Quenched invariance principle for random walks in balanced random environment

We consider random walks in a balanced random environment in $\mathbb{Z}^d$, $d\geq 2$. We first prove an invariance principle (for $d\ge2$) and the transience of the random walks when $d\ge 3$ (recurrence when $d=2$) in an ergodic environment which is not uniformly elliptic but satisfies certain moment condition. Then, using percolation arguments, we show that under mere ellipticity, the above results hold for random walks in i.i.d. balanced environments.Comment: Published online in Probab. Theory Relat. Fields, 05 Oct 2010. Typo (in journal version) corrected in (26

Pharmaceutical induction of ApoE secretion by multipotent mesenchymal stromal cells (MSCs)

<p>Abstract</p> <p>Background</p> <p>Apolipoprotein E (ApoE) is a molecular scavenger in the blood and brain. Aberrant function of the molecule causes formation of protein and lipid deposits or "plaques" that characterize Alzheimer's disease (AD) and atherosclerosis. There are three human isoforms of ApoE designated ε2, ε3, and ε4. Each isoform differentially affects the structure and function of the protein and thus the development of disease. Homozygosity for ApoE ε4 is associated with atherosclerosis and Alzheimer's disease whereas ApoE ε2 and ε3 tend to be protective. Furthermore, the ε2 form may cause forms of hyperlipoproteinemia. Therefore, introduction of ApoE ε3 may be beneficial to patients that are susceptible to or suffering from these diseases. Mesenchymal stem cells or multipotent mesenchymal stromal cells (MSCs) are adult progenitor cells found in numerous tissues. They are easily expanded in culture and engraft into host tissues when administered appropriately. Furthermore, MSCs are immunosuppressive and have been reported to engraft as allogeneic transplants. In our previous study, mouse MSCs (mMSCs) were implanted into the brains of ApoE null mice, resulting in production of small amounts of ApoE in the brain and attenuation of cognitive deficits. Therefore human MSCs (hMSCs) are a promising vector for the administration of ApoE ε3 in humans.</p> <p>Results</p> <p>Unlike mMSCs, hMSCs were found not to express ApoE in culture; therefore a molecular screen was performed for compounds that induce expression. PPARγ agonists, neural stem cell conditioned medium, osteo-inductive media, dexamethasone, and adipo-inductive media (AIM) were tested. Of the conditions tested, only AIM or dexamethasone induced sustained secretion of ApoE in MSCs and the duration of secretion was only limited by the length of time MSCs could be sustained in culture. Upon withdrawal of the inductive stimuli, the ApoE secretion persisted for a further 14 days.</p> <p>Conclusion</p> <p>The data demonstrated that pre-treatment and perhaps co-administration of MSCs homozygous for ApoE ε3 and dexamethasone may represent a novel therapy for severe instances of AD, atherosclerosis and other ApoE-related diseases.</p

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

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

Slowdown for time inhomogeneous branching Brownian motion

We consider the maximal displacement of one dimensional branching Brownian motion with (macroscopically) time varying profiles. For monotone decreasing variances, we show that the correction from linear displacement is not logarithmic but rather proportional to $T^{1/3}$. We conjecture that this is the worse case correction possible

Boundary driven zero-range processes in random media

The stationary states of boundary driven zero-range processes in random media with quenched disorder are examined, and the motion of a tagged particle is analyzed. For symmetric transition rates, also known as the random barrier model, the stationary state is found to be trivial in absence of boundary drive. Out of equilibrium, two further cases are distinguished according to the tail of the disorder distribution. For strong disorder, the fugacity profiles are found to be governed by the paths of normalized $\alpha$-stable subordinators. The expectations of integrated functions of the tagged particle position are calculated for three types of routes.Comment: 23 page

Random walks in space time mixing environments

We prove that random walks in random environments, that are exponentially mixing in space and time, are almost surely diffusive, in the sense that their scaling limit is given by the Wiener measure.Comment: 28 page

One-component plasma on a spherical annulus and a random matrix ensemble

The two-dimensional one-component plasma at the special coupling \beta = 2 is known to be exactly solvable, for its free energy and all of its correlations, on a variety of surfaces and with various boundary conditions. Here we study this system confined to a spherical annulus with soft wall boundary conditions, paying special attention to the resulting asymptotic forms from the viewpoint of expected general properties of the two-dimensional plasma. Our study is motivated by the realization of the Boltzmann factor for the plasma system with \beta = 2, after stereographic projection from the sphere to the complex plane, by a certain random matrix ensemble constructed out of complex Gaussian and Haar distributed unitary matrices.Comment: v2, typos and references corrected, 24 pages, 1 figur

On the power and the systematic biases of the detection of chromosomal inversions by paired-end genome sequencing

One of the most used techniques to study structural variation at a genome level is paired-end mapping (PEM). PEM has the advantage of being able to detect balanced events, such as inversions and translocations. However, inversions are still quite difficult to predict reliably, especially from high-throughput sequencing data. We simulated realistic PEM experiments with different combinations of read and library fragment lengths, including sequencing errors and meaningful base-qualities, to quantify and track down the origin of false positives and negatives along sequencing, mapping, and downstream analysis. We show that PEM is very appropriate to detect a wide range of inversions, even with low coverage data. However, % of inversions located between segmental duplications are expected to go undetected by the most common sequencing strategies. In general, longer DNA libraries improve the detectability of inversions far better than increments of the coverage depth or the read length. Finally, we review the performance of three algorithms to detect inversions -SVDetect, GRIAL, and VariationHunter-, identify common pitfalls, and reveal important differences in their breakpoint precisions. These results stress the importance of the sequencing strategy for the detection of structural variants, especially inversions, and offer guidelines for the design of future genome sequencing projects