146 research outputs found
Preasymptotic Convergence of Randomized Kaczmarz Method
Kaczmarz method is one popular iterative method for solving inverse problems,
especially in computed tomography. Recently, it was established that a
randomized version of the method enjoys an exponential convergence for
well-posed problems, and the convergence rate is determined by a variant of the
condition number. In this work, we analyze the preasymptotic convergence
behavior of the randomized Kaczmarz method, and show that the low-frequency
error (with respect to the right singular vectors) decays faster during first
iterations than the high-frequency error. Under the assumption that the inverse
solution is smooth (e.g., sourcewise representation), the result explains the
fast empirical convergence behavior, thereby shedding new insights into the
excellent performance of the randomized Kaczmarz method in practice. Further,
we propose a simple strategy to stabilize the asymptotic convergence of the
iteration by means of variance reduction. We provide extensive numerical
experiments to confirm the analysis and to elucidate the behavior of the
algorithms.Comment: 20 page
Structured Sparsity: Discrete and Convex approaches
Compressive sensing (CS) exploits sparsity to recover sparse or compressible
signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity
is also used to enhance interpretability in machine learning and statistics
applications: While the ambient dimension is vast in modern data analysis
problems, the relevant information therein typically resides in a much lower
dimensional space. However, many solutions proposed nowadays do not leverage
the true underlying structure. Recent results in CS extend the simple sparsity
idea to more sophisticated {\em structured} sparsity models, which describe the
interdependency between the nonzero components of a signal, allowing to
increase the interpretability of the results and lead to better recovery
performance. In order to better understand the impact of structured sparsity,
in this chapter we analyze the connections between the discrete models and
their convex relaxations, highlighting their relative advantages. We start with
the general group sparse model and then elaborate on two important special
cases: the dispersive and the hierarchical models. For each, we present the
models in their discrete nature, discuss how to solve the ensuing discrete
problems and then describe convex relaxations. We also consider more general
structures as defined by set functions and present their convex proxies.
Further, we discuss efficient optimization solutions for structured sparsity
problems and illustrate structured sparsity in action via three applications.Comment: 30 pages, 18 figure
Precision Tests of the Standard Model
30 páginas, 11 figuras, 11 tablas.-- Comunicación presentada al 25º Winter Meeting on Fundamental Physics celebrado del 3 al 8 de MArzo de 1997 en Formigal (España).Precision measurements of electroweak observables provide stringent tests of the Standard Model structure and an accurate determination of its parameters. An overview of the present experimental status is presented.This work has been supported in part
by CICYT (Spain) under grant No. AEN-96-1718.Peer reviewe
Interaction of consumer preferences and climate policies in the global transition to low-carbon vehicles
Burgeoning demands for mobility and private vehicle ownership undermine global efforts to reduce energy-related greenhouse gas emissions. Advanced vehicles powered by low-carbon sources of electricity or hydrogen offer an alternative to conventional fossil-fuelled technologies. Yet, despite ambitious pledges and investments by governments and automakers, it is by no means clear that these vehicles will ultimately reach mass-market consumers. Here, we develop state-of-the-art representations of consumer preferences in multiple, global energy- economy models, specifically focusing on the non-financial preferences of individuals. We employ these enhanced model formulations to analyse the potential for a low-carbon vehicle revolution up to mid-century. Our analysis shows that a diverse set of measures targeting vehicle buyers is necessary for driving widespread adoption of clean technologies. Carbon pricing alone is insufficient for bringing low-carbon vehicles to mass market, though it can certainly play a supporting role in ensuring a decarbonised energy supply
Low Complexity Regularization of Linear Inverse Problems
Inverse problems and regularization theory is a central theme in contemporary
signal processing, where the goal is to reconstruct an unknown signal from
partial indirect, and possibly noisy, measurements of it. A now standard method
for recovering the unknown signal is to solve a convex optimization problem
that enforces some prior knowledge about its structure. This has proved
efficient in many problems routinely encountered in imaging sciences,
statistics and machine learning. This chapter delivers a review of recent
advances in the field where the regularization prior promotes solutions
conforming to some notion of simplicity/low-complexity. These priors encompass
as popular examples sparsity and group sparsity (to capture the compressibility
of natural signals and images), total variation and analysis sparsity (to
promote piecewise regularity), and low-rank (as natural extension of sparsity
to matrix-valued data). Our aim is to provide a unified treatment of all these
regularizations under a single umbrella, namely the theory of partial
smoothness. This framework is very general and accommodates all low-complexity
regularizers just mentioned, as well as many others. Partial smoothness turns
out to be the canonical way to encode low-dimensional models that can be linear
spaces or more general smooth manifolds. This review is intended to serve as a
one stop shop toward the understanding of the theoretical properties of the
so-regularized solutions. It covers a large spectrum including: (i) recovery
guarantees and stability to noise, both in terms of -stability and
model (manifold) identification; (ii) sensitivity analysis to perturbations of
the parameters involved (in particular the observations), with applications to
unbiased risk estimation ; (iii) convergence properties of the forward-backward
proximal splitting scheme, that is particularly well suited to solve the
corresponding large-scale regularized optimization problem
Efficient Sparse Coding in Early Sensory Processing: Lessons from Signal Recovery
Sensory representations are not only sparse, but often overcomplete: coding units significantly outnumber the input units. For models of neural coding this overcompleteness poses a computational challenge for shaping the signal processing channels as well as for using the large and sparse representations in an efficient way. We argue that higher level overcompleteness becomes computationally tractable by imposing sparsity on synaptic activity and we also show that such structural sparsity can be facilitated by statistics based decomposition of the stimuli into typical and atypical parts prior to sparse coding. Typical parts represent large-scale correlations, thus they can be significantly compressed. Atypical parts, on the other hand, represent local features and are the subjects of actual sparse coding. When applied on natural images, our decomposition based sparse coding model can efficiently form overcomplete codes and both center-surround and oriented filters are obtained similar to those observed in the retina and the primary visual cortex, respectively. Therefore we hypothesize that the proposed computational architecture can be seen as a coherent functional model of the first stages of sensory coding in early vision
Compressive Inverse Scattering I. High Frequency SIMO Measurements
Inverse scattering from discrete targets with the
single-input-multiple-output (SIMO), multiple-input-single-output (MISO) or
multiple-input-multiple-output (MIMO) measurements is analyzed by compressed
sensing theory with and without the Born approximation. High frequency analysis
of (probabilistic) recoverability by the -based
minimization/regularization principles is presented. In the absence of noise,
it is shown that the -based solution can recover exactly the target of
sparsity up to the dimension of the data either with the MIMO measurement for
the Born scattering or with the SIMO/MISO measurement for the exact scattering.
The stability with respect to noisy data is proved for weak or widely separated
scatterers. Reciprocity between the SIMO and MISO measurements is analyzed.
Finally a coherence bound (and the resulting recoverability) is proved for
diffraction tomography with high-frequency, few-view and limited-angle
SIMO/MISO measurements.Comment: A new section on diffraction tomography added; typos fixed; new
figures adde
The Properties of Lion Roars and Electron Dynamics in Mirror Mode Waves Observed by the Magnetospheric MultiScale Mission
Mirror mode waves are ubiquitous in the Earth's magnetosheath, in particular behind the quasi‐perpendicular shock. Embedded in these nonlinear structures, intense lion roars are often observed. Lion roars are characterized by whistler wave packets at a frequency ∼100 Hz, which are thought to be generated in the magnetic field minima. In this study, we make use of the high time resolution instruments on board the Magnetospheric MultiScale mission to investigate these waves and the associated electron dynamics in the quasi‐perpendicular magnetosheath on 22 January 2016. We show that despite a core electron parallel anisotropy, lion roars can be generated locally in the range 0.05–0.2fce by the perpendicular anisotropy of electrons in a particular energy range. We also show that intense lion roars can be observed up to higher frequencies due to the sharp nonlinear peaks of the signal, which appear as sharp spikes in the dynamic spectra. As a result, a high sampling rate is needed to estimate correctly their amplitude, and the latter might have been underestimated in previous studies using lower time resolution instruments. We also present for the first‐time 3‐D high time resolution electron velocity distribution functions in mirror modes. We demonstrate that the dynamics of electrons trapped in the mirror mode structures are consistent with the Kivelson and Southwood (1996) model. However, these electrons can also interact with the embedded lion roars: first signatures of electron quasi‐linear pitch angle diffusion and possible signatures of nonlinear interaction with high‐amplitude wave packets are presented. These processes can lead to electron untrapping from mirror modes
Brazil in the Era of Fascism: The “New State” of Getúlio Vargas
The New State established in Brazil by Getúlio Vargas (1937–1945) is the most important case of the institutionalisation of a dictatorship of the fascism era in Latin America. During this time, an impressive spectrum of authoritarian regimes was established, some of which were very instable and poorly institutionalised, while others were more consolidated. Roger Griffin coined the concept of para-fascism for some of them, and the “New State” of Getúlio Vargas in Brazil is a paradigmatic case. In this essay, we analyse the processes of institutional reform in 1930s Brazil paying particular attention to how domestic political actors look at institutional models of fascism and corporatism.info:eu-repo/semantics/publishedVersio
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