Probabilistic D-Clustering

We present a new iterative method for probabilistic clustering of data. Given clusters, their centers and the distances of data points from these centers, the probability of cluster membership at any point is assumed inversely proportional to the distance from (the center of) the cluster in question. This assumption is our working principle. The method is a generalization, to several centers, of theWeiszfeld method for solving the Fermat–Weber location problem. At each iteration, the distances (Euclidean, Mahalanobis, etc.) from the cluster centers are computed for all data points, and the centers are updated as convex combinations of these points, with weights determined by the above principle. Computations stop when the centers stop moving.     

Number crunching vs. number theory: computers and FLT,from Kummer to SWAC (1850–1960), and beyond

The present article discusses the computational tools (both conceptual and material) used in various attempts to deal with individual cases of FLT, as well as the changing historical contexts in which these tools were developed and used, and affected research. It also explores the changing conceptions about the role of computations within the overall disciplinary picture of number theory, how they influenced research on the theorem, and the kinds of general insights thus achieved. After an overview of Kummer’s contributions and its immediate influence, I present work that favored intensive computations of particular cases of FLT as a legitimate, fruitful, and worth-pursuing number-theoretical endeavor, and that were part of a coherent and active, but essentially low-profile tradition within nineteenth century number theory. This work was related to table making activity that was encouraged by institutions and individuals whose motivations came mainly from applied mathematics, astronomy, and engineering, and seldom from number theory proper. A main section of the article is devoted to the fruitful collaboration between Harry S. Vandiver and Emma and Dick Lehmer. I show how their early work led to the hesitant introduction of electronic computers for research related with FLT. Their joint work became a milestone for computer-assisted activity in number theory at large.     

AUTOMATIC DECISION-MAKING： NEURAL FIRING AND RESPONSE

1. Introduction This is the fourth exposition on theAnalytic Hierarchy Process. It is true thatmany decisions we make subconsciously ariseout of our physical and biological needs andderive from the pressure to survive physically.We also make subconsciou…     

MAN-MACHINE COLLABORATED KNOWLEDGE CREATION IN HWMSE

1 Introduction Science of complexity and complex systems is a relatively new area In wide fields from chemistry, biology, environment, geo-science, climatology to economics and sociology, complexity has been studied from diverse views and understandings Systems science, which could be traced back to Ludwig von Bertalanffy’foundational work on general system theory, plays an active role in complexity studies From system perspectives, relevant concepts often include interaction, feedback, evol…     

Preparation and characteristics of flexible all-organic thin-film field-effect transistor

Much attention has been attracted to organic thin-film field-effect transistors (OTFFETs) in the past decades[1—4]. Because of their lower cost and easier preparation, OTFFETs are considered to be useful in driving liquid crystal displays (LCD) and organic light-emitting diodes (OLED). Furthermore, flexible OTFFETs will be one of the most useful electronic devices for flexible active matrix driving circuits. OTFFETs based on pentacene single crystal have been reported to be of g…     

GROUP SIZE AND PARALLELISM EFFECTS IN TASKS WITHHETEROGENEOUS LEVELS OF DIFFICULTY：A STOCHASTIC ORDER APPROACH

We consider tasks where in order to perform them it is sufficient that one member of a group will know how to do it. We are interested in the effect of task difficulty, and variability of that difficulty, on group performance, and in particular on the marginal contribution of an additional number to the performance of groups of different size. We explore the implications of various stochastic orders over task difficulty and variability. Some intuitive conjectures are shown to be false.     

STUDIES ON HORIZONTAL COMPETITION AMONG HOMOGENOUS RETAILERS THROUGH AGENT-BASED SIMULATION

1. Introduction A supply chain is a network composed osuppliers, manufacturers, retailers, etc., whichcooperate to offer a kind of goods or servicesThese supply chain members cooperate andcompete with each other to maximize theiown profits. For example,…     

Resonance Light-Scattering Spectroscopy Study on Interaction between Gold Colloid and Thiol Containing Pharmaceutical

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Phylogeny constructed by using diversity increment

A new approach based on the concept of the diversity increment is applied to reconstruct a phylogeny. The phylogeny of the Eutherian orders use concatenated H-stranded amino acid sequences, and the result is consistent with the commonly accepted one for the Eutherians. Foundation item: Supported by the National Natural Science Foundation of China ( 30170214) and the Open Foundation of the State Key Laboratory of Software Engineer, Wuhan University, China. Biography: Shi Feng ( 1966- ), male, Ph. D, Associate professor, research direction: bioinformatics.