Resonances for "large" ergodic systems in one dimension: a review

The present note reviews recent results on resonances for one-dimensional quantum ergodic systems constrained to a large box. We restrict ourselves to one dimensional models in the discrete case. We consider two type of ergodic potentials on the half-axis, periodic potentials and random potentials. For both models, we describe the behavior of the resonances near the real axis for a large typical sample of the potential. In both cases, the linear density of their real parts is given by the density of states of the full ergodic system. While in the periodic case, the resonances distribute on a nice analytic curve (once their imaginary parts are suitably renormalized), In the random case, the resonances (again after suitable renormalization of both the real and imaginary parts) form a two dimensional Poisson cloud

Cluster and virial expansions for the multi-species tonks gas

We consider a mixture of non-overlapping rods of different lengths ℓk moving in R or Z. Our main result are necessary and sufficient convergence criteria for the expansion of the pressure in terms of the activities zk and the densities ρk. This provides an explicit example against which to test known cluster expansion criteria, and illustrates that for non-negative interactions, the virial expansion can converge in a domain much larger than the activity expansion. In addition, we give explicit formulas that generalize the well-known relation between non-overlapping rods and labelled rooted trees. We also prove that for certain choices of the activities, the system can undergo a condensation transition akin to that of the zero-range process. The key tool is a fixed point equation for the pressure

A Survey on the Krein-von Neumann Extension, the corresponding Abstract Buckling Problem, and Weyl-Type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains

In the first (and abstract) part of this survey we prove the unitary equivalence of the inverse of the Krein--von Neumann extension (on the orthogonal complement of its kernel) of a densely defined, closed, strictly positive operator, $S\geq \varepsilon I_{\mathcal{H}}$ for some $\varepsilon >0$ in a Hilbert space $\mathcal{H}$ to an abstract buckling problem operator. This establishes the Krein extension as a natural object in elasticity theory (in analogy to the Friedrichs extension, which found natural applications in quantum mechanics, elasticity, etc.). In the second, and principal part of this survey, we study spectral properties for $H_{K,\Omega}$, the Krein--von Neumann extension of the perturbed Laplacian $-\Delta+V$ (in short, the perturbed Krein Laplacian) defined on $C^\infty_0(\Omega)$, where $V$ is measurable, bounded and nonnegative, in a bounded open set $\Omega\subset\mathbb{R}^n$ belonging to a class of nonsmooth domains which contains all convex domains, along with all domains of class $C^{1,r}$, $r>1/2$.Comment: 68 pages. arXiv admin note: extreme text overlap with arXiv:0907.144

Advanced backcross QTL mapping of resistance to Fusarium head blight and plant morphological traits in a Triticum macha × T. aestivum population

While many reports on genetic analysis of Fusarium head blight (FHB) resistance in bread wheat have been published during the past decade, only limited information is available on FHB resistance derived from wheat relatives. In this contribution, we report on the genetic analysis of FHB resistance derived from Triticum macha (Georgian spelt wheat). As the origin of T. macha is in the Caucasian region, it is supposed that its FHB resistance differs from other well-investigated resistance sources. To introduce valuable alleles from the landrace T. macha into a modern genetic background, we adopted an advanced backcross QTL mapping scheme. A backcross-derived recombinant-inbred line population of 321 BC2F3 lines was developed from a cross of T. macha with the Austrian winter wheat cultivar Furore. The population was evaluated for Fusarium resistance in seven field experiments during four seasons using artificial inoculations. A total of 300 lines of the population were genetically fingerprinted using SSR and AFLP markers. The resulting linkage map covered 33 linkage groups with 560 markers. Five novel FHB-resistance QTL, all descending from T. macha, were found on four chromosomes (2A, 2B, 5A, 5B). Several QTL for morphological and developmental traits were mapped in the same population, which partly overlapped with FHB-resistance QTL. Only the 2BL FHB-resistance QTL co-located with a plant height QTL. The largest-effect FHB-resistance QTL in this population mapped at the spelt-type locus on chromosome 5A and was associated with the wild-type allele q, but it is unclear whether q has a pleiotropic effect on FHB resistance or is closely linked to a nearby resistance QTL

A systematic review of the incidence of schizophrenia: the distribution of rates and the influence of sex, urbanicity, migrant status and methodology

BACKGROUND: Understanding variations in the incidence of schizophrenia is a crucial step in unravelling the aetiology of this group of disorders. The aims of this review are to systematically identify studies related to the incidence of schizophrenia, to describe the key features of these studies, and to explore the distribution of rates derived from these studies. METHODS: Studies with original data related to the incidence of schizophrenia (published 1965–2001) were identified via searching electronic databases, reviewing citations and writing to authors. These studies were divided into core studies, migrant studies, cohort studies and studies based on Other Special Groups. Between- and within-study filters were applied in order to identify discrete rates. Cumulative plots of these rates were made and these distributions were compared when the underlying rates were sorted according to sex, urbanicity, migrant status and various methodological features. RESULTS: We identified 100 core studies, 24 migrant studies, 23 cohort studies and 14 studies based on Other Special Groups. These studies, which were drawn from 33 countries, generated a total of 1,458 rates. Based on discrete core data for persons (55 studies and 170 rates), the distribution of rates was asymmetric and had a median value (10%–90% quantile) of 15.2 (7.7–43.0) per 100,000. The distribution of rates was significantly higher in males compared to females; the male/female rate ratio median (10%–90% quantile) was 1.40 (0.9–2.4). Those studies conducted in urban versus mixed urban-rural catchment areas generated significantly higher rate distributions. The distribution of rates in migrants was significantly higher compared to native-born; the migrant/native-born rate ratio median (10%–90% quantile) was 4.6 (1.0–12.8). Apart from the finding that older studies reported higher rates, other study features were not associated with significantly different rate distributions (e.g. overall quality, methods related to case finding, diagnostic confirmation and criteria, the use of age-standardization and age range). CONCLUSIONS: There is a wealth of data available on the incidence of schizophrenia. The width and skew of the rate distribution, and the significant impact of sex, urbanicity and migrant status on these distributions, indicate substantial variations in the incidence of schizophrenia

Sufficient Conditions for Uniform Bounds in Abstract Polymer Systems and Explorative Partition Schemes

We present several new sufficient conditions for uniform boundedness of the reduced correlations and free energy of an abstract polymer system in a complex multidisc around zero fugacity. They resolve a discrepancy between two incomparable and previously known extensions of Dobrushin’s classic condition. All conditions arise from an extension of the tree-operator approach introduced by Fernández and Procacci combined with a novel family of partition schemes of the spanning subgraph complex of a cluster. The key technique is the increased transfer of structural information from the partition scheme to a tree-operator on an enhanced space

Nash equilibria of Cauchy-random zero-sum and coordination matrix games

Nash equilibrium, Support size, Cauchy distribution, Zero-sum game, Coordination game,