916 resultados para Linear differential systems
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We wish to construct a realization theory of stable neural networks and use this theory to model the variety of stable dynamics apparent in natural data. Such a theory should have numerous applications to constructing specific artificial neural networks with desired dynamical behavior. The networks used in this theory should have well understood dynamics yet be as diverse as possible to capture natural diversity. In this article, I describe a parameterized family of higher order, gradient-like neural networks which have known arbitrary equilibria with unstable manifolds of known specified dimension. Moreover, any system with hyperbolic dynamics is conjugate to one of these systems in a neighborhood of the equilibrium points. Prior work on how to synthesize attractors using dynamical systems theory, optimization, or direct parametric. fits to known stable systems, is either non-constructive, lacks generality, or has unspecified attracting equilibria. More specifically, We construct a parameterized family of gradient-like neural networks with a simple feedback rule which will generate equilibrium points with a set of unstable manifolds of specified dimension. Strict Lyapunov functions and nested periodic orbits are obtained for these systems and used as a method of synthesis to generate a large family of systems with the same local dynamics. This work is applied to show how one can interpolate finite sets of data, on nested periodic orbits.
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Science Foundation Ireland (07/CE/11147); Irish Research Council for Science Engineering and Technology (Embark Initiative)
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This thesis is concerned with uniformly convergent finite element and finite difference methods for numerically solving singularly perturbed two-point boundary value problems. We examine the following four problems: (i) high order problem of reaction-diffusion type; (ii) high order problem of convection-diffusion type; (iii) second order interior turning point problem; (iv) semilinear reaction-diffusion problem. Firstly, we consider high order problems of reaction-diffusion type and convection-diffusion type. Under suitable hypotheses, the coercivity of the associated bilinear forms is proved and representation results for the solutions of such problems are given. It is shown that, on an equidistant mesh, polynomial schemes cannot achieve a high order of convergence which is uniform in the perturbation parameter. Piecewise polynomial Galerkin finite element methods are then constructed on a Shishkin mesh. High order convergence results, which are uniform in the perturbation parameter, are obtained in various norms. Secondly, we investigate linear second order problems with interior turning points. Piecewise linear Galerkin finite element methods are generated on various piecewise equidistant meshes designed for such problems. These methods are shown to be convergent, uniformly in the singular perturbation parameter, in a weighted energy norm and the usual L2 norm. Finally, we deal with a semilinear reaction-diffusion problem. Asymptotic properties of solutions to this problem are discussed and analysed. Two simple finite difference schemes on Shishkin meshes are applied to the problem. They are proved to be uniformly convergent of second order and fourth order respectively. Existence and uniqueness of a solution to both schemes are investigated. Numerical results for the above methods are presented.
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This thesis is concerned with uniformly convergent finite element methods for numerically solving singularly perturbed parabolic partial differential equations in one space variable. First, we use Petrov-Galerkin finite element methods to generate three schemes for such problems, each of these schemes uses exponentially fitted elements in space. Two of them are lumped and the other is non-lumped. On meshes which are either arbitrary or slightly restricted, we derive global energy norm and L2 norm error bounds, uniformly in the diffusion parameter. Under some reasonable global assumptions together with realistic local assumptions on the solution and its derivatives, we prove that these exponentially fitted schemes are locally uniformly convergent, with order one, in a discrete L∞norm both outside and inside the boundary layer. We next analyse a streamline diffusion scheme on a Shishkin mesh for a model singularly perturbed parabolic partial differential equation. The method with piecewise linear space-time elements is shown, under reasonable assumptions on the solution, to be convergent, independently of the diffusion parameter, with a pointwise accuracy of almost order 5/4 outside layers and almost order 3/4 inside the boundary layer. Numerical results for the above schemes are presented. Finally, we examine a cell vertex finite volume method which is applied to a model time-dependent convection-diffusion problem. Local errors away from all layers are obtained in the l2 seminorm by using techniques from finite element analysis.
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In the last decade, we have witnessed the emergence of large, warehouse-scale data centres which have enabled new internet-based software applications such as cloud computing, search engines, social media, e-government etc. Such data centres consist of large collections of servers interconnected using short-reach (reach up to a few hundred meters) optical interconnect. Today, transceivers for these applications achieve up to 100Gb/s by multiplexing 10x 10Gb/s or 4x 25Gb/s channels. In the near future however, data centre operators have expressed a need for optical links which can support 400Gb/s up to 1Tb/s. The crucial challenge is to achieve this in the same footprint (same transceiver module) and with similar power consumption as today’s technology. Straightforward scaling of the currently used space or wavelength division multiplexing may be difficult to achieve: indeed a 1Tb/s transceiver would require integration of 40 VCSELs (vertical cavity surface emitting laser diode, widely used for short‐reach optical interconnect), 40 photodiodes and the electronics operating at 25Gb/s in the same module as today’s 100Gb/s transceiver. Pushing the bit rate on such links beyond today’s commercially available 100Gb/s/fibre will require new generations of VCSELs and their driver and receiver electronics. This work looks into a number of state‐of-the-art technologies and investigates their performance restraints and recommends different set of designs, specifically targeting multilevel modulation formats. Several methods to extend the bandwidth using deep submicron (65nm and 28nm) CMOS technology are explored in this work, while also maintaining a focus upon reducing power consumption and chip area. The techniques used were pre-emphasis in rising and falling edges of the signal and bandwidth extensions by inductive peaking and different local feedback techniques. These techniques have been applied to a transmitter and receiver developed for advanced modulation formats such as PAM-4 (4 level pulse amplitude modulation). Such modulation format can increase the throughput per individual channel, which helps to overcome the challenges mentioned above to realize 400Gb/s to 1Tb/s transceivers.
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Localized molecular orbitals (LMOs) are much more compact representations of electronic degrees of freedom than canonical molecular orbitals (CMOs). The most compact representation is provided by nonorthogonal localized molecular orbitals (NOLMOs), which are linearly independent but are not orthogonal. Both LMOs and NOLMOs are thus useful for linear-scaling calculations of electronic structures for large systems. Recently, NOLMOs have been successfully applied to linear-scaling calculations with density functional theory (DFT) and to reformulating time-dependent density functional theory (TDDFT) for calculations of excited states and spectroscopy. However, a challenge remains as NOLMO construction from CMOs is still inefficient for large systems. In this work, we develop an efficient method to accelerate the NOLMO construction by using predefined centroids of the NOLMO and thereby removing the nonlinear equality constraints in the original method ( J. Chem. Phys. 2004 , 120 , 9458 and J. Chem. Phys. 2000 , 112 , 4 ). Thus, NOLMO construction becomes an unconstrained optimization. Its efficiency is demonstrated for the selected saturated and conjugated molecules. Our method for fast NOLMO construction should lead to efficient DFT and NOLMO-TDDFT applications to large systems.
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We describe a strategy for Markov chain Monte Carlo analysis of non-linear, non-Gaussian state-space models involving batch analysis for inference on dynamic, latent state variables and fixed model parameters. The key innovation is a Metropolis-Hastings method for the time series of state variables based on sequential approximation of filtering and smoothing densities using normal mixtures. These mixtures are propagated through the non-linearities using an accurate, local mixture approximation method, and we use a regenerating procedure to deal with potential degeneracy of mixture components. This provides accurate, direct approximations to sequential filtering and retrospective smoothing distributions, and hence a useful construction of global Metropolis proposal distributions for simulation of posteriors for the set of states. This analysis is embedded within a Gibbs sampler to include uncertain fixed parameters. We give an example motivated by an application in systems biology. Supplemental materials provide an example based on a stochastic volatility model as well as MATLAB code.
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Morphine induces antinociception by activating mu opioid receptors (muORs) in spinal and supraspinal regions of the CNS. (Beta)arrestin-2 (beta)arr2), a G-protein-coupled receptor-regulating protein, regulates the muOR in vivo. We have shown previously that mice lacking (beta)arr2 experience enhanced morphine-induced analgesia and do not become tolerant to morphine as determined in the hot-plate test, a paradigm that primarily assesses supraspinal pain responsiveness. To determine the general applicability of the (beta)arr2-muOR interaction in other neuronal systems, we have, in the present study, tested (beta)arr2 knock-out ((beta)arr2-KO) mice using the warm water tail-immersion paradigm, which primarily assesses spinal reflexes to painful thermal stimuli. In this test, the (beta)arr2-KO mice have greater basal nociceptive thresholds and markedly enhanced sensitivity to morphine. Interestingly, however, after a delayed onset, they do ultimately develop morphine tolerance, although to a lesser degree than the wild-type (WT) controls. In the (beta)arr2-KO but not WT mice, morphine tolerance can be completely reversed with a low dose of the classical protein kinase C (PKC) inhibitor chelerythrine. These findings provide in vivo evidence that the muOR is differentially regulated in diverse regions of the CNS. Furthermore, although (beta)arr2 appears to be the most prominent and proximal determinant of muOR desensitization and morphine tolerance, in the absence of this mechanism, the contributions of a PKC-dependent regulatory system become readily apparent.
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Mechanisms for the evolution of convergent behavioral traits are largely unknown. Vocal learning is one such trait that evolved multiple times and is necessary in humans for the acquisition of spoken language. Among birds, vocal learning is evolved in songbirds, parrots, and hummingbirds. Each time similar forebrain song nuclei specialized for vocal learning and production have evolved. This finding led to the hypothesis that the behavioral and neuroanatomical convergences for vocal learning could be associated with molecular convergence. We previously found that the neural activity-induced gene dual specificity phosphatase 1 (dusp1) was up-regulated in non-vocal circuits, specifically in sensory-input neurons of the thalamus and telencephalon; however, dusp1 was not up-regulated in higher order sensory neurons or motor circuits. Here we show that song motor nuclei are an exception to this pattern. The song nuclei of species from all known vocal learning avian lineages showed motor-driven up-regulation of dusp1 expression induced by singing. There was no detectable motor-driven dusp1 expression throughout the rest of the forebrain after non-vocal motor performance. This pattern contrasts with expression of the commonly studied activity-induced gene egr1, which shows motor-driven expression in song nuclei induced by singing, but also motor-driven expression in adjacent brain regions after non-vocal motor behaviors. In the vocal non-learning avian species, we found no detectable vocalizing-driven dusp1 expression in the forebrain. These findings suggest that independent evolutions of neural systems for vocal learning were accompanied by selection for specialized motor-driven expression of the dusp1 gene in those circuits. This specialized expression of dusp1 could potentially lead to differential regulation of dusp1-modulated molecular cascades in vocal learning circuits.
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To investigate the neural systems that contribute to the formation of complex, self-relevant emotional memories, dedicated fans of rival college basketball teams watched a competitive game while undergoing functional magnetic resonance imaging (fMRI). During a subsequent recognition memory task, participants were shown video clips depicting plays of the game, stemming either from previously-viewed game segments (targets) or from non-viewed portions of the same game (foils). After an old-new judgment, participants provided emotional valence and intensity ratings of the clips. A data driven approach was first used to decompose the fMRI signal acquired during free viewing of the game into spatially independent components. Correlations were then calculated between the identified components and post-scanning emotion ratings for successfully encoded targets. Two components were correlated with intensity ratings, including temporal lobe regions implicated in memory and emotional functions, such as the hippocampus and amygdala, as well as a midline fronto-cingulo-parietal network implicated in social cognition and self-relevant processing. These data were supported by a general linear model analysis, which revealed additional valence effects in fronto-striatal-insular regions when plays were divided into positive and negative events according to the fan's perspective. Overall, these findings contribute to our understanding of how emotional factors impact distributed neural systems to successfully encode dynamic, personally-relevant event sequences.
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© 2015 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.A key component in calculations of exchange and correlation energies is the Coulomb operator, which requires the evaluation of two-electron integrals. For localized basis sets, these four-center integrals are most efficiently evaluated with the resolution of identity (RI) technique, which expands basis-function products in an auxiliary basis. In this work we show the practical applicability of a localized RI-variant ('RI-LVL'), which expands products of basis functions only in the subset of those auxiliary basis functions which are located at the same atoms as the basis functions. We demonstrate the accuracy of RI-LVL for Hartree-Fock calculations, for the PBE0 hybrid density functional, as well as for RPA and MP2 perturbation theory. Molecular test sets used include the S22 set of weakly interacting molecules, the G3 test set, as well as the G2-1 and BH76 test sets, and heavy elements including titanium dioxide, copper and gold clusters. Our RI-LVL implementation paves the way for linear-scaling RI-based hybrid functional calculations for large systems and for all-electron many-body perturbation theory with significantly reduced computational and memory cost.
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All biological phenomena depend on molecular recognition, which is either intermolecular like in ligand binding to a macromolecule or intramolecular like in protein folding. As a result, understanding the relationship between the structure of proteins and the energetics of their stability and binding with others (bio)molecules is a very interesting point in biochemistry and biotechnology. It is essential to the engineering of stable proteins and to the structure-based design of pharmaceutical ligands. The parameter generally used to characterize the stability of a system (the folded and unfolded state of the protein for example) is the equilibrium constant (K) or the free energy (deltaG(o)), which is the sum of enthalpic (deltaH(o)) and entropic (deltaS(o)) terms. These parameters are temperature dependent through the heat capacity change (deltaCp). The thermodynamic parameters deltaH(o) and deltaCp can be derived from spectroscopic experiments, using the van't Hoff method, or measured directly using calorimetry. Along with isothermal titration calorimetry (ITC), differential scanning calorimetry (DSC) is a powerful method, less described than ITC, for measuring directly the thermodynamic parameters which characterize biomolecules. In this article, we summarize the principal thermodynamics parameters, describe the DSC approach and review some systems to which it has been applied. DSC is much used for the study of the stability and the folding of biomolecules, but it can also be applied in order to understand biomolecular interactions and can thus be an interesting technique in the process of drug design.
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For pt.I. see ibid. vol.1, p.301 (1985). In the first part of this work a general definition of an inverse problem with discrete data has been given and an analysis in terms of singular systems has been performed. The problem of the numerical stability of the solution, which in that paper was only briefly discussed, is the main topic of this second part. When the condition number of the problem is too large, a small error on the data can produce an extremely large error on the generalised solution, which therefore has no physical meaning. The authors review most of the methods which have been developed for overcoming this difficulty, including numerical filtering, Tikhonov regularisation, iterative methods, the Backus-Gilbert method and so on. Regularisation methods for the stable approximation of generalised solutions obtained through minimisation of suitable seminorms (C-generalised solutions), such as the method of Phillips (1962), are also considered.
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Because only 10% of individuals infected with Mycobacterium tuberculosis will eventually develop disease, antigens that are recognized differently by the immune systems of infected healthy and diseased subjects may constitute potential vaccine candidates. Here, the heparin-binding hemagglutinin adhesin (HBHA) is identified as such an antigen. Lymphocytes from 60% of healthy infected individuals (n=25) produced interferon (IFN)-gamma after stimulation with HBHA, compared with only 4% of patients with active tuberculosis (n=24). In the responders, both CD4(+) and CD8(+) cells secreted HBHA-specific IFN-gamma, and the antigen was presented by both major histocompatibility complex class I and II molecules. In contrast to the reduced ability of patients with tuberculosis to produce HBHA-specific IFN-gamma, most of them (82%) produced anti-HBHA antibodies, compared with 36% of the infected healthy subjects. These observations indicate that HBHA is recognized differently by the immune systems of patients with tuberculosis and infected healthy individuals and might provide a marker for protection against tuberculosis.
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The powerful general Pacala-Hassell host-parasitoid model for a patchy environment, which allows host density–dependent heterogeneity (HDD) to be distinguished from between-patch, host density–independent heterogeneity (HDI), is reformulated within the class of the generalized linear model (GLM) family. This improves accessibility through the provision of general software within well–known statistical systems, and allows a rich variety of models to be formulated. Covariates such as age class, host density and abiotic factors may be included easily. For the case where there is no HDI, the formulation is a simple GLM. When there is HDI in addition to HDD, the formulation is a hierarchical generalized linear model. Two forms of HDI model are considered, both with between-patch variability: one has binomial variation within patches and one has extra-binomial, overdispersed variation within patches. Examples are given demonstrating parameter estimation with standard errors, and hypothesis testing. For one example given, the extra-binomial component of the HDI heterogeneity in parasitism is itself shown to be strongly density dependent.