Approach to Equilibrium for a Class of Random Quantum Models of Infinite Range

We consider random generalizations of a quantum model of infinite range introduced by Emch and Radin. The generalizations allow a neat extension from the class l (1) of absolutely summable lattice potentials to the optimal class l (2) of square summable potentials first considered by Khanin and Sinai and generalised by van Enter and van Hemmen. The approach to equilibrium in the case of a Gaussian distribution is proved to be faster than for a Bernoulli distribution for both short-range and long-range lattice potentials. While exponential decay to equilibrium is excluded in the nonrandom l (1) case, it is proved to occur for both short and long range potentials for Gaussian distributions, and for potentials of class l (2) in the Bernoulli case. Open problems are discussed.

Limit theorems for sequences of random trees

We consider a random tree and introduce a metric in the space of trees to define the ""mean tree"" as the tree minimizing the average distance to the random tree. When the resulting metric space is compact we have laws of large numbers and central limit theorems for sequence of independent identically distributed random trees. As application we propose tests to check if two samples of random trees have the same law.

Predicting random effects with an expanded finite population mixed model

Prediction of random effects is an important problem with expanding applications. In the simplest context, the problem corresponds to prediction of the latent value (the mean) of a realized cluster selected via two-stage sampling. Recently, Stanek and Singer [Predicting random effects from finite population clustered samples with response error. J. Amer. Statist. Assoc. 99, 119-130] developed best linear unbiased predictors (BLUP) under a finite population mixed model that outperform BLUPs from mixed models and superpopulation models. Their setup, however, does not allow for unequally sized clusters. To overcome this drawback, we consider an expanded finite population mixed model based on a larger set of random variables that span a higher dimensional space than those typically applied to such problems. We show that BLUPs for linear combinations of the realized cluster means derived under such a model have considerably smaller mean squared error (MSE) than those obtained from mixed models, superpopulation models, and finite population mixed models. We motivate our general approach by an example developed for two-stage cluster sampling and show that it faithfully captures the stochastic aspects of sampling in the problem. We also consider simulation studies to illustrate the increased accuracy of the BLUP obtained under the expanded finite population mixed model. (C) 2007 Elsevier B.V. All rights reserved.

Asymmetric Ramsey Properties of Random Graphs Involving Cliques

Consider the following problem: Forgiven graphs G and F(1),..., F(k), find a coloring of the edges of G with k colors such that G does not contain F; in color i. Rodl and Rucinski studied this problem for the random graph G,,, in the symmetric case when k is fixed and F(1) = ... = F(k) = F. They proved that such a coloring exists asymptotically almost surely (a.a.s.) provided that p <= bn(-beta) for some constants b = b(F,k) and beta = beta(F). This result is essentially best possible because for p >= Bn(-beta), where B = B(F, k) is a large constant, such an edge-coloring does not exist. Kohayakawa and Kreuter conjectured a threshold function n(-beta(F1,..., Fk)) for arbitrary F(1), ..., F(k). In this article we address the case when F(1),..., F(k) are cliques of different sizes and propose an algorithm that a.a.s. finds a valid k-edge-coloring of G(n,p) with p <= bn(-beta) for some constant b = b(F(1),..., F(k)), where beta = beta(F(1),..., F(k)) as conjectured. With a few exceptions, this algorithm also works in the general symmetric case. We also show that there exists a constant B = B(F,,..., Fk) such that for p >= Bn(-beta) the random graph G(n,p) a.a.s. does not have a valid k-edge-coloring provided the so-called KLR-conjecture holds. (C) 2008 Wiley Periodicals, Inc. Random Struct. Alg., 34, 419-453, 2009

Prediction of the economic activity from the short and long-term interest rate differential: new evidences in Chile and the United States of America cases

The purpose of this work is to verify the stability of the relationship between real activity and interest rate spread. The test is based on Chen (1988) and Osorio and Galea (2006). The analysis is applied to Chile and the United States, from 1980 to 1999. In general, in both cases the relationship was statistically significant in early 80s, but a break point is found in both countries during that decades, suggesting that the relationship depends on the monetary rule follow by the Central Bank.

A New Approach to the Prediction of Partition Coefficients in Water/Organic Interfaces

In the present work, a new approach for the determination of the partition coefficient in different interfaces based on the density function theory is proposed. Our results for log P(ow) considering a n-octanol/water interface for a large super cell for acetone -0.30 (-0.24) and methane 0.95 (0.78) are comparable with the experimental data given in parenthesis. We believe that these differences are mainly related to the absence of van der Walls interactions and the limited number of molecules considered in the super cell. The numerical deviations are smaller than that observed for interpolation based tools. As the proposed model is parameter free, it is not limited to the n-octanol/water interface.

PREDICTION OF METAL CATION TOXICITY TO THE BIOLUMINESCENT FUNGUS GERRONEMA VIRIDILUCENS

A correlation between the physicochemical properties of mono- [Li(I), K(I), Na(I)] and divalent [Cd(II), Cu(II), Mn(II), Ni(II), Co(II), Zn(II), Mg(II), Ca(II)] metal cations and their toxicity (evaluated by the free ion median effective concentration. EC50(F)) to the naturally bioluminescent fungus Gerronema viridilucens has been studied using the quantitative ion character activity relationship (QICAR) approach. Among the 11 ionic parameters used in the current study, a univariate model based on the covalent index (X(m)(2)r) proved to be the most adequate for prediction of fungal metal toxicity evaluated by the logarithm of free ion median effective concentration (log EC50(F)): log EC50(F) = 4.243 (+/-0.243) -1.268 (+/-0.125).X(m)(2)r (adj-R(2) = 0.9113, Alkaike information criterion [AIC] = 60.42). Additional two- and three-variable models were also tested and proved less suitable to fit the experimental data. These results indicate that covalent bonding is a good indicator of metal inherent toxicity to bioluminescent fungi. Furthermore, the toxicity of additional metal ions [Ag(I), Cs(I), Sr(II), Ba(II), Fe(II), Hg(II), and Pb(II)] to G. viridilucens was predicted, and Pb was found to be the most toxic metal to this bioluminescent fungus (EC50(F)): Pb(II) > Ag(I) > Hg(I) > Cd(II) > Cu(II) > Co(II) Ni(II) > Mn(II) > Fe(II) approximate to Zn(II) > Mg(II) approximate to Ba(II) approximate to Cs(I) > Li(I) > K(I) approximate to Na(I) approximate to Sr(II)> Ca(II). Environ. Toxicol. Chem. 2010;29:2177-2181. (C) 2010 SETAC

Improved Prediction of Hydrocarbon Flash Points from Boiling Point Data

Flash points (T(FP)) of hydrocarbons are calculated from their flash point numbers, N(FP), with the relationship T(FP) (K) = 23.369N(FP)(2/3) + 20.010N(FP)(1/3) + 31.901 In turn, the N(FP) values can be predicted from experimental boiling point numbers (Y(BP)) and molecular structure with the equation N(FP) = 0.987 Y(BP) + 0.176D + 0.687T + 0.712B - 0.176 where D is the number of olefinic double bonds in the structure, T is the number of triple bonds, and B is the number of aromatic rings. For a data set consisting of 300 diverse hydrocarbons, the average absolute deviation between the literature and predicted flash points was 2.9 K.

Simultaneous prediction of symptom severity and cause in data from a test battery for Parkinson patients, using machine learning methods

The main purpose of this thesis project is to prediction of symptom severity and cause in data from test battery of the Parkinson’s disease patient, which is based on data mining. The collection of the data is from test battery on a hand in computer. We use the Chi-Square method and check which variables are important and which are not important. Then we apply different data mining techniques on our normalize data and check which technique or method gives good results.The implementation of this thesis is in WEKA. We normalize our data and then apply different methods on this data. The methods which we used are Naïve Bayes, CART and KNN. We draw the Bland Altman and Spearman’s Correlation for checking the final results and prediction of data. The Bland Altman tells how the percentage of our confident level in this data is correct and Spearman’s Correlation tells us our relationship is strong. On the basis of results and analysis we see all three methods give nearly same results. But if we see our CART (J48 Decision Tree) it gives good result of under predicted and over predicted values that’s lies between -2 to +2. The correlation between the Actual and Predicted values is 0,794in CART. Cause gives the better percentage classification result then disability because it can use two classes.