α∈Q nαt , nα in Z, which is constructed using the action of the monodromy on the mixed Hodge structure on the cohomology of the Milnor fiber at x. When f has an isolated singularity at x, all nα are in N, and the exponents of f , counted with multiplicity nα, are exactly the rational numbers α with nα not zero. Let us assume now that the singular locus of f is a curve Γ, having r local componen...

For a given convex polygon with inner angle no less than 3π and boundary edge bounded by [l, αl] for 1 ≤ α ≤ 1.4, where l is a given standard bar’s length, we investigate the problem of triangulating the polygon using some Steiner points such that (i) the length of each edge in triangulation is bounded by [βl, 2l], where β is a given constant and meets 0 < β ≤ 1 2 , and (ii) the number of non-s...

In this note we show that a non-degenerated polytope in IRn with n+k, 1 ≤ k < n, vertices is far from any symmetric body. We provide the asymptotically sharp estimates for the asymmetry constant of such polytopes. 0 Introduction and notations The canonical Euclidean inner product in IR is denoted by 〈·, ·〉, the norm in `p is denoted by ‖ · ‖p, 1 ≤ p ≤ ∞. By a convex body K ⊂ IR we shall always ...

We study the topological entropy of chaotic repellers formed by those points in a given chaotic attractor that never visit some small forbidden hole-region in the phase space. The hole is a set of points in the phase space that have a sequence α = (α0α1 . . . αl−1) as the first l letters in their itineraries. We point out that the difference between the topological entropies of the attractor an...

Whole human genome oligo microarrays were employed to systematically investigate the differential expression characteristics of associated mRNAs, which were found in the signal transduction pathway of β2 integrins in peripheral blood mononuclear cells (PBMCs) between patients with symptomatic pulmonary embolism (PE) and controls. A total of 20 cases of PE patients and twenty gender‑ and age‑mat...

BACKGROUND Isoflurane in clinical use is a racemate of S- and R-isoflurane. Previous studies have demonstrated that the effects of S-isoflurane on relevant anesthetic targets might be modestly stronger (less than 2-fold) than R-isoflurane. The X-ray crystallographic structure of the immunological target, leukocyte function-associated antigen-1 (LFA-1) with racemic isoflurane suggested that only...

Wavelength is one of the most important resources in Wavelength Division Multiplexing(WDM) networks. In optical routing, we are given a set of communication paths (or ligthpaths) in a WDM network and we must assign a wavelength to each path so that paths sharing a link must be assigned with different wavelengths. By properly choosing a set of nodes that are equipped with wavelength converters, ...

LFA-1 activation plays a major role in reducing the velocity of rolling leukocytes and causing firm adhesion to the endothelium. The signaling cascades that cause LFA-1 activation during this process have been described through mostly correlative experiments, but the precise occurrence and location of LFA-1 activation in response to specific signals has not been directly shown. Tim Springer’s g...

The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones polynomial and arise in Witten-Chern-Simons theory. The braiding and fusion of anyonic excitations in quantum Hall electron liquids and 2D-magnets are modeled by modular functors, opening a new possibility...

In a recent paper Richards and Zheng compute the determinant of a matrix whose entries are given by beta-type integrals, thereby generalising an earlier result by Dixon and Varchenko. They then use their result to obtain a generalisation of the famous Selberg integral. In this note we point out that the Selberg-generalisation of Richards and Zheng is a special case of an integral over Jack poly...