### 1On the Identifiability of Overcomplete Dictionaries via the Minimisation Principle Underlying K-SVD

, 2013

"... This article gives theoretical insights into the performance of K-SVD, a dictionary learning algorithm that has gained significant popularity in practical applications. The particular question studied here is when a dictionary Φ ∈ Rd×K can be recovered as local minimum of the minimisation criterion ..."

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This article gives theoretical insights into the performance of K-SVD, a dictionary learning algorithm that has gained significant popularity in practical applications. The particular question studied here is when a dictionary Φ ∈ Rd×K can be recovered as local minimum of the minimisation criterion underlying K-SVD from a set of N training signals yn = Φxn. A theoretical analysis of the problem leads to two types of identifiability results assuming the training signals are generated from a tight frame with coefficients drawn from a random symmetric distribution. First asymptotic results showing, that in expectation the generating dictionary can be recovered exactly as a local minimum of the K-SVD criterion if the coefficient distribution exhibits sufficient decay. This decay can be characterised by the coherence of the dictionary and the `1-norm of the coefficients. Based on the asymptotic results it is further demonstrated that given a finite number of training samples N, such that N / logN = O(K3d), except with probability O(N−Kd) there is a local minimum of the K-SVD criterion within distance O(KN−1/4) to the generating dictionary. Index Terms dictionary learning, sparse coding, K-SVD, finite sample size, sampling complexity, dictionary identification, minimisation criterion, sparse representation 1

### Subspace Communication

, 2014

"... We are surrounded by electronic devices that take advantage of wireless technologies, from our computer mice, which require little amounts of information, to our cellphones, which demand increasingly higher data rates. Until today, the coexistence of such a variety of services has been guaranteed by ..."

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We are surrounded by electronic devices that take advantage of wireless technologies, from our computer mice, which require little amounts of information, to our cellphones, which demand increasingly higher data rates. Until today, the coexistence of such a variety of services has been guaranteed by a fixed assignment of spectrum resources by regulatory agencies. This has resulted into a blind alley, as current wireless spectrum has become an expensive and a scarce resource. However, recent measurements in dense areas paint a very different picture: there is an actual underutilization of the spectrum by legacy sys-tems. Cognitive radio exhibits a tremendous promise for increasing the spectral efficiency for future wireless systems. Ideally, new secondary users would have a perfect panorama of the spectrum usage, and would opportunistically communicate over the available re-sources without degrading the primary systems. Yet in practice, monitoring the spectrum resources, detecting available resources for opportunistic communication, and transmit-ting over the resources are hard tasks. This thesis addresses the tasks of monitoring, de-

### COSMOLOGICAL MODELS OF MODIFIED GRAVITY

, 2013

"... The recent discovery of dark energy has prompted an investigation of ways in which the accelerated expansion of the universe can be realized. In this dissertation, we present two separate projects related to dark energy. The first project analyzes a class of braneworld models in which multiple brane ..."

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The recent discovery of dark energy has prompted an investigation of ways in which the accelerated expansion of the universe can be realized. In this dissertation, we present two separate projects related to dark energy. The first project analyzes a class of braneworld models in which multiple branes float in a five-dimensional anti-de Sitter bulk, while the second investigates a class of dark energy models from an effective field theory perspective. Investigations of models including extra dimensions have led to modifications of gravity involving a number of interesting features. In particular, the Randall-Sundrum model is well-known for achieving an amelioration of the hierarchy problem. However, the basic model relies on Minkowski branes and is subject to solar system constraints in the absence of a radion stabilization mechanism. We present a method by which a four-dimensional low-energy description can be obtained for braneworld scenarios, allowing for a number of generalizations to the original models. This method is applied to orbifolded and uncompactified N-brane models, deriving an effective four-dimensional action. The parameter space of this theory is constrained using observational evidence, and it is found that the generalizations do not weaken solar system constraints on the original model. Furthermore, we find that general

### under a Creative Commons Attribution Non-Commercial No Derivatives

, 2013

"... the condition that they attribute it, that they do not use it for commercial purposes and that they do not alter, transform or build upon it. For any reuse or redistribution, researchers must make clear to others the licence terms of this work. ..."

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the condition that they attribute it, that they do not use it for commercial purposes and that they do not alter, transform or build upon it. For any reuse or redistribution, researchers must make clear to others the licence terms of this work.

### Yang-Mills theory

, 2013

"... We calculate the three-point functions of pure Landau gauge QCD and investigate their influence on the propagators. As expected, the ghost-gluon vertex leads only to minor modifications, while the three-gluon vertex has a sizeable impact on the mid-momentum regime of the gluon propaga-tor. We descri ..."

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We calculate the three-point functions of pure Landau gauge QCD and investigate their influence on the propagators. As expected, the ghost-gluon vertex leads only to minor modifications, while the three-gluon vertex has a sizeable impact on the mid-momentum regime of the gluon propaga-tor. We describe an effective model of the three-gluon vertex that includes contributions from the neglected two-loop diagrams and thus allows to obtain propagators in good agreement with lattice results. We also determine the three-gluon vertex from these propagators and find good agree-ment with lattice results as well. In turn, these results allow us to assess the effect of the missing two-loop diagrams in the gluon propagator equation. Finally, we present the first self-consistent calculation that includes all two-and three-point functions. From quarks and gluons to hadronic matter: A bridge too far?

### P o S(QCD-TNT-III)018 On propagators and vertices of Landau gauge Yang-Mills theory

, 2013

"... We calculate the three-point functions of pure Landau gauge QCD and investigate their influence on the propagators. As expected, the ghost-gluon vertex leads only to minor modifications, while the three-gluon vertex has a sizeable impact on the mid-momentum regime of the gluon propaga-tor. We descri ..."

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We calculate the three-point functions of pure Landau gauge QCD and investigate their influence on the propagators. As expected, the ghost-gluon vertex leads only to minor modifications, while the three-gluon vertex has a sizeable impact on the mid-momentum regime of the gluon propaga-tor. We describe an effective model of the three-gluon vertex that includes contributions from the neglected two-loop diagrams and thus allows to obtain propagators in good agreement with lattice results. We also determine the three-gluon vertex from these propagators and find good agree-ment with lattice results as well. In turn, these results allow us to assess the effect of the missing two-loop diagrams in the gluon propagator equation. Finally, we present the first self-consistent calculation that includes all two-and three-point functions. From quarks and gluons to hadronic matter: A bridge too far?

### Name:...................................... Date:....................................

, 2010

"... belowground functioning of tropical biomes ..."

### E-Journal Article

"... Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, ..."

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, Rodriguez-Moreno and Peña (

*2013*) emphasize an important role of CDS prices as a basis of robust systemic risk measures. JEL*C*50 G10 G*15*The novelty of the paper lies in the use of the cross-correlation function (CCF) approach which allows to examine the presence of two types of causality (causality