Asymptotics of Plancherel-type random partitions

We present a solution to a problem suggested by Philippe Biane: We prove that a certain Plancherel-type probability distribution on partitions converges, as partitions get large, to a new determinantal random point process on the set {0,1,2,...} of nonnegative integers. This can be viewed as an edge limit ransition. The limit process is determined by a correlation kernel on {0,1,2,...} which is expressed through the Hermite polynomials, we call it the discrete Hermite kernel. The proof is based on a simple argument which derives convergence of correlation kernels from convergence of unbounded self-adjoint difference operators. Our approach can also be applied to a number of other probabilistic models. As an example, we discuss a bulk limit for one more Plancherel-type model of random partitions.Comment: AMS TeX, 19 pages. Version 2: minor typos fixe

Edge scaling limits for a family of non-Hermitian random matrix ensembles

A family of random matrix ensembles interpolating between the GUE and the Ginibre ensemble of $n\times n$ matrices with iid centered complex Gaussian entries is considered. The asymptotic spectral distribution in these models is uniform in an ellipse in the complex plane, which collapses to an interval of the real line as the degree of non-Hermiticity diminishes. Scaling limit theorems are proven for the eigenvalue point process at the rightmost edge of the spectrum, and it is shown that a non-trivial transition occurs between Poisson and Airy point process statistics when the ratio of the axes of the supporting ellipse is of order $n^{-1/3}$. In this regime, the family of limiting probability distributions of the maximum of the real parts of the eigenvalues interpolates between the Gumbel and Tracy-Widom distributions.Comment: 44 page

Influence Diffusion in Social Networks under Time Window Constraints

We study a combinatorial model of the spread of influence in networks that generalizes existing schemata recently proposed in the literature. In our model, agents change behaviors/opinions on the basis of information collected from their neighbors in a time interval of bounded size whereas agents are assumed to have unbounded memory in previously studied scenarios. In our mathematical framework, one is given a network $G=(V,E)$, an integer value $t(v)$ for each node $v\in V$, and a time window size $\lambda$. The goal is to determine a small set of nodes (target set) that influences the whole graph. The spread of influence proceeds in rounds as follows: initially all nodes in the target set are influenced; subsequently, in each round, any uninfluenced node $v$ becomes influenced if the number of its neighbors that have been influenced in the previous $\lambda$ rounds is greater than or equal to $t(v)$. We prove that the problem of finding a minimum cardinality target set that influences the whole network $G$ is hard to approximate within a polylogarithmic factor. On the positive side, we design exact polynomial time algorithms for paths, rings, trees, and complete graphs.Comment: An extended abstract of a preliminary version of this paper appeared in: Proceedings of 20th International Colloquium on Structural Information and Communication Complexity (Sirocco 2013), Lectures Notes in Computer Science vol. 8179, T. Moscibroda and A.A. Rescigno (Eds.), pp. 141-152, 201

Extending the square root method to account for additive forecast noise in ensemble methods

A square root approach is considered for the problem of accounting for model noise in the forecast step of the ensemble Kalman filter (EnKF) and related algorithms. The primary aim is to replace the method of simulated, pseudo-random additive so as to eliminate the associated sampling errors. The core method is based on the analysis step of ensemble square root filters, and consists in the deterministic computation of a transform matrix. The theoretical advantages regarding dynamical consistency are surveyed, applying equally well to the square root method in the analysis step. A fundamental problem due to the limited size of the ensemble subspace is discussed, and novel solutions that complement the core method are suggested and studied. Benchmarks from twin experiments with simple, low-order dynamics indicate improved performance over standard approaches such as additive, simulated noise, and multiplicative inflation

Phase transitions in contagion processes mediated by recurrent mobility patterns

Human mobility and activity patterns mediate contagion on many levels, including the spatial spread of infectious diseases, diffusion of rumors, and emergence of consensus. These patterns however are often dominated by specific locations and recurrent flows and poorly modeled by the random diffusive dynamics generally used to study them. Here we develop a theoretical framework to analyze contagion within a network of locations where individuals recall their geographic origins. We find a phase transition between a regime in which the contagion affects a large fraction of the system and one in which only a small fraction is affected. This transition cannot be uncovered by continuous deterministic models due to the stochastic features of the contagion process and defines an invasion threshold that depends on mobility parameters, providing guidance for controlling contagion spread by constraining mobility processes. We recover the threshold behavior by analyzing diffusion processes mediated by real human commuting data.Comment: 20 pages of Main Text including 4 figures, 7 pages of Supplementary Information; Nature Physics (2011

Pope Farm Expansion Project

Final project for INAG 248: Topics in Sustainable Agriculture (Spring 2021). University of Maryland, College Park.The group of students provided recommendations to M-NCPPC Montgomery County Parks by planting diverse types of vegetables and other crops that will benefit the community in growing familiar crops which they will be able to use appropriately and be able to feed their families while considering the harvesting and transportation of these foods to the people in the Pope Farm and creating the outline of the vegetable crops that the team recommends.Montgomery County Parks (MoCo

Detecting aseismic strain transients from seismicity data

Author Posting. © American Geophysical Union, 2011. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 116 (2011): B06305, doi:10.1029/2010JB007537.Aseismic deformation transients such as fluid flow, magma migration, and slow slip can trigger changes in seismicity rate. We present a method that can detect these seismicity rate variations and utilize these anomalies to constrain the underlying variations in stressing rate. Because ordinary aftershock sequences often obscure changes in the background seismicity caused by aseismic processes, we combine the stochastic Epidemic Type Aftershock Sequence model that describes aftershock sequences well and the physically based rate- and state-dependent friction seismicity model into a single seismicity rate model that models both aftershock activity and changes in background seismicity rate. We implement this model into a data assimilation algorithm that inverts seismicity catalogs to estimate space-time variations in stressing rate. We evaluate the method using a synthetic catalog, and then apply it to a catalog of M ≥ 1.5 events that occurred in the Salton Trough from 1990 to 2009. We validate our stressing rate estimates by comparing them to estimates from a geodetically derived slip model for a large creep event on the Obsidian Buttes fault. The results demonstrate that our approach can identify large aseismic deformation transients in a multidecade long earthquake catalog and roughly constrain the absolute magnitude of the stressing rate transients. Our method can therefore provide a way to detect aseismic transients in regions where geodetic resolution in space or time is poor.This work was supported by NSF EAR grant 0738641 and USGS NEHRP grant G10AP00004

Coordination of Chromosome Segregation and Cell Division in Staphylococcus aureus

Productive bacterial cell division and survival of progeny requires tight coordination between chromosome segregation and cell division to ensure equal partitioning of DNA. Unlike rod-shaped bacteria that undergo division in one plane, the coccoid human pathogen Staphylococcus aureus divides in three successive orthogonal planes, which requires a different spatial control compared to rod-shaped cells. To gain a better understanding of how this coordination between chromosome segregation and cell division is regulated in S. aureus, we investigated proteins that associate with FtsZ and the divisome. We found that DnaK, a well-known chaperone, interacts with FtsZ, EzrA and DivIVA, and is required for DivIVA stability. Unlike in several rod shaped organisms, DivIVA in S. aureus associates with several components of the divisome, as well as the chromosome segregation protein, SMC. This data, combined with phenotypic analysis of mutants, suggests a novel role for S. aureus DivIVA in ensuring cell division and chromosome segregation are coordinated