Large disturbances in power systems often initiate complex interactions between continuous dynamics and discrete events. Such behaviour can be modeled in a systematic way by a set of differential-algebraic equations, modified to incorporate impulse (state reset) action and constraint switching. The paper presents a practical object-oriented approach to implementing the DAIS model. The systemati...

The paper presents an overview of the inverse problems associated with applications of underwater acoustics. The problems are classified into four main categories, according to the recoverable quantities : Acoustic source localization, bottom identification, ocean acoustic tomography and target recognition. The paper gives emphasis to the three first categories, and includes methods to solve th...

Given a square matrix A, the inverse subspace problem is concerned with determining a closest matrix to A with a prescribed invariant subspace. When A is Hermitian, the closest matrix may be required to be Hermitian. We measure distance in the Frobenius norm and discuss applications to Krylov subspace methods for the solution of large-scale linear systems of equations and eigenvalue problems as...

This thesis comments on the use of Bregman distances in the context of singular regularization schemes for inverse problems. According to previous works the use of Bregman distances in combination with variational frameworks, based on singular regularization energies, leads to improved approximations of inverse problems solutions. The Bregman distance has become a powerful tool for the analysis...

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Several recent experiments in biology study systems composed of several interacting elements, for example neuron networks. Normally, measurements describe only the collective behavior of the system, even if in most cases we would like to characterize how its different parts interact. The goal of this thesis is to extract information about the microscopic interactions as a function of their coll...

We consider a sequence space model of statistical linear inverse problems where we need to estimate a function f from indirect noisy observations. Let a nite set of linear estimators be given. Our aim is to mimic the estimator in that has the smallest risk on the true f. Under general conditions, we show that this can be achieved by simple minimization of unbiased risk estimator, provided the s...

Within this chapter we present recent results on sparse recovery algorithms for inverse and ill-posed problems, i.e. we focus on those inverse problems in which we can assume that the solution has a sparse series expansion with respect to a preassigned basis or frame. The presented approaches to approximate solutions of inverse problems are limited to iterative strategies that essentially rely ...

ion is not needed. Inverse problems 531 Theorem 6.13. Two Gaussian measures μi = N (mi, Ci), i = 1, 2, on a Hilbert space H are either singular or equivalent. They are equivalent if and only if the following three conditions hold: (i) Im(C 1 ) = Im(C 1/2 2 ) := E, (ii) m1 −m2 ∈ E, (iii) the operator T := ( C−1/2 1 C 1/2 2 )( C−1/2 1 C 1/2 2 )∗ − I is Hilbert–Schmidt in E. In particular, choosin...

this paper is devoted to the proof of the unique solvability ofthe inverse problems for second-order differential operators withregular singularities. it is shown that the potential functioncan be determined from spectral data, also we prove a uniquenesstheorem in the inverse problem.