The semiclassical--Sobolev orthogonal polynomials: a general approach

We say that the polynomial sequence $(Q^{(\lambda)}_n)$ is a semiclassical Sobolev polynomial sequence when it is orthogonal with respect to the inner product $$_S= +\lambda <{{\bf u}}, {{\mathscr D}p \,{\mathscr D}r}>,$$ where ${\bf u}$ is a semiclassical linear functional, ${\mathscr D}$ is the differential, the difference or the $q$--difference operator, and $\lambda$ is a positive constant. In this paper we get algebraic and differential/difference properties for such polynomials as well as algebraic relations between them and the polynomial sequence orthogonal with respect to the semiclassical functional $\bf u$. The main goal of this article is to give a general approach to the study of the polynomials orthogonal with respect to the above nonstandard inner product regardless of the type of operator ${\mathscr D}$ considered. Finally, we illustrate our results by applying them to some known families of Sobolev orthogonal polynomials as well as to some new ones introduced in this paper for the first time.Comment: 23 pages, special issue dedicated to Professor Guillermo Lopez lagomasino on the occasion of his 60th birthday, accepted in Journal of Approximation Theor

Community, work and family in diverse contexts and changing times

The 8th International Community, Work and Family conference took place in Malta at the Valletta campus of the University of Malta between the 23rd to the 25th May 2019. In a pre-COVID-19 world with no traveling restrictions, the conference brought together over 100 experts, academics, and students from a broad range of countries and disciplines to focus on the theme of Community, Work and Family in Diverse Contexts and Changing Times. The research presented during the conference highlights some of the challenges that communities, organizations and families are facing in the twenty-first century across diverse and rapidly changing contexts. The topics presented spanned from broad studies that analyze the work-life interface of well-studied groups such as fathers and mothers, to other clusters that are generally less well-researched such as the police and the military, migrants, solo entrepreneurs, the LGBTIQ community, and those who work with people with special needs. The recurrent theme of the gendered division of labor and work-life measures was discussed by various researchers, as were the issues of flexible work, family policy, and the impact of technology. It was refreshing to note that various researchers focused on the issue of community as a source of support, whilst others explored how peer, supervisor and management support impacts work-life issues. Overall, the conference provided a diverse and rich range of scholarly material upon which to develop this special issue for Community, Work & Family. [...

The Gromov Norm of the Product of Two Surfaces

We make an estimation of the value of the Gromov norm of the Cartesian product of two surfaces. Our method uses a connection between these norms and the minimal size of triangulations of the products of two polygons. This allows us to prove that the Gromov norm of this product is between 32 and 52 when both factors have genus 2. The case of arbitrary genera is easy to deduce form this one.Comment: The journal version contains an error that invalidates one direction of the main theorem. The present version contains an erratum, at the end, explaining thi

Correlations between 21 cm Radiation and the CMB from Active Sources

Neutral hydrogen is ubiquitous, absorbing and emitting 21 cm radiation throughout much of the Universe's history. Active sources of perturbations, such as cosmic strings, would generate simultaneous perturbations in the distribution of neutral hydrogen and in the Cosmic Microwave Background (CMB) radiation from recombination. Moving strings would create wakes leading to 21 cm brightness fluctuations, while also perturbing CMB light via the Gott-Kaiser-Stebbins effect. This would lead to spatial correlations between the 21 cm and CMB anisotropies. Passive sources, like inflationary perturbations, predict no cross correlations prior to the onset of reionization. Thus, observation of any cross correlation between CMB and 21 cm radiation from dark ages would constitute evidence for new physics. We calculate the cosmic string induced correlations between CMB and 21 cm and evaluate their observability.Comment: 8 pages, 5 figure

Development of a Tool to Recreate the Mars Science Laboratory Aerothermal Environment

The Mars Science Laboratory will enter the Martian atmosphere in 2012 with multiple char depth sensors and in-depth thermocouples in its heatshield. The aerothermal environment experienced by MSL may be computationally recreated using the data from the sensors and a material response program, such as the Fully Implicit Ablation and Thermal (FIAT) response program, through the matching of the char depth and thermocouple predictions of the material response program to the sensor data. A tool, CHanging Inputs from the Environment of FIAT (CHIEF), was developed to iteratively change different environmental conditions such that FIAT predictions match within certain criteria applied to an external data set. The computational environment is changed by iterating on the enthalpy, pressure, or heat transfer coefficient at certain times in the trajectory. CHIEF was initially compared against arc-jet test data from the development of the MSL heatshield and then against simulated sensor data derived from design trajectories for MSL. CHIEF was able to match char depth and in-depth thermocouple temperatures within the bounds placed upon it for these cases. Further refinement of CHIEF to compare multiple time points and assign convergence criteria may improve accuracy

Probing the first galaxies with the SKA

Observations of anisotropies in the brightness temperature of the 21 cm line of neutral hydrogen from the period before reionization would shed light on the dawn of the first stars and galaxies. In this paper, we use large-scale semi-numerical simulations to analyse the imprint on the 21 cm signal of spatial fluctuations in the Lyman-alpha flux arising from the clustering of the first galaxies. We show that an experiment such as the Square Kilometer Array (SKA) can probe this signal at the onset of reionization, giving us important information about the UV emission spectra of the first stars and characterizing their host galaxies. SKA-pathfinders with ~ 10% of the full collecting area should be capable of making a statistical detection of the 21 cm power spectrum at redshifts z 67 MHz). We then show that the SKA should be able to measure the three dimensional power spectrum as a function of the angle with the line of sight and discuss the use of the redshift space distortions as a way to separate out the different components of the 21 cm power spectrum. We demonstrate that, at least on large scales where the Lyman-alpha fluctuations are linear, they can be used as a model independent way to extract the power spectra due to these Lyman-alpha fluctuations.Comment: 13 pages, 17 figures. New version to match version accepted by A&A. Improved discussions on the Lyman-alpha simulation, adiabatic cooling fluctuations, the Fisher matrix approach and the Poisson term calculation. New version of the code available at: http://www.SimFast21.or

Intensity Coding in Two-Dimensional Excitable Neural Networks

In the light of recent experimental findings that gap junctions are essential for low level intensity detection in the sensory periphery, the Greenberg-Hastings cellular automaton is employed to model the response of a two-dimensional sensory network to external stimuli. We show that excitable elements (sensory neurons) that have a small dynamical range are shown to give rise to a collective large dynamical range. Therefore the network transfer (gain) function (which is Hill or Stevens law-like) is an emergent property generated from a pool of small dynamical range cells, providing a basis for a "neural psychophysics". The growth of the dynamical range with the system size is approximately logarithmic, suggesting a functional role for electrical coupling. For a fixed number of neurons, the dynamical range displays a maximum as a function of the refractory period, which suggests experimental tests for the model. A biological application to ephaptic interactions in olfactory nerve fascicles is proposed.Comment: 17 pages, 5 figure

Contribution of Cross-Correlations to the 21cm Angular Power Spectrum in the Epoch of Reionization

Measurement of the 21cm hyperfine transition of neutral hydrogen provides a unique probe of the epoch of reionization and the Dark Ages. Three major mechanisms are believed to dominate the radiation process: emission from neutral hydrogen surrounding the ionized bubbles of first galaxies and/or quasars, emission from neutral hydrogen inside minihalos, and absorption of diffuse neutral hydrogen against the cosmic microwave background. In the present work, by simply combining the existing analytic models for the three mechanisms, we investigate the contribution of cross-correlation between these three components to the total 21cm angular power spectrum, in the sense that neutral hydrogen associated with different radiation processes traces the large-scale structures of underlying density perturbations. While the overall 21cm power spectrum remains almost unchanged with the inclusion of the cross-correlations, the cross-correlation may play a key role in the determination of the 21cm power spectrum during the transition of 21cm radiation from emission-dominated phase to absorption-dominated phase at redshift z~20. A significant suppression in the 21cm angular power spectrum during this transition is anticipated as the result of negative contribution of the cross-correlation between the absorption of diffuse neutral hydrogen and the emission components. Therefore, an accurate prediction of the cosmic 21cm power spectrum should take the cross-correlation into account especially at the transition phase.Comment: 10 pages, 4 figures, accepted for publication in MNRA

Consensus: guidelines: best practices for detection, assessment and management of suspected acute drug-induced liver injury during clinical trials in patients with nonalcoholic steatohepatitis

BACKGROUND: The last decade has seen a rapid growth in the number of clinical trials enrolling patients with nonalcoholic fatty liver disease and nonalcoholic steatohepatitis (NASH). Due to the underlying chronic liver disease, patients with NASH often require different approaches to the assessment and management of suspected drug-induced liver injury (DILI) compared to patients with healthy livers. However, currently no regulatory guidelines or position papers systematically address best practices pertaining to DILI in NASH clinical trials. AIMS: This publication focuses on best practices concerning the detection, monitoring, diagnosis and management of suspected acute DILI during clinical trials in patients with NASH. METHODS: This is one of several papers developed by the IQ DILI Initiative, comprised of members from 15 pharmaceutical companies, in collaboration with DILI experts from academia and regulatory agencies. This paper is based on extensive literature review, and discussions between industry members with expertise in drug safety and DILI experts from outside industry to achieve consensus on common questions related to this topic. RESULTS: Recommended best practices are outlined pertaining to hepatic inclusion and exclusion criteria, monitoring of liver tests, DILI detection, approach to a suspected DILI signal, causality assessment and hepatic discontinuation rules. CONCLUSIONS: This paper provides a framework for the approach to assessment and management of suspected acute DILI during clinical trials in patients with NASH