Nonnegative trigonometric polynomials

An extremal problem for the coefficients of sine polynomials, which are nonnegative in [0,π] , posed and discussed by Rogosinski and Szego is under consideration. An analog of the Fejér-Riesz representation of nonnegative general trigonometric and cosine polynomials is proved for nonnegative sine polynomials. Various extremal sine polynomials for the problem of Rogosinski and Szego are obtained explicitly. Associated cosine polynomials k n (θ) are constructed in such a way that { k n (θ) } are summability kernels. Thus, the L p , pointwise and almost everywhere convergence of the corresponding convolutions, is established. © 2002 Springer-Verlag New York Inc.

Polinômios irredutíveis: critérios e aplicações

Pós-graduação em Matemática em Rede Nacional - IBILCE

Zeros of classical orthogonal polynomials of a discrete variable

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Future value based single assignment program representations and optimizations

An optimizing compiler internal representation fundamentally affects the clarity, efficiency and feasibility of optimization algorithms employed by the compiler. Static Single Assignment (SSA) as a state-of-the-art program representation has great advantages though still can be improved. This dissertation explores the domain of single assignment beyond SSA, and presents two novel program representations: Future Gated Single Assignment (FGSA) and Recursive Future Predicated Form (RFPF). Both FGSA and RFPF embed control flow and data flow information, enabling efficient traversal program information and thus leading to better and simpler optimizations. We introduce future value concept, the designing base of both FGSA and RFPF, which permits a consumer instruction to be encountered before the producer of its source operand(s) in a control flow setting. We show that FGSA is efficiently computable by using a series T1/T2/TR transformation, yielding an expected linear time algorithm for combining together the construction of the pruned single assignment form and live analysis for both reducible and irreducible graphs. As a result, the approach results in an average reduction of 7.7%, with a maximum of 67% in the number of gating functions compared to the pruned SSA form on the SPEC2000 benchmark suite. We present a solid and near optimal framework to perform inverse transformation from single assignment programs. We demonstrate the importance of unrestricted code motion and present RFPF. We develop algorithms which enable instruction movement in acyclic, as well as cyclic regions, and show the ease to perform optimizations such as Partial Redundancy Elimination on RFPF.

Integrated fossil and molecular data reconstruct bat echolocation

Molecular and morphological data have important roles in illuminating evolutionary history. DNA data often yield well resolved phylogenies for living taxa, but are generally unattainable for fossils. A distinct advantage of morphology is that some types of morphological data may be collected for extinct and extant taxa. Fossils provide a unique window on evolutionary history and may preserve combinations of primitive and derived characters that are not found in extant taxa. Given their unique character complexes, fossils are critical in documenting sequences of character transformation over geologic time and may elucidate otherwise ambiguous patterns of evolution that are not revealed by molecular data alone. Here, we employ a methodological approach that allows for the integration of molecular and paleontological data in deciphering one of the most innovative features in the evolutionary history of mammals—laryngeal echolocation in bats. Molecular data alone, including an expanded data set that includes new sequences for the A2AB gene, suggest that microbats are paraphyletic but do not resolve whether laryngeal echolocation evolved independently in different microbat lineages or evolved in the common ancestor of bats and was subsequently lost in megabats. When scaffolds from molecular phylogenies are incorporated into parsimony analyses of morphological characters, including morphological characters for the Eocene taxa Icaronycteris, Archaeonycteris, Hassianycteris, and Palaeochiropteryx, the resulting trees suggest that laryngeal echolocation evolved in the common ancestor of fossil and extant bats and was subsequently lost in megabats. Molecular dating suggests that crown-group bats last shared a common ancestor 52 to 54 million years ago.

Flightless brown kiwis of New Zealand possess extremely subdivided population structure and cryptic species like small mammals.

Using allozymes and mtDNA sequences from the cytochrome b gene, we report that the brown kiwi has the highest levels of genetic structuring observed in birds. Moreover, the mtDNA sequences are, with two minor exceptions, diagnostic genetic markers for each population investigated, even though they are among the more slowly evolving coding regions in this genome. A major unexpected finding was the concordant split in molecular phylogenies between brown kiwis in the southern South Island and elsewhere in New Zealand. This basic phylogeographic boundary halfway down the South Island coincides with a fixed allele difference in the Hb nuclear locus and strongly suggests that two morphologically cryptic species are currently merged under one polytypic species. This is another striking example of how molecular genetic assays can detect phylogenetic discontinuities that are not reflected in traditional morphologically based taxonomies. However, reanalysis of the morphological characters by using phylogenetic methods revealed that the reason for this discordance is that most are primitive and thus are phylogenetically uninformative. Shared-derived morphological characters support the same relationships evident in the molecular phylogenies and, in concert with the molecular data, suggest that as brown kiwis colonized northward from the southern South Island, they retained many primitive characters that confounded earlier systematists. Strong subdivided population structure and cryptic species in brown kiwis seem to have evolved relatively recently as a consequence of Pleistocene range disjunctions, low dispersal power, and genetic drift in small populations.

Formal group laws and hypergraph colorings

Thesis (Ph.D.)--University of Washington, 2016-06

An evolutionary framework for studies of hibernation and short-term torpor

Data from diverse studies endorse ideas that short term torpor and hibernation are expressions of ancient characters. In evolutionary terms, their basic mechanisms are probably plesiomorphic (= ancestral/primitive) and physiologically similar. This contrasts with the alternate view that they are apomorphic (= derived, specialized), arising independently in many taxa from homeothermic ancestry by numerous apparent convergences. This paper explores some of the implications of accepting the plesiomorphic interpretation. Hibernation is, of course, a complex phenomenon that has undergone variations and refinements in different mammalian lineages. The argument is not that hibernation in total is a plesiomorphic character, but that it is built upon fundamental processes that are. Taking this view provides a framework for research that emphasizes the value of comparative studies, particularly of reptiles and birds. Studies of reptiles, for example, might unravel the mystery about periodic arousals. A plesiomorphic framework also explains the most extreme examples of hibernation as derived specializations from ancestry in which heterothermy is more about energy management than escape from cold. It cautions against using low body temperature (Tb) alone to diagnose torpor, emphasizes the need to distinguish between constitutional eurythermy (plesiomorphic) and constitutional stenothermy (apomorphic), and leads to a parsimonious theory about the evolution of endothermy. The paper proposes that brown adipose tissue (BAT) is apomorphic within eutheria and highlights the conundrum posed by the occurrence of both nonshivering thermogenesis (NST) and rapid arousal from hibernation in noneutherian mammals that lack BAT and uncoupling protein 1 (UCP1). It endorses the likely existence of a different, ancient and widespread mechanism for regulatory NST in mammals.

Spatial correlations between beta-amyloid (Abeta) deposits and blood vessels in early-onset Alzheimer's disease

In cases of late-onset Alzheimer’s disease (AD), there is a spatial correlation between the classsic ‘cored’ type of Beta-amyloid (Abeta) deposit and the large vertically penetrating arterioles in the cerebral cortex suggesting that blood vessels are involved in the pathogenesis of the classic deposits. In this chapter, the spatial correlations between the diffuse, primitive, and classic Abeta deposits and blood vessels were studied in 10 cases of early-onset AD in the age range 40 – 65 years. Sections of frontal cortex were immunostained with antibodies against Abeta?and with collagen IV to reveal the Abeta deposits and blood vessel profiles. In the early-onset cases as a whole, all types of Abeta? deposit and blood vessel profiles were distributed in clusters. There was a positive spatial correlation between the clusters of the diffuse Abeta deposits and the larger (>10µm) and smaller diameter (<10?m) blood vessel profiles in one and three cases respectively. The primitive and classic Abeta deposits were spatially correlated with larger and smaller blood vessels both in three and four cases respectively. Spatial correlations between the Abeta deposits and blood vessels may be more prevalent in cases expressing amyloid precursor protein (APP) than presenilin 1 (PSEN1) mutations. Apolipoprotein E (Apo E) genotype of the patient did not appear to influence the spatial correlation with blood vessel profiles. The data suggest that the larger diameter blood vessels are less important in the pathogenesis of the classic Abeta deposits in early-onset compared with late-onset AD.

The spatial patterns of beta-amyloid (Abeta) deposits and neurofibrillary tangles (NFT) in late-onset sporadic Alzheimer's disease

The spatial patterns of beta-amyloid (Abeta) deposits and neurofibrillary tangles (NFT) were studied in areas of the cerebral cortex in 16 patients with the late-onset, sporadic form of Alzheimer’s disease (AD). Diffuse, primitive, and classic Abeta deposits and NFT were aggregated into clusters; the clusters being regularly distributed parallel to the pia mater in many areas. In a significant proportion of regions, the sizes of the regularly distributed clusters approximated to those of the cells of origin of the cortico-cortical projections. The diffuse and primitive Abeta deposits exhibited a similar range of spatial patterns but the classic Abeta deposits occurred less frequently in large clusters >6400microm. In addition, the NFT often occurred in larger regularly distributed clusters than the Abeta deposits. The location, size, and distribution of the clusters of Abeta deposits and NFT supports the hypothesis that AD is a 'disconnection syndrome' in which degeneration of specific cortico-cortical and cortico-hippocampal pathways results in synaptic disconnection and the formation of clusters of NFT and Abeta deposits.

Quantitative differences in beta/A4 protein subtypes in the parahippocampal gyrus and frontal cortex in Alzheimer's disease

The density of diffuse, primitive and classic beta/A4 protein deposits was estimated in sulci and gyri in the frontal cortex and parahippocampal gyrus (PHG) in 8 cases of Alzheimer's disease. Total beta/A4 deposit density was similar in the frontal cortex and PHG but the ratio of primitive and classic deposits to the total was greater in the PHG compared with the frontal cortex. Total beta/A4 deposit density was greater in the depths of the sulci, but the proportions of the various beta/A4 subtypes were similar in sulci and gyri. Hence, increased density of primitive and classic deposits in the PHG could reflect enhanced conversion of diffuse to mature deposits whereas increased density of mature beta/A4 subtypes in sulci versus gyri may reflect increased beta/A4 deposition in the sulci.

Beta-amyloid deposition in the temporal lobe of patients with dementia with Lewy bodies:Comparison with non-demented cases and Alzheimer's disease

β-Amyloid (Aβ) deposition in regions of the temporal lobe in patients with dementia with Lewy bodies (DLB) was compared with elderly, non-demented (ND) cases and with Alzheimer's disease (AD). The distribution, density and clustering patterns of diffuse, primitive and classic Aβ deposits were similar in 'pure' DLB and ND cases. The distribution of Aβ deposits and the densities of the diffuse and primitive deposits were similar in 'mixed' DLB/AD cases compared with AD. However, the density of the classic deposits was significantly lower in DLB/AD compared with AD. In addition, the primitive Aβ deposits occurred more often in small, regularly spaced clusters in the tissue and less often in a single large cluster in DLB/AD compared with 'pure' AD. These results suggest that pure DLB and AD are distinct disorders which can coexist in some patients. However, the Aβ pathology of DLB/AD cases is not identical to that observed in patients with AD alone. (C) 2000 S. Karger AG, Basel.

Spatial correlations between beta-amyloid (A beta) deposits and blood vessels in familial Alzheimer's disease

In sporadic Alzheimer’s disease (SAD), the classic (‘dense-cored’) ß-amyloid (Aß) deposits are aggregated around the larger blood vessels in the upper laminae of the cerebral cortex. To determine whether a similar relationship exists in familial AD (FAD), the spatial correlations between the diffuse, primitive, and classic ß-amyloid (Aß deposits and blood vessels were studied in ten FAD cases including cases linked to amyloid precursor protein (APP) and presenilin (PSEN) gene mutations and expressing apolipoprotein E (apo E) allele E4. Sections of frontal cortex were immunolabelled with antibodies against Aß and with collagen IV to reveal the Aß deposits and blood vessel profiles. In the FAD cases as a whole, Aßdeposits were distributed in clusters. There was a positive spatial correlation between the clusters of the diffuse Aßdeposits and the larger (>10 µm) and smaller diameter (<10 µm) blood vessels in one and three cases respectively. The primitive Aß deposits were spatially correlated with larger and smaller blood vessels each in four cases and the classic deposits in three and four cases respectively. Apo E genotype of the patient did not influence spatial correlation with blood vessels. Hence, spatial correlations between the classic deposits and larger diameter blood vessels were significantly less frequent in FAD compared with SAD. It was concluded that both Aß deposit morphology and AD subtype determine spatial correlations with blood vessels in AD.

Spatial patterns of β-amyloid (Aβ) deposits in familial and sporadic Alzheimer's disease

The spatial patterns of the diffuse, primitive, and classic β-amyloid (Aβ) deposits were compared in cortical regions in early-onset familial Alzheimer's disease (EO-FAD) linked to mutations of the amyloid precursor protein APP) or presenilin 1 (PSEN1) genes, late-onset familial AD (LO-FAD), and sporadic AD (SAD). The objective was to determine whether genetic factors influenced the spatial patterns of the Aβ deposits. Aβ deposits were distributed either in clusters which were regularly distributed parallel to the pia mater or in larger, non-regularly distributed clusters. There were no significant differences in spatial pattern of the diffuse deposits between patient groups but mean cluster size of the diffuse deposits was larger in FAD compared with SAD. Primitive Aβ deposits were more frequently distributed in regular clusters and less frequently distributed in large clusters in FAD compared with SAD. Classic Aβ deposits were more frequently distributed in regularly spaced clusters and less frequently distributed in large clusters in LO-FAD compared with EO-FAD. There were no significant differences in the spatial patterns or cluster sizes of Aβ deposits in cases classified according to apolipoprotein E (APOE) genotype. These results suggest (1) greater deposition of Aβ in the form of clusters of diffuse deposits in FAD, (2) a greater proportion of diffuse deposits may be converted to primitive deposits in SAD, (3) classic deposits are more widely distributed in EO-FAD, and (4) the presence of APOE allele ε4 has little effect on the spatial patterns of Aβ deposits.

The spatial patterns of beta-amyloid (Abeta) deposits in dementia with Lewy bodies and Alzheimer’s disease

The spatial patterns of diffuse, primitive and classic beta-amyloid (Abeta) deposits were studied in regions of the temporal lobe in cases of ‘pure’ Dementai with Lewy bodies (DLB), cases of DLB with associated Alzheimer’s disease (AD) (DLB/AD) and cases of ‘pure’ AD. Abeta deposits occurred in clusters in all patient groups. In the majority of brain areas studied, either a single large (=6400 micron) cluster of Abeta deposits was present or Abeta deposits occurred in smaller clusters which were regularly distributed parallel to the tissue boundary. No significant differences in the spatial patterns of Abeta deposits were observed in ‘pure’ DLB compared with DLB/AD. The spatial patterns of Abeta deposits in DLB/AD cases were generally similar to those observed in AD. However, in DLB/AD the primitive deposits occurred less often in a single large cluster and more often in smaller, regularly spaced clusters than in ‘pure’ AD. The data suggest a more specific pattern of degeneration associated with Abeta deposition in DLB/AD cases compared with ‘pure’ AD.