Glauber dynamics on nonamenable graphs: Boundary conditions and mixing time

We study the stochastic Ising model on finite graphs with n vertices and bounded degree and analyze the effect of boundary conditions on the mixing time. We show that for all low enough temperatures, the spectral gap of the dynamics with (+)-boundary condition on a class of nonamenable graphs, is strictly positive uniformly in n. This implies that the mixing time grows at most linearly in n. The class of graphs we consider includes hyperbolic graphs with sufficiently high degree, where the best upper bound on the mixing time of the free boundary dynamics is polynomial in n, with exponent growing with the inverse temperature. In addition, we construct a graph in this class, for which the mixing time in the free boundary case is exponentially large in n. This provides a first example where the mixing time jumps from exponential to linear in n while passing from free to (+)-boundary condition. These results extend the analysis of Martinelli, Sinclair and Weitz to a wider class of nonamenable graphs.Comment: 31 pages, 4 figures; added reference; corrected typo

A Combinatorial Optimization Approach to the Selection of Statistical Units

In the case of some large statistical surveys, the set of units that will constitute the scope of the survey must be selected. We focus on the real case of a Census of Agriculture, where the units are farms. Surveying each unit has a cost and brings a different portion of the whole information. In this case, one wants to determine a subset of units producing the minimum total cost for being surveyed and representing at least a certain portion of the total information. Uncertainty aspects also occur, because the portion of information corresponding to each unit is not perfectly known before surveying it. The proposed approach is based on combinatorial optimization, and the arising decision problems are modeled as multidimensional binary knapsack problems. Experimental results show the effectiveness of the proposed approach

Stochastically Stable Quenched Measures

We analyze a class of stochastically stable quenched measures. We prove that stochastic stability is fully characterized by an infinite family of zero average polynomials in the covariance matrix entries.Comment: 13 page

Glauber dynamics on hyperbolic graphs : boundary conditions and mixing time

We study a continuous time Glauber dynamics reversible with respect to the Ising model on hyperbolic graphs and analyze the effect of boundary conditions on the mixing time. Specifically, we consider the dynamics on an $n$-vertex ball of the hyperbolic graph $H(v,s)$, where $v$ is the number of neighbors of each vertex and $s$ is the number of sides of each face, conditioned on having $(+)$-boundary. If $v>4$, $s>3$ and for all low enough temperatures (phase coexistence region) we prove that the spectral gap of this dynamics is bounded below by a constant independent of $n$. This implies that the mixing time grows at most linearly in $n$, in contrast to the free boundary case where it is polynomial with exponent growing with the inverse temperature $b$. Such a result extends to hyperbolic graphs the work done by Martinelli, Sinclair and Weitz for the analogous system on regular tree graphs, and provides a further example of influence of the boundary condition on the mixing time

Random walks in a one-dimensional L\'evy random environment

We consider a generalization of a one-dimensional stochastic process known in the physical literature as L\'evy-Lorentz gas. The process describes the motion of a particle on the real line in the presence of a random array of marked points, whose nearest-neighbor distances are i.i.d. and long-tailed (with finite mean but possibly infinite variance). The motion is a continuous-time, constant-speed interpolation of a symmetric random walk on the marked points. We first study the quenched random walk on the point process, proving the CLT and the convergence of all the accordingly rescaled moments. Then we derive the quenched and annealed CLTs for the continuous-time process.Comment: Final version to be published in J. Stat. Phys. 23 pages. (Changes from v1: Theorem 2.4 and Corollary 2.6 have been removed.

Coordinated actions of microRNAs with other epigenetic factors regulate skeletal muscle development and adaptation

Epigenetics plays a pivotal role in regulating gene expression in development, in response to cellular stress or in disease states, in virtually all cell types. MicroRNAs (miRNAs) are short, non-coding RNA molecules that mediate RNA silencing and regulate gene expression. miRNAs were discovered in 1993 and have been extensively studied ever since. They can be expressed in a tissue-specific manner and play a crucial role in tissue development and many biological processes. miRNAs are responsible for changes in the cell epigenome because of their ability to modulate gene expression post-transcriptionally. Recently, numerous studies have shown that miRNAs and other epigenetic factors can regulate each other or cooperate in regulating several biological processes. On the one hand, the expression of some miRNAs is silenced by DNA methylation, and histone modifications have been demonstrated to modulate miRNA expression in many cell types or disease states. On the other hand, miRNAs can directly target epigenetic factors, such as DNA methyltransferases or histone deacetylases, thus regulating chromatin structure. Moreover, several studies have reported coordinated actions between miRNAs and other epigenetic mechanisms to reinforce the regulation of gene expression. This paper reviews multiple interactions between miRNAs and epigenetic factors in skeletal muscle development and in response to stimuli or disease

A min-cut approach to functional regionalization, with a case study of the Italian local labour market areas

In several economical, statistical and geographical applications, a territory must be subdivided into functional regions. Such regions are not fixed and politically delimited, but should be identified by analyzing the interactions among all its constituent localities. This is a very delicate and important task, that often turns out to be computationally difficult. In this work we propose an innovative approach to this problem based on the solution of minimum cut problems over an undirected graph called here transitions graph. The proposed procedure guarantees that the obtained regions satisfy all the statistical conditions required when considering this type of problems. Results on real-world instances show the effectiveness of the proposed approach

Patient satisfaction after auditory implant surgery. ten-year experience from a single implanting unit center

Conclusions: The satisfaction rate of the subjects with an auditory implant appears strictly related to the resulting auditory improvement, and the surgical variables would play a prevailing role in respect to the esthetic factors. Objectives: To assess the rate of satisfaction in subjects who underwent the surgical application of an auditory device at a single Implanting Center Unit. Method: A series of validated questionnaires has been administered to subjects who underwent the surgical application of different auditory devices. The Glasgow Benefit Inventory (GBI), the Visual Analog Scale (VAS), and the Abbreviated Profile of Hearing Aid Benefit (APHAB) have been used to compare the implanted situation with the hearing-aided one; a percutaneous bone conductive implant (pBCI) with an active middle ear implant (AMEI) on the round window in mixed hearing loss; and an invisible, fully-implantable device with a frankly and bulky semi-implantable device. Results: The mean GBI scores were higher in Vibrant Soundbridge (VSB)VR and BonebridgeVR subjects, without significant differences among the various devices. The mean VAS score increased for all the devices in comparison with the conventional hearing aid. The mean APHAB score was similarly better in the implanted condition as total and partial scores

Pointwise estimates and exponential laws in metastable systems via coupling methods

We show how coupling techniques can be used in some metastable systems to prove that mean metastable exit times are almost constant as functions of the starting microscopic configuration within a "meta-stable set." In the example of the Random Field Curie Weiss model, we show that these ideas can also be used to prove asymptotic exponentiallity of normalized metastable escape times.Comment: Published in at http://dx.doi.org/10.1214/10-AOP622 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org