Non-Deterministic Closure Theory and Universal Arrows

Traditional closure theory discusses the closure operations on orders with graph-theoretic methods, or the reflectors on skeletal categories with category-theoretic methods. Both approaches are confined, like most of classical mathematics, to total and deterministic operations. So traditional closure theory makes it possible to define the semantics of the while-do commands only for terminating and deterministic programming. This paper outlines a closure theory for relations which transcend totality and determinism. For the sake of conciseness, the language used is that of graph theory but the methods are category-theoretic and some hints are offered for a possible translation into the language of category theory. Our basic idea is that closure relations consist of universal arrows in the sense of category theory. The new closure theory is appropriate for defining a semantics of the while-do commands both for terminating, deterministic programming and for non-terminating, non-deterministic programming.     

Universal abelian covers of superisolated singularities

We give explicit examples of Gorenstein surface singularities with integral homology sphere link, which are not complete intersections. Their existence was shown by Luengo–Velasco, Melle–Hernández and Némethi, thereby providing counterexamples to the universal abelian covering conjecture of Neumann and Wahl (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Reader's Guide to Gacs's “Positive Rates” Paper

Peter Gacs's monograph, which follows this article, provides a counterexample to the important Positive Rates Conjecture. This conjecture, which arose in the late 1960's, was based on very plausible arguments, some of which come from statistical mechanics. During the long gestation period of the Gacs example, there has been a great deal of skepticism about the validity of his work. The construction and verification of Gacs's counterexample are unavoidably complex, and as a consequence, his paper is quite lengthy. But because of the novelty of the techniques and the significance of the result, his work deserves to become widely known. This reader's guide is intended both as a cheap substitute for reading the whole thing, as well as a warm-up for those who want to plumb its depths.     

Some geometric and dynamical properties of the Urysohn space

This is a survey article about the geometry and dynamical properties of the Urysohn space. Most of the results presented here are part of the author's Ph.D. thesis and were published in the articles [J. Melleray, Stabilizers of closed sets in the Urysohn space, Fund. Math. 189 (1) (2006) 53-60; J. Melleray, Compact metrizable groups are isometry groups of compact metric spaces, Proc. Amer. Math. Soc. 136 (4) (2008) 1451; J. Melleray, On the geometry of Urysohn's universal metric space, Topology Appl. 154 (2007) 384-403]; a few results are new, most notably the fact that Iso(U) is not divisible.     

Equilibrium folding and unfolding dynamics to reveal detailed free energy landscape of src SH3 protein by magnetic tweezers

Src SH3 protein domain is a typical two-state protein which has been confirmed by research of denaturant-induced unfolding dynamics. Force spectroscopy experiments by optical tweezers and atomic force microscopy have measured the force-dependent unfolding rates with different kinds of pulling geometry. However, the equilibrium folding and unfolding dynamics at constant forces has not been reported. Here, using stable magnetic tweezers, we performed equilibrium folding and unfolding dynamic measurement and force-jump measurement of src SH3 domain with tethering points at its N-and C-termini. From the obtained force-dependent transition rates, a detailed two-state free energy landscape of src SH3 protein is constructed with quantitative information of folding free energy, transition state barrier height and position,which exemplifies the capability of magnetic tweezers to study protein folding and unfolding dynamics.     

SOME DYNAMICAL PROPERTIES OF THE UNIVERSAL UNFOLDING OF PITCHFORK

From the point of view of dynamics,the phenomenon of mode jumpingin the imperfect pitchfork problem is discussed.The dynamical mechanism of modeljumping of structures,such as plate and shell,that is brought about by the extremurninstability,is explained.Finally,we give numerical simulation to show the validity ofour results.     

On random frequent universality

We give a probabilistic construction of frequently hypercyclic or universal entire functions using Birkhoff?s ergodic Theorem. We apply the same ideas to construct random frequently universal vectors for the polynomials of the weighted backward shift on the classical real or complex ?^p${?}^p$ space.     

Overlap Cycles for Steiner Quadruple Systems

Steiner quadruple systems are set systems in which every triple is contained in a unique quadruple. It is well known that Steiner quadruple systems of order v, or SQS(v), exist if and only if . Universal cycles, introduced by Chung, Diaconis, and Graham in 1992, are a type of cyclic Gray code. Overlap cycles are generalizations of universal cycles that were introduced in 2010 by Godbole, et al. Using Hanani's SQS constructions, we show that for every with there exists an SQS(v) that admits a 1‐overlap cycle.     

Developing an algorithm for compression, multiplexing and enhancement of multiple images

Image compression is one of the important fields that has useful applications in data storage and transmission. In this research a new algorithm is developed and tested for multiple-image compression and enhancement. The algorithm, in addition, is applied to multiple noisy images. Also, the effect of compression ratio on the peak signal to noise ratio (PSNR) is explored by applying different compression ratios. The developed algorithm gives good compression and noise immunity. It can be used for storage/transmission of encrypted and compressed information.