Let D be a b-wise independent distribution over {0, 1}m. Let E be the “noise” distribution over {0, 1}m where the bits are independent and each bit is 1 with probability η/2. We study which tests f : {0, 1}m → [−1, 1] are ε-fooled by D + E, i.e., |E[f(D+E)]−E[f(U)]| ≤ ε where U is the uniform distribution. We show that D+E ε-fools product tests f : ({0, 1}n)k → [−1, 1] given by the product of k...

We consider the random Schrödinger operator−ε−2∆(d) +ξ (ε)(x), with ∆(d) the discrete Laplacian on Zd and ξ (ε)(x) are bounded and independent random variables, on sets of the form Dε := {x ∈ Zd : xε ∈ D} for D bounded, open and with a smooth boundary, and study the statistics of the Dirichlet eigenvalues in the limit ε ↓ 0. Assuming Eξ (ε)(x) = U(xε) holds for some bounded and continuous funct...

In this paper which is an extended version of an article submitted to the Finite Volumes for Complex Applications V conference, we design a finite-volume based numerical scheme for the solution of the nonlinear balance equations of RNG variants of the well-known k − ε model and the v − f system encountered in the k − ε− v − f model which can be seen as an extension of first order turbulence mod...

Given nonnegative real sequences a = (αk)k∈Z and b = (βk)k∈Z we study the generated summation operator Sa,b(x) := ( αk [∑ l<k βlxl ]) k∈Z , x = (xk)k∈Z , regarded as a mapping from `p(Z) to `q(Z). We give necessary and sufficient conditions for the boundedness of Sa,b and prove optimal estimates for its entropy numbers relative to the summation properties of a and b. Our results are applied to ...

Fitch graphs G = (X,E) are di-graphs that are explained by {⊗, 1}-edge-labeled rooted trees with leaf set X: there is an arc xy ∈ E if and only if the unique path in T that connects the least common ancestor lca(x, y) of x and y with y contains at least one edge with label 1. In practice, Fitch graphs represent xenology relations, i.e., pairs of genes x and y for which a horizontal gene transfe...

Given an LLL-basis B of dimension n = hk we accelerate slide-reduction with blocksize k to run under a reasonable assumption in 1 6 nh log1+ε α local SVP-computations in dimension k, where α ≥ 4 3 measures the quality of the given LLL-basis and ε is the quality of slide-reduction. If the given basis B is already slide-reduced for blocksize k/2 then the number of local SVP-computations for slide...

This paper proves that for every positive integers n, k and any positive number ε, we can explicitly construct a DAG G with n+O(k1+ε) vertices and a constant degree such that even after removing any k vertices from G, the remaining digraph still contains an n-vertex dipath. This paper also proves that for every positive integers n, k and any positive number ε, we can explicitly construct a grap...

Magnetic and structural aspects of the annealing-induced transformation of rapidly-solidified Mn55Al45 ribbons from the as-quenched metastable antiferromagnetic (AF) ε-phase to the target ferromagnetic (FM) L10 τ-phase are investigated. The as-solidified material exhibits a majority hexagonal ε-MnAl phase revealing a large exchange bias shift below a magnetic blocking temperature TB~95 K (Hex~1...