Description:
Using eigenvalue analysis, it was shown by Erdos et al. that, with the exception of C4, there are no graphs of diameter 2, maximum degree d and d2 vertices. In this paper, we show that graphs of diameter 2, maximum degree d and d2-1 vertices do not exist for most values of d, when d is even, and we conjecture that they do not exist for any even d greater than 4.
Description:
Using eigenvalue analysis, it was shown by Erdos et al. that, with the exception of C4, there are no graphs of diameter 2, maximum degree d and d2 vertices. In this paper, we show that graphs of diameter 2, maximum degree d and d2-1 vertices do not exist for most values of d, when d is even, and we conjecture that they do not exist for any even d greater than 4.
Description:
This paper introduces the notion of piecewise partially separable functions and studies their properties. We also consider some of many applications of these functions. Finally, we consider the problem of minimizing of piecewise partially separable functions and develop an algorithm for its solution. This algorithm exploits the structure of such functions. We present the results of preliminary numerical experiments.
Description:
This paper introduces the notion of piecewise partially separable functions and studies their properties. We also consider some of many applications of these functions. Finally, we consider the problem of minimizing of piecewise partially separable functions and develop an algorithm for its solution. This algorithm exploits the structure of such functions. We present the results of preliminary numerical experiments.
Description:
The degree/diameter problem is to determine the largest graphs or digraphs of given maximum degree and given diameter. This paper deals with directed graphs. General upper bounds, called Moore bounds, exist for the largest possible order of such digraphs of maximum degree d and diameter k. It is known that simulated annealing and genetic algorithm are effective techniques to identify global optimization solutions. This paper describes our attempt to build a Hybrid Simulated Annealing and Genetic Algorithm (HSAGA) that can be used to construct larger digraphs, and displays our preliminary results obtained by HSAGA.
Description:
The characterization of important complexity classes by logical descriptions has been an important and prolific area of Descriptive complexity. However, the central focus of the research has been the study of classes like P, NP, L and NL, corresponding to decision problems (e.g. the characterization of NP by Fagin [Fag74] and of P by Gradel [E. 91]). In contrast, optimization problems have received much less attention. Optimization problems corresponding to the NP class have been characterized in terms of logic expressions by Papadimitriou and Yannakakis, Panconesi and Ranjan, Kolaitis and Thakur, Khanna et al, and by Zimand. In this paper, we attempt to characterize the optimization versions of P via expressions in second order logic, many of them using universal Horn formulae with successor relations. These results nicely complement those of Kolaitis and Thakur [KT94] for polynomially bounded NP-optimization problems. The polynomially bounded versions of maximization and minimization problems are treated first, and then the maximization problems in the not necessarily polynomially bounded class.
Description:
The characterization of important complexity classes by logical descriptions has been an important and prolific area of Descriptive complexity. However, the central focus of the research has been the study of classes like P, NP, L and NL, corresponding to decision problems (e.g. the characterization of NP by Fagin [Fag74] and of P by Gradel [E. 91]). In contrast, optimization problems have received much less attention. Optimization problems corresponding to the NP class have been characterized in terms of logic expressions by Papadimitriou and Yannakakis, Panconesi and Ranjan, Kolaitis and Thakur, Khanna et al, and by Zimand. In this paper, we attempt to characterize the optimization versions of P via expressions in second order logic, many of them using universal Horn formulae with successor relations. These results nicely complement those of Kolaitis and Thakur [KT94] for polynomially bounded NP-optimization problems. The polynomially bounded versions of maximization and minimization problems are treated first, and then the maximization problems in the not necessarily polynomially bounded class.
Description:
Data have been collected for many years in different scientific (industrial, medical) research groups. Very often these groups kept all the the they could collect. It is possible that the data contains a lot of noisy features which do not bring any information, but make the problem more complicated. The additional study of eliminating non-informative and selecting informative features is very important in the area of Data Mining. There are several feature selection methods which were developed for supervised classification. The area of feature selection for unsupervised classification is not so developed. In this paper we present a new feature selection approach for unsupervised classification, based on clustering and nonsmooth optimisation techniques.
Description:
Drug-drug interaction is one of the important problems of Adverse Drug Reaction (ADR). In this paper we develop an optimization approach for the study of this problem. This approach is based on drug-reaction relationships represented in the form of a vector of weights, which can be defined as a solution to some global optimization problem. Although this approach can be used for solving many ADR problems, we concentrate here only on drug-drug interactions. Based on drug-reaction relationships, we formulate this problem as an optimization problem. The approach is applied to different classes of reactions from the Australian Adverse Drug Reaction Advisory Committee (ADRAC) database.
Description:
Drug-drug interaction is one of the important problems of Adverse Drug Reaction (ADR). In this paper we develop an optimization approach for the study of this problem. This approach is based on drug-reaction relationships represented in the form of a vector of weights, which can be defined as a solution to some global optimization problem. Although this approach can be used for solving many ADR problems, we concentrate here only on drug-drug interactions. Based on drug-reaction relationships, we formulate this problem as an optimization problem. The approach is applied to different classes of reactions from the Australian Adverse Drug Reaction Advisory Committee (ADRAC) database.
Description:
In 1960, Hoffman and Singleton investigated the existence of Moore graphs of diameter 2 (graphs of maximum degree d and d² + 1 vertices), and found that such graphs exist only for d = 2; 3; 7 and possibly 57. In 1980, Erdös et al., using eigenvalue analysis, showed that, with the exception of C4, there are no graphs of diameter 2, maximum degree d and d² vertices. In this paper, we show that graphs of diameter 2, maximum degree d and d² - 1 vertices do not exist for most values of d with d ≥ 6, and conjecture that they do not exist for any d ≥ 6.
Description:
This article develops a combinatorial algorithm for a class of codes extending BCH codes and constructed with finite state automata. Our algorithm computes the largest number of errors that the extended codes can correct, and finds a generator for eachoptimal code in this class of extensions. The question of finding codes with largest possible information rates remains open.
Description:
It is well known that apart from the Petersen graph there are no Moore graphs of degree 3. As a cubic graph must have an even number of vertices, there are no graphs of maximum degree 3 and
Description:
By an (a, d)-edge-antimagic total labeling of a graph G(V, E) we mean a bijective function f from V(G) u E(G) onto the set. { 1, 2, ... ,ǀV(C)ǀ+IE(G)I} such that the set of all the edge-weights, w(uv) ,.... f(u) + f(uv) + f(v), uv C E (G), is {a, a+ d, a+ 2d, . . . , a + (lE(G)I-1)d}, for two integers a > 0 and d
Description:
By an (a, d)-edge-antimagic total labeling of a graph G(V, E) we mean a bijective function f from V(G) u E(G) onto the set. { 1, 2, ... ,ǀV(C)ǀ+IE(G)I} such that the set of all the edge-weights, w(uv) ,.... f(u) + f(uv) + f(v), uv C E (G), is {a, a+ d, a+ 2d, . . . , a + (lE(G)I-1)d}, for two integers a > 0 and d
Description:
In this paper we develop an optimization approach for the study of Adverse Drug Reaction (ADR) problems. This approach is based on drug-reaction relationships represented in the form of a vector weights, which can be defined as a solution to some global optimization problem. Although it can be used for solving many ADR problems, we concentrate on the problem of accurate identification of drugs that are responsible for reactions that have occurred. Based on drug-reaction relationships, we formulate this problem as an optimization problem. The approach is applied to Australian Adverse Drug Reaction Advisory Committee (ADRAC) database. We take a comprehensive approach to considering all reaction classes which combines 18 SOC (System Organ Class), as well as the sub-classes of reaction classes Blood, Body, Neurological and Cardiovascular. The numerical experiments provided high accuracy in prediction of suspected drugs reported in ADRAC database.
Description:
This articles develops a combinatorial algorithm for a class of codes extending BCH codes and constructed with finite state automata. Ou algorithm computes the largest number of errors that the extended codes can correct, and finds a generator for each optimal code in this class of extensions. The question of finding codes with largest possible information rates remains open.