Eigenvalue Separation in Some Random Matrix Models

The eigenvalue density for members of the Gaussian orthogonal and unitary ensembles follows the Wigner semi-circle law. If the Gaussian entries are all shifted by a constant amount c/Sqrt(2N), where N is the size of the matrix, in the large N limit a single eigenvalue will separate from the support of the Wigner semi-circle provided c > 1. In this study, using an asymptotic analysis of the secular equation for the eigenvalue condition, we compare this effect to analogous effects occurring in general variance Wishart matrices and matrices from the shifted mean chiral ensemble. We undertake an analogous comparative study of eigenvalue separation properties when the size of the matrices are fixed and c goes to infinity, and higher rank analogues of this setting. This is done using exact expressions for eigenvalue probability densities in terms of generalized hypergeometric functions, and using the interpretation of the latter as a Green function in the Dyson Brownian motion model. For the shifted mean Gaussian unitary ensemble and its analogues an alternative approach is to use exact expressions for the correlation functions in terms of classical orthogonal polynomials and associated multiple generalizations. By using these exact expressions to compute and plot the eigenvalue density, illustrations of the various eigenvalue separation effects are obtained.Comment: 25 pages, 9 figures include

Expansion Potential for Irrigation within the Mississippi Delta Region

17.6 million acres, or 73 percent, of the Mississippi Delta Region is currently cropland and possesses the physical characteristics of slope, texture and soil type which are recommended for irrigation. Economic feasibility of expanding irrigation by flood, furrow and center pivot methods were examined under 24 scenarios representing two sets of crop prices, yield levels, production costs, opportunity costs and six crop rotations. Irrigation was economically feasible for 56 to 100 percent of the cropland across all scenarios. Approximately 88 percent of the cropland can be economically irrigated with flood or furrow in its present form, 8 percent yield highest net returns if furrow irrigated following land forming and 4 percent can be economically irrigated only with center pivot systems

Weighing Neutrinos with Galaxy Cluster Surveys

Large future galaxy cluster surveys, combined with cosmic microwave background observations, can achieve a high sensitivity to the masses of cosmologically important neutrinos. We show that a weak lensing selected sample of ~100,000 clusters could tighten the current upper bound on the sum of masses of neutrino species by an order of magnitude, to a level of 0.03 eV. Since this statistical sensitivity is below the best existing lower limit on the mass of at least one neutrino species, a future detection is likely, provided that systematic errors can be controlled to a similar level.Comment: 4 pages, 1 figure, version accepted for publication in PR

Modular networks emerge from multiconstraint optimization

Modular structure is ubiquitous among complex networks. We note that most such systems are subject to multiple structural and functional constraints, e.g., minimizing the average path length and the total number of links, while maximizing robustness against perturbations in node activity. We show that the optimal networks satisfying these three constraints are characterized by the existence of multiple subnetworks (modules) sparsely connected to each other. In addition, these modules have distinct hubs, resulting in an overall heterogeneous degree distribution.Comment: 5 pages, 4 figures; Published versio

Some Like It Hot: Linking Diffuse X-ray Luminosity, Baryonic Mass, and Star Formation Rate in Compact Groups of Galaxies

We present an analysis of the diffuse X-ray emission in 19 compact groups of galaxies (CGs) observed with Chandra. The hottest, most X-ray luminous CGs agree well with the galaxy cluster X-ray scaling relations in $L_X-T$ and $L_X-\sigma$, even in CGs where the hot gas is associated with only the brightest galaxy. Using Spitzer photometry, we compute stellar masses and classify HCGs 19, 22, 40, and 42 and RSCGs 32, 44, and 86 as fossil groups using a new definition for fossil systems that includes a broader range of masses. We find that CGs with total stellar and HI masses $\gtrsim10^{11.3}$ M$_\odot$ are often X-ray luminous, while lower-mass CGs only sometimes exhibit faint, localized X-ray emission. Additionally, we compare the diffuse X-ray luminosity against both the total UV and 24 $\mu$m star formation rates of each CG and optical colors of the most massive galaxy in each of the CGs. The most X-ray luminous CGs have the lowest star formation rates, likely because there is no cold gas available for star formation, either because the majority of the baryons in these CGs are in stars or the X-ray halo, or due to gas stripping from the galaxies in CGs with hot halos. Finally, the optical colors that trace recent star formation histories of the most massive group galaxies do not correlate with the X-ray luminosities of the CGs, indicating that perhaps the current state of the X-ray halos is independent of the recent history of stellar mass assembly in the most massive galaxies.Comment: 20 pages, 7 figures, accepted for publication in Ap

Rethinking the patient: using Burden of Treatment Theory to understand the changing dynamics of illness

<b>Background</b> In this article we outline Burden of Treatment Theory, a new model of the relationship between sick people, their social networks, and healthcare services. Health services face the challenge of growing populations with long-term and life-limiting conditions, they have responded to this by delegating to sick people and their networks routine work aimed at managing symptoms, and at retarding - and sometimes preventing - disease progression. This is the new proactive work of patient-hood for which patients are increasingly accountable: founded on ideas about self-care, self-empowerment, and self-actualization, and on new technologies and treatment modalities which can be shifted from the clinic into the community. These place new demands on sick people, which they may experience as burdens of treatment.<p></p> <b>Discussion</b> As the burdens accumulate some patients are overwhelmed, and the consequences are likely to be poor healthcare outcomes for individual patients, increasing strain on caregivers, and rising demand and costs of healthcare services. In the face of these challenges we need to better understand the resources that patients draw upon as they respond to the demands of both burdens of illness and burdens of treatment, and the ways that resources interact with healthcare utilization.<p></p> <b>Summary</b> Burden of Treatment Theory is oriented to understanding how capacity for action interacts with the work that stems from healthcare. Burden of Treatment Theory is a structural model that focuses on the work that patients and their networks do. It thus helps us understand variations in healthcare utilization and adherence in different healthcare settings and clinical contexts

The Clumping Transition in Niche Competition: a Robust Critical Phenomenon

We show analytically and numerically that the appearance of lumps and gaps in the distribution of n competing species along a niche axis is a robust phenomenon whenever the finiteness of the niche space is taken into account. In this case depending if the niche width of the species $\sigma$ is above or below a threshold $\sigma_c$, which for large n coincides with 2/n, there are two different regimes. For $\sigma > sigma_c$ the lumpy pattern emerges directly from the dominant eigenvector of the competition matrix because its corresponding eigenvalue becomes negative. For $\sigma </- sigma_c$ the lumpy pattern disappears. Furthermore, this clumping transition exhibits critical slowing down as $\sigma$ is approached from above. We also find that the number of lumps of species vs. $\sigma$ displays a stair-step structure. The positions of these steps are distributed according to a power-law. It is thus straightforward to predict the number of groups that can be packed along a niche axis and it coincides with field measurements for a wide range of the model parameters.Comment: 16 pages, 7 figures; http://iopscience.iop.org/1742-5468/2010/05/P0500

Construction of the Soudan 2 detector

Progress in the construction of the Soudan 2 nucleon decay detector which is being built at the Soudan iron mine in Minnesota is discussed. The expected event rate and characteristics of low energy neutrino events, muon events, multiple muon events, and other cosmic ray phenomena are discussed

On the Prior Sensitivity of Thompson Sampling

The empirically successful Thompson Sampling algorithm for stochastic bandits has drawn much interest in understanding its theoretical properties. One important benefit of the algorithm is that it allows domain knowledge to be conveniently encoded as a prior distribution to balance exploration and exploitation more effectively. While it is generally believed that the algorithm's regret is low (high) when the prior is good (bad), little is known about the exact dependence. In this paper, we fully characterize the algorithm's worst-case dependence of regret on the choice of prior, focusing on a special yet representative case. These results also provide insights into the general sensitivity of the algorithm to the choice of priors. In particular, with $p$ being the prior probability mass of the true reward-generating model, we prove $O(\sqrt{T/p})$ and $O(\sqrt{(1-p)T})$ regret upper bounds for the bad- and good-prior cases, respectively, as well as \emph{matching} lower bounds. Our proofs rely on the discovery of a fundamental property of Thompson Sampling and make heavy use of martingale theory, both of which appear novel in the literature, to the best of our knowledge.Comment: Appears in the 27th International Conference on Algorithmic Learning Theory (ALT), 201