Hitting spheres on hyperbolic spaces

For a hyperbolic Brownian motion on the Poincar\'e half-plane $\mathbb{H}^2$, starting from a point of hyperbolic coordinates $z=(\eta, \alpha)$ inside a hyperbolic disc $U$ of radius $\bar{\eta}$, we obtain the probability of hitting the boundary $\partial U$ at the point $(\bar \eta,\bar \alpha)$. For $\bar{\eta} \to \infty$ we derive the asymptotic Cauchy hitting distribution on $\partial \mathbb{H}^2$ and for small values of $\eta$ and $\bar \eta$ we obtain the classical Euclidean Poisson kernel. The exit probabilities $\mathbb{P}_z\{T_{\eta_1}<T_{\eta_2}\}$ from a hyperbolic annulus in $\mathbb{H}^2$ of radii $\eta_1$ and $\eta_2$ are derived and the transient behaviour of hyperbolic Brownian motion is considered. Similar probabilities are calculated also for a Brownian motion on the surface of the three dimensional sphere. For the hyperbolic half-space $\mathbb{H}^n$ we obtain the Poisson kernel of a ball in terms of a series involving Gegenbauer polynomials and hypergeometric functions. For small domains in $\mathbb{H}^n$ we obtain the $n$-dimensional Euclidean Poisson kernel. The exit probabilities from an annulus are derived also in the $n$-dimensional case

Surface tension fluctuations and a new spinodal point in glass-forming liquids

The dramatic slowdown of glass-forming liquids has been variously linked to increasing dynamic and static correlation lengths. Yet, empirical evidence is insufficient to decide among competing theories. The random first order theory (RFOT) links the dynamic slowdown to the growth of amorphous static order, whose range depends on a balance between configurational entropy and surface tension. This last quantity is expected to vanish when the temperature surpasses a spinodal point beyond which there are no metastable states. Here we measure for the first time the surface tension in a model glass-former, and find that it vanishes at the energy separating minima from saddles, demonstrating the existence of a spinodal point for amorphous metastable order. Moreover, the fluctuations of surface tension become smaller for lower temperatures, in quantitative agreement with recent theoretical speculation that spatial correlations in glassy systems relax nonexponentially because of the narrowing of the surface tension distribution.Comment: 6 pages, 5 figure

A phase-separation perspective on dynamic heterogeneities in glass-forming liquids

We study dynamic heterogeneities in a model glass-former whose overlap with a reference configuration is constrained to a fixed value. The system phase-separates into regions of small and large overlap, so that dynamical correlations remain strong even for asymptotic times. We calculate an appropriate thermodynamic potential and find evidence of a Maxwell's construction consistent with a spinodal decomposition of two phases. Our results suggest that dynamic heterogeneities are the expression of an ephemeral phase-separating regime ruled by a finite surface tension

Numerical simulations of liquids with amorphous boundary conditions

It has recently become clear that simulations under amorphpous boundary conditions (ABCs) can provide valuable information on the dynamics and thermodynamics of disordered systems with no obvious ordered parameter. In particular, they allow to detect a correlation length that is not measurable with standard correlation functions. Here we explain what exactly is meant by ABCs, discuss their relation with point-to-set correlations and briefly describe some recent results obtained with this technique.Comment: Presented at STATPHYS 2

Towards an Achievable Performance for the Loop Nests

Numerous code optimization techniques, including loop nest optimizations, have been developed over the last four decades. Loop optimization techniques transform loop nests to improve the performance of the code on a target architecture, including exposing parallelism. Finding and evaluating an optimal, semantic-preserving sequence of transformations is a complex problem. The sequence is guided using heuristics and/or analytical models and there is no way of knowing how close it gets to optimal performance or if there is any headroom for improvement. This paper makes two contributions. First, it uses a comparative analysis of loop optimizations/transformations across multiple compilers to determine how much headroom may exist for each compiler. And second, it presents an approach to characterize the loop nests based on their hardware performance counter values and a Machine Learning approach that predicts which compiler will generate the fastest code for a loop nest. The prediction is made for both auto-vectorized, serial compilation and for auto-parallelization. The results show that the headroom for state-of-the-art compilers ranges from 1.10x to 1.42x for the serial code and from 1.30x to 1.71x for the auto-parallelized code. These results are based on the Machine Learning predictions.Comment: Accepted at the 31st International Workshop on Languages and Compilers for Parallel Computing (LCPC 2018

FETR-ALS Study Protocol: A Randomized Clinical Trial of Fecal Microbiota Transplantation in Amyotrophic Lateral Sclerosis

Background and Rationale: Among the key players in the pathogenesis of Amyotrophic Lateral Sclerosis (ALS), microglia and T regulatory lymphocytes (Treg) are candidate cells for modifying the course of the disease. The gut microbiota (GM) acts by shaping immune tolerance and regulating the Treg number and suppressive function, besides circulating neuropeptides, and other immune cells that play in concert through the gut-brain axis. Previous mouse models have shown an altered enteric flora in early stage ALS, pointing to a possible GM role in ALS pathogenesis. Fecal Microbial Transplantation (FMT) is a well-known therapeutic intervention used to re-establish the proper microenvironment and to modulate enteric and systemic immunity. Methods: We are going to perform a multicenter randomized double-blind clinical trial employing FMT as a therapeutic intervention for ALS patients (NCT0376632). Forty-two ALS patients, at an early stage, will be enrolled with a 2:1 allocation ratio (28 FMT-treated patients vs. 14 controls). Study duration will be 12 months per patient. Three endoscopic procedures for intestinal biopsies in FMT and control groups are predicted at baseline, month 6 and month 12; at baseline and at month 6 fresh feces from healthy donors will be infused at patients in the intervention arm. The primary outcome is a significant change in Treg number between FMT-treated patients and control arm from baseline to month 6. Secondary outcomes include specific biological aims, involving in-depth analysis of immune cells and inflammatory status changes, central and peripheral biomarkers of ALS, besides comprehensive analysis of the gut, saliva and fecal microbiota. Other secondary aims include validated clinical outcomes of ALS (survival, forced vital capacity, and modifications in ALSFRS-R), besides safety and quality of life. Expected Results: We await FMT to increase Treg number and suppressive functionality, switching the immune system surrounding motorneurons to an anti-inflammatory, neuroprotective status. Extensive analysis on immune cell populations, cytokines levels, and microbiota (gut, fecal and saliva) will shed light on early processes possibly leading the degenerative ALS course. Conclusions: This is the first trial with FMT as a potential intervention to modify immunological response to ALS and disease progression at an early stage

Aging and relaxation near Random Pinning Glass Transitions

Pinning particles at random in supercooled liquids is a promising route to make substantial progress on the glass transition problem. Here we develop a mean-field theory by studying the equilibrium and non-equilibrium dynamics of the spherical p-spin model in presence of a fraction c of pinned spins. Our study shows the existence of two dynamic critical lines: one corresponding to usual Mode Coupling transitions and the other one to dynamic spinodal transitions. Quenches in the portion of the c - T phase diagram delimited by those two lines leads to aging. By extending our results to finite dimensional systems we predict non-interrupted aging only for quenches on the ideal glass transition line and two very different types of equilibrium relaxations for quenches below and above it.Comment: 7 pages, 4 figure