‘aging’ scaling property typical of glassy dynamics when σ → 0. 4) A progression from normal diffusiveness to subdiffusive behavior and finally to a stop in the growth of the mean square displacement as demonstrated by the use of a repeated-cell map. (see Fig. 3) The existence of this analogy is perhaps not accidental since the limit of vanishing noise amplitude σ → 0 involves loss of ergodicity.

We study the distribution of maximum likelihood estimate (MLE) in high-dimensional logistic models, where covariates are Gaussian with an arbitrary covariance structure. prove that limit large problems holding ratio between number p and sample size n constant, every finite list MLE coordinates follows a multivariate normal distribution. Concretely, jth coordinate βˆj is asymptotically normally ...

We generalize the notion of symmetries of propositional formulas in conjunctive normal form to modal formulas. Our framework uses the coinductive models introduced in [4] and, hence, the results apply to a wide class of modal logics including, for example, hybrid logics. Our main result shows that the symmetries of a modal formula preserve entailment: if σ is a symmetry of φ then φ |= ψ if and ...

1 Background We derive the sampling distribution of the SAM (significance analysis for microarrays) statistic introduced by Tusher et al. (2001). The statistic resembles the t-statistic, but has an additional regularizing term in the denominator, which is a constant for a given dataset. We first introduce some notation and the SAM statistic, and then proceed to derive an approximate sampling di...

Proof of Corollary 1. Assume that X has only terminal singularities. Then Codim(Σ ⊂ X) ≥ 3. By Theorem, Σ has no codimension 3 irreducible components. Therefore Codim(Σ ⊂ X) ≥ 4. Conversely, assume Codim(Σ ⊂ X) ≥ 4. Take a resolution f : Y → X of X and denote by {Ei} the f -exceptional divisors. Since X has canonical singularities, we have KY = f KX +ΣaiEi with non-negative integers ai. One can...

We generalize the notion of symmetries of propositional formulas in conjunctive normal form to modal formulas. Our framework uses the coinductive models introduced in [4] and, hence, the results apply to a wide class of modal logics including, for example, hybrid logics. Our main result shows that the symmetries of a modal formula preserve entailment: if σ is a symmetry of φ then φ |= ψ if and ...

Let T be a tree with induced partial order . We investigate centered Gaussian processes X = (X t)t∈T represented as X t = σ(t) ∑ v t α(v)ξv for given weight functions α and σ on T and with (ξv)v∈T i.i.d. standard normal. In a first part we treat general trees and weights and derive necessary and sufficient conditions for the a.s. boundedness of X in terms of compactness properties of (T, d). He...

Porous silicon samples were prepared by electrochemical etching method for different etching times. The structural properties of porous silicon (PS) samples were determined from the Atomic Force Microscopy (AFM) measurements. The surface mean root square roughness (σ rms) changes as function of porosity were studied, and the influence of etching time on porosity and roughness was studied too. U...