Rapid computation of LL-functions attached to Maass forms

Let $L$ be a degree-$2$ $L$-function associated to a Maass cusp form. We explore an algorithm that evaluates $t$ values of $L$ on the critical line in time $O(t^{1+\varepsilon})$. We use this algorithm to rigorously compute an abundance of consecutive zeros and investigate their distribution

Bounds and algorithms for the K-Bessel function of imaginary order

AbstractUsing the paths of steepest descent, we prove precise bounds with numerical implied constants for the modified Bessel function${K}_{ir} (x)$of imaginary order and its first two derivatives with respect to the order. We also prove precise asymptotic bounds on more general (mixed) derivatives without working out numerical implied constants. Moreover, we present an absolutely and rapidly convergent series for the computation of${K}_{ir} (x)$and its derivatives, as well as a formula based on Fourier interpolation for computing with many values of$r$. Finally, we have implemented a subset of these features in a software library for fast and rigorous computation of${K}_{ir} (x)$.</jats:p

Using bijective maps to improve free energy estimates

We derive a fluctuation theorem for generalized work distributions, related to bijective mappings of the phase spaces of two physical systems, and use it to derive a two-sided constraint maximum likelihood estimator of their free energy difference which uses samples from the equilibrium configurations of both systems. As an application, we evaluate the chemical potential of a dense Lennard-Jones fluid and study the construction and performance of suitable maps.Comment: 17 pages, 11 figure

Numerical computation of Maass waveforms and an application to cosmology

We compute numerically eigenvalues and eigenfunctions of the Laplacian in a three-dimensional hyperbolic space. Applying the results to cosmology, we demonstrate that the methods learned in quantum chaos can be used in other fields of research.Comment: A version of the paper with high resolution figures is available at http://www.physik.uni-ulm.de/theo/qc/publications.htm

The physics of angular momentum radio

Wireless communications, radio astronomy and other radio science applications are predominantly implemented with techniques built on top of the electromagnetic linear momentum (Poynting vector) physical layer. As a supplement and/or alternative to this conventional approach, techniques rooted in the electromagnetic angular momentum physical layer have been advocated, and promising results from proof-of-concept radio communication experiments using angular momentum were recently published. This sparingly exploited physical observable describes the rotational (spinning and orbiting) physical properties of the electromagnetic fields and the rotational dynamics of the pertinent charge and current densities. In order to facilitate the exploitation of angular momentum techniques in real-world implementations, we present a systematic, comprehensive theoretical review of the fundamental physical properties of electromagnetic angular momentum observable. Starting from an overview that puts it into its physical context among the other Poincar\'e invariants of the electromagnetic field, we describe the multi-mode quantized character and other physical properties that sets electromagnetic angular momentum apart from the electromagnetic linear momentum. These properties allow, among other things, a more flexible and efficient utilization of the radio frequency spectrum. Implementation aspects are discussed and illustrated by examples based on analytic and numerical solutions.Comment: Fixed LaTeX rendering errors due to inconsistencies between arXiv's LaTeX machine and texlive in OpenSuSE 13.

Are GSTM1 Null and GSTT1 Null Risk Factor of Autism Spectrum Disorder? a Preliminary Study

Background: Low plasma total glutathione (tGSH) levels, elevated levels of oxidized glutathione (GSSG) and low ratios of tGSH to GSSG in autism were reported. Glutathione S-transferases (GST) are antioxidant enzymes that play important role in cellular detoxification and the excretion of environmental pollutants including heavy metals. Glutathione S-transferase mu (GSTM1) and Glutathione S-transferase theta (GSTT1) are known to be highly polymorphic. Homozygous deletions of these genes result in lack ofenzyme activity and impaired the ability to excrete metals including mercury. Combined effects of mercury (Hg) accumulation coupled with decreased levels of antioxidants (low glutathione and antioxidant enzymes) contribute to the phenotypic presentation of autism spectrum disorder (ASD). Association of GSTM1 null genotype with autism has been reported. Therefore the preliminary study was performed to investigate the role of GSTM1 null and GSTT1 null as risk factor of ASD associated with phenotype expression.Method: Fifty one ASD patients were recruited from special need & autism school and 45 controls from Semarang & Solo. Blood veins samples were collected and genomic DNA was extracted by salting-out method in CEBIOR Semarang. Genotyping for GSTM1 and GSTT1 gene was done in UMBI Malaysia. Multiplex PCR was performed and PCR products were separated on 1.2 % agarose gel, stained with ethidium bromide and visualized on UV transiluminator. GSTM1 & GSTT1 gene product is about 625 bp and 459 bp. Absence of GSTM1 and GSTT1 gene band was interpreted as GSTM1 null & GSTT1 null.Results: The frequency of GSTM1 null and GSTT1 null in ASD higher compared with control group but the difference is not statistically significant (p=0.357, OR=0.504; 95% CI 0.117-2.168 and p=0.364, OR=0.674; 95% CI 0.287-1.580). There is also no statistically different in the distribution of GSTM1 null and GSTT1 null between mild to moderately autistic and severely autistic (p=0.983, OR=0.980; 95% CI 0.158-6.095 and p=0.439, OR=1.633; 95% CI 0.471-5.656).Conclusion: GSTM1 null and GSTT1 null are not risk factor of ASD. Further investigations are needed with a bigger sample size, analyzing multiple GST genes and GST activity determination to find out the gene susceptibility of ASD and factors that contribute to the phenotype expression of ASD

A Competence-Based Course Authoring Concept for Learning Platforms with Legacy Assignment Tools

This paper is concerned with several of the most important aspects of Competence-Based Learning (CBL): course authoring, assignments, and categorization of learning content. The latter is part of the so-called Bologna Process (BP) and can effectively be supported by integrating knowledge resources like, e.g., standardized skill and competence taxonomies into the target implementation approach, aiming at making effective use of an open integration architecture while fostering the interoperability of hybrid knowledge-based e-learning solutions. Modern scenarios ask for interoperable software solutions to seamlessly integrate existing e-learning infrastructures and legacy tools with innovative technologies while being cognitively efficient to handle. In this way, prospective users are enabled to use them without learning overheads. At the same time, methods of Learning Design (LD) in combination with CBL are getting more and more important for production and maintenance of easy to facilitate solutions. We present our approach of developing a competence-based course-authoring and assignment support software. It is bridging the gaps between contemporary Learning Management Systems (LMS) and established legacy learning infrastructures by embedding existing resources via Learning Tools Interoperability (LTI). Furthermore, the underlying conceptual architecture for this integration approach will be explained. In addition, a competence management structure based on knowledge technologies supporting standardized skill and competence taxonomies will be introduced. The overall goal is to develop a software solution which will not only flawlessly merge into a legacy platform and several other learning environments, but also remain intuitively usable. As a proof of concept, the so-called platform independent conceptual architecture model will be validated by a concrete use case scenario

Utilization of photon orbital angular momentum in the low-frequency radio domain

We show numerically that vector antenna arrays can generate radio beams which exhibit spin and orbital angular momentum characteristics similar to those of helical Laguerre-Gauss laser beams in paraxial optics. For low frequencies (< 1 GHz), digital techniques can be used to coherently measure the instantaneous, local field vectors and to manipulate them in software. This opens up for new types of experiments that go beyond those currently possible to perform in optics, for information-rich radio physics applications such as radio astronomy, and for novel wireless communication concepts.Comment: 4 pages, 5 figures. Changed title, identical to the paper published in PR

Occurrence of periodic Lam\'e functions at bifurcations in chaotic Hamiltonian systems

We investigate cascades of isochronous pitchfork bifurcations of straight-line librating orbits in some two-dimensional Hamiltonian systems with mixed phase space. We show that the new bifurcated orbits, which are responsible for the onset of chaos, are given analytically by the periodic solutions of the Lam\'e equation as classified in 1940 by Ince. In Hamiltonians with C_${2v}$ symmetry, they occur alternatingly as Lam\'e functions of period 2K and 4K, respectively, where 4K is the period of the Jacobi elliptic function appearing in the Lam\'e equation. We also show that the two pairs of orbits created at period-doubling bifurcations of touch-and-go type are given by two different linear combinations of algebraic Lam\'e functions with period 8K.Comment: LaTeX2e, 22 pages, 14 figures. Version 3: final form of paper, accepted by J. Phys. A. Changes in Table 2; new reference [25]; name of bifurcations "touch-and-go" replaced by "island-chain

About ergodicity in the family of limacon billiards

By continuation from the hyperbolic limit of the cardioid billiard we show that there is an abundance of bifurcations in the family of limacon billiards. The statistics of these bifurcation shows that the size of the stable intervals decreases with approximately the same rate as their number increases with the period. In particular, we give numerical evidence that arbitrarily close to the cardioid there are elliptic islands due to orbits created in saddle node bifurcations. This shows explicitly that if in this one parameter family of maps ergodicity occurs for more than one parameter the set of these parameter values has a complicated structure.Comment: 17 pages, 9 figure