Rate of parity violation from measure concentration

We present a geometric argument determining the kinematic (phase-space) factor contributing to the relative rate at which degrees of freedom of one chirality come to dominate over degrees of freedom of opposite chirality, in models with parity violation. We rely on the measure concentration of a subset of a Euclidean cube which is controlled by an isoperimetric inequality. We provide an interpretation of this result in terms of ideas of Statistical Mechanics.Comment: 10 pages, no figure

Exponential and moment inequalities for U-statistics

A Bernstein-type exponential inequality for (generalized) canonical U-statistics of order 2 is obtained and the Rosenthal and Hoffmann-J{\o}rgensen inequalities for sums of independent random variables are extended to (generalized) U-statistics of any order whose kernels are either nonnegative or canonicalComment: 22 page

Smooth analysis of the condition number and the least singular value

Let \a be a complex random variable with mean zero and bounded variance. Let $N_{n}$ be the random matrix of size $n$ whose entries are iid copies of \a and $M$ be a fixed matrix of the same size. The goal of this paper is to give a general estimate for the condition number and least singular value of the matrix $M + N_{n}$, generalizing an earlier result of Spielman and Teng for the case when \a is gaussian. Our investigation reveals an interesting fact that the "core" matrix $M$ does play a role on tail bounds for the least singular value of $M+N_{n}$. This does not occur in Spielman-Teng studies when \a is gaussian. Consequently, our general estimate involves the norm $\|M\|$. In the special case when $\|M\|$ is relatively small, this estimate is nearly optimal and extends or refines existing results.Comment: 20 pages. An erratum to the published version has been adde

The phytobenthos of the Hornsund fiord, SW Spitsbergen

The species composition and biomass of material collected in the summers 1981 and 1983 from 69 stations in the Hornsund fiord were analysed. 48 macroalgal taxa were found: 13 green algae, 18 brown algae and 17 red algae. 19 of these taxa were not reported from the nearby Isfjorden. The overall biomass for the littoral zone varied from 0 to 216gnT2 formalin d.w., although in J of samples the biomass was between 20 and 80 gm_z. The dominant species were Fucus distichus, Acrosiphonia duriusada and Pilayella littoralis. Using cluster analysis, an attempt was made to delimit regions with a characteristic species composition. The results obtained, however, do not permit this in the littoral zone of the Hornsund fiord