1,064 research outputs found
Non-signalling energy use in the brain.
Energy use limits the information processing power of the brain. However, apart from the ATP used to power electrical signalling, a significant fraction of the brain's energy consumption is not directly related to information processing. The brain spends just under half of its energy on non-signalling processes, but it remains poorly understood which tasks are so energetically costly for the brain. We review existing experimental data on subcellular processes that may contribute to this non-signalling energy use, and provide modelling estimates, to try to assess the magnitude of their ATP consumption and consider how their changes in pathology may compromise neuronal function. As a main result, surprisingly little consensus exists on the energetic cost of actin treadmilling, with estimates ranging from < 1% of the brain's global energy budget up to one-half of neuronal energy use. Microtubule treadmilling and protein synthesis have been estimated to account for very small fractions of the brain's energy budget, whereas there is stronger evidence that lipid synthesis and mitochondrial proton leak are energetically expensive. Substantial further research is necessary to close these gaps in knowledge about the brain's energy-expensive non-signalling tasks
Beyond convergence rates: Exact recovery with Tikhonov regularization with sparsity constraints
The Tikhonov regularization of linear ill-posed problems with an
penalty is considered. We recall results for linear convergence rates and
results on exact recovery of the support. Moreover, we derive conditions for
exact support recovery which are especially applicable in the case of ill-posed
problems, where other conditions, e.g. based on the so-called coherence or the
restricted isometry property are usually not applicable. The obtained results
also show that the regularized solutions do not only converge in the
-norm but also in the vector space (when considered as the
strict inductive limit of the spaces as tends to infinity).
Additionally, the relations between different conditions for exact support
recovery and linear convergence rates are investigated.
With an imaging example from digital holography the applicability of the
obtained results is illustrated, i.e. that one may check a priori if the
experimental setup guarantees exact recovery with Tikhonov regularization with
sparsity constraints
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
Inverse Problems in a Bayesian Setting
In a Bayesian setting, inverse problems and uncertainty quantification (UQ)
--- the propagation of uncertainty through a computational (forward) model ---
are strongly connected. In the form of conditional expectation the Bayesian
update becomes computationally attractive. We give a detailed account of this
approach via conditional approximation, various approximations, and the
construction of filters. Together with a functional or spectral approach for
the forward UQ there is no need for time-consuming and slowly convergent Monte
Carlo sampling. The developed sampling-free non-linear Bayesian update in form
of a filter is derived from the variational problem associated with conditional
expectation. This formulation in general calls for further discretisation to
make the computation possible, and we choose a polynomial approximation. After
giving details on the actual computation in the framework of functional or
spectral approximations, we demonstrate the workings of the algorithm on a
number of examples of increasing complexity. At last, we compare the linear and
nonlinear Bayesian update in form of a filter on some examples.Comment: arXiv admin note: substantial text overlap with arXiv:1312.504
The equivalence of fluctuation scale dependence and autocorrelations
We define optimal per-particle fluctuation and correlation measures, relate
fluctuations and correlations through an integral equation and show how to
invert that equation to obtain precise autocorrelations from fluctuation scale
dependence. We test the precision of the inversion with Monte Carlo data and
compare autocorrelations to conditional distributions conventionally used to
study high- jet structure.Comment: 10 pages, 9 figures, proceedings, MIT workshop on correlations and
fluctuations in relativistic nuclear collision
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
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