577 research outputs found
Analysis of A Nonsmooth Optimization Approach to Robust Estimation
In this paper, we consider the problem of identifying a linear map from
measurements which are subject to intermittent and arbitarily large errors.
This is a fundamental problem in many estimation-related applications such as
fault detection, state estimation in lossy networks, hybrid system
identification, robust estimation, etc. The problem is hard because it exhibits
some intrinsic combinatorial features. Therefore, obtaining an effective
solution necessitates relaxations that are both solvable at a reasonable cost
and effective in the sense that they can return the true parameter vector. The
current paper discusses a nonsmooth convex optimization approach and provides a
new analysis of its behavior. In particular, it is shown that under appropriate
conditions on the data, an exact estimate can be recovered from data corrupted
by a large (even infinite) number of gross errors.Comment: 17 pages, 9 figure
Sparse phase retrieval via group-sparse optimization
This paper deals with sparse phase retrieval, i.e., the problem of estimating
a vector from quadratic measurements under the assumption that few components
are nonzero. In particular, we consider the problem of finding the sparsest
vector consistent with the measurements and reformulate it as a group-sparse
optimization problem with linear constraints. Then, we analyze the convex
relaxation of the latter based on the minimization of a block l1-norm and show
various exact recovery and stability results in the real and complex cases.
Invariance to circular shifts and reflections are also discussed for real
vectors measured via complex matrices
Finding sparse solutions of systems of polynomial equations via group-sparsity optimization
The paper deals with the problem of finding sparse solutions to systems of
polynomial equations possibly perturbed by noise. In particular, we show how
these solutions can be recovered from group-sparse solutions of a derived
system of linear equations. Then, two approaches are considered to find these
group-sparse solutions. The first one is based on a convex relaxation resulting
in a second-order cone programming formulation which can benefit from efficient
reweighting techniques for sparsity enhancement. For this approach, sufficient
conditions for the exact recovery of the sparsest solution to the polynomial
system are derived in the noiseless setting, while stable recovery results are
obtained for the noisy case. Though lacking a similar analysis, the second
approach provides a more computationally efficient algorithm based on a greedy
strategy adding the groups one-by-one. With respect to previous work, the
proposed methods recover the sparsest solution in a very short computing time
while remaining at least as accurate in terms of the probability of success.
This probability is empirically analyzed to emphasize the relationship between
the ability of the methods to solve the polynomial system and the sparsity of
the solution.Comment: Journal of Global Optimization (2014) to appea
On Conditions for Uniqueness in Sparse Phase Retrieval
The phase retrieval problem has a long history and is an important problem in
many areas of optics. Theoretical understanding of phase retrieval is still
limited and fundamental questions such as uniqueness and stability of the
recovered solution are not yet fully understood. This paper provides several
additions to the theoretical understanding of sparse phase retrieval. In
particular we show that if the measurement ensemble can be chosen freely, as
few as 4k-1 phaseless measurements suffice to guarantee uniqueness of a
k-sparse M-dimensional real solution. We also prove that 2(k^2-k+1) Fourier
magnitude measurements are sufficient under rather general conditions
Nonlinear Compressive Particle Filtering
Many systems for which compressive sensing is used today are dynamical. The
common approach is to neglect the dynamics and see the problem as a sequence of
independent problems. This approach has two disadvantages. Firstly, the
temporal dependency in the state could be used to improve the accuracy of the
state estimates. Secondly, having an estimate for the state and its support
could be used to reduce the computational load of the subsequent step. In the
linear Gaussian setting, compressive sensing was recently combined with the
Kalman filter to mitigate above disadvantages. In the nonlinear dynamical case,
compressive sensing can not be used and, if the state dimension is high, the
particle filter would perform poorly. In this paper we combine one of the most
novel developments in compressive sensing, nonlinear compressive sensing, with
the particle filter. We show that the marriage of the two is essential and that
neither the particle filter or nonlinear compressive sensing alone gives a
satisfying solution.Comment: Accepted to CDC 201
The Self-Employment of Immigrants and Natives in Sweden
Earlier studies on entrepreneurship and self-employment among immigrants call attention to the fact that also the "market" for self-employment or entrepreneurs consists of a supply and demand side as well as the interaction between these two. More recent research suggests that a mix of personal resources, the surrounding structural context of markets, competition and the current political and economic environment, all acting together are seen as determining factors affecting self-employment by immigrants. However, few studies have been able to quantify the importance of these different aspects that determine ethnic self-employment. The central aim of this paper is therefore, by using multilevel regression, to quantify the role the country of birth respectively labour market area plays for understanding individual differences in self-employment. Using register data on individuals for the year of 2007 for the entire Swedish population we have in this study a unique opportunity to quantify the relative importance of the self-employers embeddedness in the social and ethnic networks (country of birth) and the regional business and public regulatory framework (labour market areas) measured. Our results suggest that of the total variation in individual differences in self-employment can 14 % (men) respectively 16 % (women) be attributed to the ethnic group and the labour market area. Furthermore, the ethnical groups accounted for 70 % (men) and 78 % (women) of this higher level variance. These results show that the social and ethnical context (measured by country of birth) and the economic environment (measured by local labour market areas) played a minor role for understanding individual differences in self-employment. These results can have important implications when planning interventions or other actions focusing on self-employment. Focusing only on ethnical groups/labour market areas might be inefficient as approximately 85 % of the variation is not explained by ethnical groups/labour market areas. Instead more general approaches or interventions focusing on other groups that capture a larger part of the variation might be more efficient.immigrants, self-employment, integration, entrepreneurship, multilevel logistic regression
Studies on Implementation of . . . High Throughput and Low Power Consumption
In this thesis we discuss design and implementation of frequency selective digital filters with high throughput and low power consumption. The thesis includes proposed arithmetic transformations of lattice wave digital filters that aim at increasing the throughput and reduce the power consumption of the filter implementation. The thesis also includes two case studies where digital filters with high throughput and low power consumption are required. A method for obtaining high throughput as well as reduced power consumption of digital filters is arithmetic transformation of the filter structure. In this thesis arithmetic transformations of first- and second-order Richards’ allpass sections composed by symmetric two-port adaptors and implemented using carry-save arithmetic are proposed. Such filter sections can be used for implementation of lattice wave digital filters and bireciprocal lattice wave digital filters. The latter structures are efficient for implementation of interpolators and decimators by factors of two. Th
Monoenergetic Gamma-Rays from Non-Minimal Kaluza-Klein Dark Matter Annihilations
We investigate monoenergetic gamma-ray signatures from annihilations of dark
matter comprised of Z^1, the first Kaluza-Klein excitation of the Z boson, in a
non-minimal Universal Extra Dimensions model. The self-interactions of the
non-Abelian Z^1 gauge boson give rise to a large number of contributing Feynman
diagrams that do not exist for annihilations of the Abelian gauge boson B^1,
which is the standard Kaluza-Klein dark matter candidate. We find that the
annihilation rate is indeed considerably larger for the Z^1 than for the B^1.
Even though relic density calculations indicate that the mass of the Z^1 should
be larger than the mass of the B^1, the predicted monoenergetic gamma fluxes
are of the same order of magnitude. We compare our results to existing
experimental limits, as well as to future sensitivities, for image air
Cherenkov telescopes, and we find that the limits are reached already with a
moderately large boost factor. The realistic prospects for detection depend on
the experimental energy resolution.Comment: 21 pages, 6 figures, REVTeX4. Minor misprints correcte
Privileged Communications-Attorney and Client
A high-dimensional regression space usually causes problems in nonlinear system identification.However, if the regression data are contained in (or spread tightly around) some manifold, thedimensionality can be reduced. This paper presents a use of dimension reduction techniques tocompose a two-step identification scheme suitable for high-dimensional identification problems withmanifold-valued regression data. Illustrating examples are also given
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