Statistical Properties and Decay of Correlations for Interval Maps with Critical Points and Singularities

We consider a class of piecewise smooth one-dimensional maps with critical points and singularities (possibly with infinite derivative). Under mild summability conditions on the growth of the derivative on critical orbits, we prove the central limit theorem and a vector-valued almost sure invariance principle. We also obtain results on decay of correlations.Comment: 18 pages, minor revisions, to appear in Communications in Mathematical Physic

Large deviations for non-uniformly expanding maps

We obtain large deviation results for non-uniformly expanding maps with non-flat singularities or criticalities and for partially hyperbolic non-uniformly expanding attracting sets. That is, given a continuous function we consider its space average with respect to a physical measure and compare this with the time averages along orbits of the map, showing that the Lebesgue measure of the set of points whose time averages stay away from the space average decays to zero exponentially fast with the number of iterates involved. As easy by-products we deduce escape rates from subsets of the basins of physical measures for these types of maps. The rates of decay are naturally related to the metric entropy and pressure function of the system with respect to a family of equilibrium states. The corrections added to the published version of this text appear in bold; see last section for a list of changesComment: 36 pages, 1 figure. After many PhD students and colleagues having pointed several errors in the statements and proofs, this is a correction to published article answering those comments. List of main changes in a new last sectio

Neuropeptide Y as a risk factor for cardiorenal disease and cognitive dysfunction in chronic kidney disease: translational opportunities and challenges

Neuropeptide Y (NPY) is a 36-amino-acid peptide member of a family also including peptide YY and pancreatic polypeptide, which are all ligands to Gi/Go coupled receptors. NPY regulates several fundamental biologic functions including appetite/satiety, sex and reproduction, learning and memory, cardiovascular and renal function and immune functions. The mesenteric circulation is a major source of NPY in the blood in man and this peptide is considered a key regulator of gut-brain cross talk. A progressive increase in circulating NPY accompanies the progression of chronic kidney disease (CKD) toward kidney failure and NPY robustly predicts cardiovascular events in this population. Furthermore, NPY is suspected as a possible player in accelerated cognitive function decline and dementia in patients with CKD and in dialysis patients. In theory, interfering with the NPY system has relevant potential for the treatment of diverse diseases from cardiovascular and renal diseases to diseases of the central nervous system. Pharmaceutical formulations for effective drug delivery and cost, as well as the complexity of diseases potentially addressable by NPY/NPY antagonists, have been a problem until now. This in part explains the slow progress of knowledge about the NPY system in the clinical arena. There is now renewed research interest in the NPY system in psychopharmacology and in pharmacology in general and new studies and a new breed of clinical trials may eventually bring the expected benefits in human health with drugs interfering with this system

Multiscale Systems, Homogenization, and Rough Paths:VAR75 2016: Probability and Analysis in Interacting Physical Systems

In recent years, substantial progress was made towards understanding convergence of fast-slow deterministic systems to stochastic differential equations. In contrast to more classical approaches, the assumptions on the fast flow are very mild. We survey the origins of this theory and then revisit and improve the analysis of Kelly-Melbourne [Ann. Probab. Volume 44, Number 1 (2016), 479-520], taking into account recent progress in $p$-variation and c\`adl\`ag rough path theory.Comment: 27 pages. Minor corrections. To appear in Proceedings of the Conference in Honor of the 75th Birthday of S.R.S. Varadha

Functional Assessment of EnvZ/OmpR Two-Component System in Shewanella oneidensis

EnvZ and OmpR constitute the bacterial two-component signal transduction system known to mediate osmotic stress response in a number of Gram-negative bacteria. In an effort to understand the mechanism through which Shewanella oneidensis senses and responds to environmental osmolarity changes, structure of the ompR-envZ operon was determined with Northern blotting assay and roles of the EnvZ/OmpR two-component system in response to various stresses were investigated with mutational analysis, quantitative reverse transcriptase PCR (qRT-PCR), and phenotype microarrays. Results from the mutational analysis and qRT-PCR suggested that the EnvZ/OmpR system contributed to osmotic stress response of S. oneidensis and very likely engaged a similar strategy employed by E. coli, which involved reciprocal regulation of two major porin coding genes. Additionally, the ompR-envZ system was also found related to cell motility. We further showed that the ompR-envZ dependent regulation of porin genes and motility resided almost completely on ompR and only partially on envZ, indicating additional mechanisms for OmpR phosphorylation. In contrast to E. coli lacking ompR-envZ, however, growth of S. oneidensis did not show a significant dependence on ompR-envZ even under osmotic stress. Further analysis with phenotype microarrays revealed that the S. oneidensis strains lacking a complete ompR-envZ system displayed hypersensitivities to a number of agents, especially in alkaline environment. Taken together, our results suggest that the function of the ompR-envZ system in S. oneidensis, although still connected with osmoregulation, has diverged considerably from that of E. coli. Additional mechanism must exist to support growth of S. oneidensis under osmotic stress

Cognitive disorders in patients with chronic kidney disease: Approaches to prevention and treatment

Background: Cognitive impairment is common in patients with chronic kidney disease (CKD), and early intervention may prevent the progression of this condition. Methods: Here, we review interventions for the complications of CKD (anemia, secondary hyperparathyroidism, metabolic acidosis, harmful effects of dialysis, the accumulation of uremic toxins) and for prevention of vascular events, interventions that may potentially be protective against cognitive impairment. Furthermore, we discuss nonpharmacological and pharmacological methods to prevent cognitive impairment and/or minimize the latter's impact on CKD patients' daily lives. Results: A particular attention on kidney function assessment is suggested during work-up for cognitive impairment. Different approaches are promising to reduce cognitive burden in patients with CKD but the availabe dedicated data are scarce. Conclusions: There is a need for studies assessing the effect of interventions on the cognitive function of patients with CKD