Efficient sorting of Bessel beams

We demonstrate the efficient sorter of Bessel beams separating both the azimuthal and radial components. This is based upon the recently reported transformation of angular to transverse momentum states. We separately identify over forty azimuthal and radial components, with a radial spacing of 1588 m<sup>−1</sup>, and outline how the device could be used to identify the two spatial dimensions simultaneously

Learning Arbitrary Statistical Mixtures of Discrete Distributions

We study the problem of learning from unlabeled samples very general statistical mixture models on large finite sets. Specifically, the model to be learned, $\vartheta$, is a probability distribution over probability distributions $p$, where each such $p$ is a probability distribution over $[n] = \{1,2,\dots,n\}$. When we sample from $\vartheta$, we do not observe $p$ directly, but only indirectly and in very noisy fashion, by sampling from $[n]$ repeatedly, independently $K$ times from the distribution $p$. The problem is to infer $\vartheta$ to high accuracy in transportation (earthmover) distance. We give the first efficient algorithms for learning this mixture model without making any restricting assumptions on the structure of the distribution $\vartheta$. We bound the quality of the solution as a function of the size of the samples $K$ and the number of samples used. Our model and results have applications to a variety of unsupervised learning scenarios, including learning topic models and collaborative filtering.Comment: 23 pages. Preliminary version in the Proceeding of the 47th ACM Symposium on the Theory of Computing (STOC15

Experimental Realization of a Single-Phase Five Level Inverter for PV Applications

voltage-controlled, single-phase, five-level inverter for photovoltaic systems using semiconductor power devices is proposed. Use of a unique, multilevel voltage source configuration allows the production of high voltage, low harmonic distortion AC outputs without using transformers or series-associated synchronized switching devices. The typical role of multi-level inverters is to generate the desired AC voltage from multiple DC voltage rails. Therefore multi-level inverters can provide high power AC outputs with good efficiency. The inverter design proposed here has superior voltage regulation, a low-distortion output and improved efficiency compared to existing multi-level inverters. Complete functionality has been verified using both MATLAB/SIMULINK simulation software and experimental trial

Track Structure and the Quality Factor for Space Radiation Cancer Risk

A major risk from exposure to space radiation is the induction of cancer and it is from estimates of this risk that the maximum career flight times of NASA space crew members are restricted by a permissible exposure limit. For the purpose of demonstrating compliance with the career limit, NASA has developed a cancer risk projection model for exposure-induced fatal cancer, in which the formulation and numerical values of the quality factor (QFNASA) are substantially different from those of the quality factor (Q) or radiation weighting factor (wR) routinely applied for radiation protection on earth. The quality factor is used to account for the increased effectiveness of radiations of high linear energy transfer (LET), compared to the effectiveness of low-LET -rays derived from epidemiological studies of the atomic-bomb survivors. The need for a special approach for space radiation is dictated by the special characteristics of the charged particles from solar radiation and especially the charged particles of high energy and charge (HZE) in galactic cosmic rays (GCR). This article considers aspects of radiation track structure in relation to the relative biological effectiveness (RBE) of HZE particles and the quality factor used for space radiation. The NASA quality factor (QFNASA) is composed of two terms, which can be interpreted as broadly representing the low- and the high-ionization-density components of the HZE particle tracks. These are discussed in turn as they relate to available experimental evidence on the biological effectiveness of such components. Also briefly described are subsequent published proposals for a reformulation of the quality factor to relate more directly to the acute -ray exposures from the atomic bombs and for further refinement of the parameter values (and their uncertainties) that determine the shape of the quality factor function. Other recent developments are also mentioned

Disease signatures are robust across tissues and experiments

Meta-analyses combining gene expression microarray experiments offer new insights into the molecular pathophysiology of disease not evident from individual experiments. Although the established technical reproducibility of microarrays serves as a basis for meta-analysis, pathophysiological reproducibility across experiments is not well established. In this study, we carried out a large-scale analysis of disease-associated experiments obtained from NCBI GEO, and evaluated their concordance across a broad range of diseases and tissue types. On evaluating 429 experiments, representing 238 diseases and 122 tissues from 8435 microarrays, we find evidence for a general, pathophysiological concordance between experiments measuring the same disease condition. Furthermore, we find that the molecular signature of disease across tissues is overall more prominent than the signature of tissue expression across diseases. The results offer new insight into the quality of public microarray data using pathophysiological metrics, and support new directions in meta-analysis that include characterization of the commonalities of disease irrespective of tissue, as well as the creation of multi-tissue systems models of disease pathology using public data

A Meinardus theorem with multiple singularities

Meinardus proved a general theorem about the asymptotics of the number of weighted partitions, when the Dirichlet generating function for weights has a single pole on the positive real axis. Continuing \cite{GSE}, we derive asymptotics for the numbers of three basic types of decomposable combinatorial structures (or, equivalently, ideal gas models in statistical mechanics) of size $n$, when their Dirichlet generating functions have multiple simple poles on the positive real axis. Examples to which our theorem applies include ones related to vector partitions and quantum field theory. Our asymptotic formula for the number of weighted partitions disproves the belief accepted in the physics literature that the main term in the asymptotics is determined by the rightmost pole.Comment: 26 pages. This version incorporates the following two changes implied by referee's remarks: (i) We made changes in the proof of Proposition 1; (ii) We provided an explanation to the argument for the local limit theorem. The paper is tentatively accepted by "Communications in Mathematical Physics" journa

Chalcogenide-glass polarization-maintaining photonic crystal fiber for mid-infrared supercontinuum generation

In this paper, we report the design and fabrication of a highly birefringent polarization-maintaining photonic crystal fiber (PM-PCF) made from chalcogenide glass, and its application to linearly-polarized supercontinuum (SC) generation in the mid-infrared region. The PM fiber was drawn using the casting method from As38Se62 glass which features a transmission window from 2 to 10 $\mu m$ and a high nonlinear index of 1.13.10$^{-17}$m$^{2}$W$^{-1}$. It has a zero-dispersion wavelength around 4.5 $\mu m$ and, at this wavelength, a large birefringence of 6.10$^{-4}$ and consequently strong polarization maintaining properties are expected. Using this fiber, we experimentally demonstrate supercontinuum generation spanning from 3.1-6.02 $\mu m$ and 3.33-5.78 $\mu m$ using femtosecond pumping at 4 $\mu m$ and 4.53 $\mu m$, respectively. We further investigate the supercontinuum bandwidth versus the input pump polarization angle and we show very good agreement with numerical simulations of the two-polarization model based on two coupled generalized nonlinear Schr\"odinger equations.Comment: 13 pages, 8 figure

Asymmetric polarity reversals, bimodal field distribution, and coherence resonance in a spherically symmetric mean-field dynamo model

Using a mean-field dynamo model with a spherically symmetric helical turbulence parameter alpha which is dynamically quenched and disturbed by additional noise, the basic features of geomagnetic polarity reversals are shown to be generic consequences of the dynamo action in the vicinity of exceptional points of the spectrum. This simple paradigmatic model yields long periods of constant polarity which are interrupted by self-accelerating field decays leading to asymmetric polarity reversals. It shows the recently discovered bimodal field distribution, and it gives a natural explanation of the correlation between polarity persistence time and field strength. In addition, we find typical features of coherence resonance in the dependence of the persistence time on the noise.Comment: 5 pages, 7 figure

Experimental Validation of a Thirteen Level H-Bridge Photovoltaic Inverter Configuration

Highly efficient and compact multilevel inverters are desirable in many applications such as wind farms, solar energy harvesting and electric vehicles. The authors present a single-phase thirteen level inverter control method employing semiconductor power devices for photovoltaic applications. The unique configuration of source inverters with multilevel voltage capabilities enables large voltages together with minimal harmonic distortion without the employment of associated harmonized switching devices or transformers. A multilevel inverter is commonly used to create a desired voltage from several dc voltage levels. Therefore multilevel inverters can satisfy the large electric power requirements for high power devices. The proposed inverter system based on a simple Hbridge inverter structure provides accurate voltage control and excellent efficiency. The proposed inverter is demonstrated using MATLAB/SIMULINK simulation software and experimental validation is executed using high-efficiency ARM controlle

Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime

Numerical simulations are used to study how fiber supercontinuum generation seeded by picosecond pulses can be actively controlled through the use of input pulse modulation. By carrying out multiple simulations in the presence of noise, we show how tailored supercontinuum Spectra with increased bandwidth and improved stability can be generated using an input envelope modulation of appropriate frequency and depth. The results are discussed in terms of the non-linear propagation dynamics and pump depletion.Comment: Aspects of this work were presented in Paper ThJ2 at OECC/ACOFT 2008, Sydney Australia 7-10 July (2008). Journal paper submitted for publication 30 July 200