Mid infrared interband cascade lasers for sensing applications

The growth of Interband Cascade Laser material to cover the wavelength range from 3–4 μm is presented along with the fabrication and characterization of Broad Area (BA) and Ridge Waveguide (RWG) devices based on this material. Pulsed operation slightly below room temperature is observed for both device types, and a strong reduction of threshold currents can be observed in the RWG lasers. Variation of the active Quantum Well width in the epitaxial structures enables laser emission in the 3–4 μm wavelength region.     

The constrained reinitialization equation for level set methods

Based on the constrained reinitialization scheme [D. Hartmann, M. Meinke, W. Schröder, Differential equation based constrained reinitialization for level set methods, J. Comput. Phys. 227 (2008) 6821–6845] a new constrained reinitialization equation incorporating a forcing term is introduced. Two formulations for high-order constrained reinitialization (HCR) are presented combining the simplicity and generality of the original reinitialization equation [M. Sussman, P. Smereka, S. Osher, A level set approach for computing solutions to incompressible two-phase flow, J. Comput. Phys. 114 (1994) 146–159] in terms of high-order standard discretization and the accuracy of the constrained reinitialization scheme in terms of interface displacement. The novel HCR schemes represent simple extensions of standard implementations of the original reinitialization equation. The results evidence the significantly increased accuracy and robustness of the novel schemes.     

The decoupling of damped linear systems in free or forced vibration

The purpose of this paper is to extend classical modal analysis to decouple any viscously damped linear system in non-oscillatory free vibration or in forced vibration. Based upon an exposition of how exponential decay in a system can be regarded as imaginary oscillations, the concept of damped modes of imaginary vibration is introduced. By phase synchronization of these real and physically excitable modes, a time-varying transformation is constructed to decouple non-oscillatory free vibration. When time drifts caused by viscous damping and by external excitation are both accounted for, a time-varying decoupling transformation for forced vibration is derived. The decoupling procedure devised herein reduces to classical modal analysis for systems that are undamped or classically damped. This paper constitutes the second and final part of a solution to the “classical decoupling problem.” Together with an earlier paper, a general methodology that requires only the solution of a quadratic eigenvalue problem is developed to decouple any damped linear system.     

Feedback cooling of a single neutral atom

We demonstrate feedback cooling of the motion of a single rubidium atom trapped in a high-finesse optical resonator to a temperature of about 160 μK. Time-dependent transmission and intensity-correlation measurements prove the reduction of the atomic position uncertainty. The feedback increases the 1/e storage time into the 1 s regime, 30 times longer than without feedback. Feedback cooling therefore rivals state-of-the-art laser cooling, but with the advantages that it requires less optical access and exhibits less optical pumping.     

Kolmogorov scaling of turbulent flow in the vicinity of the wall

How to scale even the simplest of turbulent flows continues to be a cause for considerable controversy. In the present research, a data base compiling results from channel flow direct numerical simulations and turbulent boundary layer experiments is employed to investigate the properties of shear and normal Reynolds stresses very close to the wall. Two types of scaling based on Kolmogorov length and velocity scales are analyzed. It is shown that it is highly likely that large length scales of the order of the channel half-width or the boundary layer thickness play an important role even in the innermost regions of wall-bounded turbulent flows, which hints at the persistence of Reynolds number effects in even high Reynolds number flows.     

Optimal Entropy-Transport problems and a new Hellinger–Kantorovich distance between positive measures

Inventiones mathematicae - We develop a full theory for the new class of Optimal Entropy-Transport problems between nonnegative and finite Radon measures in general topological spaces. These...     

Concentration for Poisson U-statistics: Subgraph counts in random geometric graphs

Concentration bounds for the probabilities $\mathbb{P}(N\ge M+r)$ and $\mathbb{P}(N\le M?r)$ are proved, where $M$ is a median or the expectation of a subgraph count $N$ associated with a random geometric graph built over a Poisson process. The lower tail bounds have a Gaussian decay and the upper tail inequalities satisfy an optimality condition. A remarkable feature is that the underlying Poisson process can have a.s. infinitely many points.The estimates for subgraph counts follow from tail inequalities for more general local Poisson U-statistics. These bounds are proved using recent general concentration results for Poisson U-statistics and techniques involving the convex distance for Poisson processes.     

Finding small somatic structural variants in exome sequencing data: a machine learning approach

Genetic variation forms the basis for diversity but can as well be harmful and cause diseases, such as tumors. Structural variants (SV) are an example of complex genetic variations that comprise of many nucleotides ranging up to several megabases. Based on recent developments in sequencing technology it has become feasable to elucidate the genetic state of a person’s genes (i.e. the exome) or even the complete genome. Here, a machine learning approach is presented to find small disease-related SVs with the help of sequencing data. The method uses differences in characteristics of mapping patterns between tumor and normal samples at a genomic locus. This way, the method aims to be directly applicable for exome sequencing data to improve detection of SVs since specific SV detection methods are currently lacking. The method has been evaluated based on a simulation study as well as with exome data of patients with acute myeloid leukemia. An implementation of the algorithm is available at https://github.com/lenz99-/svmod.