Rosette Central Configurations, Degenerate central configurations and bifurcations

In this paper we find a class of new degenerate central configurations and bifurcations in the Newtonian $n$-body problem. In particular we analyze the Rosette central configurations, namely a coplanar configuration where $n$ particles of mass $m_1$ lie at the vertices of a regular $n$-gon, $n$ particles of mass $m_2$ lie at the vertices of another $n$-gon concentric with the first, but rotated of an angle $\pi/n$, and an additional particle of mass $m_0$ lies at the center of mass of the system. This system admits two mass parameters $\mu=m_0/m_1$ and \ep=m_2/m_1. We show that, as $\mu$ varies, if $n> 3$, there is a degenerate central configuration and a bifurcation for every \ep>0, while if $n=3$ there is a bifurcations only for some values of $\epsilon$.Comment: 16 pages, 6 figure

On two-dimensional surface attractors and repellers on 3-manifolds

We show that if $f: M^3\to M^3$ is an $A$-diffeomorphism with a surface two-dimensional attractor or repeller $\mathcal B$ and $M^2_ \mathcal B$ is a supporting surface for $\mathcal B$, then $\mathcal B = M^2_{\mathcal B}$ and there is $k\geq 1$ such that: 1) $M^2_{\mathcal B}$ is a union $M^2_1\cup...\cup M^2_k$ of disjoint tame surfaces such that every $M^2_i$ is homeomorphic to the 2-torus $T^2$. 2) the restriction of $f^k$ to $M^2_i$ $(i\in\{1,...,k\})$ is conjugate to Anosov automorphism of $T^2$

Geometric Integration of Hamiltonian Systems Perturbed by Rayleigh Damping

Explicit and semi-explicit geometric integration schemes for dissipative perturbations of Hamiltonian systems are analyzed. The dissipation is characterized by a small parameter $\epsilon$, and the schemes under study preserve the symplectic structure in the case $\epsilon=0$. In the case $0<\epsilon\ll 1$ the energy dissipation rate is shown to be asymptotically correct by backward error analysis. Theoretical results on monotone decrease of the modified Hamiltonian function for small enough step sizes are given. Further, an analysis proving near conservation of relative equilibria for small enough step sizes is conducted. Numerical examples, verifying the analyses, are given for a planar pendulum and an elastic 3--D pendulum. The results are superior in comparison with a conventional explicit Runge-Kutta method of the same order

A striking correspondence between the dynamics generated by the vector fields and by the scalar parabolic equations

The purpose of this paper is to enhance a correspondence between the dynamics of the differential equations $\dot y(t)=g(y(t))$ on $\mathbb{R}^d$ and those of the parabolic equations $\dot u=\Delta u +f(x,u,\nabla u)$ on a bounded domain $\Omega$. We give details on the similarities of these dynamics in the cases $d=1$, $d=2$ and $d\geq 3$ and in the corresponding cases $\Omega=(0,1)$, $\Omega=\mathbb{T}^1$ and dim($\Omega$)$\geq 2$ respectively. In addition to the beauty of such a correspondence, this could serve as a guideline for future research on the dynamics of parabolic equations

Adaptation of the generic PDE's results to the notion of prevalence

Many generic results have been proved, especially concerning the qualitative behaviour of solutions of partial differential equations. Recently, a new notion of "almost always", the prevalence, has been developped for vectorial spaces. This notion is interesting since, for example, prevalence sets are equivalent to the full Lebesgue measure sets in finite dimensional spaces. The purpose of this article is to adapt the generic PDE's results to the notion of prevalence. In particular, we consider the cases where Sard-Smale theorems or arguments of analytic perturbations of the parameters are used

Environmental Factors in the Relapse and Recurrence of Inflammatory Bowel Disease:A Review of the Literature

The causes of relapse in patients with Crohn's disease (CD) and ulcerative colitis (UC) are largely unknown. This paper reviews the epidemiological and clinical data on how medications (non-steroidal anti-inflammatory drugs, estrogens and antibiotics), lifestyle factors (smoking, psychological stress, diet and air pollution) may precipitate clinical relapses and recurrence. Potential biological mechanisms include: increasing thrombotic tendency, imbalances in prostaglandin synthesis, alterations in the composition of gut microbiota, and mucosal damage causing increased permeability

Field and Laboratory Studies Provide Insights into the Meaning of Day-Time Activity in a Subterranean Rodent (Ctenomys aff. knighti), the Tuco-Tuco

South American subterranean rodents (Ctenomys aff. knighti), commonly known as tuco-tucos, display nocturnal, wheel-running behavior under light-dark (LD) conditions, and free-running periods >24 h in constant darkness (DD). However, several reports in the field suggested that a substantial amount of activity occurs during daylight hours, leading us to question whether circadian entrainment in the laboratory accurately reflects behavior in natural conditions. We compared circadian patterns of locomotor activity in DD of animals previously entrained to full laboratory LD cycles (LD12∶12) with those of animals that were trapped directly from the field. In both cases, activity onsets in DD immediately reflected the previous dark onset or sundown. Furthermore, freerunning periods upon release into DD were close to 24 h indicating aftereffects of prior entrainment, similarly in both conditions. No difference was detected in the phase of activity measured with and without access to a running wheel. However, when individuals were observed continuously during daylight hours in a semi-natural enclosure, they emerged above-ground on a daily basis. These day-time activities consisted of foraging and burrow maintenance, suggesting that the designation of this species as nocturnal might be inaccurate in the field. Our study of a solitary subterranean species suggests that the circadian clock is entrained similarly under field and laboratory conditions and that day-time activity expressed only in the field is required for foraging and may not be time-dictated by the circadian pacemaker

Basal LAT-diacylglycerol-RasGRP1 Signals in T Cells Maintain TCRα Gene Expression

In contrast to the well-characterized T cell receptor (TCR) signaling pathways that induce genes that drive T cell development or polarization of naïve CD4 T cells into the diverse TH1, TH2, TH17 and Treg lineages, it is unclear what signals maintain specific gene expression in mature resting T cells. Resting T cells residing in peripheral lymphoid organs exhibit low-level constitutive signaling. Whereas tonic signals in B cells are known to be critical for survival, the roles of tonic signals in peripheral T cells are unknown. Here we demonstrate that constitutive signals in Jurkat T cell lines are transduced via the adapter molecule LAT and the Ras exchange factor RasGRP1 to maintain expression of TCRα mRNA and surface expression of the TCR/CD3 complex. Independent approaches of reducing basal activity through the LAT-diacylglycerol-RasGRP pathway led to reduced constitutive Ras-MEK-ERK signals and decreased TCRα mRNA and surface TCR expression in Jurkat cells. However, loss of TCR expression takes several days in these cell line experiments. In agreement with these in vitro approaches, inducible deletion of Lat in vivo results in reduced TCRα mRNA- and surface TCR- expression in a delayed temporal manner as well. Lastly, we demonstrate that loss of basal LAT-RasGRP signals appears to lead to silencing or repression of TCRα transcription. We postulate that basal LAT-diacylglycerol-RasGRP signals fulfill a regulatory function in peripheral T lymphocytes by maintaining proper gene expression programs