Spectral Synthesis of Jordan Operators

AbstractThe purpose of this paper is to extend results of J. Wermer (1952, Proc. Amer. Math. Soc.3, 270–277), L. Brown et al. (1960, Trans. Amer. Math. Soc.96, 162–183), and D. Sarason (1972, J. Reine Agnew. Math.252, 1–15; 1966, Pacific J. Math.17, 511–517) on spectral subspaces of diagonalizable operators on separable complex Hilbert space to the class of so-called Jordan operators or infinite direct sums of Jordan cells

Mate Choice and the Evolutionary Stability of a Fixed Threshold in a Sequential Search Strategy

The sequential search strategy is a prominent model of searcher behavior, derived as a rule by which females might sample and choose a mate from a distribution of prospective partners. The strategy involves a threshold criterion against which prospective mates are evaluated. The optimal threshold depends on the attributes of prospective mates, which are likely to vary across generations or within the lifetime of searchers due to stochastic environmental events. The extent of this variability and the cost to acquire information on the distribution of the quality of prospective mates determine whether a learned or environmentally canalized threshold is likely to be favored. In this paper, we determine conditions on cross-generational perturbations of the distribution of male phenotypes that allow for the evolutionary stability of an environmentally canalized threshold. In particular, we derive conditions under which there is a genetically determined threshold that is optimal over an evolutionary time scale in comparison to any other unlearned threshold. These considerations also reveal a simple algorithm by which the threshold could be learned

Functional annotations of diabetes nephropathy susceptibility loci through analysis of genome-wide renal gene expression in rat models of diabetes mellitus

<p>Abstract</p> <p>Background</p> <p>Hyperglycaemia in diabetes mellitus (DM) alters gene expression regulation in various organs and contributes to long term vascular and renal complications. We aimed to generate novel renal genome-wide gene transcription data in rat models of diabetes in order to test the responsiveness to hyperglycaemia and renal structural changes of positional candidate genes at selected diabetic nephropathy (DN) susceptibility loci.</p> <p>Methods</p> <p>Both Affymetrix and Illumina technologies were used to identify significant quantitative changes in the abundance of over 15,000 transcripts in kidney of models of spontaneous (genetically determined) mild hyperglycaemia and insulin resistance (Goto-Kakizaki-GK) and experimentally induced severe hyperglycaemia (Wistar-Kyoto-WKY rats injected with streptozotocin [STZ]).</p> <p>Results</p> <p>Different patterns of transcription regulation in the two rat models of diabetes likely underlie the roles of genetic variants and hyperglycaemia severity. The impact of prolonged hyperglycaemia on gene expression changes was more profound in STZ-WKY rats than in GK rats and involved largely different sets of genes. These included genes already tested in genetic studies of DN and a large number of protein coding sequences of unknown function which can be considered as functional and, when they map to DN loci, positional candidates for DN. Further expression analysis of rat orthologs of human DN positional candidate genes provided functional annotations of known and novel genes that are responsive to hyperglycaemia and may contribute to renal functional and/or structural alterations.</p> <p>Conclusion</p> <p>Combining transcriptomics in animal models and comparative genomics provides important information to improve functional annotations of disease susceptibility loci in humans and experimental support for testing candidate genes in human genetics.</p

Mate choice decisions by searchers

For more than two decades rudimentary versions of the fixed sample and sequential search strategies have provided the primary theoretical foundation for the study of mate choice decisions by searchers. The theory that surrounds these models has expanded markedly over this time period. In this paper, we review and extend results derived from these models, with a focus on the empirical analysis of searcher behavior. The basic models are impractical for empirical purposes because they rely on the assumption that searchers—and, for applied purposes, researchers—assess prospective mates based on their quality, the fitness consequences of mate choice decisions. Here we expound versions of the models that are more empirically useful, reformulated to reflect decisions based on male phenotypic characters. For some organisms, it may be possible to use preference functions to derive predictions from the reformulated models and thereby avoid difficulties associated with the measurement of male quality per se. But predictions derived from the two models are difficult to differentiate empirically, regardless of how the models are formulated. Here we develop ideas that illustrate how this goal might be accomplished. In addition, we clarify how the variability of male quality should be evaluated and we extend what is known about how this variability influences searcher behavior under each model. More general difficulties associated with the empirical study of mate choice decisions by searchers are also discussed [Current Zoology 59 (2): 184–199, 2013]