Relaxation Dynamics of Point Vortices

We study a model describing relaxation dynamics of point vortices, from quasi-stationary state to the stationary state. It takes the form of a mean field equation of Brownian point vortices derived from Chavanis, and is formulated by our previous work as a limit equation of the patch model studied by Robert-Someria. This model is subject to the micro-canonical statistic laws; conservation of energy, that of mass, and increasing of the entropy. We study the existence and nonexistence of the global-in-time solution. It is known that this profile is controlled by a bound of the negative inverse temperature. Here we prove a rigorous result for radially symmetric case. Hence E/M2 large and small imply the global-in-time and blowup in finite time of the solution, respectively. Where E and M denote the total energy and the total mass, respectively.

Diffusive and Anti-Diffusive Behavior for Kinetic Models of Opinion Dynamics

In the present paper, we study a class of nonlinear integro-differential equations of a kinetic type describing the dynamics of opinion for two types of societies: conformist ( σ = 1 ) and anti-conformist ( σ = - 1 ). The essential role is played by the symmetric nature of interactions. The class may be related to the mesoscopic scale of description. This means that we are going to statistically describe an individual state of an agent of the system. We show that the corresponding equations result at the macroscopic scale in two different pictures: anti-diffusive ( σ = 1 ) and diffusive ( σ = - 1 ). We provide a rigorous result on the convergence. The result captures the macroscopic behavior resulting from the mesoscopic one. In numerical examples, we observe both unipolar and bipolar behavior known in political sciences.

Comparative Analysis of Simple Additive Weighting Method and Weighted Product Method to New Employee Recruitment Decision Support System (DSS) at PT. Warta Media Nusantara

Issue handling of inadvertence situations in the decision-making process of recruiting new employees at PT. Warta Media Nusantara that use criteria value of interviews, field test, a psychological test and medical check-up requires Multi Attribute Decision Making (MADM) as an auxiliary method of decision-making on the prospective eligible employee to be accepted in the company. There are various MADM methods, such as Simple Additive Weighting (SAW) method and Weighted Product (WP) method. Both of these methods are known as the most common method used in handling MADM issues, so in this study both methods are applied to the DSS and analyzed the differences in terms of obtained results and the execution time required for each method. The results of the study of the application of SAW and WP methods in the recruitment of new employees DSS there are some differences in the results of the candidates rank order and the differences in execution time of each method. The differences in rank order of these methods are due to the effects of alternative values, weighting criteria, and the calculation method. WP method is able to provide more rigorous result than SAW method, while the difference in execution time of SAW and WP methods explains that the execution time of SAW method relatively quick because SAW calculation method has a simpler process than the process of WP calculation methods

ROLE OF HURST EXPONENT IN PREDICTION OF MARKET EFFICIENCY IN KSE-100 INDEX

Purpose:- This paper aims to investigate the Efficient Market Hypothesis (EMH) and validity of Random Walk Model (RWM) in KSE-100 index starting from 1992 till 2014 taking monthly averages of index. Methodology:- Main focus of the paper is to evaluate the efficiency in KSE-100 index with respect to application of Hurst Exponent and Rescaled Ranged Statistics. Although many researchers have previously explained the working of EMH in KSE-100 index but rarely anyone has explained it using Hurst Exponent Analysis on over all longest period since the establishment of KSE-100 index Feb, 1992 to Dec, 2014. Annual Rescaled Range Statistics are also calculated to explain the good or bad years according to Estimated Hurst Statistics. All statistical analysis has been performed on Gretl which gives the good grasp over Hurst Exponent Analysis. Results:- The results revealed that overall KSE-100 index is not following the random walk and is not performing efficiently, and yearly break up shows that market was persistent in few years but mostly it was antipersistent (long-run memory prevails). Practical Implication:- Implementing Hurst Exponent Analysis enabled us to get rigorous result about performance of the Pakistan stock market in terms of efficiency that implied chances of arbitrage opportunity prevail significantly.

Verification methods: Rigorous results using floating-point arithmetic

A classical mathematical proof is constructed using pencil and paper. However, there are many ways in which computers may be used in a mathematical proof. But ‘proof by computer’, or even the use of computers in the course of a proof, is not so readily accepted (the December 2008 issue of the Notices of the American Mathematical Society is devoted to formal proofs by computer).In the following we introduce verification methods and discuss how they can assist in achieving a mathematically rigorous result. In particular we emphasize how floating-point arithmetic is used.

A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART XI: PERIOD-2 RULES

The 11th part of our tour through one-dimensional binary Cellular Automata concerns period-2 rules, which form the second group in our classification of the 88 globally-independent CA rules according to the properties of their periodic orbits. In this article, we display the basin tree diagrams of all period-2 rules along with their time-2 characteristic functions, and then we prove that all rules belonging to group 2 have robust period-2 ω-limit orbits for any finite, and infinite, bit string length. This rigorous result, which pairs with the one about period-1 rules given in the tenth installment of our chronicle, confirms what we stated about period-2 rules on the basis of empirical evidence. In the second part of this tutorial, we introduce the notion of quasi global-equivalence and prove that there are only 82 quasi globally-independent CA rules. For the first time, we show that the space-time patterns of globally-independent local rules can depend on each other, and we present an example of quasi-global transformation. We also define the super string 𝄞, and its unique decimal representation x𝄞, dubbed the super decimal, which provides a completely transparent yet rigorous proof that rule [Formula: see text] is chaotic when L → ∞. Moreover, we present the basin tree generation formulas, which uncover the analytical relationships between basin trees of globally-equivalent rules. Last but not least, for pedagogical and epistemological reasons, we conclude this paper with the selection of rule[Formula: see text], instead of rule [Formula: see text], as the prototypic universal Turing machine for our future discourse.

A Spectral Approach to Analysing Belief Propagation for 3-Colouring

Belief propagation (BP) is a message-passing algorithm that computes the exact marginal distributions at every vertex of a graphical model without cycles. While BP is designed to work correctly on trees, it is routinely applied to general graphical models that may contain cycles, in which case neither convergence, nor correctness in the case of convergence is guaranteed. Nonetheless, BP has gained popularity as it seems to remain effective in many cases of interest, even when the underlying graph is ‘far’ from being a tree. However, the theoretical understanding of BP (and its new relative survey propagation) when applied to CSPs is poor.Contributing to the rigorous understanding of BP, in this paper we relate the convergence of BP to spectral properties of the graph. This encompasses a result for random graphs with a ‘planted’ solution; thus, we obtain the first rigorous result on BP for graph colouring in the case of a complex graphical structure (as opposed to trees). In particular, the analysis shows how belief propagation breaks the symmetry between the 3! possible permutations of the colour classes.

ON A SPECTRAL THEOREM FOR DEFORMATION QUANTIZATION

We give a construction of an eigenstate for a non-critical level of the Hamiltonian function, and investigate the contribution of Morse critical points to the spectral decomposition. We compare the rigorous result with the series obtained by a perturbation theory. As an example the relation to the spectral asymptotics is discussed.