Large Deviations Behavior of the Logarithmic Error Probability of Random Codes

This work studies the deviations of the error exponent of the constant composition code ensemble around its expectation, known as the error exponent of the typical random code (TRC). In particular, it is shown that the probability of randomly drawing a codebook whose error exponent is smaller than the TRC exponent is exponentially small; upper and lower bounds for this exponent are given, which coincide in some cases. In addition, the probability of randomly drawing a codebook whose error exponent is larger than the TRC exponent is shown to be double–exponentially small; upper and lower bounds to the double–exponential exponent are given. The results suggest that codebooks whose error exponent is larger than the error exponent of the TRC are extremely rare. The key ingredient in the proofs is a new large deviations result of type class enumerators with dependent variables

Observation of Biexcitonic Optical Bistability and Optical Limiting in CuCl

Experimental evidence for the occurrence of optical bistability using the biexciton two-photon resonance in CuCl is presented. These observations agree with recent theoretical predictions that require an intensity of 10 MW/cm2 and 10-μm-thick etalons with 90% reflective coatings. Earlier much less demanding predictions neglected two important physical effects: unsaturable background absorption at the biexciton from the tail of the exciton resonance and broadening of the biexciton resonance with intensity

Specifying computer-supported collaboration scripts

Collaboration scripts are activity programs which aim to foster collaborative learning by structuring interaction between learners. Computer-supported collaboration scripts generally suffer from the problem of being restrained to a specific learning platform and learning context. A standardization of collaboration scripts first requires a specification of collaboration scripts that integrates multiple perspectives from computer science, education and psychology. So far, only few and limited attempts at such specifications have been made. This paper aims to consolidate and expand these approaches in light of recent findings and to propose a generic framework for the specification of collaboration scripts. The framework enables a description of collaboration scripts using a small number of components (participants, activities, roles, resources and groups) and mechanisms (task distribution, group formation and sequencing)

Maximizing Neumann fundamental tones of triangles

We prove sharp isoperimetric inequalities for Neumann eigenvalues of the Laplacian on triangular domains. The first nonzero Neumann eigenvalue is shown to be maximal for the equilateral triangle among all triangles of given perimeter, and hence among all triangles of given area. Similar results are proved for the harmonic and arithmetic means of the first two nonzero eigenvalues

Force measurements of a superconducting-film actuator for a cryogenic interferometric gravitational-wave detector

We measured forces applied by an actuator with a YBCO film at near 77 K for the Large-scale Cryogenic Gravitational-wave Telescope (LCGT) project. An actuator consisting of both a YBCO film of 1.6 micrometers thickness and 0.81 square centimeters area and a solenoid coil exerted a force of up to 0.2 mN on a test mass. The presented actuator system can be used to displace the mirror of LCGT for fringe lock of the interferometer.Comment: 9 pages, 3 figure

Effects of soybean lipid infusion on triglyceride and unbound free fatty acid levels in preterm infants

© 2018 Informa UK Limited, trading as Taylor & Francis Group Objective: To determine the plasma triglyceride (TG) and unbound free fatty acid (FFAu) levels in infants treated with increasing dosages of soybean lipid, intralipid (IL), infusion. Study design: TG and FFAu levels were measured in 78 preterm infants (BW 500–2000 g; GA 23–34 weeks) using the fluorescent probe ADIFAB2 and enzymatic method. Results: The infants’ BW was 1266.2 ± 440.7 g and GA 28.8 ± 3.1 weeks. TG levels were 77.4 ± 50 mg/dL, 140.2 ± 188 mg/dL (p \u3c .04 compared to levels during low dose IL infusion) and 135.6 ± 118 mg/dL (p \u3c .004), respectively during increased IL rates. FFAu levels were 17.7 ± 13 nM, 47.3 ± 102.8 nM (p = .07) and 98 ± 234 nM (p = .03). TG levels correlated with IL dose, the rate of IL administration, and FFAu levels. TG and FFAu levels were higher in infants below 28 weeks’ gestation Conclusions: Increasing dosage of IL is associated with increasing levels of TG and FFAu, especially in infants below 29 weeks of gestation. The increased level of FFAu suggests inefficient cellular utilization

A remark on an overdetermined problem in Riemannian Geometry

Let $(M,g)$ be a Riemannian manifold with a distinguished point $O$ and assume that the geodesic distance $d$ from $O$ is an isoparametric function. Let $\Omega\subset M$ be a bounded domain, with $O \in \Omega$, and consider the problem $\Delta_p u = -1$ in $\Omega$ with $u=0$ on $\partial \Omega$, where $\Delta_p$ is the $p$-Laplacian of $g$. We prove that if the normal derivative $\partial_{\nu}u$ of $u$ along the boundary of $\Omega$ is a function of $d$ satisfying suitable conditions, then $\Omega$ must be a geodesic ball. In particular, our result applies to open balls of $\mathbb{R}^n$ equipped with a rotationally symmetric metric of the form $g=dt^2+\rho^2(t)\,g_S$, where $g_S$ is the standard metric of the sphere.Comment: 8 pages. This paper has been written for possible publication in a special volume dedicated to the conference "Geometric Properties for Parabolic and Elliptic PDE's. 4th Italian-Japanese Workshop", organized in Palinuro in May 201

High Resolution Mid-Infrared Imaging of Ultraluminous Infrared Galaxies

Observations of ultraluminous infrared galaxies (ULIRGs) with an achieved resolution approaching the diffraction limit in the mid-infrared from 8 - 25 $\mu$m using the Keck Telescopes are reported. We find extremely compact structures, with spatial scales of $< 0.3''$ (diameter) in six of the seven ULIRGs observed. These compact sources emit between 30% and 100% of the mid-infrared energy from these galaxies. We have utilized the compact mid-infrared structures as a diagnostic of whether an AGN or a compact (100 -- 300 pc) starburst is the primary power source in these ULIRGs. In Markarian 231, the upper limit on the diameter of the 12.5 $\mu$m source, 0.13$''$, shows that the size of the infrared source must increase with increasing wavelength, consistent with AGN models. In IRAS 05189-2524 and IRAS 08572+3915 there is strong evidence that the source size increases with increasing wavelength. This suggests heating by a central source rather than an extended luminosity source, consistent with the optical classification as an AGN. The compact mid-infrared sources seen in the other galaxies cannot be used to distinguish the ultimate luminosity source. If these ULIRGs are powered by compact starbursts, the star formation rates seen in the central few hundred parsecs far exceed the global rates seen in nearby starburst galaxies, and approach the surface brightness of individual clusters in nearby starburst galaxies.Comment: 33pages, 6 tables, 5 figures, Accepted for publication in A

Structural Stability and Renormalization Group for Propagating Fronts

A solution to a given equation is structurally stable if it suffers only an infinitesimal change when the equation (not the solution) is perturbed infinitesimally. We have found that structural stability can be used as a velocity selection principle for propagating fronts. We give examples, using numerical and renormalization group methods.Comment: 14 pages, uiucmac.tex, no figure