A Recursion Formula for Moments of Derivatives of Random Matrix Polynomials

We give asymptotic formulae for random matrix averages of derivatives of characteristic polynomials over the groups USp(2N), SO(2N) and O^-(2N). These averages are used to predict the asymptotic formulae for moments of derivatives of L-functions which arise in number theory. Each formula gives the leading constant of the asymptotic in terms of determinants of hypergeometric functions. We find a differential recurrence relation between these determinants which allows the rapid computation of the (k+1)-st constant in terms of the k-th and (k-1)-st. This recurrence is reminiscent of a Toda lattice equation arising in the theory of \tau-functions associated with Painlev\'e differential equations

Magnitude and Extent of Contaminated Sediment and Toxicity in Chesapeake Bay

INTRODUCTION: This report summarizes the results of NOAA's sediment toxicity, chemistry, and benthic community studies in the Chesapeake Bay estuary. As part of the National Status and Trends (NS&T) Program, NOAA has conducted studies to determine the spatial extent and severity of chemical contamination and associated adverse biological effects in coastal bays and estuaries of the United States since 1991. Sediment contamination in U.S. coastal areas is a major environmental issue because of its potential toxic effects on biological resources and often, indirectly, on human health. Thus, characterizing and delineating areas of sediment contamination and toxicity and demonstrating their effect(s) on benthic living resources are viewed as important goals of coastal resource management. Benthic community studies have a history of use in regional estuarine monitoring programs and have been shown to be an effective indicator for describing the extent and magnitude of pollution impacts in estuarine ecosystems, as well as for assessing the effectiveness of management actions. Chesapeake Bay is the largest estuarine system in the United States. Including tidal tributaries, the Bay has approximately 18,694 km of shoreline (more than the entire US West Coast). The watershed is over 165,000 km2 (64,000 miles2), and includes portions of six states (Delaware, Maryland, New York, Pennsylvania, Virginia, and West Virginia) and the District of Columbia. The population of the watershed exceeds 15 million people. There are 150 rivers and streams in the Chesapeake drainage basin. Within the watershed, five major rivers - the Susquehanna, Potomac, Rappahannock, York and James - provide almost 90% of the freshwater to the Bay. The Bay receives an equal volume of water from the Atlantic Ocean. In the upper Bay and tributaries, sediments are fine-grained silts and clays. Sediments in the middle Bay are mostly made of silts and clays derived from shoreline erosion. In the lower Bay, by contrast, the sediments are sandy. These particles come from shore erosion and inputs from the Atlantic Ocean. The introduction of European-style agriculture and large scale clearing of the watershed produced massive shifts in sediment dynamics of the Bay watershed. As early as the mid 1700s, some navigable rivers were filled in by sediment and sedimentation caused several colonial seaports to become landlocked. Toxic contaminants enter the Bay via atmospheric deposition, dissolved and particulate runoff from the watershed or direct discharge. While contaminants enter the Bay from several sources, sediments accumulate many toxic contaminants and thus reveal the status of input for these constituents. In the watershed, loading estimates indicate that the major sources of contaminants are point sources, stormwater runoff, atmospheric deposition, and spills. Point sources and urban runoff in the Bay proper contribute large quantities of contaminants. Pesticide inputs to the Bay have not been quantified. Baltimore Harbor and the Elizabeth River remain among the most contaminated areas in the Unites States. In the mainstem, deep sediment core analyses indicate that sediment accumulation rates are 2-10 times higher in the northern Bay than in the middle and lower Bay, and that sedimentation rates are 2-10 times higher than before European settlement throughout the Bay (NOAA 1998). The core samples show a decline in selected PAH compounds over the past several decades, but absolute concentrations are still 1 to 2 orders of magnitude above 'pristine' conditions. Core data also indicate that concentrations of PAHs, PCBs and, organochlorine pesticides do not demonstrate consistent trends over 25 years, but remain 10 times lower than sediments in the tributaries. In contrast, tri-butyl-tin (TBT) concentrations in the deep cores have declined significantly since it=s use was severely restricted. (PDF contains 241 pages

On realizations of polynomial algebras with three generators via deformed oscillator algebras

We present the most general polynomial Lie algebra generated by a second order integral of motion and one of order M, construct the Casimir operator, and show how the Jacobi identity provides the existence of a realization in terms of deformed oscillator algebra. We also present the classical analog of this construction for the most general Polynomial Poisson algebra. Two specific classes of such polynomial algebras are discussed that include the symmetry algebras observed for various 2D superintegrable systems.Comment: 28 page

Exponential-family Random Network Models

Random graphs, where the connections between nodes are considered random variables, have wide applicability in the social sciences. Exponential-family Random Graph Models (ERGM) have shown themselves to be a useful class of models for representing com- plex social phenomena. We generalize ERGM by also modeling nodal attributes as random variates, thus creating a random model of the full network, which we call Exponential-family Random Network Models (ERNM). We demonstrate how this framework allows a new formu- lation for logistic regression in network data. We develop likelihood-based inference for the model and an MCMC algorithm to implement it. This new model formulation is used to analyze a peer social network from the National Lon- gitudinal Study of Adolescent Health. We model the relationship between substance use and friendship relations, and show how the results differ from the standard use of logistic regression on network data

An inevitable wave of prescription drug monitoring programs in the context of prescription opioids: pros, cons and tensions

BACKGROUND: In an effort to control non-medical use and/or medical abuse of prescription drugs, particularly prescription opioids, electronic prescription drug monitoring programs (PDMP) have been introduced in North-American countries, Australia and some parts of Europe. Paradoxically, there are simultaneous pressures to increase opioid prescribing for the benefit of individual patients and to reduce it for the sake of public health, and this pressure warrants a delicate balance of appropriate therapeutic uses of these drugs with the risk of developing dependence. This article discusses pros and cons of PDMP in reducing diversion of prescription opioids, without hampering access to those medications for those with genuine needs, and highlights tensions around PDMP implementation. DISCUSSION: PDMPs may help alleviate diversion, over-prescription and fraudulent prescribing/dispensing; prompt drug treatment referrals; avoid awkward drug urine test; and inform spatial changes in prescribing practices and help designing tailored interventions. Fear of legal retribution, privacy and data security, potential confusion about addiction and pseudo-addiction, and potential undue pressure of detecting misuse/diversion - are the major problems. There are tensions about unintended consequence of excessive regulatory enforcements, corresponding collateral damages particularly about inadequate prescribing for patients with genuine needs, and mandatory consultation requirements of PDMP. SUMMARY: In this era of information technology PDMP is likely to flourish and remain with us for a long time. A clear standard of practice against which physicians' care will be judged may expedite the utilisation of PDMP. In addition, adequate training on addiction and pain management along with public awareness, point-of-supply data entry from pharmacy, point-of-care real-time access to data, increasing access to addiction treatment and appropriate regulatory enforcement preferably through healthcare administration, together, may help remove barriers to PDMP use

Symmetry groupoids and admissible vector fields for coupled cell networks

The space of admissible vector fields, consistent with the structure of a network of coupled dynamical systems, can be specified in terms of the network's symmetry groupoid. The symmetry groupoid also determines the robust patterns of synchrony in the network – those that arise because of the network topology. In particular, synchronous cells can be identified in a canonical manner to yield a quotient network. Admissible vector fields on the original network induce admissible vector fields on the quotient, and any dynamical state of such an induced vector field can be lifted to the original network, yielding an analogous state in which certain sets of cells are synchronized. In the paper, necessary and sufficient conditions are specified for all admissible vector fields on the quotient to lift in this manner. These conditions are combinatorial in nature, and the proof uses invariant theory for the symmetric group. Also the symmetry groupoid of a quotient is related to that of the original network, and it is shown that there is a close analogy with the usual normalizer symmetry that arises in group-equivariant dynamics