Limit operators, collective compactness, and the spectral theory of infinite matrices

In the first half of this memoir we explore the interrelationships between the abstract theory of limit operators (see e.g. the recent monographs of Rabinovich, Roch and Silbermann (2004) and Lindner (2006)) and the concepts and results of the generalised collectively compact operator theory introduced by Chandler-Wilde and Zhang (2002). We build up to results obtained by applying this generalised collectively compact operator theory to the set of limit operators of an operator (its operator spectrum). In the second half of this memoir we study bounded linear operators on the generalised sequence space , where and is some complex Banach space. We make what seems to be a more complete study than hitherto of the connections between Fredholmness, invertibility, invertibility at infinity, and invertibility or injectivity of the set of limit operators, with some emphasis on the case when the operator is a locally compact perturbation of the identity. Especially, we obtain stronger results than previously known for the subtle limiting cases of and . Our tools in this study are the results from the first half of the memoir and an exploitation of the partial duality between and and its implications for bounded linear operators which are also continuous with respect to the weaker topology (the strict topology) introduced in the first half of the memoir. Results in this second half of the memoir include a new proof that injectivity of all limit operators (the classic Favard condition) implies invertibility for a general class of almost periodic operators, and characterisations of invertibility at infinity and Fredholmness for operators in the so-called Wiener algebra. In two final chapters our results are illustrated by and applied to concrete examples. Firstly, we study the spectra and essential spectra of discrete Schrödinger operators (both self-adjoint and non-self-adjoint), including operators with almost periodic and random potentials. In the final chapter we apply our results to integral operators on .

Mapping of composite hadrons into elementary hadrons and effective hadronic Hamiltonians

A mapping technique is used to derive in the context of constituent quark models effective Hamiltonians that involve explicit hadron degrees of freedom. The technique is based on the ideas of mapping between physical and ideal Fock spaces and shares similarities with the quasiparticle method of Weinberg. Starting with the Fock-space representation of single-hadron states, a change of representation is implemented by a unitary transformation such that composites are redescribed by elementary Bose and Fermi field operators in an extended Fock space. When the unitary transformation is applied to the microscopic quark Hamiltonian, effective, hermitian Hamiltonians with a clear physical interpretation are obtained. Applications and comparisons with other composite-particle formalisms of the recent literature are made using the nonrelativistic quark model. (C) 1998 Academic Press.

Anderson-like Transition for a Class of Random Sparse Models in d >= 2 Dimensions

We show that the Kronecker sum of d >= 2 copies of a random one-dimensional sparse model displays a spectral transition of the type predicted by Anderson, from absolutely continuous around the center of the band to pure point around the boundaries. Possible applications to physics and open problems are discussed briefly.

On degeneracy and invariances of random fields paths with applications in Gaussian process modelling

We study pathwise invariances and degeneracies of random fields with motivating applications in Gaussian process modelling. The key idea is that a number of structural properties one may wish to impose a priori on functions boil down to degeneracy properties under well-chosen linear operators. We first show in a second order set-up that almost sure degeneracy of random field paths under some class of linear operators defined in terms of signed measures can be controlled through the two first moments. A special focus is then put on the Gaussian case, where these results are revisited and extended to further linear operators thanks to state-of-the-art representations. Several degeneracy properties are tackled, including random fields with symmetric paths, centred paths, harmonic paths, or sparse paths. The proposed approach delivers a number of promising results and perspectives in Gaussian process modelling. In a first numerical experiment, it is shown that dedicated kernels can be used to infer an axis of symmetry. Our second numerical experiment deals with conditional simulations of a solution to the heat equation, and it is found that adapted kernels notably enable improved predictions of non-linear functionals of the field such as its maximum.

Knowledge beliefs and attitudes of squash venue operators relating to use of protective eyewear

Sports venues are in a position to potentially influence the safety practices of their patrons. This study examined the knowledge, beliefs and attitudes of venue operators that could influence the use of protective eyewear by squash players. A 50% random sample of all private and public squash venues affiliated with the Victorian Squash Federation in metropolitan Melbourne was selected. Face-to-face interviews were conducted with 15 squash venue operators during August 2001. Interviews were transcribed and content and thematic analyses were performed. The content of the interviews covered five topics: (1) overall injury risk perception, (2) eye injury occurrence, (3) knowledge, behaviors, attitudes and beliefs associated with protective eyewear, (4) compulsory protective eyewear and (5) availability of protective eyewear at venues. Venue operators were mainly concerned with the severe nature of eye injuries, rather than the relatively low incidence of these injuries. Some venue operators believed that players should wear any eyewear, rather than none at all, and believed that more players should use protective eyewear. Generally, they did not believe that players with higher levels of experience and expertise needed to wear protective eyewear when playing. Only six venues had at least one type of eyewear available for players to hire or borrow or to purchase. Operators expressed a desire to be informed about correct protective eyewear. Appropriate protective eyewear is not readily available at squash venues. Better-informed venue operators may be more likely to provide suitable protective eyewear.

On Multi-Dimensional Random Walk Models Approximating Symmetric Space-Fractional Diffusion Processes

Mathematics Subject Classification: 26A33, 47B06, 47G30, 60G50, 60G52, 60G60.

On The Cauchy Problem for Non Effectively Hyperbolic Operators, The Ivrii-Petkov-Hörmander Condition and the Gevrey Well Posedness

2000 Mathematics Subject Classification: 35L15, Secondary 35L30.

Elementary classroom teachers' knowledge of tort liability for negligence

The purpose of this research study was to investigate the legal knowledge of Florida's public elementary classroom teachers in the area of tort liability for negligence. A second purpose of the study was to assess the knowledge of school law in the area of negligence according to specific variables to determine if significant differences in knowledge existed among groups of teachers classified by: years of teaching experience, whether or not teachers took a school law course or inservice, college degree held and whether or not teachers had administrative experience. A validated survey instrument consisting of 22 scenarios based on decided court cases in the United States was utilized. These cases included court decisions ranging from 1938–1994, and represented the categories of duty and standard of care, proper instruction, proper supervision, proper maintenance, field trips, and post-injury treatment. ^ A random sample of 420 elementary classroom teachers were sent the survey instrument to complete, and a total of 309 surveys were returned producing a return rate of 77%. The results of this research study revealed that the overall level of legal knowledge of public elementary classroom teachers in the State of Florida produced a mean percent correct of 53%. The range of scores varied from 18%–82%, with the approximate average of correct answers of 12 out of 22. The category of proper instruction produced the lowest mean percent correct of 35%, and the area of post-injury treatment yielded the highest mean percent correct of 78%. ^ The findings of this study emphasize the necessity of preparing teachers regarding their legal rights, duties and responsibilities. The need for teachers to receive training at the preservice and inservice levels has become clear by this study. ^

Biased Random-key Genetic Algorithms For The Winner Determination Problem In Combinatorial Auctions.

Abstract In this paper, we address the problem of picking a subset of bids in a general combinatorial auction so as to maximize the overall profit using the first-price model. This winner determination problem assumes that a single bidding round is held to determine both the winners and prices to be paid. We introduce six variants of biased random-key genetic algorithms for this problem. Three of them use a novel initialization technique that makes use of solutions of intermediate linear programming relaxations of an exact mixed integer-linear programming model as initial chromosomes of the population. An experimental evaluation compares the effectiveness of the proposed algorithms with the standard mixed linear integer programming formulation, a specialized exact algorithm, and the best-performing heuristics proposed for this problem. The proposed algorithms are competitive and offer strong results, mainly for large-scale auctions.

Synthesis and structural characterization of block and random low molecular weight copolymers composed of L-lactic acid and isosorbide succinate moieties

Isosorbide succinate moieties were incorporated into poly(L-lactide) (PLLA) backbone in order to obtain a new class of biodegradable polymer with enhanced properties. This paper describes the synthesis and characterization of four types of low molecular weight copolymers. Copolymer I was obtained from monomer mixtures of L-lactide, isosorbide, and succinic anhydride; II from oligo(L-lactide) (PLLA), isosorbide, and succinic anhydride; III from oligo(isosorbide succinate) (PIS) and L-lactide; and IV from transesterification reactions between PLLA and PIS. MALDI-TOFMS and 13C-NMR analyses gave evidence that co-oligomerization was successfully attained in all cases. The data suggested that the product I is a random co-oligomer and the products II-IV are block co-oligomers.

Consumo e comportamento alimentar entre adolescentes brasileiros: Pesquisa Nacional de Saúde do Escolar (PeNSE), 2009

O objetivo deste artigo é descrever características de consumo e comportamento alimentar de adolescentes brasileiros e sua associação com fatores sociodemográficos. Estudou-se, em 2009, amostra representativa de alunos do 9º ano do ensino fundamental de escolas públicas e privadas das 26 capitais brasileiras e do Distrito Federal. Utilizou-se questionário autoaplicável sobre atributos sociodemográficos, consumo e comportamento alimentar, entre outros. Estimativas dos indicadores construídos foram apresentadas para o total da população e por sexo. A associação de cada um dos indicadores com variáveis sociodemográficas foi examinada por meio de regressão logística. A maioria dos adolescentes consumia regularmente feijão (62,6%), leite (53,6%) e guloseimas (50,9%), realizava pelo menos o almoço ou o jantar com a mãe ou responsável (62,6%) e comia assistindo televisão ou estudando (50,9%). Em geral, as meninas estavam mais expostas a práticas alimentares não desejáveis, e o melhor nível socioeconômico associou-se a maiores prevalências dos indicadores estudados. Os resultados revelaram consumo regular dos marcadores de alimentação não saudável e consumo inferior ao recomendado dos de alimentação saudável, apontando a necessidade de ações de promoção de saúde dirigidas a jovens.

Influence of memory in deterministic walks in random media: Analytical calculation within a mean-field approximation

Consider a random medium consisting of N points randomly distributed so that there is no correlation among the distances separating them. This is the random link model, which is the high dimensionality limit (mean-field approximation) for the Euclidean random point structure. In the random link model, at discrete time steps, a walker moves to the nearest point, which has not been visited in the last mu steps (memory), producing a deterministic partially self-avoiding walk (the tourist walk). We have analytically obtained the distribution of the number n of points explored by the walker with memory mu=2, as well as the transient and period joint distribution. This result enables us to explain the abrupt change in the exploratory behavior between the cases mu=1 (memoryless walker, driven by extreme value statistics) and mu=2 (walker with memory, driven by combinatorial statistics). In the mu=1 case, the mean newly visited points in the thermodynamic limit (N >> 1) is just < n >=e=2.72... while in the mu=2 case, the mean number < n > of visited points grows proportionally to N(1/2). Also, this result allows us to establish an equivalence between the random link model with mu=2 and random map (uncorrelated back and forth distances) with mu=0 and the abrupt change between the probabilities for null transient time and subsequent ones.

Effect of Low-Level Laser Therapy on Malondialdehyde Concentration in Random Cutaneous Flap Viability

Objective: The aim of this study was to assess the effects of 830 and 670 nm laser on malondialdehyde (MDA) concentration in random skin-flap survival. Background Data: Low-level laser therapy (LLLT) has been reported to be successful in stimulating the formation of new blood vessels and activating superoxide-dismutase delivery, thus helping the inhibition of free-radical action and consequently reducing necrosis. Materials and Methods: Thirty Wistar rats were used and divided into three groups, with 10 rats in each one. A random skin flap was raised on the dorsum of each animal. Group 1 was the control group; group 2 received 830 nm laser radiation; and group 3 was submitted to 670 nm laser radiation. The animals underwent laser therapy with 36 J/cm(2) energy density immediately after surgery and on the 4 days subsequent to surgery. The application site of the laser radiation was 1 point, 2.5 cm from the flap's cranial base. The percentage of the skin-flap necrosis area was calculated 7 days postoperative using the paper-template method, and a skin sample was collected immediately after as a way of determining the MDA concentration. Results: Statistically significant differences were found between the necrosis percentages, with higher values seen in group 1 compared with groups 2 and 3. Groups 2 and 3 did not present statistically significant differences (p > 0.05). Group 3 had a lower concentration of MDA values compared to the control group (p < 0.05). Conclusion: LLLT was effective in increasing the random skin-flap viability in rats, and the 670 nm laser was efficient in reducing the MDA concentration.

Multi-trait and random regression mature weight heritability and breeding value estimates in Nelore cattle

Mature weight breeding values were estimated using a multi-trait animal model (MM) and a random regression animal model (RRM). Data consisted of 82 064 weight records from 8 145 animals, recorded from birth to eight years of age. Weights at standard ages were considered in the MM. All models included contemporary groups as fixed effects, and age of dam (linear and quadratic effects) and animal age as covariates. In the RRM, mean trends were modelled through a cubic regression on orthogonal polynomials of animal age and genetic maternal and direct and maternal permanent environmental effects were also included as random. Legendre polynomials of orders 4, 3, 6 and 3 were used for animal and maternal genetic and permanent environmental effects, respectively, considering five classes of residual variances. Mature weight (five years) direct heritability estimates were 0.35 (MM) and 0.38 (RRM). Rank correlation between sires' breeding values estimated by MM and RRM was 0.82. However, selecting the top 2% (12) or 10% (62) of the young sires based on the MM predicted breeding values, respectively 71% and 80% of the same sires would be selected if RRM estimates were used instead. The RRM modelled the changes in the (co) variances with age adequately and larger breeding value accuracies can be expected using this model.

Random X Inactivation and Extensive Mosaicism in Human Placenta Revealed by Analysis of Allele-Specific Gene Expression along the X Chromosome

Imprinted inactivation of the paternal X chromosome in marsupials is the primordial mechanism of dosage compensation for X-linked genes between females and males in Therians. In Eutherian mammals, X chromosome inactivation (XCI) evolved into a random process in cells from the embryo proper, where either the maternal or paternal X can be inactivated. However, species like mouse and bovine maintained imprinted XCI exclusively in extraembryonic tissues. The existence of imprinted XCI in humans remains controversial, with studies based on the analyses of only one or two X-linked genes in different extraembryonic tissues. Here we readdress this issue in human term placenta by performing a robust analysis of allele-specific expression of 22 X-linked genes, including XIST, using 27 SNPs in transcribed regions. We show that XCI is random in human placenta, and that this organ is arranged in relatively large patches of cells with either maternal or paternal inactive X. In addition, this analysis indicated heterogeneous maintenance of gene silencing along the inactive X, which combined with the extensive mosaicism found in placenta, can explain the lack of agreement among previous studies. Our results illustrate the differences of XCI mechanism between humans and mice, and highlight the importance of addressing the issue of imprinted XCI in other species in order to understand the evolution of dosage compensation in placental mammals.