New features of modulational instability of partially coherent light; importance of the incoherence spectrum

It is shown that the properties of the modulational instability of partially coherent waves propagating in a nonlinear Kerr medium depend crucially on the profile of the incoherent field spectrum. Under certain conditions, the incoherence may even enhance, rather than suppress, the instability. In particular, it is found that the range of modulationally unstable wave numbers does not necessarily decrease monotonously with increasing degree of incoherence and that the modulational instability may still exist even when long wavelength perturbations are stable.Comment: 4 pages, 2 figures, submitted to Phys. Rev. Let

Partially incoherent optical vortices in self-focusing nonlinear media

We observe stable propagation of spatially localized single- and double-charge optical vortices in a self-focusing nonlinear medium. The vortices are created by self-trapping of partially incoherent light carrying a phase dislocation, and they are stabilized when the spatial incoherence of light exceeds a certain threshold. We confirm the vortex stabilization effect by numerical simulations and also show that the similar mechanism of stabilization applies to higher-order vortices.Comment: 4 pages and 6 figures (including 3 experimental figures

Grouping time series by pairwise measures of redundancy

A novel approach is proposed to group redundant time series in the frame of causality. It assumes that (i) the dynamics of the system can be described using just a small number of characteristic modes, and that (ii) a pairwise measure of redundancy is sufficient to elicit the presence of correlated degrees of freedom. We show the application of the proposed approach on fMRI data from a resting human brain and gene expression profiles from HeLa cell culture.Comment: 4 pages, 8 figure

Exact soliton solutions, shape changing collisions and partially coherent solitons in coupled nonlinear Schroedinger equations

We present the exact bright one-soliton and two-soliton solutions of the integrable three coupled nonlinear Schroedinger equations (3-CNLS) by using the Hirota method, and then obtain them for the general $N$-coupled nonlinear Schroedinger equations (N-CNLS). It is pointed out that the underlying solitons undergo inelastic (shape changing) collisions due to intensity redistribution among the modes. We also analyse the various possibilities and conditions for such collisions to occur. Further, we report the significant fact that the various partial coherent solitons (PCS) discussed in the literature are special cases of the higher order bright soliton solutions of the N-CNLS equations.Comment: 4 pages, RevTex, 1 EPS figure To appear in Physical Review Letter

Universality in Systems with Power-Law Memory and Fractional Dynamics

There are a few different ways to extend regular nonlinear dynamical systems by introducing power-law memory or considering fractional differential/difference equations instead of integer ones. This extension allows the introduction of families of nonlinear dynamical systems converging to regular systems in the case of an integer power-law memory or an integer order of derivatives/differences. The examples considered in this review include the logistic family of maps (converging in the case of the first order difference to the regular logistic map), the universal family of maps, and the standard family of maps (the latter two converging, in the case of the second difference, to the regular universal and standard maps). Correspondingly, the phenomenon of transition to chaos through a period doubling cascade of bifurcations in regular nonlinear systems, known as "universality", can be extended to fractional maps, which are maps with power-/asymptotically power-law memory. The new features of universality, including cascades of bifurcations on single trajectories, which appear in fractional (with memory) nonlinear dynamical systems are the main subject of this review.Comment: 23 pages 7 Figures, to appear Oct 28 201

Discrete wavelet transform de-noising in eukaryotic gene splicing

<p>Abstract</p> <p>Background</p> <p>This paper compares the most common digital signal processing methods of exon prediction in eukaryotes, and also proposes a technique for noise suppression in exon prediction. The specimen used here which has relevance in medical research, has been taken from the public genomic database - GenBank.</p> <p>Methods</p> <p>Here exon prediction has been done using the digital signal processing methods viz. binary method, EIIP (electron-ion interaction psuedopotential) method and filter methods. Under filter method two filter designs, and two approaches using these two designs have been tried. The discrete wavelet transform has been used for de-noising of the exon plots.</p> <p>Results</p> <p>Results of exon prediction based on the methods mentioned above, which give values closest to the ones found in the NCBI database are given here. The exon plot de-noised using discrete wavelet transform is also given.</p> <p>Conclusion</p> <p>Alterations to the proven methods as done by the authors, improves performance of exon prediction algorithms. Also it has been proven that the discrete wavelet transform is an effective tool for de-noising which can be used with exon prediction algorithms.</p

Multivariate Iyengar type inequalities for radial functions

Here we present a variety of multivariate Iyengar type inequalities for radial functions defined on the shell and ball. Our approach is based on the polar coordinates in R^N, N>=2, and the related multivariate polar integration formula. Via this method we transfer well-known univariate Iyengar type inequalities and uni-variate author’s related results into multivariate Iyengar inequalities

Statistical Theory for Incoherent Light Propagation in Nonlinear Media

A novel statistical approach based on the Wigner transform is proposed for the description of partially incoherent optical wave dynamics in nonlinear media. An evolution equation for the Wigner transform is derived from a nonlinear Schrodinger equation with arbitrary nonlinearity. It is shown that random phase fluctuations of an incoherent plane wave lead to a Landau-like damping effect, which can stabilize the modulational instability. In the limit of the geometrical optics approximation, incoherent, localized, and stationary wave-fields are shown to exist for a wide class of nonlinear media.Comment: 4 pages, REVTeX4. Submitted to Physical Review E. Revised manuscrip

COVID-19 unmasked global collaboration protocol:Longitudinal cohort study examining mental health of young children and caregivers during the pandemic

Background: Early empirical data shows that school-aged children, adolescents and adults are experiencing elevated levels of anxiety and depression during the COVID-19 pandemic. Currently, there is very little research on mental health outcomes for young children. Objectives: To describe the formation of a global collaboration entitled, 'COVID-19 Unmasked'. The collaborating researchers aim to (1) describe and compare the COVID-19 related experiences within and across countries; (2) examine mental health outcomes for young children (1 to 5 years) and caregivers over a 12-month period during the COVID-19 pandemic; (3) explore the trajectories/time course of psychological outcomes of the children and parents over this period and (4) identify the risk and protective factors for different mental health trajectories. Data will be combined from all participating countries into one large open access cross-cultural dataset to facilitate further international collaborations and joint publications. Methods: COVID-19 Unmasked is an online prospective longitudinal cohort study. An international steering committee was formed with the aim of starting a global collaboration. Currently, partnerships have been formed with 9 countries (Australia, Cyprus, Greece, the Netherlands, Poland, Spain, Turkey, the UK, and the United States of America). Research partners have started to start data collection with caregivers of young children aged 1-5 years old at baseline, 3-months, 6-months, and 12-months. Caregivers are invited to complete an online survey about COVID-19 related exposure and experiences, child's wellbeing, their own mental health, and parenting. Data analysis: Primary study outcomes will be child mental health as assessed by scales from the Patient-Reported Outcomes Measurement Information System - Early Childhood (PROMIS-EC) and caregiver mental health as assessed by the Depression Anxiety Stress Scale (DASS-21). The trajectories/time course of mental health difficulties and the impact of risk and protective factors will be analysed using hierarchical linear models, accounting for nested effects (e.g. country) and repeated measures