Search results for: generalized Kullback-Leibler divergence

Authors: Ana Serafimovic, Karthik Devarajan

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Non-negative matrix factorization approximates a high dimensional non-negative matrix V as the product of two non-negative matrices, W and H, and allows only additive linear combinations of data, enabling it to learn parts with representations in reality. It has been successfully applied in the analysis and interpretation of high dimensional data arising in neuroscience, computational biology, and natural language processing, to name a few. The objective of this paper is to assess a hybrid algorithm for non-negative matrix factorization with multiplicative updates. The method aims to minimize the symmetric version of Kullback-Leibler divergence known as intrinsic information and assumes that the noise is signal-dependent and that it originates from an arbitrary distribution from the exponential family. It is a generalization of currently available algorithms for Gaussian, Poisson, gamma and inverse Gaussian noise. We demonstrate the potential usefulness of the new generalized algorithm by comparing its performance to the baseline methods which also aim to minimize symmetric divergence measures.

Keywords: non-negative matrix factorization, dimension reduction, clustering, intrinsic information, symmetric information divergence, signal-dependent noise, exponential family, generalized Kullback-Leibler divergence, dual divergence

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Authors: Neda Lovričević, Đilda Pečarić, Josip Pečarić

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The Jensen functional in its discrete form is brought in relation to the Csiszar divergence functional, this time via its monotonicity property. This approach presents a generalization of the previously obtained results that made use of interpolating Jensen-type inequalities. Thus the monotonicity property is integrated with the Zipf-Mandelbrot law and applied to f-divergences for probability distributions that originate from the Csiszar divergence functional: Kullback-Leibler divergence, Hellinger distance, Bhattacharyya distance, chi-square divergence, total variation distance. The Zipf-Mandelbrot and the Zipf law are widely used in various scientific fields and interdisciplinary and here the focus is on the aspect of the mathematical inequalities.

Keywords: Jensen functional, monotonicity, Csiszar divergence functional, f-divergences, Zipf-Mandelbrot law

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Authors: Jyh-Yang Wu, Sheng-Gwo Chen

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In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem with a generalized finite difference method and obeys the conservation law on discrete closed surfaces. We use the similar method to solve the Cahn-Hilliard equations on evolving spherical surfaces and observe stability results in our numerical simulations.

Keywords: conservation laws, diffusion equations, Cahn-Hilliard equations, evolving surfaces

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Authors: Christian Lavault

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In this paper, the generalized fractional integral operators of two generalized Mittag-Leffler type functions are investigated. The special cases of interest involve the generalized M-series and K-function, both introduced by Sharma. The two pairs of theorems established herein generalize recent results about left- and right-sided generalized fractional integration operators applied here to the M-series and the K-function. The note also results in important applications in physics and mathematical engineering.

Keywords: Fox–Wright Psi function, generalized hypergeometric function, generalized Riemann– Liouville and Erdélyi–Kober fractional integral operators, Saigo's generalized fractional calculus, Sharma's M-series and K-function

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Authors: Vishal Jaunky, Jonas Grafström

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The development of the European Union’s (EU) single economic market and rapid technological change has resulted in major structural changes in EU’s member states economies. The general liberalization process that the countries has undergone together has convinced the governments of the member states of need to upgrade their economic and training systems in order to be able to face the economic globalization. Several signs of economic convergence have been found but less is known about the knowledge production. This paper addresses the convergence pattern of technological innovation in 13 European Union (EU) states over the time period 1990-2011 by means of parametric and non-parametric techniques. Parametric approaches revolve around the neoclassical convergence theories. This paper reveals divergence of both the β and σ types. Further, we found evidence of stochastic divergence and non-parametric convergence approach such as distribution dynamics shows a tendency towards divergence. This result is supported with the occurrence of γ-divergence. The policies of the EU to reduce technological gap among its member states seem to be missing its target, something that can have negative long run consequences for the market.

Keywords: convergence, patents, panel data, European union

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Authors: Benedict Barnes, Anthony Y. Aidoo

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A Divergence Regularization Method (DRM) is used to regularize the ill-posed Helmholtz equation where the boundary deflection is inhomogeneous in a Hilbert space H. The DRM incorporates a positive integer scaler which homogenizes the inhomogeneous boundary deflection in Cauchy problem of the Helmholtz equation. This ensures the existence, as well as, uniqueness of solution for the equation. The DRM restores all the three conditions of well-posedness in the sense of Hadamard.

Keywords: divergence regularization method, Helmholtz equation, ill-posed inhomogeneous Cauchy boundary conditions

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Authors: M. V. Belubekyan, S. R. Martirosyan

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On the example of an elastic rectangular plate streamlined by a supersonic gas flow, we have investigated the phenomenon of divergence and of panel flatter of the overrunning of the gas flow at a free edge under assumption of the presence of concentrated inertial masses and moments at the free edge. We applied a new approach of finding of solution of these problems, which was developed based on the algorithm for an analytical solution finding. This algorithm is easy to use for theoretical studies for the wides circle of nonconservative problems of linear elastic stability. We have established the relation between the characteristics of natural vibrations of the plate and velocity of the streamlining gas flow, which enables one to draw some conclusions on the stability of disturbed motion of the plate depending on the parameters of the system plate-flow. Its solution shows that either the divergence or the localized divergence and the flutter instability are possible. The regions of the stability and instability in space of parameters of the problem are identified. We have investigated the dynamic behavior of the disturbed motion of the panel near the boundaries of region of the stability. The safe and dangerous boundaries of region of the stability are found. The transition through safe boundary of the region of the stability leads to the divergence or localized divergence arising in the vicinity of free edge of the rectangular plate. The transition through dangerous boundary of the region of the stability leads to the panel flutter. The deformations arising at the flutter are more dangerous to the skin of the modern aircrafts and rockets resulting to the loss of the strength and appearance of the fatigue cracks.

Keywords: stability, elastic plate, divergence, localized divergence, supersonic panels flutter

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Authors: Menghzheng Yao

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Generalized social trust among Chinese has been declining in the past few decades, making the search for its causes necessary. Drawing on the symbolic interaction theory and the 2012 Chinese General Social Survey data, this research investigated the impact of people’s socialization preferences and frequencies on their perceptions of generalized social trust in China. This research also took a preliminary step towards understanding the spatial differences of the generalized social trust using the ArcGIS software. The results show that respondents who interacted with their neighbors more frequently were more likely to have higher levels of perceptions of generalized social trust. Several demographics were also significantly related to perception of generalized social trust. Elderly and better educated Chinese and people with higher self-perceived social status were associated with greater levels of generalized social trust perception, while urban dwellers and religious respondents expressed lower levels of such perception. Implications for future research and policy are discussed.

Keywords: China, generalized social trust, symbolic interaction, ArcGIS

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Authors: M. Y. Bakeir

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Rough set theory is a recent approach for reasoning about data. It has achieved a large amount of applications in various real-life fields. The main idea of rough sets corresponds to the lower and upper set approximations. These two approximations are exactly the interior and the closure of the set with respect to a certain topology on a collection U of imprecise data acquired from any real-life field. The base of the topology is formed by equivalence classes of an equivalence relation E defined on U using the available information about data. The theory of generalized topology was studied by Cs´asz´ar. It is well known that generalized topology in the sense of Cs´asz´ar is a generalization of the topology on a set. On the other hand, many important collections of sets related with the topology on a set form a generalized topology. The notion of Nano topology was introduced by Lellis Thivagar, which was defined in terms of approximations and boundary region of a subset of an universe using an equivalence relation on it. The purpose of this paper is to introduce a new generalized topology in terms of rough set called nano generalized topology

Keywords: rough sets, topological space, generalized topology, nano topology

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Authors: Li-Zhi Liao

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The central path has played the key role in the interior point method. However, the convergence of the central path may not be true even in some convex programming problems with linear constraints. In this paper, the generalized central paths are introduced for convex programming. One advantage of the generalized central paths is that the paths will always converge to some optimal solutions of the convex programming problem for any initial interior point. Some additional theoretical properties for the generalized central paths will be also reported.

Keywords: central path, convex programming, generalized central path, interior point method

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Authors: Rada Somkhuean, Sa-aat Niwitpong, Suparat Niwitpong

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This paper presents the generalized p-values for testing the difference between two future population means when the variances are unknown, in both cases for when the variances are equal and unequal. We also derive a closed form expression of the upper bound of the proposed generalized p-value.

Keywords: generalized p-value, two future population means, upper bound, variances

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Authors: Shohei Maruyama, Yasuo Matsuyama, Sachiyo Aburatani

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The development of the method to annotate unknown gene functions is an important task in bioinformatics. One of the approaches for the annotation is The identification of the metabolic pathway that genes are involved in. Gene expression data have been utilized for the identification, since gene expression data reflect various intracellular phenomena. However, it has been difficult to estimate the gene function with high accuracy. It is considered that the low accuracy of the estimation is caused by the difficulty of accurately measuring a gene expression. Even though they are measured under the same condition, the gene expressions will vary usually. In this study, we proposed a feature extraction method focusing on the variability of gene expressions to estimate the genes' metabolic pathway accurately. First, we estimated the distribution of each gene expression from replicate data. Next, we calculated the similarity between all gene pairs by KL divergence, which is a method for calculating the similarity between distributions. Finally, we utilized the similarity vectors as feature vectors and trained the multiclass SVM for identifying the genes' metabolic pathway. To evaluate our developed method, we applied the method to budding yeast and trained the multiclass SVM for identifying the seven metabolic pathways. As a result, the accuracy that calculated by our developed method was higher than the one that calculated from the raw gene expression data. Thus, our developed method combined with KL divergence is useful for identifying the genes' metabolic pathway.

Keywords: metabolic pathways, gene expression data, microarray, Kullback–Leibler divergence, KL divergence, support vector machines, SVM, machine learning

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Authors: Philippe Gugler

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This contribution reflects some important questions regarding inter alia the economic development occurring in the light of the ASEAN’s goal of creating the ASEAN Economic Community (AEC) by 2015. We observe a continuing economic growth of GDP per capita over recent years despite the negative effects of the world economic crisis. IMF forecasts indicate that this trend will continue. The paper focuses on the analysis and comparison of economic growth trends of ASEAN countries.

Keywords: ASEAN, convergence, divergence, economic growth, globalization, integration

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Authors: A. K. Sethi, R. N. Patra, B. Nayak

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In this paper, we have considered Friedmann-Robertson-Walker (FRW) metric with generalized Chaplygin gas which has viscosity in the context of Lyra geometry. The viscosity is considered in two different ways (i.e. zero viscosity, non-constant r (rho)-dependent bulk viscosity) using constant deceleration parameter which concluded that, for a special case, the viscous generalized Chaplygin gas reduces to modified Chaplygin gas. The represented model indicates on the presence of Chaplygin gas in the Universe. Observational constraints are applied and discussed on the physical and geometrical nature of the Universe.

Keywords: bulk viscosity, lyra geometry, generalized chaplygin gas, cosmology

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Authors: M. H. M. Rashid

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Given H a Hilbert space and B(H) the algebra of bounded linear operator in H, let δAB denote the generalized derivation defined by A and B. The main objective of this article is to study Weyl type theorems for generalized derivation for (A,B) satisfying a couple of Fuglede.

Keywords: Fuglede Property, Weyl’s theorem, generalized derivation, Aluthge transform

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Authors: Heidar Jafarizadeh, Hossein Keshtkar, Ahmad Sohankar

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Heat transfer and turbulent flow structure have been studied in a divergent ribbed duct with a varying duct geometry with Reynolds numbers of 7000 to 90000 using numerical methods. In this study, we confirmed our numerical results of a ribbed duct with an Initial slope of zero to 3 degree by comparing them to experimental data we had and investigated the impact of the ducts divergence on heat transfer and flow pattern in the 2-dimensional flow. Then we investigated the effect of tilting the ribs, on heat transfer and flow behavior. We achieved this by changing the ribs angles from a range of 40 to 75 degrees in a divergent duct and simulated the flow in 3-dimensions. Our results show that with an increase in duct divergence, heat transfer increases linearly and the coefficient of friction increases exponentially. As the results show, a duct with a divergence angle of 1.5 degree presents better thermal performance in comparison with all the angle range’s we studied. Besides, a ribbed duct with 40 degree rib orientation had the best thermal performance considering the simultaneous effects of pressure drop and heat transfer which were imposed on it.

Keywords: divergent ribbed duct, heat transfer, thermal performance, turbulent flow structure

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Authors: Fatemeh Mohammadi Aghjeh Mashhad

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In this paper, we give several ways for computing generalized local homology modules by using Gorenstein flat resolutions. Also, we find some bounds for vanishing of generalized local homology modules.

Keywords: a-adic completion functor, generalized local homology modules, Gorenstein flat modules

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Authors: Ahmad Termimi Ab Ghani, Kojiro Higuchi

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In this paper, we present some results of simultaneous infinite games. We mainly work with generalized reachability games and Buechi games. These games are two-player concurrent games where each player chooses simultaneously their moves at each step. Our goal is to give simple expressions of values for each game. Moreover, we are interested in the question of what type of optimal (ε-optimal) strategy exists for both players depending on the type of games. We first show the determinacy (optimal value) and optimal (ε-optimal) strategies in generalized reachability games. We provide a simple expressions of value of this game and prove the existence of memoryless randomized ε-optimal strategy for Player I in any generalized reachability games. We then observe games with more complex objectives, games with Buechi objectives. We present how to compute an ε-optimal strategies and approximate a value of game in some way. Specifically, the results of generalized reachability games are used to show the value of Buechi games can be approximated as values of some generalized reachability games.

Keywords: optimal Strategies, generalized reachability games, Buechi games

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Authors: A. S. Issa, S. K. Q. AL-Omari

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In this paper, we investigate certain spaces of generalized functions for the Fourier and Fourier type integral transforms. We discuss convolution theorems and establish certain spaces of distributions for the considered integrals. The new Fourier type integral is well-defined, linear, one-to-one and continuous with respect to certain types of convergences. Many properties and an inverse problem are also discussed in some details.

Keywords: Boehmian, Fourier integral, Fourier type integral, generalized quotient

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Authors: Ruchi, A. M. Acu, Purshottam N. Agrawal

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The purpose of this paper to introduce the Durrmeyer type modification of q-generalized-Bernstein operators which include the Bernstein polynomials in the particular α = 0. We investigate the rate of convergence by means of the Lipschitz class and the Peetre’s K-functional. Also, we define the bivariate case of Durrmeyer type modification of q-generalized-Bernstein operators and study the degree of approximation with the aid of the partial modulus of continuity and the Peetre’s K-functional. Finally, we introduce the GBS (Generalized Boolean Sum) of the Durrmeyer type modification of q- generalized-Bernstein operators and investigate the approximation of the Bögel continuous and Bögel differentiable functions with the aid of the Lipschitz class and the mixed modulus of smoothness.

Keywords: Bögel continuous, Bögel differentiable, generalized Boolean sum, Peetre’s K-functional, Lipschitz class, mixed modulus of smoothness

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Authors: Dzmitry M. Kabanau, Vladimir V. Kabanov, Yahor V. Lebiadok, Denis V. Shabrov, Pavel V. Shpak, Gevork T. Mikaelyan, Alexandr P. Bunichev

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This article is deal with the experimental investigations of the laser diode matrixes (LDM) based on the AlGaAs/GaAs heterostructures (lasing wavelength 790-880 nm) to find optimal LDM parameters for active vision systems. In particular, the dependence of LDM radiation pulse power on the pulse duration and LDA active layer heating as well as the LDM radiation divergence are discussed.

Keywords: active vision systems, laser diode matrixes, thermal properties, radiation divergence

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Authors: An Chengrui, Yin Zi, Wu Bingbing, Ma Yuanzhu, Jin Kaixiu, Chen Xiao, Ouyang Hongwei

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Single cell RNA sequence (scRNA-seq) is one of the effective tools to study transcriptomics of biological processes. Recently, similarity measurement of cells is Euclidian distance or its derivatives. However, the process of scRNA-seq is a multi-variate Bernoulli event model, thus we hypothesize that it would be more efficient when the divergence between cells is valued with relative entropy than Euclidian distance. In this study, we compared the performances of Euclidian distance, Spearman correlation distance and Relative Entropy using scRNA-seq data of the early, medial and late stage of limb development generated in our lab. Relative Entropy is better than other methods according to cluster potential test. Furthermore, we developed KL-SNE, an algorithm modifying t-SNE whose definition of divergence between cells Euclidian distance to Kullback–Leibler divergence. Results showed that KL-SNE was more effective to dissect cell heterogeneity than t-SNE, indicating the better performance of relative entropy than Euclidian distance. Specifically, the chondrocyte expressing Comp was clustered together with KL-SNE but not with t-SNE. Surprisingly, cells in early stage were surrounded by cells in medial stage in the processing of KL-SNE while medial cells neighbored to late stage with the process of t-SNE. This results parallel to Heatmap which showed cells in medial stage were more heterogenic than cells in other stages. In addition, we also found that results of KL-SNE tend to follow Gaussian distribution compared with those of the t-SNE, which could also be verified with the analysis of scRNA-seq data from another study on human embryo development. Therefore, it is also an effective way to convert non-Gaussian distribution to Gaussian distribution and facilitate the subsequent statistic possesses. Thus, relative entropy is potentially a better way to determine the divergence of cells in scRNA-seq data analysis.

Keywords: Single cell RNA sequence, Similarity measurement, Relative Entropy, KL-SNE, t-SNE

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Authors: Marianna Bolla

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The aim of this paper is to compare spectral, discrepancy, and degree properties of expanding graph sequences. As we can prove equivalences and implications between them and the definition of the generalized (multiclass) quasirandomness of Lovasz–Sos (2008), they can be regarded as generalized quasirandom properties akin to the equivalent quasirandom properties of the seminal Chung-Graham-Wilson paper (1989) in the one-class scenario. Since these properties are valid for deterministic graph sequences, irrespective of stochastic models, the partial implications also justify for low-dimensional embedding of large-scale graphs and for discrepancy minimizing spectral clustering.

Keywords: generalized random graphs, multiway discrepancy, normalized modularity spectra, spectral clustering

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Authors: Rana Rimawi, Ayman Baklizi

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Skewed distributions are important models that are frequently used in applications. Generalized distributions form a class of skewed distributions and gain widespread use in applications because of their flexibility in data analysis. More specifically, the Generalized Logistic Distribution with its different types has received considerable attention recently. In this study, based on progressively type-II censored data, we will consider point estimation in type II Generalized Logistic Distribution (Type II GLD). We will develop several estimators for its unknown parameters, including maximum likelihood estimators (MLE), Bayes estimators and linear estimators (BLUE). The estimators will be compared using simulation based on the criteria of bias and Mean square error (MSE). An illustrative example of a real data set will be given.

Keywords: point estimation, type II generalized logistic distribution, progressive censoring, maximum likelihood estimation

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Authors: Serge Provost, Abdous Saboor

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A q-analogue of the generalized extreme value distribution which includes the Gumbel distribution is introduced. The additional parameter q allows for increased modeling flexibility. The resulting distribution can have a finite, semi-infinite or infinite support. It can also produce several types of hazard rate functions. The model parameters are determined by making use of the method of maximum likelihood. It will be shown that it compares favourably to three related distributions in connection with the modeling of a certain hydrological data set.

Keywords: extreme value theory, generalized extreme value distribution, goodness-of-fit statistics, Gumbel distribution

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Authors: Aleksandar Hatzivelkos

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The term ”compromise” is mostly used casually within the social choice theory. It is usually used as a mere result of the social choice function, and this omits its deeper meaning and ramifications. This paper is based on a mathematical model for the description of a compromise as a version of the Sorites paradox. It introduces a formal definition of d-measure of divergence from a compromise and models a notion of compromise that is often used only colloquially. Such a model for vagueness phenomenon, which lies at the core of the notion of compromise enables the introduction of new mathematical structures. In order to maximize compromise, different methods can be used. In this paper, we explore properties of a social welfare function TdM (from Total d-Measure), which is defined as a function which minimizes the total sum of d-measures of divergence over all possible linear orderings. We prove that TdM satisfy strict Pareto principle and behaves well asymptotically. Furthermore, we show that for certain domain restrictions, TdM satisfy positive responsiveness and IIIA (intense independence of irrelevant alternatives) thus being equivalent to Borda count on such domain restriction. This result gives new opportunities in social choice, especially when there is an emphasis on compromise in the decision-making process.

Keywords: borda count, compromise, measure of divergence, minimization

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Authors: Niloofar Fariborzi, Hamzeh Alipour, Kourosh Azizi, Neda Eskandarzade, Abozar Ghorbani

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The family Parvoviridae consists of a large diversity of single-stranded DNA viruses, which cause mild to severe diseases in both vertebrates and invertebrates. The Parvoviridae are classified into three subfamilies: Parvovirinae infect vertebrates, Densovirinae infects invertebrates, while Hamaparovirinae infects both vertebrates and invertebrates. Except for the NS1 region, which is the prime criterion for phylogeny analysis, other parts of the parvoviruses genome, such as UTRs, are diverse even among closely related viruses or within the same genus. It is believed that host switching in parvoviruses may be related to genetic changes in regions other than NS1; therefore, whole-genome screening is valuable for studying parvoviruses' host-virus interactions. The aim of this study was to analyze genome organization and phylogeny of the complete genome sequence of the 132 Paroviridae family members, focusing on viruses that infect invertebrates. The maximum and minimum divergence within each subfamily belonged to Densovirinae and Parvovirinae, respectively. The greatest evolutionary divergence was between Hamaparovirinae and Parvovirinae. Unclassified viruses were mostly from Parovirinae and had the highest divergence to densoviruses and the lowest divergence to Parovirinae viruses. In a phylogenetic tree, all hamparoviruses were found in the center of densoviruses, with the exception of Syngnathid Ichthamaparvovirus 1 (NC_055527), which was positioned between two Parvovirinae members (NC _022089 and NC_038544). The proximity of hamparoviruses members to some densoviruses strengthens the possibility that densoviruses may be the ancestors of hamaparoviruses or vice versa. Therefore, examination and phylogeny analysis of the whole genome is necessary to understand Parvoviridae family host selection.

Keywords: densoviruses, parvoviridae, bioinformatics, phylogeny

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Authors: Yu-Chen Wei

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The relationship between organizational human capital and organizational effectiveness have been a common topic of interest to organization researchers. Much of this research has concluded that higher human capital can predict greater organizational outcomes. Whereas human capital research has traditionally focused on organizations, the current study turns to the team level human capital. In addition, there are no known empirical studies assessing the effect of human capital divergence on team performance. Team human capital refers to the sum of knowledge, ability, and experience embedded in team members. Team human capital divergence is defined as the variation of human capital within a team. This study is among the first to assess the role of human capital divergence as a moderator of the effect of team human capital on team performance. From the traditional perspective, team human capital represents the collective ability to solve problems and reducing operational risk of all team members. Hence, the higher team human capital, the higher the team performance. This study further employs social learning theory to explain the relationship between team human capital and team performance. According to this theory, the individuals will look for progress by way of learning from teammates in their teams. They expect to have upper human capital, in turn, to achieve high productivity, obtain great rewards and career success eventually. Therefore, the individual can have more chances to improve his or her capability by learning from peers of the team if the team members have higher average human capital. As a consequence, all team members can develop a quick and effective learning path in their work environment, and in turn enhance their knowledge, skill, and experience, leads to higher team performance. This is the first argument of this study. Furthermore, the current study argues that human capital divergence is negative to a team development. For the individuals with lower human capital in the team, they always feel the pressure from their outstanding colleagues. Under the pressure, they cannot give full play to their own jobs and lose more and more confidence. For the smart guys in the team, they are reluctant to be colleagues with the teammates who are not as intelligent as them. Besides, they may have lower motivation to move forward because they are prominent enough compared with their teammates. Therefore, human capital divergence will moderate the relationship between team human capital and team performance. These two arguments were tested in 510 team-seasons drawn from major league baseball (1998–2014). Results demonstrate that there is a positive relationship between team human capital and team performance which is consistent with previous research. In addition, the variation of human capital within a team weakens the above relationships. That is to say, an individual working with teammates who are comparable to them can produce better performance than working with people who are either too smart or too stupid to them.

Keywords: human capital divergence, team human capital, team performance, team level research

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Authors: Omenogor, Happy Dumbi

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This paper examines the areas of convergence and divergence between English and Ųkwųanį (a language in Nigeria) vowel systems with particular emphasis on the front vowels. It specifies areas of difficulty for the average Ųkwųanį users of English and Ųkwųanį L1 users of English as a second language. The paper explains the nature of contrastive analysis, the geographical locations where Ųkwųanį is spoken as mother tongue as well as English and Ųkwųanį front vowels. The principles of establishing phonemes, minimal pairs in Ųkwųanį as well as the vowel charts in both languages are among the issues highlighted in this paper.

Keywords: convergence, divergence, English, Ukwųanį

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Authors: Ana Barbir, S. Ivelic Bradanovic, D. Pecaric, J. Pecaric

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We proved a converse to Sherman's inequality. Using the concept of f-divergence we obtained some inequalities for the well-known entropies, such as Shannon entropies that have many applications in many applied sciences, for example, in information theory, biology and economics Zipf-Mandelbrot law gave improvement in account for the low-rankwords in corpus. Applications of Zipf-Mandelbrot law can be found in linguistics, information sciences and also mostly applicable in ecological eld studies. We also introduced an entropy by applying the Zipf-Mandelbrot law and derived some related inequalities.

Keywords: f-divergence, majorization inequality, Sherman inequality, Zipf-Mandelbrot entropy

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