We give a non trivial upper bound, Fh(g, N), for the size of a Bh[g] subset of {1, ...., N} when g > 1. In particular, we prove F2(g, N) ≤ 1.864(gN) + 1 Fh(g, N) ≤ 1 (1 + cosh(π/h))1/h (hh!gN), h > 2. On the other hand we exhibit B2[g] subsets of {1, ...., N} with g + [g/2] √ g + 2[g/2] N + o(N) elements. 1. Upper bounds Let h ≥ 2, g ≥ 1 be integers. A subset A of integers is called a Bh[g]-seq...

MicroRNAs (miRNAs) and copy number variations (CNVs) are two newly discovered genetic elements that have revolutionized the field of molecular biology and genetics. By performing in silico whole genome analysis, we demonstrate that both the number of miRNAs that target genes found in CNV regions as well as the number of miRNA-binding sites are significantly higher than those of genes found in n...

the interaction of brilliant green with herring sperm dna was investigated in detail by spectrometric methods in γ-cyclodextrin systems. on the condition of physiological ph, brilliant green prefers to form the 1:1 inclusion complex with γ-cyclodextrin.all the evidences indicated that the binding modes between γ-cyclodextrin-brilliant green and dna were grooving binding and partial non-classica...

In 2006 illegal immigrants represented four percent of the total number of US residents, and comparable figures hold also for other advanced destination countries. If governments are not able or willing to stick to their “official” immigration policy, why do they set such policies in the first place? The purpose of this paper is to address this apparent puzzle, by developing a political agency ...

In this paper we obtain a best upper bound for the ratio of the extreme values of positive numbers in terms of the arithmetic-geometric means ratio. This has immediate consequences for condition numbers of matrices and the standard deviation of equiprobable events. It also allows for a refinement of Schwarz’s vector inequality.

The normwise distance of a matrix A to the nearest singular matrix is well known to be equal to ‖A‖/cond(A) for norms being subordinate to a vector norm. However, there is no hope to find a similar formula or even a simple algorithm for computing the componentwise distance to the nearest singular matrix for general matrices. This is because Rohn and Poljak [7] showed that this is an NP -hard pr...

Let b ≥ 2 be an integer and ξ be an irrational real number. Among other results, we establish an explicit lower bound for the number of distinct blocks of n digits occurring in the b-ary expansion of ξ.

Models of transcription are often built around a picture of RNA polymerase and transcription factors (TFs) acting on a single copy of a promoter. However, most TFs are shared between multiple genes with varying binding affinities. Beyond that, genes often exist at high copy number-in multiple identical copies on the chromosome or on plasmids or viral vectors with copy numbers in the hundreds. U...

The Pythagoras number of a ring A is the smallest integer p A = p ≥ 1 such that any sum of squares of A is a sum of p squares, and p A = +∞ if such an integer does not exist. This is a very delicate invariant whose study has deserved a lot of attention from specialists in number theory, quadratic forms, real algebra, and real geometry. Wellknown examples are the following: p = 4 (Lagrange’s fam...

We discuss the performance of the convex approximations introduced by Van der Vlerk [2004] for the class of integer recourse problems with totally unimodular (TU) recourse matrices. We show that the main result in Van der Vlerk [2004] needs stronger assumptions, so that a performance guarantee for the convex approximations is lacking in general. In order to obtain such a performance guarantee, ...