On positive solutions and the Omega limit set for a class of delay differential equations

This paper studies the positive solutions of a class of delay differential equations with two delays. These equations originate from the modeling of hematopoietic cell populations. We give a sufficient condition on the initial function for $t\leq 0$ such that the solution is positive for all time $t>0$. The condition is "optimal". We also discuss the long time behavior of these positive solutions through a dynamical system on the space of continuous functions. We give a characteristic description of the $\omega$ limit set of this dynamical system, which can provide informations about the long time behavior of positive solutions of the delay differential equation.Comment: 15 pages, 2 figure

Cartoons kill: casualties in animated recreational theater in an objective observational new study of kids' introduction to loss of life.

Objectives To assess the risk of on-screen death of important characters in children’s animated films versus dramatic films for adults. Design Kaplan-Meier survival analysis with Cox regression comparing time to first on-screen death. Setting Authors’ television screens, with and without popcorn. Participants Important characters in 45 top grossing children’s animated films and a comparison group of 90 top grossing dramatic films for adults. Main outcome measures Time to first on-screen death. Results Important characters in children’s animated films were at an increased risk of death compared with characters in dramatic films for adults (hazard ratio 2.52, 95% confidence interval 1.30 to 4.90). Risk of on-screen murder of important characters was higher in children’s animated films than in comparison films (2.78, 1.02 to 7.58). Conclusions Rather than being the innocuous form of entertainment they are assumed to be, children’s animated films are rife with on-screen death and murder

Complex Dynamics and Multistability in a Damped Harmonic Oscillator with Delayed Negative Feedback

A center manifold reduction and numerical calculations are used to demonstrate the presence of limit cycles, two-tori, and multistability in the damped harmonic oscillator with delayed negative feedback. This model is the prototype of a mechanical system operating with delayed feedback. Complex dynamics are thus seen to arise in very plausible and commonly occurring mechanical and neuromechanical feedback systems

Sustained IFN signaling is associated with delayed development of SARS-CoV-2-specific immunity.

Plasma RNAemia, delayed antibody responses and inflammation predict COVID-19 outcomes, but the mechanisms underlying these immunovirological patterns are poorly understood. We profile 782 longitudinal plasma samples from 318 hospitalized patients with COVID-19. Integrated analysis using k-means reveals four patient clusters in a discovery cohort: mechanically ventilated critically-ill cases are subdivided into good prognosis and high-fatality clusters (reproduced in a validation cohort), while non-critical survivors segregate into high and low early antibody responders. Only the high-fatality cluster is enriched for transcriptomic signatures associated with COVID-19 severity, and each cluster has distinct RBD-specific antibody elicitation kinetics. Both critical and non-critical clusters with delayed antibody responses exhibit sustained IFN signatures, which negatively correlate with contemporaneous RBD-specific IgG levels and absolute SARS-CoV-2-specific B and CD4 <sup>+</sup> T cell frequencies. These data suggest that the "Interferon paradox" previously described in murine LCMV models is operative in COVID-19, with excessive IFN signaling delaying development of adaptive virus-specific immunity

Select strengths and biases of models in representing the Arctic winter boundary layer over sea ice: the Larcform 1 single column model intercomparison

Weather and climate models struggle to represent lower tropospheric temperature and moisture profiles and surface fluxes in Arctic winter, partly because they lack or misrepresent physical processes that are specific to high latitudes. Observations have revealed two preferred states of the Arctic winter boundary layer. In the cloudy state, cloud liquid water limits surface radiative cooling, and temperature inversions are weak and elevated. In the radiatively clear state, strong surface radiative cooling leads to the build-up of surface-based temperature inversions. Many large-scale models lack the cloudy state, and some substantially underestimate inversion strength in the clear state. Here, the transformation from a moist to a cold dry air mass is modeled using an idealized Lagrangian perspective. The trajectory includes both boundary layer states, and the single-column experiment is the first Lagrangian Arctic air formation experiment (Larcform 1) organized within GEWEX GASS (Global atmospheric system studies). The intercomparison reproduces the typical biases of large-scale models: some models lack the cloudy state of the boundary layer due to the representation of mixed-phase microphysics or to the interaction between micro- and macrophysics. In some models, high emissivities of ice clouds or the lack of an insulating snow layer prevent the build-up of surface-based inversions in the radiatively clear state. Models substantially disagree on the amount of cloud liquid water in the cloudy state and on turbulent heat fluxes under clear skies. Observations of air mass transformations including both boundary layer states would allow for a tighter constraint of model behavior

Model theory of finite and pseudofinite groups

This is a survey, intended both for group theorists and model theorists, concerning the structure of pseudofinite groups, that is, infinite models of the first-order theory of finite groups. The focus is on concepts from stability theory and generalisations in the context of pseudofinite groups, and on the information this might provide for finite group theory

Structured models of cell migration incorporating molecular binding processes

The dynamic interplay between collective cell movement and the various molecules involved in the accompanying cell signalling mechanisms plays a crucial role in many biological processes including normal tissue development and pathological scenarios such as wound healing and cancer. Information about the various structures embedded within these processes allows a detailed exploration of the binding of molecular species to cell-surface receptors within the evolving cell population. In this paper we establish a general spatio-temporal-structural framework that enables the description of molecular binding to cell membranes coupled with the cell population dynamics. We first provide a general theoretical description for this approach and then illustrate it with two examples arising from cancer invasion

Quantitative Analysis of Mechanisms That Govern Red Blood Cell Age Structure and Dynamics during Anaemia

Mathematical modelling has proven an important tool in elucidating and quantifying mechanisms that govern the age structure and population dynamics of red blood cells (RBCs). Here we synthesise ideas from previous experimental data and the mathematical modelling literature with new data in order to test hypotheses and generate new predictions about these mechanisms. The result is a set of competing hypotheses about three intrinsic mechanisms: the feedback from circulating RBC concentration to production rate of immature RBCs (reticulocytes) in bone marrow, the release of reticulocytes from bone marrow into the circulation, and their subsequent ageing and clearance. In addition we examine two mechanisms specific to our experimental system: the effect of phenylhydrazine (PHZ) and blood sampling on RBC dynamics. We performed a set of experiments to quantify the dynamics of reticulocyte proportion, RBC concentration, and erythropoietin concentration in PHZ-induced anaemic mice. By quantifying experimental error we are able to fit and assess each hypothesis against our data and recover parameter estimates using Markov chain Monte Carlo based Bayesian inference. We find that, under normal conditions, about 3% of reticulocytes are released early from bone marrow and upon maturation all cells are released immediately. In the circulation, RBCs undergo random clearance but have a maximum lifespan of about 50 days. Under anaemic conditions reticulocyte production rate is linearly correlated with the difference between normal and anaemic RBC concentrations, and their release rate is exponentially correlated with the same. PHZ appears to age rather than kill RBCs, and younger RBCs are affected more than older RBCs. Blood sampling caused short aperiodic spikes in the proportion of reticulocytes which appear to have a different developmental pathway than normal reticulocytes. We also provide evidence of large diurnal oscillations in serum erythropoietin levels during anaemia

Práticas de regulação das aprendizagens de estagiários do 1º ciclo do ensino básico de Portugal

O estudo sobre as práticas de regulação das aprendizagens de estagiários do 1º ciclo do ensino básico permitiu-nos concluir que, resultante da prática da avaliação formativa contínua, a regulação incide, sobretudo, nas dificuldades de aprendizagem dos alunos. Utilizam estratégias de regulação corretivas, mas também, de regulação interativa. Mais condicionadas foram as estratégias de regulação dos diferentes ritmos de trabalho e de aprendizagem dos alunos