From First Lyapunov Coefficients to Maximal Canards

Hopf bifurcations in fast-slow systems of ordinary differential equations can be associated with surprising rapid growth of periodic orbits. This process is referred to as canard explosion. The key step in locating a canard explosion is to calculate the location of a special trajectory, called a maximal canard, in parameter space. A first-order asymptotic expansion of this location was found by Krupa and Szmolyan in the framework of a "canard point"-normal-form for systems with one fast and one slow variable. We show how to compute the coefficient in this expansion using the first Lyapunov coefficient at the Hopf bifurcation thereby avoiding use of this normal form. Our results connect the theory of canard explosions with existing numerical software, enabling easier calculations of where canard explosions occur.Comment: preprint version - for final version see journal referenc

Relativistic Langevin Dynamics in Expanding Media

We study the consequences of different realizations of diffusion processes in relativistic Langevin simulations. We elaborate on the Ito-Stratonovich dilemma by showing how microscopically calculated transport coefficients as obtained from a Boltzmann/Fokker-Planck equation can be implemented to lead to an unambiguous realization of the Langevin process. Pertinent examples within the pre-point (Ito) and post-point (H\"anggi-Klimontovich) Langevin prescriptions are worked out explicitly. Deviations from this implementation are shown to generate variants of the Boltzmann distribution as the stationary (equilibrium) solutions. Finally, we explicitly verify how the Lorentz invariance of the Langevin process is maintained in the presence of an expanding medium, including the case of an "elliptic flow" transmitted to a Brownian test particle. This is particularly relevant for using heavy-flavor diffusion as a quantitative tool to diagnose transport properties of QCD matter as created in ultrarelativistic heavy-ion collisions.Comment: 8 pages, 4 figures; v2: Reference adde

Stochastic Processes Crossing from Ballistic to Fractional Diffusion with Memory: Exact Results

We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (sub- or super-diffusion) at longer times. Using the standard non-Markovian diffusion equation we demonstrate how to choose the memory kernel to exactly respect the two different asymptotics of the diffusion process. Having done so we solve for the probability distribution function (pdf) as a continuous function which evolves inside a ballistically expanding domain. This general solution agrees for long times with the pdf obtained within the continuous random walk approach but it is much superior to this solution at shorter times where the effect of the ballistic regime is crucial

Through the Microbial Looking Glass: Premature Labor, Preeclampsia, and Gestational Diabetes: A Scoping Review

The influence of microbial factors on adverse perinatal outcomes has become the focal point of recent investigations, with particular interest in the role of the microbiome and probiotic interventions. The purpose of this scoping review was to identify and critique the most recent evidence about these factors as they relate to pregnancies complicated by preeclampsia (PEC), preterm birth (PTB), and gestational diabetes mellitus (GDM). Four databases (PubMed, EMBASE, Web of Science, and Cochrane) were searched for articles published in English in the last 10 years with the concepts of the microbiome, probiotics, and PEC, PTB, or GDM. Forty-nine articles were eligible for full-text review. Five articles were excluded, leaving 44 articles that met all the eligibility criteria. The relationships between the microbiome and the risk for PEC, PTB, and GDM are not fully elucidated, although probiotic interventions seem beneficial in decreasing PEC and GDM risk. Probiotic interventions targeting bacterial vaginosis and elimination of infection in women at risk for PTB appear to be beneficial. More research is needed to understand the contributions of the microbiome to adverse perinatal outcomes. Probiotic interventions appear to be effective in reducing risk for select outcomes

Energy loss of a heavy quark produced in a finite-size quark-gluon plasma

We study the energy loss of an energetic heavy quark produced in a high temperature quark-gluon plasma and travelling a finite distance before emerging in the vacuum. While the retardation time of purely collisional energy loss is found to be of the order of the Debye screening length, we find that the contributions from transition radiation and the Ter-Mikayelian effect do not compensate, leading to a reduction of the zeroth order (in an opacity expansion) energy loss.Comment: QM2006 Proceedings; caption of fig 1 and ref [7] modified in v

Persistent recruitment of somatosensory cortex during active maintenance of hand images in working memory

Working memory (WM) supports temporary maintenance of task-relevant information. This process is associated with persistent activity in the sensory cortex processing the information (e.g., visual stimuli activate visual cortex). However, we argue here that more multifaceted stimuli moderate this sensory-locked activity and recruit distinctive cortices. Specifically, perception of bodies recruits somatosensory cortex (SCx) beyond early visual areas (suggesting embodiment processes). Here we explore persistent activation in processing areas beyond the sensory cortex initially relevant to the modality of the stimuli. Using visual and somatosensory evoked-potentials in a visual WM task, we isolated different levels of visual and somatosensory involvement during encoding of body and non-body-related images. Persistent activity increased in SCx only when maintaining body images in WM, whereas visual/posterior regions' activity increased significantly when maintaining non-body images. Our results bridge WM and embodiment frameworks, supporting a dynamic WM process where the nature of the information summons specific processing resources

Immunological basis of differences in disease resistance in the chicken

Genetic resistance to diseases is a multigenic trait governed mainly by the immune system and its interactions with many physiologic and environmental factors. In the adaptive immunity, T cell and B cell responses, the specific recognition of antigens and interactions between antigen presenting cells, T cells and B cells are crucial. It occurs through a network of mediator proteins such as the molecules of the major histocompatibility complex (MHC), T cell receptors, immunoglobulins and secreted proteins such as the cytokines and antibodies. The diversity of these proteins that mainly is due to an intrinsic polymorphism of the genes causes phenotypic variation in disease resistance. The well-known linkage of MHC polymorphism and Marek's disease resistance difference represents a classic model revealing immunological factors in resistance differences and diversity of mediator molecules. The molecular bases in any resistance variation to infectious pathogens are vaguely understood. This paper presents a review of the major immune mediators involved in resistance and susceptibility to infectious diseases and their functional mechanisms in the chicken. The genetic interaction of disease resistance with production traits and the environment is mentioned

The exact evaluation of the corner-to-corner resistance of an M x N resistor network: Asymptotic expansion

We study the corner-to-corner resistance of an M x N resistor network with resistors r and s in the two spatial directions, and obtain an asymptotic expansion of its exact expression for large M and N. For M = N, r = s =1, our result is R_{NxN} = (4/pi) log N + 0.077318 + 0.266070/N^2 - 0.534779/N^4 + O(1/N^6).Comment: 12 pages, re-arranged section

Mass and eccentricity constraints on the planetary debris orbiting the white dwarf WD 1145+017

Being the first of its kind, the white dwarf WD 1145+017 exhibits a complex system of disintegrating debris which offers a unique opportunity to study its disruption process in real time. Even with plenty of transit observations there are no clear constraints on the masses or eccentricities of such debris. Using N-body simulations, we show that masses greater than ≃1020 kg (a tenth of the mass of Ceres) or orbits that are not nearly circular (eccentricity > 10−3) dramatically increase the chances of the system becoming unstable within 2 yr, which would contrast with the observational data over this timespan. We also provide a direct comparison between transit phase shifts detected in the observations and by our numerical simulations