Fractal Properties of Robust Strange Nonchaotic Attractors in Maps of Two or More Dimensions

We consider the existence of robust strange nonchaotic attractors (SNA's) in a simple class of quasiperiodically forced systems. Rigorous results are presented demonstrating that the resulting attractors are strange in the sense that their box-counting dimension is N+1 while their information dimension is N. We also show how these properties are manifested in numerical experiments.Comment: 9 pages, 14 figure

Toxoplasma gondii Inhibits Apoptosis in Infected Cells by Caspase Inactivation and NF-κB Activation

Our experiments aimed to clarify the mechanism by which host cell apoptosis is inhibited by infection with the intracellular protozoan parasite, Toxoplasma gondii (T. gondii). Mouse spleen cells were cultured in 6-well plates with RPMI 1640/10% FBS at 37℃, in a 5% CO2 atmosphere. Apoptosis of spleen cells was induced by actinomycin-D (AD) treatment for 1 h prior to infection with T. gondii. A variety of assays were used to assess the progression of apoptosis: DNA size analysis on agarose gel electrophoresis, flow cytometry with annexin V/PI staining, and analysis of expression levels of Bcl-2 family and NF-κB mRNA and proteins by RT-PCR, Western blotting, and EMSA. Additionally, transmission electron microscopy (TEM) was performed to observe changes in cell morphology. Fragmentation of DNA was inhibited in spleen cells treated with AD and T. gondii 5 h and 18 h post infection, respectively, and flow cytometry studies showed a decreased apoptotic rates in AD and T. gondii treated spleen cells. We observed decreased expression of Bax mRNA and protein, while levels of Bcl-2 mRNA remained constant in spleen cells treated with AD and T. gondii. Caspase 3 and PARP were inactivated in cells treated with AD and T. gondii, and increased levels of cleaved caspase 8 were also observed. Analysis of EMSA and Western blot data suggests that activation of transcription factor NF-κB may be involved in the blockade of apoptosis by T. gondii. TEM analysis showed nuclear fragmentation and chromatin condensation occurring in spleen cells treated with AD; however, such apoptosis-associated morphological changes were not observed in cells treated with both AD and T. gondii tachyzoites. Together, these data show that T. gondii infection inhibits AD induced apoptosis via caspase inactivation and NF-κB activation in mouse spleen cells

On Nonlinear Stochastic Balance Laws

We are concerned with multidimensional stochastic balance laws. We identify a class of nonlinear balance laws for which uniform spatial $BV$ bounds for vanishing viscosity approximations can be achieved. Moreover, we establish temporal equicontinuity in $L^1$ of the approximations, uniformly in the viscosity coefficient. Using these estimates, we supply a multidimensional existence theory of stochastic entropy solutions. In addition, we establish an error estimate for the stochastic viscosity method, as well as an explicit estimate for the continuous dependence of stochastic entropy solutions on the flux and random source functions. Various further generalizations of the results are discussed

Deficiency of peroxiredoxin 2 exacerbates angiotensin II-induced abdominal aortic aneurysm

Abdominal aortic aneurysm: Potential enzyme biomarker identified An enzyme with antioxidant properties may provide a biomarker and therapeutic agent to help treat abdominal aortic aneurysm (AAA). AAA involves the structural deterioration of the aorta through chronic inflammation and oxidative stress, and can trigger life-threatening artery rupture. An antioxidant enzyme called peroxiredoxin 2 (PRDX2) is increased in patients with ruptures, but whether its role in AAA is beneficial or detrimental is unclear. Goo Taeg Oh at the Ewha Womans University in Seoul, Jong-Gil Park at the Korea Research Institute of Bioscience and Biotechnology, Daejeon, South Korea, and co-workers examined the effect of PRDX2 on AAA progression. PRDX2 suppressed structural damage in mice, limiting artery dilation and protein degradation. Loss of PRDX2 accelerated AAA development. Measuring levels of PRDX2 may indicate AAA severity in patients, while boosting the enzyme could repair aortic damage

Tunable Lyapunov exponent in inverse magnetic billiards

The stability properties of the classical trajectories of charged particles are investigated in a two dimensional stadium-shaped inverse magnetic domain, where the magnetic field is zero inside the stadium domain and constant outside. In the case of infinite magnetic field the dynamics of the system is the same as in the Bunimovich billiard, i.e., ergodic and mixing. However, for weaker magnetic fields the phase space becomes mixed and the chaotic part gradually shrinks. The numerical measurements of the Lyapunov exponent (performed with a novel method) and the integrable/chaotic phase space volume ratio show that both quantities can be smoothly tuned by varying the external magnetic field. A possible experimental realization of the arrangement is also discussed.Comment: 4 pages, 6 figure

Thermodynamic formalism for systems with Markov dynamics

The thermodynamic formalism allows one to access the chaotic properties of equilibrium and out-of-equilibrium systems, by deriving those from a dynamical partition function. The definition that has been given for this partition function within the framework of discrete time Markov chains was not suitable for continuous time Markov dynamics. Here we propose another interpretation of the definition that allows us to apply the thermodynamic formalism to continuous time. We also generalize the formalism --a dynamical Gibbs ensemble construction-- to a whole family of observables and their associated large deviation functions. This allows us to make the connection between the thermodynamic formalism and the observable involved in the much-studied fluctuation theorem. We illustrate our approach on various physical systems: random walks, exclusion processes, an Ising model and the contact process. In the latter cases, we identify a signature of the occurrence of dynamical phase transitions. We show that this signature can already be unravelled using the simplest dynamical ensemble one could define, based on the number of configuration changes a system has undergone over an asymptotically large time window.Comment: 64 pages, LaTeX; version accepted for publication in Journal of Statistical Physic

Hypoxia promotes liver stage malaria infection in primary human hepatocytes in vitro

Homeostasis of mammalian cell function strictly depends on balancing oxygen exposure to maintain energy metabolism without producing excessive reactive oxygen species. In vivo, cells in different tissues are exposed to a wide range of oxygen concentrations, and yet in vitro models almost exclusively expose cultured cells to higher, atmospheric oxygen levels. Existing models of liver stage malaria that utilize primary human hepatocytes typically exhibit low in vitro infection efficiencies, possibly due to missing microenvironmental support signals. One cue that may influence the infection capacity of cultured human hepatocytes is the dissolved oxygen concentration. We developed a microscale human liver platform comprised of precisely patterned primary human hepatocytes and nonparenchymal cells (MPCC) to model liver stage malaria, but the oxygen concentrations are typically higher in the in vitro liver platform than anywhere along the hepatic sinusoid. Indeed, we observed that liver stage Plasmodium parasite development in vivo correlates with hepatic sinusoidal oxygen gradients. Therefore, we hypothesized that in vitro liver stage malaria infection efficiencies may improve under hypoxia. Using the infection of MPCCs with P. berghei or P. yoelii as a model, we observed that ambient hypoxia resulted in increased survival of exo-erythrocytic forms (EEFs) in hepatocytes, and improved parasite development in a subset of surviving EEFs, based on EEF size. Further, the effective cell surface oxygen tensions (pO2) experienced by the hepatocytes, as predicted by a mathematical model, were systematically perturbed by varying culture parameters like hepatocyte density and media height, uncovering an optimal cell surface pO2 to maximize the number of mature EEFs. Initial mechanistic experiments reveal that treatment of primary human hepatocytes with the hypoxia mimetic, cobalt (II) chloride, as well as a HIF-1α activator, dimethyloxalylglycine, also enhance P. berghei infection, suggesting that the effect of hypoxia on infection is mediated in part by host-dependent HIF-1α mechanisms.Bill & Melinda Gates Foundation (Award 51066)Howard Hughes Medical Institut

Random walks and polymers in the presence of quenched disorder

After a general introduction to the field, we describe some recent results concerning disorder effects on both `random walk models', where the random walk is a dynamical process generated by local transition rules, and on `polymer models', where each random walk trajectory representing the configuration of a polymer chain is associated to a global Boltzmann weight. For random walk models, we explain, on the specific examples of the Sinai model and of the trap model, how disorder induces anomalous diffusion, aging behaviours and Golosov localization, and how these properties can be understood via a strong disorder renormalization approach. For polymer models, we discuss the critical properties of various delocalization transitions involving random polymers. We first summarize some recent progresses in the general theory of random critical points : thermodynamic observables are not self-averaging at criticality whenever disorder is relevant, and this lack of self-averaging is directly related to the probability distribution of pseudo-critical temperatures $T_c(i,L)$ over the ensemble of samples $(i)$ of size $L$. We describe the results of this analysis for the bidimensional wetting and for the Poland-Scheraga model of DNA denaturation.Comment: 17 pages, Conference Proceedings "Mathematics and Physics", I.H.E.S., France, November 200

Serum Response Factor Regulates Immediate Early Host Gene Expression in Toxoplasma gondii-Infected Host Cells

Toxoplasma gondii is a wide spread pathogen that can cause severe and even fatal disease in fetuses and immune-compromised hosts. As an obligate intracellular parasite, Toxoplasma must alter the environment of its host cell in order to establish its replicative niche. This is accomplished, in part, by secretion of factors into the host cell that act to modulate processes such as transcription. Previous studies demonstrated that genes encoding transcription factors such as c-jun, junB, EGR1, and EGR2 were amongst the host genes that were the most rapidly upregulated following infection. In cells stimulated with growth factors, these genes are regulated by a transcription factor named Serum Response Factor. Serum Response Factor is a ubiquitously expressed DNA binding protein that regulates growth and actin cytoskeleton genes via MAP kinase or actin cytoskeletal signaling, respectively. Here, we report that Toxoplasma infection leads to the rapid activation of Serum Response Factor. Serum Response Factor activation is a Toxoplasma-specific event since the transcription factor is not activated by the closely related protozoan parasite, Neospora caninum. We further demonstrate that Serum Response Factor activation requires a parasite-derived secreted factor that signals via host MAP kinases but independently of the host actin cytoskeleton. Together, these data define Serum Response Factor as a host cell transcription factor that regulates immediate early gene expression in Toxoplasma-infected cells