their statistical characteristics were researched. The results of the analysis have shown that the estimates of the Hurst exponent, which were obtained for the stationary realisations using the considered methods, are biased normal random variables. For each method the bias depends on the true value of the degrees self-similarity of the process and length of time series. Those estimates which are obtained by the DFA method and the wavelet transformation have the minimal bias. Standard deviations of the estimates depending on the estimation method and decrease, while the length of the series increases. Those estimates which are obtained by using the wavelet analysis have the minimal standard deviation. In the case of a nonstationary time series, represented by a trend and additive fractal noise, more accurate evaluation is obtained using the DFA method. This method allows estimating the Hurst exponent for experimental data with trend components of virtually any kind. The greatest difficulty in estimating, presents a series with a periodic trend component. It is desirable in addition to investigate the spectrum of the wavelet energy, which is demonstrated in the structure of the time series. In the presence of a slight trend, the wavelet-estimation is quite effective.

Keywords: Hurst exponent, estimate of the Hurst exponent, self-similar stochastic process, nonstationary time series, methods for estimating the Hurst exponent.

ACM Classification Keywords: G.3 Probability and statistics - Time series analysis, Stochastic processes, G.1 Numerical analysis, G.1.2 Approximation - Wavelets and fractals.

Link:

COMPARATIVE ANALYSIS FOR ESTIMATING OF THE HURST EXPONET FOR STATIONARY AND NONSTATIONARY TIME SERIES

Ludmila Kirichenko, Tamara Radivilova, Zhanna Deineko

http://foibg.com/ijitk/ijitk-vol05/ijitk05-4-p05.pdf

Abstract: The problem under consideration is to find a synchronizing sequence for a logic network with memory. A novel method is proposed that is based on formulation of the task as the Boolean satisfiability problem solved with any standard SAT solver. The developed method allows creating a Boolean equation presenting the problem in conjunctive normal form.

Keywords: design automation, verification, testing.

ACM Classification Keywords: B.6.2 Logic Design: Reliability and Testing; B.6.2 Reliability and Testing: Error-checking.

Link:

SEARCH ALGORITHM FOR SHORTEST SYNCHRONIZING SEQUENCES USING BOOLEAN SATISFIABILITY

Liudmila Cheremisinova

http://foibg.com/ijitk/ijitk-vol05/ijitk05-4-p04.pdf

Abstract: The main current concepts in overall Quality of Service (QoS) considerations in telecommunication systems, in documents of the leading standardization organizations, are found and put together. At least fifteen Open Issues for further study are formulated. Proposed are: Work Definitions of Communication and Telecommunication; A Reference Model of a Telecommunication System; Definitions of Overall Telecommunication Network and System Performance; Two Telecommunication System States’ modelling approaches are described; Parameters’ Classification Based on Their Values' Establishing Method is proposed, for the needs of design models; The necessity of Causal Classification of Values in Telecommunication Systems’ Models is argued; The necessity of Overall Telecommunication System’s Parameters’ Notation System is argued and a set of requirements is listed. An initial step of such notation system, proposed and used by authors is described.

Keywords: Telecommunication Systems, Telecommunication Network, Overall Quality of Service, Multi-Conceptual? Models, Models Scalability

ACM Classification Keywords: C.4 Performance of Systems, H.1.2 User/Machine Systems, I.6 Simulation and Modelling, I.6.0 General, H.1.2 User/Machine Systems, K.6 Management of Computing and Information Systems, K.6.0 Genera.

Link:

OVERALL QOS REFERENCING IN TELECOMMUNICATION SYSTEMS – SOME CURRENT CONCEPTS AND OPEN ISSUES

Stoyan Poryazov, Emiliya Saranova

http://foibg.com/ijitk/ijitk-vol05/ijitk05-4-p03.pdf

Abstract: This paper presents a new approach for creating conferences CD based HTML presentation of published papers for off-line reading. A couple of advances techniques has been deployed to automate process of creation like Java script engine, SQL database integration, full text search engine. The approach offers a good integration with online conference management systems for direct data exchange, friendly user interface and good compatibility with majority of contemporary HTML browsers.

Key Words: Java script, SQL, PHP, Database, Open Source, Linux.

Link:

AUTOMATED CONFERENCE CD-ROM BUILDER – AN OPEN SOURCE APPROACH

Stefan Karastanev

http://foibg.com/ijitk/ijitk-vol05/ijitk05-4-p02.pdf

Abstract: Current research on digital libraries (DL) is mostly focused on the generation of large collections of multimedia resources and regular tools for their indexing and retrieval. However, digital libraries should provide more than advanced content maintenance and retrieval services. They should aid the users in their content observation, knowledge acquisition and better satisfying their needs, interests and wishes. This paper presents an extension of the current DL functionality with content analyzing services. The main goal is to reach implicit and hidden data, content, rules and facts, dependences and tendencies, valid for the content in the DL repository, to synthesize and summarize the collected data in order to use them in various investigations and learning. These services also observe the DL tracking services’ output and provide different inferences for the frequency of service usage, failed requests, user logs and activities, etc., assisting the DL environment maintenance through the generation of inferences about its stability, flexibility, and reliability. This interpretation of DL analyzing services is not proposed and analyzed until now. We try to push up a new research point, aiming to aid user’s work in the DL environment.

Keywords: Digital Libraries, Services, Content Analysis, East-Christian? Iconographical Art.

ACM Classification Keywords: H.3.5 Online Information Services – Web-based services, H.3.7 Digital Libraries – Collection, Dissemination, System issues

Link:

CONTENT ANALYZING AND SYNTHESIZING SERVICES IN A DIGITAL LIBRARY

Desislava Paneva-Marinova?, Maxim Goynov, Radoslav Pavlov

http://foibg.com/ijitk/ijitk-vol05/ijitk05-4-p01.pdf

Abstract: The purpose of this work is to investigate how the Business Rules approach (very promising) can be used for the purposes of feasible and efficient software modernization (very needed). The processes of the forward and backward reengineering of legacy software systems are presented through identification of the main players. Their responsibilities, assigned tasks and expected deliverables are described. Some reasons for need of instrumental tools to support the process are given.

Keywords: software development, software modernization, business rules, extracting business rules.

ACM Classification Keywords: D.2.1 Requirements/Specifications, D.2.7 Distribution, Maintenance, and Enhancement.

Link:

EXTRACTING BUSINES RULES – HYPE OR HOPE FOR SOFTWARE MODERNIZATION

Neli Maneva, Krassimir Manev

http://foibg.com/ijita/vol18/ijita18-4-p08.pdf

Abstract: Wide introduction of the process-oriented systems for today is connected with the fact that they allow to formalize knowledge about business processes at the enterprises companies, organizations. At the same time, construction of business processes’ formal models require a lot of time and material costs, and it is the subject to influence of the human factor because it is often carry out with participation of experts and executors the purposes of which can be not coincided with the purposes of modeled business processes and enterprise overall aims. The given contradiction can lead to a divergence between real business process and its developed model. It can lead to construction of inadequate models of business processes. One of the important approaches to the decision of the given problem is realized on the basis of methodology of business processes intelligent analysis. The intelligent analysis is directed on reception of really carried out business processes’ models on the basis of research of events registration magazines of such processes.

Keywords: business processes, Petri net, implicit selection, logic net, predicate.

ACM Classification Keywords: C.4 Performance of systems - Modeling techniques, J.1 Administrative data processing - Business

Link:

EFFECTIVE CONSTRUCTIVE MODELS OF IMPLICIT SELECTION IN BUSINESS PROCESSES

Nataliya Golyan, Vera Golyan, Olga Kalynychenko

http://foibg.com/ijita/vol18/ijita18-4-p07.pdf