Quasirandomness in hypergraphs

An $n$-vertex graph $G$ of edge density $p$ is considered to be quasirandom if it shares several important properties with the random graph $G(n,p)$. A well-known theorem of Chung, Graham and Wilson states that many such `typical' properties are asymptotically equivalent and, thus, a graph $G$ possessing one such property automatically satisfies the others. In recent years, work in this area has focused on uncovering more quasirandom graph properties and on extending the known results to other discrete structures. In the context of hypergraphs, however, one may consider several different notions of quasirandomness. A complete description of these notions has been provided recently by Towsner, who proved several central equivalences using an analytic framework. We give short and purely combinatorial proofs of the main equivalences in Towsner's result.Comment: 19 page

Large-scale albuminuria screen for nephropathy models in chemically induced mouse mutants

Background/Aim: Phenotype-driven screening of a great pool of randomly mutant mice and subsequent selection of animals showing symptoms equivalent to human kidney diseases may result in the generation of novel suitable models for the study of the pathomechanisms and the identification of genes involved in kidney dysfunction. Methods: We carried out a large-scale analysis of ethylnitrosourea (ENU)-induced mouse mutants for albuminuria by using qualitative SDS-polyacrylamide gel electrophoresis. Results: The primary albuminuria screen preceded the comprehensive phenotypic mutation analysis in a part of the mice of the Munich ENU project to avoid loss of mutant animals as a consequence of prolonged suffering from severe nephropathy. The primary screen detected six confirmed phenotypic variants in 2,011 G1 animals screened for dominant mutations and no variant in 48 G3 pedigrees screened for recessive mutations. Further breeding experiments resulted in two lines showing a low phenotypic penetrance of albuminuria. The secondary albuminuria screen was carried out in mutant lines which were established in the Munich ENU project without preceding primary albuminuria analysis. Two lines showing increased plasma urea levels were chosen to clarify if severe kidney lesions are involved in the abnormal phenotype. This analysis revealed severe albuminuria in mice which are affected by a recessive mutation leading to increased plasma urea and cholesterol levels. Conclusion: Thus, the phenotypic selection of ENU-induced mutants according to the parameter proteinuria in principle demonstrates the feasibility to identify nephropathy phenotypes in ENU-mutagenized mice. Copyright (C) 2005 S. Karger AG, Basel

Minimum and maximum against k lies

A neat 1972 result of Pohl asserts that [3n/2]-2 comparisons are sufficient, and also necessary in the worst case, for finding both the minimum and the maximum of an n-element totally ordered set. The set is accessed via an oracle for pairwise comparisons. More recently, the problem has been studied in the context of the Renyi-Ulam liar games, where the oracle may give up to k false answers. For large k, an upper bound due to Aigner shows that (k+O(\sqrt{k}))n comparisons suffice. We improve on this by providing an algorithm with at most (k+1+C)n+O(k^3) comparisons for some constant C. The known lower bounds are of the form (k+1+c_k)n-D, for some constant D, where c_0=0.5, c_1=23/32=0.71875, and c_k=\Omega(2^{-5k/4}) as k goes to infinity.Comment: 11 pages, 3 figure

Emerging Role of Nuclear Medicine in Oral and Maxillofacial Surgery

During the past several years, nuclear medicine has emerged as one of the most useful imaging studies in oral and maxillofacial surgery, not only in diagnosis and staging but also in the management plan and follow-up protocols of many cancer or inflammatory diseases. Nuclear medicine has in addition a special place in treating several benign and malignant diseases. The practicing maxillofacial surgeon’s knowledge of nuclear medicine capabilities and advantages and disadvantages of each modality is crucial in his or her daily work. The purpose of this chapter is to clarify the important role of nuclear medicine in diagnosis and treatment of oral and maxillofacial region pathologies as well as its indications and limitations in the daily practice of the oral and maxillofacial surgeon

Organized Current Patterns in Disordered Conductors

We present a general theory of current deviations in straight current carrying wires with random imperfections, which quantitatively explains the recent observations of organized patterns of magnetic field corrugations above micron-scale evaporated wires. These patterns originate from the most efficient electron scattering by Fourier components of the wire imperfections with wavefronts along the $\pm 45^{\circ}$ direction. We show that long range effects of surface or bulk corrugations are suppressed for narrow wires or wires having an electrically anisotropic resistivity

Imaging geometry through dynamics: the observable representation

For many stochastic processes there is an underlying coordinate space, $V$, with the process moving from point to point in $V$ or on variables (such as spin configurations) defined with respect to $V$. There is a matrix of transition probabilities (whether between points in $V$ or between variables defined on $V$) and we focus on its ``slow'' eigenvectors, those with eigenvalues closest to that of the stationary eigenvector. These eigenvectors are the ``observables,'' and they can be used to recover geometrical features of $V$