1,088 research outputs found
Non-signalling energy use in the developing rat brain
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
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
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
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
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
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 Penalty Term
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 of the regularized solutions in dependence of the noise
level . 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 .Comment: 15 page
Necessary conditions for variational regularization schemes
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
Consider a nonlinear ill-posed operator equation where is
defined on a Banach space . In general, for solving this equation
numerically, a finite dimensional approximation of and an approximation of
are required. Moreover, in general the given data \yd of 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
--space
Besov priors for Bayesian inverse problems
We consider the inverse problem of estimating a function 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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