On Stepanov almost-periodic oscillations and their discretizations

The relationship between Carathéodory almost-periodic (a.p.) solutions and their discretizations is clarified for differential equations and inclusions in Banach spaces. Our investigation was stimulated by an old result of Meisters [Proc. Am. Math. Soc. 10 (1959), pp. 113–119] about Bohr a.p. solutions which we generalize in several directions. Unlike for functions, Stepanov and Bohr a.p. sequences are shown to coincide. A particular attention is paid to purely (i.e. non-uniformly continuous) Stepanov a.p. solutions. Many ideas are explained in detail by means of examples illustrated.     

Comparative study of microscopic charge dynamics in crystalline acceptor-substituted oligothiophenes

By performing microscopic charge transport simulations for a set of crystalline dicyanovinyl-substituted oligothiophenes, we find that the internal acceptor-donor-acceptor molecular architecture combined with thermal fluctuations of dihedral angles results in large variations of local electric fields, substantial energetic disorder, and pronounced Poole-Frenkel behavior, which is unexpected for crystalline compounds. We show that the presence of static molecular dipoles causes large energetic disorder, which is mostly reduced not by compensation of dipole moments in a unit cell but by molecular polarizabilities. In addition, the presence of a well-defined π-stacking direction with strong electronic couplings and short intermolecular distances turns out to be disadvantageous for efficient charge transport since it inhibits other transport directions and is prone to charge trapping.     

Large deviations estimates for the multiscale analysis of heart rate variability

In the realm of multiscale signal analysis, multifractal analysis provides a natural and rich framework to measure the roughness of a time series. As such, it has drawn special attention of both mathematicians and practitioners, and led them to characterize relevant physiological factors impacting the heart rate variability. Notwithstanding these considerable progresses, multifractal analysis almost exclusively developed around the concept of Legendre singularity spectrum, for which efficient and elaborate estimators exist, but which are structurally blind to subtle features like non-concavity or, to a certain extent, non scaling of the distributions. Large deviations theory allows bypassing these limitations but it is only very recently that performing estimators were proposed to reliably compute the corresponding large deviations singularity spectrum. In this article, we illustrate the relevance of this approach, on both theoretical objects and on human heart rate signals from the Physionet public database. As conjectured, we verify that large deviations principles reveal significant information that otherwise remains hidden with classical approaches, and which can be reminiscent of some physiological characteristics. In particular we quantify the presence/absence of scale invariance of RR signals.     

Faciliation of Mandarin tone perception by visual speech in clear and degraded audio: implications for cochlear implants

Cochlear implant (CI) users in tone language environments report great difficulty in perceiving lexical tone. This study investigated the augmentation of simulated cochlear implant audio by visual (facial) speech information for tone. Native speakers of Mandarin and Australian English were asked to discriminate between minimal pairs of Mandarin tones in five conditions: Auditory-Only, Auditory-Visual, CI-simulated Auditory-Only, CI-simulated Auditory-Visual, and Visual-Only (silent video). Discrimination in CI-simulated audio conditions was poor compared with normal audio, and varied according to tone pair, with tone pairs with strong non-F0 cues discriminated the most easily. The availability of visual speech information also improved discrimination in the CI-simulated audio conditions, particularly on tone pairs with strong durational cues. In the silent Visual-Only condition, both Mandarin and Australian English speakers discriminated tones above chance levels. Interestingly, tone-nai?ve listeners outperformed native listeners in the Visual-Only condition, suggesting firstly that visual speech information for tone is available, and may in fact be under-used by normal-hearing tone language perceivers, and secondly that the perception of such information may be language-general, rather than the product of language-specific learning. This may find application in the development of methods to improve tone perception in CI users in tone language environments.     

Relative intensity noise and frequency noise of a compact Brillouin laser made of As38Se62 suspended-core chalcogenide fiber

Relative intensity noise and frequency noise have been measured for the first time for a single-frequency Brillouin chalcogenide As38Se62 fiber laser. This is also the first demonstration of a compact suspended-core fiber Brillouin laser, which exhibits a low threshold power of 22 mW and a slope efficiency of 26% for nonresonant pumping.     

Epicatechin B-ring conjugates: first enantioselective synthesis and evidence for their occurrence in human biological fluids

Herein, the first enantioselective total synthesis of a number of biologically relevant (-)-epicatechin conjugates is described. The success of this synthesis relied on (i) optimized conditions for the stereospecific cyclization step leading to the catechin C ring; on (ii) efficient conjugation reactions; and on (iii) optimized deprotection sequences. These standard compounds have been subsequently used to elucidate for the first time the pattern of (-)-epicatechin conjugates present in four different human biological fluids following (-)-epicatechin absorption.     

Regioselective Cu(I)-catalyzed tandem A3-coupling/decarboxylative coupling to 3-amino-1,4-enynes

An efficient and novel copper-mediated protocol for the synthesis of 3-amino-1,4-enynes from glyoxylic acid, an amine, and an alkyne was developed. This new reaction involving two sequential C-C bond formations is air and moisture tolerant and proceeds via a tandem A(3)-coupling and a selective decarboxylative coupling.     

1,4-bis-(3-hydroxy-4-oxo-4H-chromen-2-yl)-benzene (bis-flavonol): synthesis, spectral properties and principle possibility of the excited state double proton transfer reaction

Synthesis and systematic investigation of the spectral-luminescent properties of “bis-flavonol” {1,4-bis-(3-hydroxy-4-oxo-4H-chromen-2-yl)-benzene} were performed. Hypothetical possibility for the double excited-state proton transfer reaction in bis-flavonol is discussed based on both quantum-chemical modeling and experimental data. Consecutive S₁*-state transfer of the two protons of the title molecule is shown to be energetically unfavorable, however, still preserving a possibility for the concerted double proton transfer in the excited dienol form.     

On an efficient splitting‐based method for solving the diffusion equation on a sphere

A novel numerical approach for solving the diffusion problem on a sphere is suggested. By using operator splitting, we develop a new method that allows constructing finite difference schemes of the second and fourth approximation orders in the spatial variables. Both schemes properly ensure the balance of mass and the energy dissipation in the L₂ ‐norm. The schemes are very cheap from the computational standpoint. Numerical results demonstrate the skillfulness of the approach in describing the diffusion dynamics on a sphere. It is shown the method can directly be extended to nonlinear diffusion problems.© 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 331–352, 2012     

Numerical Measure of a Complex Matrix

We introduce a natural probability measure over the numerical range of a complex matrix A ∈ M _n( \input amssym $\Bbb C$ ). This numerical measure μ_A can be defined as the law of the random variable 〈AX, X〉 ∈ \input amssym $\Bbb C$ when the vector X ∈ \input amssym $\Bbb C$ ⁿ is uniformly distributed on the unit sphere. If the matrix A is normal, we show that μ_A has a piecewise polynomial density f_A, which can be identified with a multivariate B‐spline. In the general (nonnormal) case, we relate the Radon transform of μ_A to the spectrum of a family of Hermitian matrices, and we deduce an explicit representation formula for the numerical density that is appropriate for theoretical and computational purposes. As an application, we show that the density f_A is polynomial in some regions of the complex plane that can be characterized geometrically, and we recover some known results about lacunae of symmetric hyperbolic systems in 2 + 1 dimensions. Finally, we prove under general assumptions that the numerical measure of a matrix A ∈ M _n (\input amssym $\Bbb C$ ) concentrates to a Dirac mass as the size n goes to infinity. © 2011 Wiley Periodicals, Inc.