Fitting Effective Diffusion Models to Data Associated with a "Glassy Potential": Estimation, Classical Inference Procedures and Some Heuristics

A variety of researchers have successfully obtained the parameters of low dimensional diffusion models using the data that comes out of atomistic simulations. This naturally raises a variety of questions about efficient estimation, goodness-of-fit tests, and confidence interval estimation. The first part of this article uses maximum likelihood estimation to obtain the parameters of a diffusion model from a scalar time series. I address numerical issues associated with attempting to realize asymptotic statistics results with moderate sample sizes in the presence of exact and approximated transition densities. Approximate transition densities are used because the analytic solution of a transition density associated with a parametric diffusion model is often unknown.I am primarily interested in how well the deterministic transition density expansions of Ait-Sahalia capture the curvature of the transition density in (idealized) situations that occur when one carries out simulations in the presence of a "glassy" interaction potential. Accurate approximation of the curvature of the transition density is desirable because it can be used to quantify the goodness-of-fit of the model and to calculate asymptotic confidence intervals of the estimated parameters. The second part of this paper contributes a heuristic estimation technique for approximating a nonlinear diffusion model. A "global" nonlinear model is obtained by taking a batch of time series and applying simple local models to portions of the data. I demonstrate the technique on a diffusion model with a known transition density and on data generated by the Stochastic Simulation Algorithm.Comment: 30 pages 10 figures Submitted to SIAM MMS (typos removed and slightly shortened

Interleukin-6 and Associated Cytokine Responses to An Acute Bout of High-intensity Interval Exercise: the Effect of Exercise Intensity and Volume

Acute increases in interleukin (IL)-6 following prolonged exercise are associated with the induction of a transient anti-inflammatory state (e.g., increases in IL-10) that is partly responsible for the health benefits of regular exercise. The purposes of this study were to investigate the IL-6–related inflammatory response to high-intensity interval exercise (HIIE) and to determine the impact of exercise intensity and volume on this response. Ten participants (5 males and 5 females) completed 3 exercise bouts of contrasting intensity and volume (LOW, MOD, and HIGH). The HIGH protocol was based upon standard HIIE protocols, while the MOD and LOW protocols were designed to enable a comparison of exercise intensity and volume with a fixed duration. Inflammatory cytokine concentrations were measured in plasma (IL-6, IL-10) and also determined the level of gene expression (IL-6, IL-10, and IL-4R) in peripheral blood. The plasma IL-6 response to exercise (reported as fold changes) was significantly greater in HIGH (2.70 ± 1.51) than LOW (1.40 ± 0.32) (P = 0.04) and was also positively correlated to the mean exercise oxygen uptake (r = 0.54, P < 0.01). However, there was no change in anti-inflammatory IL-10 or IL-4R responses in plasma or at the level of gene expression. HIIE caused a significant increase in IL-6 and was greater than that seen in low-intensity exercise of the same duration. The increases in IL-6 were relatively small in magnitude, and appear to have been insufficient to induce the acute systemic anti-inflammatory effects, which are evident following longer duration exercise

Response of an Afro-Palearctic bird migrant to glaciation cycles

We combine tracks of a long-distance migratory bird with high–temporal resolution climate data to reconstruct habitat availability month by month for the past 120,000 y. The seasonal changes of suitable habitat in the past imply that continued seasonal migration was necessary during the glacial maxima. Genomic-based estimates of effective population size indicate that more generally migratory lifestyles can be beneficially adapted to various climatic conditions. Our results provide a major step forward in understanding how migratory species will fare in the future and have important implications for how we understand the role of migration in the distribution of species and potentially speciation

Host resources and parasite traits interact to determine the optimal combination of host parasite‐mitigation strategies

Organisms have evolved diverse strategies to manage parasite infections. Broadly, hosts may avoid infection by altering behaviour, resist infection by targeting parasites or tolerate infection by repairing associated damage. The effectiveness of a strategy depends on interactions between, for example, resource availability, parasite traits (virulence, life‐history) and the host itself (nutritional status, immunopathology). To understand how these factors shape host parasite‐mitigation strategies, we developed a mathematical model of within‐host, parasite‐immune dynamics in the context of helminth infections. The model incorporated host nutrition and resource allocation to different mechanisms of immune response: larval parasite prevention; adult parasite clearance; damage repair (tolerance). We also considered a non‐immune strategy: avoidance via anorexia, reducing intake of infective stages. Resources not allocated to immune processes promoted host condition, whereas harm due to parasites and immunopathology diminished it. Maximising condition (a proxy for fitness), we determined optimal host investment for each parasite‐mitigation strategy, singly and combined, across different environmental resource levels and parasite trait values. Which strategy was optimal varied with scenario. Tolerance generally performed well, especially with high resources. Success of the different resistance strategies (larval prevention or adult clearance) tracked relative virulence of larval and adult parasites: slowly maturing, highly damaging larvae favoured prevention; rapidly maturing, less harmful larvae favoured clearance. Anorexia was viable only in the short term, due to reduced host nutrition. Combined strategies always outperformed any lone strategy: these were dominated by tolerance, with some investment in resistance.Choice of parasite mitigation strategy has profound consequences for hosts, impacting their condition, survival and reproductive success. We show that the efficacy of different strategies is highly dependent on timescale, parasite traits and resource availability. Models that integrate such factors can inform the collection and interpretation of empirical data, to understand how those drivers interact to shape host immune responses in natural systems

Long-term temporal trends in gastrointestinal parasite infection in wild Soay sheep

Monitoring the prevalence and abundance of parasites over time is important for addressing their potential impact on host life histories, immunological profiles and their influence as a selective force. Only long-term ecological studies have the potential to shed light on both the temporal trends in infection prevalence and abundance and the drivers of such trends, because of their ability to dissect drivers that may be confounded over shorter time scales. Despite this, only a relatively small number of such studies exist. Here, we analysed changes in the prevalence and abundance of gastrointestinal parasites in the wild Soay sheep population of St. Kilda across 31 years. The host population density (PD) has increased across the study, and PD is known to increase parasite transmission, but we found that PD and year explained temporal variation in parasite prevalence and abundance independently. Prevalence of both strongyle nematodes and coccidian microparasites increased during the study, and this effect varied between lambs, yearlings and adults. Meanwhile, abundance of strongyles was more strongly linked to host PD than to temporal (yearly) dynamics, while abundance of coccidia showed a strong temporal trend without any influence of PD. Strikingly, coccidian abundance increased 3-fold across the course of the study in lambs, while increases in yearlings and adults were negligible. Our decades-long, intensive, individual-based study will enable the role of environmental change and selection pressures in driving these dynamics to be determined, potentially providing unparalleled insight into the drivers of temporal variation in parasite dynamics in the wild

Green function techniques in the treatment of quantum transport at the molecular scale

The theoretical investigation of charge (and spin) transport at nanometer length scales requires the use of advanced and powerful techniques able to deal with the dynamical properties of the relevant physical systems, to explicitly include out-of-equilibrium situations typical for electrical/heat transport as well as to take into account interaction effects in a systematic way. Equilibrium Green function techniques and their extension to non-equilibrium situations via the Keldysh formalism build one of the pillars of current state-of-the-art approaches to quantum transport which have been implemented in both model Hamiltonian formulations and first-principle methodologies. We offer a tutorial overview of the applications of Green functions to deal with some fundamental aspects of charge transport at the nanoscale, mainly focusing on applications to model Hamiltonian formulations.Comment: Tutorial review, LaTeX, 129 pages, 41 figures, 300 references, submitted to Springer series "Lecture Notes in Physics