The Affine Uncertainty Principle, Associated Frames and Applications in Signal Processing

Uncertainty relations play a prominent role in signal processing, stating that a signal can not be simultaneously concentrated in the two related domains of the corresponding phase space. In particular, a new uncertainty principle for the affine group, which is directly related to the wavelet transform has lead to a new minimizing waveform. In this thesis, a frame construction is proposed which leads to approximately tight frames based on this minimizing waveform. Frame properties such as the diagonality of the frame operator as well as lower and upper frame bounds are analyzed. Additionally, three applications of such frame constructions are introduced: inpainting of missing audio data, detection of neuronal spikes in extracellular recorded data and peak detection in MALDI imaging data

Patient Reported Outcomes in Chronic Inflammatory Diseases: Current State, Limitations and Perspectives

Chronic inflammatory diseases (CID) are emerging disorders which do not only affect specific organs with respective clinical symptoms but can also affect various aspects of life, such as emotional distress, anxiety, fatigue and quality of life. These facets of chronic disease are often not recognized in the therapy of CID patients. Furthermore, the symptoms and patient-reported outcomes often do not correlate well with the actual inflammatory burden. The discrepancy between patient-reported symptoms and objectively assessed disease activity can indeed be instructive for the treating physician to draw an integrative picture of an individual's disease course. This poses a challenge for the design of novel, more comprehensive disease assessments. In this mini-review, we report on the currently available patient-reported outcomes, the unmet needs in the field of chronic inflammatory diseases and the challenges of addressing these

Comparison of Variational Approaches for the Exactly Solvable 1/r-Hubbard Chain

We study Hartree-Fock, Gutzwiller, Baeriswyl, and combined Gutzwiller-Baeriswyl wave functions for the exactly solvable one-dimensional $1/r$-Hubbard model. We find that none of these variational wave functions is able to correctly reproduce the physics of the metal-to-insulator transition which occurs in the model for half-filled bands when the interaction strength equals the bandwidth. The many-particle problem to calculate the variational ground state energy for the Baeriswyl and combined Gutzwiller-Baeriswyl wave function is exactly solved for the~$1/r$-Hubbard model. The latter wave function becomes exact both for small and large interaction strength, but it incorrectly predicts the metal-to-insulator transition to happen at infinitely strong interactions. We conclude that neither Hartree-Fock nor Jastrow-type wave functions yield reliable predictions on zero temperature phase transitions in low-dimensional, i.e., charge-spin separated systems.Comment: 23 pages + 3 figures available on request; LaTeX under REVTeX 3.

The H\"older Inequality for KMS States

We prove a H\"older inequality for KMS States, which generalises a well-known trace-inequality. Our results are based on the theory of non-commutative $L_p$-spaces.Comment: 10 page

Genome-wide protein–DNA binding dynamics suggest a molecular clutch for transcription factor function

Dynamic access to genetic information is central to organismal development and environmental response. Consequently, genomic processes must be regulated by mechanisms that alter genome function relatively rapidly1-4. Conventional chromatin immunoprecipitation (ChIP) experiments measure transcription factor (TF) occupancy5, but are blind to kinetics and are poor predictors of TF function at a given locus. To measure TF binding dynamics genome-wide, we performed competition ChIP6,7 with a sequence-specific S. cerevisiae transcription factor, Rap18. Rap1 binding dynamics and Rap1 occupancy were only weakly correlated (R2 = 0.14), but binding dynamics were more strongly linked to function than occupancy. Long Rap1 residence was coupled to transcriptional activation, while fast binding turnover, which we term “treadmilling”, was linked to low transcriptional output. Thus, DNA-binding events that appear identical by conventional ChIP may have starkly different underlying modes of interaction that lead to opposing functional outcomes. We propose that TF binding turnover is a major point of regulation in determining the functional consequences of transcription factor binding, and is mediated in large part by control of competition between TFs and nucleosomes. Our model (Supplementary Fig. 1) predicts a clutch-like mechanism that rapidly engages a treadmilling transcription factor into a stable binding state, or vice-versa, to modulate TF function

Schwieriger Atemweg bei Neurofibromatose Typ 1 mit Einblutung

Ein 44-jähriger Mann entwickelte eine rasch grössenprogrediente Schwellung am Hals mit zunehmender Dyspnoe nach dem Verzehr von erdnusshaltigen Schokolinsen. Fremdanamnestisch bestand eine NF1 und eine schwere Allergie auf Erdnüsse

Wehrl entropy, Lieb conjecture and entanglement monotones

We propose to quantify the entanglement of pure states of $N \times N$ bipartite quantum system by defining its Husimi distribution with respect to $SU(N)\times SU(N)$ coherent states. The Wehrl entropy is minimal if and only if the pure state analyzed is separable. The excess of the Wehrl entropy is shown to be equal to the subentropy of the mixed state obtained by partial trace of the bipartite pure state. This quantity, as well as the generalized (R{\'e}nyi) subentropies, are proved to be Schur--convex, so they are entanglement monotones and may be used as alternative measures of entanglement