Widely-tunable mid-infrared frequency comb source based on difference frequency generation

We report on a mid-IR frequency comb source of unprecedented tunability covering the entire 3-10 μm molecular fingerprint region. The system is based on difference frequency generation in a GaSe crystal pumped by a 151 MHz Yb:fiber frequency comb. The process was seeded with Raman-shifted solitons generated in a highly nonlinear suspended-core fiber with the same source. Average powers up to 1.5 mW were achieved at the 4.7 μm wavelength.     

Phase Retrieval from Gabor Measurements

Compressed sensing investigates the recovery of sparse signals from linear measurements. But often, in a wide range of applications, one is given only the absolute values (squared) of the linear measurements. Recovering such signals (not necessarily sparse) is known as the phase retrieval problem. We consider this problem in the case when the measurements are time-frequency shifts of a suitably chosen generator, i.e. coming from a Gabor frame. We prove an easily checkable injectivity condition for recovery of any signal from all \(N^2\) time-frequency shifts, and for recovery of sparse signals, when only some of those measurements are given.     

A Smooth 3D Model for Fiber Lay-Down Processes

We present an improved three-dimensional stochastic model concerning the fiber lay-down in the production process of nonwoven materials. The model describes the position of the deposited fibers on a conveyor belt, which is determined by a system of stochastic differential equations. Here we remove a drawback of a previous 3D model, that is the non-smoothness of the fiber paths. Besides the derivation of the smooth 3D model we show its connection to the non-smooth model in a white noise limit. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

De Rham Cohomology and Hodge Decomposition For Quantum Groups

Let be one of the N²-dimensionalbicovariant first order differential calculi for the quantumgroups GL_q(N), SL_q(N), SO_q(N), or Sp_q(N), where q is a transcendentalcomplex number and z is a regular parameter. It is shown thatthe de Rham cohomology of Woronowicz' external algebra coincides with the de Rham cohomologiesof its left-coinvariant, its right-coinvariant and its (two-sided)coinvariant subcomplexes. In the cases GL_q(N) and SL_q(N) thecohomology ring is isomorphic to the coinvariant external algebra and to the vector space of harmonic forms. We prove a Hodge decomposition theorem in thesecases. The main technical tool is the spectral decompositionof the quantum Laplace-Beltrami operator. 2000 MathematicalSubject Classification: 46L87, 58A12, 81R50.     

On the Visualization of Patient Specific Arterial Geometries Using the Virtual Histology

The simulation of a balloon–angioplasty (clinical treatment of atherosclerotically degenerated arteries) requires information of the anatomical and physiological composition of the arterial wall. The intravascular ultrasound and the interpretation by a virtual histology provide cross–sectional images of the diseased arterial walls where the different components are characterized by color–coding. Using these information and the reconstruction of the vessel path from biplane angiography the patient specific data are visualized and discretized. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Théorème de l’Indice et Formule des Traces

Our purpose is to obtain a geometric formula as explicit as possible for the L ² index of a Dirac operator over a locally symmetric space of finite volume, generalizing Arthur’s formula for the Euler–Poincaré caracteristic (Arthur in Invent Math 97:257–290, 1989).     

Aspects of a Phase Transition in High-Dimensional Random Geometry

A phase transition in high-dimensional random geometry is analyzed as it arises in a variety of problems. A prominent example is the feasibility of a minimax problem that represents the extremal case of a class of financial risk measures, among them the current regulatory market risk measure Expected Shortfall. Others include portfolio optimization with a ban on short-selling, the storage capacity of the perceptron, the solvability of a set of linear equations with random coefficients, and competition for resources in an ecological system. These examples shed light on various aspects of the underlying geometric phase transition, create links between problems belonging to seemingly distant fields, and offer the possibility for further ramifications.     

Modified Darboux transformations with foreign auxiliary equations

We construct a new type of first-order Darboux transformations for the stationary Schrödinger equation. In contrast to the conventional case, our Darboux transformations support arbitrary (foreign) auxiliary equations. We show that among other applications, our formalism can be used to systematically construct Darboux transformations for Schrödinger equations with energy-dependent potentials, including a recent result (Lin et al., 2007) [16] as a special case.     

Terahertz near-field imaging using subwavelength plasmonic apertures and a quantum cascade laser source

The first demonstration, to our knowledge, of near-field imaging using subwavelength plasmonic apertures with a terahertz quantum cascade laser source is presented. "Bull's-eye" apertures, featuring subwavelength circular apertures flanked by periodic annular corrugations were created using a novel fabrication method. A fivefold increase in intensity was observed for plasmonic apertures over plain apertures of the same diameter. Detailed studies of the transmitted beam profiles were undertaken for apertures with both planarized and corrugated exit facets, with the former producing spatially uniform intensity profiles and subwavelength spatial resolution. Finally, a proof-of-concept imaging experiment is presented, where an inhomogeneous pharmaceutical drug coating is investigated.     

Suppression of Diagonal Peaks in TROSY-Type H NMR NOESY Spectra of N-Labeled Proteins

A novel method for suppression of diagonal peaks in the amide region of NOESY NMR spectra of ¹⁵N-labeled proteins is presented. The method is particularly useful for larger proteins at high magnetic fields where interference between dipolar and chemical shift anisotropy relaxation mechanisms results in large TROSY effects, i.e., large differences in ¹H^N linewidths depending on the spin state of attached ¹⁵N nuclei. In this limit the new TROSY NOESY method does not compromise sensitivity. It is demonstrated using a perdeuterated ¹⁵N-labeled protein sample, Neural Cell Adhesion Molecule 213–308 (NCAM) from rat, in H₂O at 800 MHz.