1,088 research outputs found

    Non-signalling energy use in the developing rat brain

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    Energy use in the brain constrains its information processing power, but only about half the brain's energy consumption is directly related to information processing. Evidence for which non-signalling processes consume the rest of the brain's energy has been scarce. For the first time, we investigated the energy use of the brain's main non-signalling tasks with a single method. After blocking each non-signalling process, we measured oxygen level changes in juvenile rat brain slices with an oxygen-sensing microelectrode and calculated changes in oxygen consumption throughout the slice using a modified diffusion equation. We found that the turnover of the actin and microtubule cytoskeleton, followed by lipid synthesis, are significant energy drains, contributing 25%, 22% and 18%, respectively, to the rate of oxygen consumption. In contrast, protein synthesis is energetically inexpensive. We assess how these estimates of energy expenditure relate to brain energy use in vivo, and how they might differ in the mature brain

    Adaptive Covariance Estimation with model selection

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    We provide in this paper a fully adaptive penalized procedure to select a covariance among a collection of models observing i.i.d replications of the process at fixed observation points. For this we generalize previous results of Bigot and al. and propose to use a data driven penalty to obtain an oracle inequality for the estimator. We prove that this method is an extension to the matricial regression model of the work by Baraud

    Parameter identification in a semilinear hyperbolic system

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    We consider the identification of a nonlinear friction law in a one-dimensional damped wave equation from additional boundary measurements. Well-posedness of the governing semilinear hyperbolic system is established via semigroup theory and contraction arguments. We then investigte the inverse problem of recovering the unknown nonlinear damping law from additional boundary measurements of the pressure drop along the pipe. This coefficient inverse problem is shown to be ill-posed and a variational regularization method is considered for its stable solution. We prove existence of minimizers for the Tikhonov functional and discuss the convergence of the regularized solutions under an approximate source condition. The meaning of this condition and some arguments for its validity are discussed in detail and numerical results are presented for illustration of the theoretical findings

    Design and Development of On-orbit Servicing CubeSat-class Satellite

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    The long term vision of the Naval Academy Satellite Team for Autonomous Robotics (NSTAR) is to lower both the risk and cost of on-orbit space system construction and repair through the use of a CubeSat robotic arm system. NSTAR developments will enable space agencies and private companies to construct large, complex structures in space at a reduced cost with greater diagnostic assessment ability. Robotic Experimental Construction Satellite (RECS) is designed as NSTAR’s second project iteration and works to meet five different capabilities for semi-autonomous orbit assembly. RECS is a 3U CubeSat with two extendable robotic arms, each with six degrees of freedom. In coordination with the launch manifest, RECS has been designed, completed, and is awaiting launch to the ISS where it will conduct testing. This type of on-orbit demonstration has never been completed on CubeSat-scale systems. A successful mission will indicate entry into a new frontier of satellites, where space systems remain in operation longer, missions are of lower cost, and the ability to complete space-based scientific research is expanded. This paper provides the details of the design and capabilities of the NSTAR system

    Numerical studies of the Lagrangian approach for reconstruction of the conductivity in a waveguide

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    We consider an inverse problem of reconstructing the conductivity function in a hyperbolic equation using single space-time domain noisy observations of the solution on the backscattering boundary of the computational domain. We formulate our inverse problem as an optimization problem and use Lagrangian approach to minimize the corresponding Tikhonov functional. We present a theorem of a local strong convexity of our functional and derive error estimates between computed and regularized as well as exact solutions of this functional, correspondingly. In numerical simulations we apply domain decomposition finite element-finite difference method for minimization of the Lagrangian. Our computational study shows efficiency of the proposed method in the reconstruction of the conductivity function in three dimensions

    Singular Value Decomposition of Operators on Reproducing Kernel Hilbert Spaces

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    Reproducing kernel Hilbert spaces (RKHSs) play an important role in many statistics and machine learning applications ranging from support vector machines to Gaussian processes and kernel embeddings of distributions. Operators acting on such spaces are, for instance, required to embed conditional probability distributions in order to implement the kernel Bayes rule and build sequential data models. It was recently shown that transfer operators such as the Perron-Frobenius or Koopman operator can also be approximated in a similar fashion using covariance and cross-covariance operators and that eigenfunctions of these operators can be obtained by solving associated matrix eigenvalue problems. The goal of this paper is to provide a solid functional analytic foundation for the eigenvalue decomposition of RKHS operators and to extend the approach to the singular value decomposition. The results are illustrated with simple guiding examples

    Sparse Regularization with lql^q Penalty Term

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    We consider the stable approximation of sparse solutions to non-linear operator equations by means of Tikhonov regularization with a subquadratic penalty term. Imposing certain assumptions, which for a linear operator are equivalent to the standard range condition, we derive the usual convergence rate O(δ)O(\sqrt{\delta}) of the regularized solutions in dependence of the noise level δ\delta. Particular emphasis lies on the case, where the true solution is known to have a sparse representation in a given basis. In this case, if the differential of the operator satisfies a certain injectivity condition, we can show that the actual convergence rate improves up to O(δ)O(\delta).Comment: 15 page

    Necessary conditions for variational regularization schemes

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    We study variational regularization methods in a general framework, more precisely those methods that use a discrepancy and a regularization functional. While several sets of sufficient conditions are known to obtain a regularization method, we start with an investigation of the converse question: How could necessary conditions for a variational method to provide a regularization method look like? To this end, we formalize the notion of a variational scheme and start with comparison of three different instances of variational methods. Then we focus on the data space model and investigate the role and interplay of the topological structure, the convergence notion and the discrepancy functional. Especially, we deduce necessary conditions for the discrepancy functional to fulfill usual continuity assumptions. The results are applied to discrepancy functionals given by Bregman distances and especially to the Kullback-Leibler divergence.Comment: To appear in Inverse Problem

    Discretization of variational regularization in Banach spaces

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    Consider a nonlinear ill-posed operator equation F(u)=yF(u)=y where FF is defined on a Banach space XX. In general, for solving this equation numerically, a finite dimensional approximation of XX and an approximation of FF are required. Moreover, in general the given data \yd of yy are noisy. In this paper we analyze finite dimensional variational regularization, which takes into account operator approximations and noisy data: We show (semi-)convergence of the regularized solution of the finite dimensional problems and establish convergence rates in terms of Bregman distances under appropriate sourcewise representation of a solution of the equation. The more involved case of regularization in nonseparable Banach spaces is discussed in detail. In particular we consider the space of finite total variation functions, the space of functions of finite bounded deformation, and the LL^\infty--space

    Besov priors for Bayesian inverse problems

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    We consider the inverse problem of estimating a function uu from noisy, possibly nonlinear, observations. We adopt a Bayesian approach to the problem. This approach has a long history for inversion, dating back to 1970, and has, over the last decade, gained importance as a practical tool. However most of the existing theory has been developed for Gaussian prior measures. Recently Lassas, Saksman and Siltanen (Inv. Prob. Imag. 2009) showed how to construct Besov prior measures, based on wavelet expansions with random coefficients, and used these prior measures to study linear inverse problems. In this paper we build on this development of Besov priors to include the case of nonlinear measurements. In doing so a key technical tool, established here, is a Fernique-like theorem for Besov measures. This theorem enables us to identify appropriate conditions on the forward solution operator which, when matched to properties of the prior Besov measure, imply the well-definedness and well-posedness of the posterior measure. We then consider the application of these results to the inverse problem of finding the diffusion coefficient of an elliptic partial differential equation, given noisy measurements of its solution.Comment: 18 page
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