The role of crossover operator in the genetic optimization of magnetic models

The Ising model, introduced almost 100 years ago by Wilhelm Lenz and Ernst Ising, is the formalism still popular as a tool to describe magnetic properties of a wide class of materials. Among many issues which arise when using this model there exist problems related to the process of finding minimum energy of the system. Since these problems are NP-hard, optimizations can either be performed for some approximated cases or be the subject of global optimization techniques. In this paper we present an analysis of the effect of different crossover operators on the efficiency of genetic algorithm used to minimize energy in the Ising model. Although it is not a benchmark tool, we hope it may be interesting as a testing tool.     

Using the Hamming distance to extend TOPSIS in a fuzzy environment

Considering the fact that, in some cases, determining precisely the exact value of attributes is difficult and that their values can be considered as fuzzy data, this paper extends the TOPSIS method for dealing with fuzzy data, and an algorithm for determining the best choice among all possible choices when the data are fuzzy is also presented. In this approach, to identify the fuzzy ideal solution and fuzzy negative ideal solution, one of the Yager indices which is used for ordering fuzzy quantities in [0, 1] is applied. Using Yager’s index leads to a procedure for choosing fuzzy ideal and negative ideal solutions directly from the data for observed alternatives. Then, the Hamming distance is proposed for calculating the distance between two triangular fuzzy numbers. Finally, an application is given, to clarify the main results developed in the paper.     

Description of weakly periodic Gibbs measures for the isingmodel on a cayley tree

We introduce the concept of a weakly periodic Gibbs measure. For the Ising model, we describe a set of such measures corresponding to normal subgroups of indices two and four in the group representation of a Cayley tree. In particular, we prove that for a Cayley tree of order four, there exist critical values T _c < T _cr of the temperature T > 0 such that there exist five weakly periodic Gibbs measures for 0 < T < T _c or T > T _cr , three weakly periodic Gibbs measures for T = T _c , and one weakly periodic Gibbs measure for T _c < T ≤ T _cr . __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 2, pp. 292–302, August, 2008.     

Correlation Function of the Two-Dimensional Ising Model on a Finite Lattice: II

We calculate the pair correlation function and the magnetic susceptibility in the anisotropic Ising model on the lattice with one infinite and one finite dimension with periodic boundary conditions imposed along the second dimension. Using the exact expressions for lattice form factors, we propose formulas for arbitrary spin matrix elements, thus providing a possibility to calculate all multipoint correlation functions in the anisotropic Ising model on cylindrical and toroidal lattices. We analyze passing to the scaling limit.     

Using a cognitive architecture with a physiological substrate to represent effects of a psychological stressor on cognition

Adding a physiological representation to a cognitive architecture offers an attractive approach to modeling the effects of stress on cognition. We introduce ACT-R/Φ, an extended version of the ACT-R cognitive architecture that includes an integrative model of physiology. The extension allows the representation of how physiology and cognition interact. This substrate was used to represent potential effects of a startle response and task-based stress during a mental arithmetic (subtraction) task. We compare predictions from two models loaded into the new hybrid architecture to models previously developed within ACT-R. General behavior differed between models in that the ACT-R/Φ models had dynamic declarative memory noise over the course of the task based on varying epinephrine levels. They attempted more subtractions but were less accurate; this more closely matched human performance than the previous ACT-R models. Using ACT-R/Φ allows a more tractable integration of current physiological and cognitive perspectives on stress. ACT-R/Φ also permits further exploration of the interaction between cognition and physiology, and the emergent effects on behavior caused by the interaction among physiological subsystems. This extension is useful for anyone exploring how the human mind can occur in and be influenced by the physical universe.     

Extremes of the internal energy of the Potts model on cubic graphs

We prove tight upper and lower bounds on the internal energy per particle (expected number of monochromatic edges per vertex) in the anti‐ferromagnetic Potts model on cubic graphs at every temperature and for all . This immediately implies corresponding tight bounds on the anti‐ferromagnetic Potts partition function. Taking the zero‐temperature limit gives new results in extremal combinatorics: the number of q‐colorings of a 3‐regular graph, for any , is maximized by a union of 's. This proves the d = 3 case of a conjecture of Galvin and Tetali.     

The entropy of Garfinkle-Horne dilaton black hole due to arbitrary spin fields

Using the membrane model which is based on brick wall model, we calculated the free energy and entropy of Garfinkle-Horne dilatonic black hole due to arbitrary spin fields. The result shows that the entropy of scalar field and the entropy of Fermionic field have similar formulas. There is only a coefficient between them.     

Using asymptotic results to obtain a confidence interval for the population median

Almost all introductory and intermediate level statistics textbooks include the topic of confidence interval for the population mean. Almost all these texts introduce the median as a robust measure of central tendency. Only a few of these books, however, cover inference on the population median and in particular confidence interval for the median. This may be due to the somewhat complex nature of the problem. This paper attempts to popularize a method that is conceptually and computationally simpler than the currently used methods in textbooks and has the promise of being more accessible to elementary/intermediate level statistics students. The method is conceptually simpler, because its development parallels that of obtaining a confidence interval for the mean and it involves concepts that are well-covered in elementary courses. It is computationally simple, because its major computational component is a smoothing method that is widely available in statistical software. For the latter reason, the proposed method is referred to as the Smoothing method. A simple R program is given that produces confidence intervals using the Smoothing method. Utilization of Minitab, SAS, and SPSS for this purpose is also discussed. A simulation study is performed to compare statistical properties of the proposed method to those of the two currently popular methods of Bootstrap and Binomial. Based on this limited simulation studies, it is observed that the Smoothing method is at least as good as, and in some respects is superior to, the Binomial and Bootstrap methods in samples of size as large or larger than 30.     

Characterizing partition functions of the spin model by rank growth

We characterize which graph invariants are partition functions of a spin model over C$\mathbb{C}$, in terms of the rank growth of associated ‘connection matrices’.     

The metastable behavior of the three-dimensional stochastic Ising model I

The metastable behavior of the stochastic Ising model in a finite three-dimensional torus is studied in the limit as the temperature goes to zero. All metastable states are characterized and a hierarchic structure is found. For a large class of initial states, the logarithmic asymptotics of the hitting time of the states are studied with all spins +l or − 1. Project supported in part by the State Education Commission of China, the National Natural Science Foundation of China, the Tianyuan Foundation and the National 863 Project.     

The Initial Drift of a 2D Droplet at Zero Temperature

We consider the 2D stochastic Ising model evolving according to the Glauber dynamics at zero temperature. We compute the initial drift for droplets which are suitable approximations of smooth domains. A specific spatial average of the derivative at time 0 of the volume variation of a droplet close to a boundary point is equal to its curvature multiplied by a direction dependent coefficient. We compute the explicit value of this coefficient.      

A note on the stochastic properties of a scale change random effects model

The scale change model in survival analysis incorporates unobserved heterogeneity through a frailty that enters the baseline hazard function to change the time scale. In this paper we examine the stochastic properties of the mixtures of scale change model and build dependence between the overall population variable and the frailty variable. We also carry out stochastic comparisons between overall population variables when their respective frailty or baseline variables are ordered in the sense of various stochastic orders. Finally, we demonstrate how the variation of the baseline variable has an effect on the model.     

On a basic definition of returns to scale

A concept that has sparked considerable interest in DEA is that of returns to scale (RTS). One of the basic and useful definitions of RTS in DEA models is based upon the PPS. In this work, a discussion about the PPS-based definition of RTS is given, leading to a modified definition of RTS which is suitable in the presence of multiple supporting hyperplanes passing through the unit under assessment. The definition provided is a simplification of a definition given by Tone.     

Improvements of the Maximum Pseudo-Likelihood Estimators in Various Spatial Statistical Models

Abstract

Maximum pseudo-likelihood estimation has hitherto been viewed as a practical but flawed alternative to maximum likelihood estimation, necessary because the maximum likelihood estimator is too hard to compute, but flawed because of its inefficiency when the spatial interactions are strong. We demonstrate that a single Newton-Raphson step starting from the maximum pseudo-likelihood estimator produces an estimator which is close to the maximum likelihood estimator in terms of its actual value, attained likelihood, and efficiency, even in the presence of strong interactions. This hybrid technique greatly increases the practical applicability of pseudo-likelihood-based estimation. Additionally, in the case of the spatial point processes, we propose a proper maximum pseudo-likelihood estimator which is different from the conventional one. The proper maximum pseudo-likelihood estimator clearly shows better performance than the conventional one does when the spatial interactions are strong.     

A network approach to the modelling of active magnetic bearings

The modelling of active magnetic bearings based on a network approach is considered. Unlike in the standard modelling approach, where a linearization of the current-force relation for the centred shaft position is used, network models permit to include the position dependence of the bearing force in the force model. This becomes necessary when model based controllers are used to stabilize a magnetically supported shaft in tracking applications.

The approach is based on the well known application of network models to magnetic circuits. Further simplifying assumptions are discussed which allow one to obtain a network with a limited number of lumped parameters describing the magnetic behaviour of a magnetic bearing. The modelling of a combined radial and axial bearing serves as an example for the application of the proposed approach. Furthermore, the fitting of the network based model to measured characteristic force curves is discussed. In this context, a method for including saturation effects in the model is sketched.