Entanglement entropy of fermions in any dimension and the Widom conjecture

We show that entanglement entropy of free fermions scales faster then area law, as opposed to the scaling $L^{d-1}$ for the harmonic lattice, for example. We also suggest and provide evidence in support of an explicit formula for the entanglement entropy of free fermions in any dimension $d$, $S\sim c(\partial\Gamma,\partial\Omega)\cdot L^{d-1}\log L$ as the size of a subsystem $L\to\infty$, where $\partial\Gamma$ is the Fermi surface and $\partial\Omega$ is the boundary of the region in real space. The expression for the constant $c(\partial\Gamma,\partial\Omega)$ is based on a conjecture due to H. Widom. We prove that a similar expression holds for the particle number fluctuations and use it to prove a two sided estimates on the entropy $S$.Comment: Final versio

A Guide to Localized Frames and Applications to Galerkin-like Representations of Operators

This chapter offers a detailed survey on intrinsically localized frames and the corresponding matrix representation of operators. We re-investigate the properties of localized frames and the associated Banach spaces in full detail. We investigate the representation of operators using localized frames in a Galerkin-type scheme. We show how the boundedness and the invertibility of matrices and operators are linked and give some sufficient and necessary conditions for the boundedness of operators between the associated Banach spaces.Comment: 32 page

Fertilization and early embryology: Use of lasers in assisted fertilization and hatching

The erbium-yttrium-aluminium-garnet (Er: YAG) laser has been applied to micromanipulation in humans. It was used in the fertilization process for both subzonal insemination (SUZI) and for partial zona dissection (PZD). Laser-assisted micromanipulation achieved significantly higher fertilization rates (34.8%) when compared to mechanical SUZI (16.1%), but use of the laser did not improve the PZD results (laser 14.8% versus mechanical 14%). The Er: YAG laser was used to assist hatching. In the mouse it significantly improved the hatching rate (80 versus 29.3%) 110 h after administration of human chorionic gonadotrophin. This technique was applied in two different centres to patients with previous in-vitro fertilization (IVF) failures. The implantation rate per embryo (14.4% laser-assisted hatching versus 6% control group) and the pregnancy rate per transfer (40 versus 16.2%) were improve

Improved osteogenic vector for non-viral gene therapy

Therapeutic compensation of deficient bone regeneration is a challenging task and a topic of on-going search for novel treatment strategies. One promising approach for improvement involves non-viral gene delivery using the bone morphogenetic protein-2 (BMP-2) gene to provide transient, local and sustained expression of the growth factor. However, since efficiency of non-viral gene delivery is low, this study focused on the improvement of a BMP-2 gene expression system, aiming for compensation of poor transfection efficiency. First, the native BMP-2 gene sequence was modified by codon optimisation and altered by inserting a highly truncated artificial intron (96 bp). Transfection of multiple cell lines and rat adipose-derived mesenchymal stem cells with plasmids harbouring the improved BMP-2 sequence led to a several fold increased expression rate and subsequent osteogenic differentiation. Additionally, comparing expression kinetics of elongation factor 1 alpha (EF1α) promoter with a state of the art CMV promoter revealed significantly higher BMP-2 expression when under the influence of the EF1α promoter. Results obtained by quantification of bone markers as well as osteogenic assays showed reduced sensitivity to promoter silencing effects of the EF1α promoter in rat adipose-derived mesenchymal stem cells. Finally, screening of several protein secretion signals using either luciferase or BMP-2 as reporter protein revealed no superior candidates for potential replacement of the native BMP-2 secretion signal. Taken together, by enhancing the exogenous BMP-2 expression system, low transfection efficiencies in therapeutic applications can be compensated, making safe non-viral systems even more suitable for tissue regeneration approaches

Quantum theta functions and Gabor frames for modulation spaces

Representations of the celebrated Heisenberg commutation relations in quantum mechanics and their exponentiated versions form the starting point for a number of basic constructions, both in mathematics and mathematical physics (geometric quantization, quantum tori, classical and quantum theta functions) and signal analysis (Gabor analysis). In this paper we try to bridge the two communities, represented by the two co--authors: that of noncommutative geometry and that of signal analysis. After providing a brief comparative dictionary of the two languages, we will show e.g. that the Janssen representation of Gabor frames with generalized Gaussians as Gabor atoms yields in a natural way quantum theta functions, and that the Rieffel scalar product and associativity relations underlie both the functional equations for quantum thetas and the Fundamental Identity of Gabor analysis.Comment: 38 pages, typos corrected, MSC class change

Approximation of Feynman path integrals with non-smooth potentials

We study the convergence in $L^2$ of the time slicing approximation of Feynman path integrals under low regularity assumptions on the potential. Inspired by the custom in Physics and Chemistry, the approximate propagators considered here arise from a series expansion of the action. The results are ultimately based on function spaces, tools and strategies which are typical of Harmonic and Time-frequency analysis.Comment: 18 page

Understanding Terrorist Organizations with a Dynamic Model

Terrorist organizations change over time because of processes such as recruitment and training as well as counter-terrorism (CT) measures, but the effects of these processes are typically studied qualitatively and in separation from each other. Seeking a more quantitative and integrated understanding, we constructed a simple dynamic model where equations describe how these processes change an organization's membership. Analysis of the model yields a number of intuitive as well as novel findings. Most importantly it becomes possible to predict whether counter-terrorism measures would be sufficient to defeat the organization. Furthermore, we can prove in general that an organization would collapse if its strength and its pool of foot soldiers decline simultaneously. In contrast, a simultaneous decline in its strength and its pool of leaders is often insufficient and short-termed. These results and other like them demonstrate the great potential of dynamic models for informing terrorism scholarship and counter-terrorism policy making.Comment: To appear as Springer Lecture Notes in Computer Science v2: vectorized 4 figures, fixed two typos, more detailed bibliograph

An optimally concentrated Gabor transform for localized time-frequency components

Gabor analysis is one of the most common instances of time-frequency signal analysis. Choosing a suitable window for the Gabor transform of a signal is often a challenge for practical applications, in particular in audio signal processing. Many time-frequency (TF) patterns of different shapes may be present in a signal and they can not all be sparsely represented in the same spectrogram. We propose several algorithms, which provide optimal windows for a user-selected TF pattern with respect to different concentration criteria. We base our optimization algorithm on $l^p$-norms as measure of TF spreading. For a given number of sampling points in the TF plane we also propose optimal lattices to be used with the obtained windows. We illustrate the potentiality of the method on selected numerical examples

A luciferase-based quick potency assay to predict chondrogenic differentiation.

Chondrogenic differentiation of adipose derived stem cells (ASC) is challenging but highly promising for cartilage repair. Large donor variability of chondrogenic differentiation potential raises the risk for transplantation of cells with reduced efficacy and a low chondrogenic potential. Therefore quick potency assays are required in order to control the potency of the isolated cells before cell transplantation. Current in vitro methods to analyze the differentiation potential are time consuming and thus, a novel enhancer and tissue-specific promoter combination was employed for the detection of chondrogenic differentiation of ASC in a novel quick potency bioassay. Human primary ASC were co-transfected with the Metridia luciferase based collagen type II reporter gene pCMVE_ACDCII-MetLuc together with a Renilla control plasmid and analyzed for their chondrogenic potential. On day 3 after chondrogenic induction, the luciferase activity was induced in all tested donors under three dimensional (3D) culture conditions and in a second approach also under 2D culture conditions. With our newly developed quick potency bioassay we can determine chondrogenic potential already after 3 days of chondrogenic induction and under 2D culture conditions. This will enhance the efficiency of testing cell functionality, which should allow in the future to predict the suitability of cells derived from individual patients for cell therapies, in a very short time and at low costs