Diluted antiferromagnets in a field seem to be in a different universality class than the random-field Ising model

We perform large-scale Monte Carlo simulations using the Machta-Newman-Chayes algorithms to study the critical behavior of both the diluted antiferromagnet in a field with 30% dilution and the random-field Ising model with Gaussian random fields for different field strengths. Analytical calculations by Cardy [Phys. Rev. B 29, 505 (1984)] predict that both models map onto each other and share the same universality class in the limit of vanishing fields. However, a detailed finite-size scaling analysis of both the Binder cumulant and the two-point finite-size correlation length suggests that even in the limit of small fields, where the mapping is expected to work, both models are not in the same universality class. Therefore, care should be taken when interpreting (experimental) data for diluted antiferromagnets in a field using the random-field Ising model. Based on our numerical data, we present analytical expressions for the phase boundaries of both models.Comment: 12 pages, 9 figures, 5 table

Periodized Radial Basis Functions (RBFs) and RBF-Vortex Method for the Barotropic Vorticity Equation.

Fluids spontaneously develop fronts, narrow spiral filaments and other features of rapid spatial variation which are very challenging for numerical methods. Like most competing numerical schemes, Radial Basis Function (RBF) methods are based on interpolation. It has been previously proved that the RBF approximation converges to the correct solution as the number of grid points increases. When the flow is varying rapidly, high accuracy requires a high density of interpolation points while smooth regions require a lower density of points. A method that can adaptively allocate more grid points to where the fronts develop and fewer grid points to where the flow is smooth is of great value in fluid simulation on the surface of a sphere. In this thesis, a method that combines the meshfree nature of RBF interpolation and the Lagrangian particle method is developed. On the one hand, the particles serving as fluid elements are advected by the velocity field such that rapidly varying regions are densely populated; on the other hand, the particles serving as RBF centers provide higher density of interpolation points and therefore give a better resolution of the regions.PhDAtmospheric, Oceanic and Space Sciences and Scientific ComputingUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/108985/1/wanderx_1.pd

Quantification of the Impact of Feature Selection on the Variance of Cross-Validation Error Estimation

<p/> <p>Given the relatively small number of microarrays typically used in gene-expression-based classification, all of the data must be used to train a classifier and therefore the same training data is used for error estimation. The key issue regarding the quality of an error estimator in the context of small samples is its accuracy, and this is most directly analyzed via the deviation distribution of the estimator, this being the distribution of the difference between the estimated and true errors. Past studies indicate that given a prior set of features, cross-validation does not perform as well in this regard as some other training-data-based error estimators. The purpose of this study is to quantify the degree to which feature selection increases the variation of the deviation distribution in addition to the variation in the absence of feature selection. To this end, we propose the coefficient of relative increase in deviation dispersion (CRIDD), which gives the relative increase in the deviation-distribution variance using feature selection as opposed to using an optimal feature set without feature selection. The contribution of feature selection to the variance of the deviation distribution can be significant, contributing to over half of the variance in many of the cases studied. We consider linear-discriminant analysis, 3-nearest-neighbor, and linear support vector machines for classification; sequential forward selection, sequential forward floating selection, and the <inline-formula><graphic file="1687-4153-2007-16354-i1.gif"/></inline-formula>-test for feature selection; and <inline-formula><graphic file="1687-4153-2007-16354-i2.gif"/></inline-formula>-fold and leave-one-out cross-validation for error estimation. We apply these to three feature-label models and patient data from a breast cancer study. In sum, the cross-validation deviation distribution is significantly flatter when there is feature selection, compared with the case when cross-validation is performed on a given feature set. This is reflected by the observed positive values of the CRIDD, which is defined to quantify the contribution of feature selection towards the deviation variance.</p

A New Stopping Criterion for BICM-ID System Based on Cross-Entropy

AbstractThis paper proposes a new stopping criterion for BICM-ID (bit-interleaved coded modulation with iterative decoding) system based on the CE (cross-entropy) stopping criterion. Unlike the conventional CE stopping criterion, the new scheme only computes and compares the cross-entropy value of the odd bits of the entire frame bits. We name the proposed new criterion as Partial-CE stopping criterion. The new criterion can reduce about 50% computation complexity of the BICM-ID receiver. Simulations comparing the new criterion with the original CE stopping criterion show that the proposed Partial-CE scheme can achieve similar performances in terms of BER and the average iteration numbers

An Explorative Study of the Effectiveness of Mobile Advertising

This study examines factors related to the effectiveness of mobile advertising. Using a large data set with 115, 899 records of ad tap through from a mobile advertising company, we identify that the influencing factors for ad tap through are application type, mobile operators, scrolling frequency, and the regional income level. We use a logit model to analyze how the probability of ad tap through is related to the identified factors. The results show that application type, mobile operators, scrolling frequency, and the regional income level all have significant effects on the likelihood whether users would tap on certain types of advertising. Based on the findings, we propose strategies for mobile advertisers to engage in effective and targeted mobile advertising