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

Fundamental noise limitations to supercontinuum generation in microstructure fiber

Broadband noise on supercontinuum spectra generated in microstructure fiber is shown to lead to amplitude fluctuations as large as 50 % for certain input laser pulse parameters. We study this noise using both experimental measurements and numerical simulations with a generalized stochastic nonlinear Schroedinger equation, finding good quantitative agreement over a range of input pulse energies and chirp values. This noise is shown to arise from nonlinear amplification of two quantum noise inputs: the input pulse shot noise and the spontaneous Raman scattering down the fiber.Comment: 16 pages with 6 figure

On the modulation instability development in optical fiber systems

Extensive numerical simulations were performed to investigate all stages of modulation instability development from the initial pulse of pico-second duration in photonic crystal fiber: quasi-solitons and dispersive waves formation, their interaction stage and the further propagation. Comparison between 4 different NLS-like systems was made: the classical NLS equation, NLS system plus higher dispersion terms, NLS plus higher dispersion and self-steepening and also fully generalized NLS equation with Raman scattering taken into account. For the latter case a mechanism of energy transfer from smaller quasi-solitons to the bigger ones is proposed to explain the dramatical increase of rogue waves appearance frequency in comparison to the systems when the Raman scattering is not taken into account.Comment: 9 pages, 54 figure

Polarization and dispersion properties of elliptical hole golden spiral photonic crystal fiber

An elliptical air-hole golden spiral photonic crystal fiber (EGS-PCF) is analyzed with the full-vectorial finite element method. The air-holes in the EGS-PCF are arranged in a spiral pattern governed by the Golden Ratio, where the design has been inspired by the optimal arrangement of seeds found in nature. The EGS-PCF exhibits extremely high birefringence (∼0.022 at operating wavelength 1550 nm) which is particularly useful for generating a polarization stable supercontinuum (SC). The fiber can also be designed to have a Zero Dispersion Wavelength (ZDW) at a suitable wavelength for only one polarization and large negative dispersion for the other, leading to a single-polarization SC. In addition, the fiber dispersion can be designed to obtain ZDWs at 800 nm and 1064 nm simultaneously, which can facilitate broadband supercontinuum generation (SCG) through multi-wavelength pumping

Golden spiral photonic crystal fiber: polarization and dispersion properties

A golden spiral photonic crystal fiber (GS-PCF) design is presented in which air holes are arranged in a spiral pattern governed by the golden ratio, where the design has been inspired by the optimal arrangement of seeds found in nature. The birefringence and polarization properties of this fiber are analyzed using a vectorial finite-element method. The fiber that is investigated shows a large modal birefringence peak value of 0.016 at an operating wavelength of 1.55 μm and exhibits highly tuneable dispersion with multiple zero dispersion wavelengths and also large normal dispersion. The GS-PCF design has identical circular air holes that potentially simplify fabrication. In light of its properties, the GS-PCF could have application as a highly birefringent fiber and in nonlinear optics, and moreover the 2D chiral nature of the pattern could yield exotic properties

Interest in bariatric surgery among obese patients with obstructive sleep apnea

BACKGROUND: Standard obstructive sleep apnea (OSA) therapies are poorly tolerated. Bariatric surgery is a potential alternative but the level of interest in this intervention among OSA patients is unknown. OBJECTIVES: Determine the proportion of OSA patients who would be interested in bariatric surgery. SETTING: Sleep clinics, United States. METHODS: Consecutive adult patients with untreated severe OSA and a body mass index of 35-45 kg/m2 were approached. Patients at low perioperative risk and no urgent indication for OSA treatment were invited to a separate informational visit about bariatric surgery as primary treatment for OSA. RESULTS: Of 767 eligible patients, 230 (30.0%) were not at low perioperative risk, 49 (6.4%) had drowsy driving, and 16 (2.1%) had no insurance coverage for bariatric surgery. Of the remaining 482 patients, over one third (35.5%) were interested in bariatric surgery. Surgical interest was 47.2% in women versus 27.6% in men (

Relativistic Brownian motion: From a microscopic binary collision model to the Langevin equation

The Langevin equation (LE) for the one-dimensional relativistic Brownian motion is derived from a microscopic collision model. The model assumes that a heavy point-like Brownian particle interacts with the lighter heat bath particles via elastic hard-core collisions. First, the commonly known, non-relativistic LE is deduced from this model, by taking into account the non-relativistic conservation laws for momentum and kinetic energy. Subsequently, this procedure is generalized to the relativistic case. There, it is found that the relativistic stochastic force is still \gd-correlated (white noise) but does \emph{no} longer correspond to a Gaussian white noise process. Explicit results for the friction and momentum-space diffusion coefficients are presented and discussed.Comment: v2: Eqs. (17c) and (28) corrected; v3: discussion extended, Eqs. (33) added, thereby connection to earlier work clarified; v4: final version, accepted for publication in Phys. Rev.