35 resultados para exponential sums


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Interest is growing around the application of lean techniques to new product introduction (NPI). Although a relatively emergent topic compared with the application of 'lean' within the factory, since 2000 there has been an exponential rise in the literature on this subject. However, much of this work focuses on describing and extolling the virtues of the 'Toyota approach' to design. Therefore, by way of a stock take for the UK, the present authors' research has set out to understand how well lean product design practices have been adopted by leading manufacturers. This has been achieved by carrying out in-depth case studies with three carefully selected manufacturers of complex engineered products. This paper describes these studies, the detailed results and subsequent findings, and concludes that both the awareness and adoption of practices is generally embryonic and far removed from the theory advocated in the literature. © IMechE 2007.

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Instability triggering and transient growth of thermoacoustic oscillations were experimentally investigated in combination with linear/nonlinear flame transfer function (FTF) methodology in a model lean-premixed gas turbine combustor operated with CH 4 and air at atmospheric pressure. A fully premixed flame with 10kW thermal power and an equivalence ratio of 0.60 was chosen for detailed characterization of the nonlinear transient behaviors. Flame transfer functions were experimentally determined by simultaneous measurements of inlet velocity fluctuations and heat release rate oscillations using a constant temperature anemometer and OH */CH * chemiluminescence emissions, respectively. The phase-resolved variation of the local flame structure at a limit cycle was measured by planar laser-induced fluorescence of OH. Simultaneous measurements of inlet velocity, OH */CH * emission, and acoustic pressure were performed to investigate the temporal evolution of the system from a stable to a limit cycle operation. This measurement allows us to describe an unsteady instability triggering event in terms of several distinct stages: (i) initiation of a small perturbation, (ii) exponential amplification, (iii) saturation, (iv) nonlinear evolution of the perturbations towards a new unstable periodic state, (v) quasi-steady low-amplitude periodic oscillation, and (vi) fully-developed high-amplitude limit cycle oscillation. Phase-plane portraits of instantaneous inlet velocity and heat release rate clearly show the presence of two different attractors. Depending on its initial position in phase space at infinitesimally small amplitude, the system evolves towards either a high-amplitude oscillatory state or a low-amplitude oscillatory state. This transient phenomenon was analyzed using frequency- and amplitude-dependent damping mechanisms, and compared to subcritical and supercritical bifurcation theories. The results presented in this paper experimentally demonstrate the hypothesis proposed by Preetham et al. based on analytical and computational solutions of the nonlinear G-equation [J. Propul. Power 24 (2008) 1390-1402]. Good quantitative agreement was obtained between measurements and predictions in terms of the conditions for the onset of triggering and the amplitude of triggered combustion instabilities. © 2011 The Combustion Institute.

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Noise and vibration from underground railways is a major source of disturbance to inhabitants near subways. To help designers meet noise and vibration limits, numerical models are used to understand vibration propagation from these underground railways. However, the models commonly assume the ground is homogeneous and neglect to include local variability in the soil properties. Such simplifying assumptions add a level of uncertainty to the predictions which is not well understood. The goal of the current paper is to quantify the effect of soil inhomogeneity on surface vibration. The thin-layer method (TLM) is suggested as an efficient and accurate means of simulating vibration from underground railways in arbitrarily layered half-spaces. Stochastic variability of the soils elastic modulus is introduced using a KL expansion; the modulus is assumed to have a log-normal distribution and a modified exponential covariance kernel. The effect of horizontal soil variability is investigated by comparing the stochastic results for soils varied only in the vertical direction to soils with 2D variability. Results suggest that local soil inhomogeneity can significantly affect surface velocity predictions; 90 percent confidence intervals showing 8 dB averages and peak values up to 12 dB are computed. This is a significant source of uncertainty and should be considered when using predictions from models assuming homogeneous soil properties. Furthermore, the effect of horizontal variability of the elastic modulus on the confidence interval appears to be negligible. This suggests that only vertical variation needs to be taken into account when modelling ground vibration from underground railways. © 2012 Elsevier Ltd. All rights reserved.

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The vibro-acoustic response of built-up structures, consisting of stiff components with low modal density and flexible components with high modal density, is sensitive to small imperfections in the flexible components. In this paper, the uncertainty of the response is considered by modeling the low modal density master system as deterministic and the high modal density subsystems in a nonparametric stochastic way, i.e., carrying a diffuse wave field, and by subsequently computing the response probability density function. The master system's mean squared response amplitude follows a singular noncentral complex Wishart distribution conditional on the subsystem energies. For a single degree of freedom, this is equivalent to a chi-square or an exponential distribution, depending on the loading conditions. The subsystem energies follow approximately a chi-square distribution when their relative variance is smaller than unity. The results are validated by application to plate structures, and good agreement with Monte Carlo simulations is found. © 2012 Acoustical Society of America.

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We consider the general problem of constructing nonparametric Bayesian models on infinite-dimensional random objects, such as functions, infinite graphs or infinite permutations. The problem has generated much interest in machine learning, where it is treated heuristically, but has not been studied in full generality in non-parametric Bayesian statistics, which tends to focus on models over probability distributions. Our approach applies a standard tool of stochastic process theory, the construction of stochastic processes from their finite-dimensional marginal distributions. The main contribution of the paper is a generalization of the classic Kolmogorov extension theorem to conditional probabilities. This extension allows a rigorous construction of nonparametric Bayesian models from systems of finite-dimensional, parametric Bayes equations. Using this approach, we show (i) how existence of a conjugate posterior for the nonparametric model can be guaranteed by choosing conjugate finite-dimensional models in the construction, (ii) how the mapping to the posterior parameters of the nonparametric model can be explicitly determined, and (iii) that the construction of conjugate models in essence requires the finite-dimensional models to be in the exponential family. As an application of our constructive framework, we derive a model on infinite permutations, the nonparametric Bayesian analogue of a model recently proposed for the analysis of rank data.

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We introduce a Gaussian process model of functions which are additive. An additive function is one which decomposes into a sum of low-dimensional functions, each depending on only a subset of the input variables. Additive GPs generalize both Generalized Additive Models, and the standard GP models which use squared-exponential kernels. Hyperparameter learning in this model can be seen as Bayesian Hierarchical Kernel Learning (HKL). We introduce an expressive but tractable parameterization of the kernel function, which allows efficient evaluation of all input interaction terms, whose number is exponential in the input dimension. The additional structure discoverable by this model results in increased interpretability, as well as state-of-the-art predictive power in regression tasks.

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Atmospheric effects can significantly degrade the reliability of free-space optical communications. One such effect is scintillation, caused by atmospheric turbulence, refers to random fluctuations in the irradiance and phase of the received laser beam. In this paper we inv stigate the use of multiple lasers and multiple apertures to mitigate scintillation. Since the scintillation process is slow, we adopt a block fading channel model and study the outage probability under the assumptions of orthogonal pulse-position modulation and non-ideal photodetection. Assuming perfect receiver channel state information (CSI), we derive the signal-to-noise ratio (SNR) exponents for the cases when the scintillation is lognormal, exponential and gammagamma distributed, which cover a wide range of atmospheric turbulence conditions. Furthermore, when CSI is also available at the transmitter, we illustrate very large gains in SNR are possible (in some cases larger than 15 dB) by adapting the transmitted power. Under a long-term power constraint, we outline fundamental design criteria via a simple expression that relates the required number of lasers and apertures for a given code rate and number of codeword blocks to completely remove system outages. Copyright © 2009 IEEE.

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The redistribution of fluorine during solid phase epitaxial regrowth (SPER) of preamorphized Si has been experimentally investigated, explained, and simulated, for different F concentrations and temperatures. We demonstrate, by a detailed analysis and modeling of F secondary ion mass spectrometry chemical-concentration profiles, that F segregates in amorphous Si during SPER by splitting in three possible states: (i) a diffusive one that migrates in amorphous Si; (ii) an interface segregated state evidenced by the presence of a F accumulation peak at the amorphous-crystal interface; (iii) a clustered F state. The interplay among these states and their roles in the F incorporation into crystalline Si are fully described. It is shown that diffusive F migrates by a trap limited diffusion mechanism and also interacts with the advancing interface by a sticking-release dynamics that regulates the amount of F segregated at the interface. We demonstrate that this last quantity determines the regrowth rate through an exponential law. On the other hand we show that neither the diffusive F nor the one segregated at the interface can directly incorporate into the crystal but F has to cluster in the amorphous phase before being incorporated in the crystal, in agreement with recent experimental observations. The trends of the model parameters as a function of the temperature are shown and discussed obtaining a clear energetic scheme of the F redistribution and incorporation in preamorphized Si. The above physical understanding and the model could have a strong impact on the use of F as a tool for optimizing the doping profiles in the fabrication of ultrashallow junctions. © 2010 The American Physical Society.

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This paper is concerned with time-domain optimal control of active suspensions. The optimal control problem formulation has been generalised by incorporating both road disturbances (ride quality) and a representation of driver inputs (handling quality) into the optimal control formulation. A regular optimal control problem as well as a risk-sensitive exponential optimal control performance index is considered. Emphasis has been given to practical considerations including the issue of state estimation in the presence of load disturbances (driver inputs). © 2012 IEEE.

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Electrostatic forces play a key role in mediating interactions between proteins. However, gaining quantitative insights into the complex effects of electrostatics on protein behavior has proved challenging, due to the wide palette of scenarios through which both cations and anions can interact with polypeptide molecules in a specific manner or can result in screening in solution. In this article, we have used a variety of biophysical methods to probe the steady-state kinetics of fibrillar protein self-assembly in a highly quantitative manner to detect how it is modulated by changes in solution ionic strength. Due to the exponential modulation of the reaction rate by electrostatic forces, this reaction represents an exquisitely sensitive probe of these effects in protein-protein interactions. Our approach, which involves a combination of experimental kinetic measurements and theoretical analysis, reveals a hierarchy of electrostatic effects that control protein aggregation. Furthermore, our results provide a highly sensitive method for the estimation of the magnitude of binding of a variety of ions to protein molecules.

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This paper considers how the provision of integrated household-level infrastructure – particularly water and environmental sanitation (including water supply, sewerage, roads, storm drainage and solid waste management) –can play a leading role in improving the conditions in slum settlements. Around 700 socio-economic interviews were carried out in India and South Africa to investigate an innovative approach called slum networking, which sees the strong correlation between slum locations and drainage paths as an opportunity for improving the wider urban environment. This recognition allows resources to be mobilised locally, thereby removing the need for external aid funding. The evidence from the 700 families shows that communities perceive water and sanitation inputs to be their top priority and are willing to contribute to the costs. If slum upgrading is led with access to integrated water and environmental sanitation at household level with community contributions to the cost of infrastructure, then slum communities subsequently invest considerably greater sums in improved housing and education, with longer term contributions to poverty alleviation, improvements in health and literacy and an increase in disposable incomes.

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An ultrasound image is created from backscattered echoes originating from both diffuse and directional scattering. It is potentially useful to separate these two components for the purpose of tissue characterization. This article presents several models for visualization of scattering fields on 3-dimensional (3D) ultrasound imaging. By scanning the same anatomy from multiple directions, we can observe the variation of specular intensity as a function of the viewing angle. This article considers two models for estimating the diffuse and specular components of the backscattered intensity: a modification of the well-known Phong reflection model and an existing exponential model. We examine 2-dimensional implementations and also propose novel 3D extensions of these models in which the probe is not constrained to rotate within a plane. Both simulation and experimental results show that improved performance can be achieved with 3D models. © 2013 by the American Institute of Ultrasound in Medicine.

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Although it is widely believed that reinforcement learning is a suitable tool for describing behavioral learning, the mechanisms by which it can be implemented in networks of spiking neurons are not fully understood. Here, we show that different learning rules emerge from a policy gradient approach depending on which features of the spike trains are assumed to influence the reward signals, i.e., depending on which neural code is in effect. We use the framework of Williams (1992) to derive learning rules for arbitrary neural codes. For illustration, we present policy-gradient rules for three different example codes - a spike count code, a spike timing code and the most general "full spike train" code - and test them on simple model problems. In addition to classical synaptic learning, we derive learning rules for intrinsic parameters that control the excitability of the neuron. The spike count learning rule has structural similarities with established Bienenstock-Cooper-Munro rules. If the distribution of the relevant spike train features belongs to the natural exponential family, the learning rules have a characteristic shape that raises interesting prediction problems.

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In this paper we consider the problem of constructing a distributed feedback law to achieve synchronization for a group of k agents whose states evolve on SO(n) and which exchange only partial state information along communication links. The partial state information is given by the action of the state on reference vectors in ℝn. We propose a gradient based control law which achieves exponential local convergence to a synchronization configuration under a rank condition on a generalized Laplacian matrix. Furthermore, we discuss the case of time-varying reference vectors and provide a convergence result for this case. The latter helps reach synchronization, requiring less communication links and weaker conditions on the instantaneous reference vectors. Our methods are illustrated on an attitude synchronization problem where agents exchange only their relative positions observed in the respective body frames. ©2009 IEEE.

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We introduce a characterization of contraction for bounded convex sets. For discrete-time multi-agent systems we provide an explicit upperbound on the rate of convergence to a consensus under the assumptions of contractiveness and (weak) connectedness (across an interval.) Convergence is shown to be exponential when either the system or the function characterizing the contraction is linear. Copyright © 2007 IFAC.