14,261 research outputs found

    The Singularities of the Wave Trace of the Basic Laplacian of a Riemannian Foliation

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    We apply techniques of microlocal analysis to the study of the transverse geometry of Riemannian foliations in order to analyze spectral invariants of the basic Laplacian acting on functions on a Riemannian foliation with a bundle-like metric. In particular, we consider the trace of the basic wave operator when the mean curvature form is basic. We extend the concept of basic functions to distributions and demonstrate the existence of the basic wave kernel. The singularities of the trace of this basic wave kernel occur at the lengths of certain geodesic arcs which are orthogonal to the closures of the leaves of the foliation. In cases when the foliation has regular closure, a complete representation of the trace of the basic wave kernel can be computed for t≠0t\not=0. Otherwise, a partial trace formula over a certain set of lengths of well-behaved geodesic arcs is obtained

    A Method to Separate Stochastic and Deterministic Information from Electrocardiograms

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    In this work we present a new idea to develop a method to separate stochastic and deterministic information contained in an electrocardiogram, ECG, which may provide new sources of information with diagnostic purposes. We assume that the ECG has information corresponding to many different processes related with the cardiac activity as well as contamination from different sources related with the measurement procedure and the nature of the observed system itself. The method starts with the application of an improuved archetypal analysis to separate the mentioned stochastic and deterministic information. From the stochastic point of view we analyze Renyi entropies, and with respect to the deterministic perspective we calculate the autocorrelation function and the corresponding correlation time. We show that healthy and pathologic information may be stochastic and/or deterministic, can be identified by different measures and located in different parts of the ECG.Comment: 4 pages, 6 figure

    Electron correlations in a C20_{20} fullerene cluster: A lattice density-functional study of the Hubbard model

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    The ground-state properties of C20_{20} fullerene clusters are determined in the framework of the Hubbard model by using lattice density-functional theory (LDFT) and scaling approximations to the interaction-energy functional. Results are given for the ground-state energy, kinetic and Coulomb energies, local magnetic moments, and charge-excitation gap, as a function of the Coulomb repulsion U/tU/t and for electron or hole doping δ\delta close half-band filling (∣δ∣≤1|\delta| \le 1). The role of electron correlations is analyzed by comparing the LDFT results with fully unrestricted Hartree-Fock (UHF) calculations which take into account possible noncollinear arrangements of the local spin-polarizations. The consequences of the spin-density-wave symmetry breaking, often found in UHF, and the implications of this study for more complex fullerene structures are discussed.Comment: 18 pages, 7 figures, Submitted to PR

    CNS Control of Glucose Metabolism: Response to Environmental Challenges

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    Over the last 15 years, considerable work has accumulated to support the role of the CNS in regulating postprandial glucose levels. As discussed in the first section of this review, the CNS receives and integrates information from afferent neurons, circulating hormones, and postprandially generated nutrients to subsequently direct changes in glucose output by the liver and glucose uptake by peripheral tissues. The second major component of this review focuses on the effects of external pressures, including high fat diet and changes to the light:dark cycle on CNS-regulating glucose homeostasis. We also discuss the interaction between these different pressures and how they contribute to the multifaceted mechanisms that we hypothesize contribute to the dysregulation of glucose in type 2 diabetes mellitus (T2DM). We argue that while current peripheral therapies serve to delay the progression of T2DM, generating combined obesity and T2DM therapies targeted at the CNS, the primary site of dysfunction for both diseases, would lead to a more profound impact on the progression of both diseases
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