Equality of averaged and quenched large deviations for random walks in random environments in dimensions four and higher

We consider large deviations for nearest-neighbor random walk in a uniformly elliptic i.i.d. environment. It is easy to see that the quenched and the averaged rate functions are not identically equal. When the dimension is at least four and Sznitman's transience condition (T) is satisfied, we prove that these rate functions are finite and equal on a closed set whose interior contains every nonzero velocity at which the rate functions vanish.Comment: 17 pages. Minor revision. In particular, note the change in the title of the paper. To appear in Probability Theory and Related Fields

Quenched large deviations for multidimensional random walk in random environment with holding times

We consider a random walk in random environment with random holding times, that is, the random walk jumping to one of its nearest neighbors with some transition probability after a random holding time. Both the transition probabilities and the laws of the holding times are randomly distributed over the integer lattice. Our main result is a quenched large deviation principle for the position of the random walk. The rate function is given by the Legendre transform of the so-called Lyapunov exponents for the Laplace transform of the first passage time. By using this representation, we derive some asymptotics of the rate function in some special cases.Comment: This is the corrected version of the paper. 24 page

The rarity of terrestrial gamma-ray flashes

We report on the first search for Terrestrial Gamma-ray Flashes (TGFs) from altitudes where they are thought to be produced. The Airborne Detector for Energetic Lightning Emissions (ADELE), an array of gamma-ray detectors, was flown near the tops of Florida thunderstorms in August/September 2009. The plane passed within 10 km horizontal distance of 1213 lightning discharges and only once detected a TGF. If these discharges had produced TGFs of the same intensity as those seen from space, every one should have been seen by ADELE. Separate and significant nondetections are established for intracloud lightning, negative cloud-to-ground lightning, and narrow bipolar events. We conclude that TGFs are not a primary triggering mechanism for lightning. We estimate the TGF-to-flash ratio to be on the order of 10^(−2) to 10^(−3) and show that TGF intensities cannot follow the well-known power-law distribution seen in earthquakes and solar flares, due to our limits on the presence of faint events

Positron clouds within thunderstorms

We report the observation of two isolated clouds of positrons inside an active thunderstorm. These observations were made by the Airborne Detector for Energetic Lightning Emissions (ADELE), an array of six gamma-ray detectors, which flew on a Gulfstream V jet aircraft through the top of an active thunderstorm in August 2009. ADELE recorded two 511 keV gamma-ray count rate enhancements, 35 seconds apart, each lasting approximately 0.2 seconds. The enhancements, which were about a factor of 12 above background, were both accompanied by electrical activity as measured by a flat-plate antenna on the underside of the aircraft. The energy spectra were consistent with a source mostly composed of positron annihilation gamma rays, with a prominent 511 keV line clearly visible in the data. Model fits to the data suggest that the aircraft was briefly immersed in clouds of positrons, more than a kilometer across. It is not clear how the positron clouds were created within the thunderstorm, but it is possible they were caused by the presence of the aircraft in the electrified environment.Comment: Accepted for publication in the Journal of Plasma Physic

Variational formulas and cocycle solutions for directed polymer and percolation models

We discuss variational formulas for the law of large numbers limits of certain models of motion in a random medium: namely, the limiting time constant for last-passage percolation and the limiting free energy for directed polymers. The results are valid for models in arbitrary dimension, steps of the admissible paths can be general, the environment process is ergodic under spatial translations, and the potential accumulated along a path can depend on the environment and the next step of the path. The variational formulas come in two types: one minimizes over gradient-like cocycles, and another one maximizes over invariant measures on the space of environments and paths. Minimizing cocycles can be obtained from Busemann functions when these can be proved to exist. The results are illustrated through 1+1 dimensional exactly solvable examples, periodic examples, and polymers in weak disorder

Alternative proof for the localization of Sinai's walk

We give an alternative proof of the localization of Sinai's random walk in random environment under weaker hypothesis than the ones used by Sinai. Moreover we give estimates that are stronger than the one of Sinai on the localization neighborhood and on the probability for the random walk to stay inside this neighborhood

Stationary cocycles and Busemann functions for the corner growth model

We study the directed last-passage percolation model on the planar square lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, out- side of the class of exactly solvable models. Stationary cocycles are constructed for this percolation model from queueing fixed points. These cocycles serve as bound- ary conditions for stationary last-passage percolation, solve variational formulas that characterize limit shapes, and yield existence of Busemann functions in directions where the shape has some regularity. In a sequel to this paper the cocycles are used to prove results about semi-infinite geodesics and the competition interface

Geodesics and the competition interface for the corner growth model

We study the directed last-passage percolation model on the planar square lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, out- side of the class of exactly solvable models. Stationary cocycles are constructed for this percolation model from queueing fixed points. These cocycles serve as bound- ary conditions for stationary last-passage percolation, solve variational formulas that characterize limit shapes, and yield existence of Busemann functions in directions where the shape has some regularity. In a sequel to this paper the cocycles are used to prove results about semi-infinite geodesics and the competition interface

Association of homocysteine and methylene tetrahydrofolate reductase (MTHFR C677T) gene polymorphism with coronary artery disease (CAD) in the population of North India

The implications of the methylene tetrahydrofolate reductase (MTHFR) gene and the level of homocysteine in the pathogenesis of coronary artery disease (CAD) have been extensively studied in various ethnic groups. Our aim was to discover the association of MTHFR (C677T) polymorphism and homocysteine level with CAD in north Indian subjects. The study group consisted of 329 angiographically proven CAD patients, and 331 age and sex matched healthy individuals as controls. MTHFR (C677T) gene polymorphism was detected based on the polymerase chain reaction and restriction digestion with HinfI. Total homocysteine plasma concentration was measured using immunoassay. T allele frequency was found to be significantly higher in patients than in the control group. We found significantly elevated levels of mean homocysteine in the patient group when compared to the control group (p = 0.00). Traditional risk factors such as diabetes, hypertension, smoking habits, a positive family history and lipid profiles (triglyceride, total cholesterol, HDL-cholesterol, LDL-cholesterol, VLDL-cholesterol), were found significantly associated through univariate analysis. Furthermore, multivariable logistics regression analysis revealed that CAD is significantly and variably associated with diabetes, hypertension, smoking, triglycerides and HDL-cholesterol. Our findings showed that MTHFR C677T polymorphism and homocysteine levels were associated with coronary artery disease in the selected population

Distinct Transcriptome Expression of the Temporal Cortex of the Primate Microcebus murinus during Brain Aging versus Alzheimer's Disease-Like Pathology

Aging is the primary risk factor of neurodegenerative disorders such as Alzheimer's disease (AD). However, the molecular events occurring during brain aging are extremely complex and still largely unknown. For a better understanding of these age-associated modifications, animal models as close as possible to humans are needed. We thus analyzed the transcriptome of the temporal cortex of the primate Microcebus murinus using human oligonucleotide microarrays (Affymetrix). Gene expression profiles were assessed in the temporal cortex of 6 young adults, 10 healthy old animals and 2 old, “AD-like” animals that presented ß-amyloid plaques and cortical atrophy, which are pathognomonic signs of AD in humans. Gene expression data of the 14,911 genes that were detected in at least 3 samples were analyzed. By SAM (significance analysis of microarrays), we identified 47 genes that discriminated young from healthy old and “AD-like” animals. These findings were confirmed by principal component analysis (PCA). ANOVA of the expression data from the three groups identified 695 genes (including the 47 genes previously identified by SAM and PCA) with significant changes of expression in old and “AD-like” in comparison to young animals. About one third of these genes showed similar changes of expression in healthy aging and in “AD-like” animals, whereas more than two thirds showed opposite changes in these two groups in comparison to young animals. Hierarchical clustering analysis of the 695 markers indicated that each group had distinct expression profiles which characterized each group, especially the “AD-like” group. Functional categorization showed that most of the genes that were up-regulated in healthy old animals and down-regulated in “AD-like” animals belonged to metabolic pathways, particularly protein synthesis. These data suggest the existence of compensatory mechanisms during physiological brain aging that disappear in “AD-like” animals. These results open the way to new exploration of physiological and “AD-like” aging in primates