919 resultados para Best algebraic approximation


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Dynamic systems involving convolution integrals with decaying kernels, of which fractionally damped systems form a special case, are non-local in time and hence infinite dimensional. Straightforward numerical solution of such systems up to time t needs O(t(2)) computations owing to the repeated evaluation of integrals over intervals that grow like t. Finite-dimensional and local approximations are thus desirable. We present here an approximation method which first rewrites the evolution equation as a coupled in finite-dimensional system with no convolution, and then uses Galerkin approximation with finite elements to obtain linear, finite-dimensional, constant coefficient approximations for the convolution. This paper is a broad generalization, based on a new insight, of our prior work with fractional order derivatives (Singh & Chatterjee 2006 Nonlinear Dyn. 45, 183-206). In particular, the decaying kernels we can address are now generalized to the Laplace transforms of known functions; of these, the power law kernel of fractional order differentiation is a special case. The approximation can be refined easily. The local nature of the approximation allows numerical solution up to time t with O(t) computations. Examples with several different kernels show excellent performance. A key feature of our approach is that the dynamic system in which the convolution integral appears is itself approximated using another system, as distinct from numerically approximating just the solution for the given initial values; this allows non-standard uses of the approximation, e. g. in stability analyses.

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Every year, approximately 62 000 people with stroke and transient ischemic attack are treated in Canadian hospitals, and the evidence suggests one-third or more will experience vascular-cognitive impairment, and/or intractable fatigue, either alone or in combination. The 2015 update of the Canadian Stroke Best Practice Recommendations: Mood, Cognition and Fatigue Module guideline is a comprehensive summary of current evidence-based recommendations for clinicians in a range of settings, who provide care to patients following stroke. The three consequences of stroke that are the focus of the this guideline (poststroke depression, vascular cognitive impairment, and fatigue) have high incidence rates and significant impact on the lives of people who have had a stroke, impede recovery, and result in worse long-term outcomes. Significant practice variations and gaps in the research evidence have been reported for initial screening and in-depth assessment of stroke patients for these conditions. Also of concern, an increased number of family members and informal caregivers may also experience depressive symptoms in the poststroke recovery phase which further impact patient recovery. These factors emphasize the need for a system of care that ensures screening occurs as a standard and consistent component of clinical practice across settings as stroke patients transition from acute care to active rehabilitation and reintegration into their community. Additionally, building system capacity to ensure access to appropriate specialists for treatment and ongoing management of stroke survivors with these conditions is another great challenge.

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CTRU, a public key cryptosystem was proposed by Gaborit, Ohler and Sole. It is analogue of NTRU, the ring of integers replaced by the ring of polynomials $\mathbb{F}_2[T]$ . It attracted attention as the attacks based on either LLL algorithm or the Chinese Remainder Theorem are avoided on it, which is most common on NTRU. In this paper we presents a polynomial-time algorithm that breaks CTRU for all recommended parameter choices that were derived to make CTRU secure against popov normal form attack. The paper shows if we ascertain the constraints for perfect decryption then either plaintext or private key can be achieved by polynomial time linear algebra attack.

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In this paper, we present an algebraic method to study and design spatial parallel manipulators that demonstrate isotropy in the force and moment distributions. We use the force and moment transformation matrices separately, and derive conditions for their isotropy individually as well as in combination. The isotropy conditions are derived in closed-form in terms of the invariants of the quadratic forms associated with these matrices. The formulation is applied to a class of Stewart platform manipulator, and a multi-parameter family of isotropic manipulators is identified analytically. We show that it is impossible to obtain a spatially isotropic configuration within this family. We also compute the isotropic configurations of an existing manipulator and demonstrate a procedure for designing the manipulator for isotropy at a given configuration. (C) 2008 Elsevier Ltd. All rights reserved.

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"Extended Clifford algebras" are introduced as a means to obtain low ML decoding complexity space-time block codes. Using left regular matrix representations of two specific classes of extended Clifford algebras, two systematic algebraic constructions of full diversity Distributed Space-Time Codes (DSTCs) are provided for any power of two number of relays. The left regular matrix representation has been shown to naturally result in space-time codes meeting the additional constraints required for DSTCs. The DSTCs so constructed have the salient feature of reduced Maximum Likelihood (ML) decoding complexity. In particular, the ML decoding of these codes can be performed by applying the lattice decoder algorithm on a lattice of four times lesser dimension than what is required in general. Moreover these codes have a uniform distribution of power among the relays and in time, thus leading to a low Peak to Average Power Ratio at the relays.

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We explore an isoparametric interpolation of total quaternion for geometrically consistent, strain-objective and path-independent finite element solutions of the geometrically exact beam. This interpolation is a variant of the broader class known as slerp. The equivalence between the proposed interpolation and that of relative rotation is shown without any recourse to local bijection between quaternions and rotations. We show that, for a two-noded beam element, the use of relative rotation is not mandatory for attaining consistency cum objectivity and an appropriate interpolation of total rotation variables is sufficient. The interpolation of total quaternion, which is computationally more efficient than the one based on local rotations, converts nodal rotation vectors to quaternions and interpolates them in a manner consistent with the character of the rotation manifold. This interpolation, unlike the additive interpolation of total rotation, corresponds to a geodesic on the rotation manifold. For beam elements with more than two nodes, however, a consistent extension of the proposed quaternion interpolation is difficult. Alternatively, a quaternion-based procedure involving interpolation of relative rotations is proposed for such higher order elements. We also briefly discuss a strategy for the removal of possible singularity in the interpolation of quaternions, proposed in [I. Romero, The interpolation of rotations and its application to finite element models of geometrically exact rods, Comput. Mech. 34 (2004) 121–133]. The strain-objectivity and path-independence of solutions are justified theoretically and then demonstrated through numerical experiments. This study, being focused only on the interpolation of rotations, uses a standard finite element discretization, as adopted by Simo and Vu-Quoc [J.C. Simo, L. Vu-Quoc, A three-dimensional finite rod model part II: computational aspects, Comput. Methods Appl. Mech. Engrg. 58 (1986) 79–116]. The rotation update is achieved via quaternion multiplication followed by the extraction of the rotation vector. Nodal rotations are stored in terms of rotation vectors and no secondary storages are required.

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We propose certain discrete parameter variants of well known simulation optimization algorithms. Two of these algorithms are based on the smoothed functional (SF) technique while two others are based on the simultaneous perturbation stochastic approximation (SPSA) method. They differ from each other in the way perturbations are obtained and also the manner in which projections and parameter updates are performed. All our algorithms use two simulations and two-timescale stochastic approximation. As an application setting, we consider the important problem of admission control of packets in communication networks under dependent service times. We consider a discrete time slotted queueing model of the system and consider two different scenarios - one where the service times have a dependence on the system state and the other where they depend on the number of arrivals in a time slot. Under our settings, the simulated objective function appears ill-behaved with multiple local minima and a unique global minimum characterized by a sharp dip in the objective function in a small region of the parameter space. We compare the performance of our algorithms on these settings and observe that the two SF algorithms show the best results overall. In fact, in many cases studied, SF algorithms converge to the global minimum.

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We propose several stochastic approximation implementations for related algorithms in flow-control of communication networks. First, a discrete-time implementation of Kelly's primal flow-control algorithm is proposed. Convergence with probability 1 is shown, even in the presence of communication delays and stochastic effects seen in link congestion indications. This ensues from an analysis of the flow-control algorithm using the asynchronous stochastic approximation (ASA) framework. Two relevant enhancements are then pursued: a) an implementation of the primal algorithm using second-order information, and b) an implementation where edge-routers rectify misbehaving flows. Next, discretetime implementations of Kelly's dual algorithm and primaldual algorithm are proposed. Simulation results a) verifying the proposed algorithms and, b) comparing the stability properties are presented.

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The problem of reconstruction of a refractive-index distribution (RID) in optical refraction tomography (ORT) with optical path-length difference (OPD) data is solved using two adaptive-estimation-based extended-Kalman-filter (EKF) approaches. First, a basic single-resolution EKF (SR-EKF) is applied to a state variable model describing the tomographic process, to estimate the RID of an optically transparent refracting object from noisy OPD data. The initialization of the biases and covariances corresponding to the state and measurement noise is discussed. The state and measurement noise biases and covariances are adaptively estimated. An EKF is then applied to the wavelet-transformed state variable model to yield a wavelet-based multiresolution EKF (MR-EKF) solution approach. To numerically validate the adaptive EKF approaches, we evaluate them with benchmark studies of standard stationary cases, where comparative results with commonly used efficient deterministic approaches can be obtained. Detailed reconstruction studies for the SR-EKF and two versions of the MR-EKF (with Haar and Daubechies-4 wavelets) compare well with those obtained from a typically used variant of the (deterministic) algebraic reconstruction technique, the average correction per projection method, thus establishing the capability of the EKF for ORT. To the best of our knowledge, the present work contains unique reconstruction studies encompassing the use of EKF for ORT in single-resolution and multiresolution formulations, and also in the use of adaptive estimation of the EKF's noise covariances. (C) 2010 Optical Society of America

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A new deterministic three-dimensional neutral and charged particle transport code, MultiTrans, has been developed. In the novel approach, the adaptive tree multigrid technique is used in conjunction with simplified spherical harmonics approximation of the Boltzmann transport equation. The development of the new radiation transport code started in the framework of the Finnish boron neutron capture therapy (BNCT) project. Since the application of the MultiTrans code to BNCT dose planning problems, the testing and development of the MultiTrans code has continued in conventional radiotherapy and reactor physics applications. In this thesis, an overview of different numerical radiation transport methods is first given. Special features of the simplified spherical harmonics method and the adaptive tree multigrid technique are then reviewed. The usefulness of the new MultiTrans code has been indicated by verifying and validating the code performance for different types of neutral and charged particle transport problems, reported in separate publications.

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Internationally there is a growing interest in the mental wellbeing of young people. However, it is unclear whether mental wellbeing is best conceptualized as a general wellbeing factor or a multidimensional construct. This paper investigated whether mental wellbeing, measured by the Mental Health Continuum-Short Form (MHC-SF), is best represented by: (1) a single-factor general model; (2) a three-factor multidimensional model or (3) a combination of both (bifactor model). 2,220 young Australians aged between 16 and 25 years completed an online survey including the MHC-SF and a range of other wellbeing and mental ill-health measures. Exploratory factor analysis supported a bifactor solution, comprised of a general wellbeing factor, and specific group factors of psychological, social and emotional wellbeing. Confirmatory factor analysis indicated that the bifactor model had a better fit than competing single and three-factor models. The MHC-SF total score was more strongly associated with other wellbeing and mental ill-health measures than the social, emotional or psychological subscale scores. Findings indicate that the mental wellbeing of young people is best conceptualized as an overarching latent construct (general wellbeing) to which emotional, social and psychological domains contribute. The MHC-SF total score is a valid and reliable measure of this general wellbeing factor.

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Fuel cells are emerging as alternate green power producers for both large power production and for use in automobiles. Hydrogen is seen as the best option as a fuel; however, hydrogen fuel cells require recirculation of unspent hydrogen. A supersonic ejector is an apt device for recirculation in the operating regimes of a hydrogen fuel cell. Optimal ejectors have to be designed to achieve best performances. The use of the vector evaluated particle swarm optimization technique to optimize supersonic ejectors with a focus on its application for hydrogen recirculation in fuel cells is presented here. Two parameters, compression ratio and efficiency, have been identified as the objective functions to be optimized. Their relation to operating and design parameters of ejector is obtained by control volume based analysis using a constant area mixing approximation. The independent parameters considered are the area ratio and the exit Mach number of the nozzle. The optimization is carried out at a particularentrainment ratio and results in a set of nondominated solutions, the Pareto front. A set of such curves can be used for choosing the optimal design parameters of the ejector.

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The problem of admission control of packets in communication networks is studied in the continuous time queueing framework under different classes of service and delayed information feedback. We develop and use a variant of a simulation based two timescale simultaneous perturbation stochastic approximation (SPSA) algorithm for finding an optimal feedback policy within the class of threshold type policies. Even though SPSA has originally been designed for continuous parameter optimization, its variant for the discrete parameter case is seen to work well. We give a proof of the hypothesis needed to show convergence of the algorithm on our setting along with a sketch of the convergence analysis. Extensive numerical experiments with the algorithm are illustrated for different parameter specifications. In particular, we study the effect of feedback delays on the system performance.

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We show that the dynamical Wigner functions for noninteracting fermions and bosons can have complex singularity structures with a number of new solutions accompanying the usual mass-shell dispersion relations. These new shell solutions are shown to encode the information of the quantum coherence between particles and antiparticles, left and right moving chiral states and/or between different flavour states. Analogously to the usual derivation of the Boltzmann equation, we impose this extended phase space structure on the full interacting theory. This extension of the quasiparticle approximation gives rise to a self-consistent equation of motion for a density matrix that combines the quantum mechanical coherence evolution with a well defined collision integral giving rise to decoherence. Several applications of the method are given, for example to the coherent particle production, electroweak baryogenesis and study of decoherence and thermalization.

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The favoured conformations of the prolyl residue have been obtained by calculating their potential energies arising from bond-angle strain, torsion-angle strain, non-bonded and electrostatic interatomic energies. In addition to the five membered ring, the peptide unit at the amino end (with ω = 180°) and the C′ atom at the carboxyl end have been taken into account. It is found that there are two local minima in the configurational space of the parameters defining the conformation, as is actually observed-one (denoted by B) with Cγ displaced on the same side as C′, which is lower in energy than the other (denoted by A) with Cγ displaced on the opposite side of C′. The other four atoms Cδ, N, Cα, Cβ are nearly in a plane. The conformations of minimum energy (for both A and B) have bond angles very close to the mean observed values while the torsion angles are well within the range observed in various structures for each type. Taking into account the fact that the influence of neighbouring molecules in a crystal structure may make the conformation of a molecule different from the minimal one, the ranges of the conformational parameters for which the energy is within 0.6 kcal/mole above the minimum value (called the "most probable range") and within 1.2 kcal/mole (called the "probable range") have been determined. The ranges thus obtained, agree well with observation, and most of the observed data lie within the most probable ranges, although differing appreciably from the conformation of minimum energy. The study has been extended, in a limited way, to the conformation of the ring in the amino acid proline. Since the nitrogen is tetrahedral in this (as contrasted with being planar in the prolyl residue), it is found that any one of the five atoms can be out of plane (either way), with the other four lying nearly in a plane. These correspond to low energy conformations (up to 1.2 kcal/mole above the minimum). One such example, in which the Cα atom is out of plane is known for dl-proline · HCl. It is also shown that in these calculations energies due to bond length distortions can be neglected to a good degree of approximation, provided the 'best' values of the bond lengths for the particular compound are used in the theoretical calculations.