Universality and the circular law for sparse random matrices

The universality phenomenon asserts that the distribution of the eigenvalues of random matrix with i.i.d. zero mean, unit variance entries does not depend on the underlying structure of the random entries. For example, a plot of the eigenvalues of a random sign matrix, where each entry is +1 or -1 with equal probability, looks the same as an analogous plot of the eigenvalues of a random matrix where each entry is complex Gaussian with zero mean and unit variance. In the current paper, we prove a universality result for sparse random n by n matrices where each entry is nonzero with probability $1/n^{1-\alpha}$ where $0<\alpha\le1$ is any constant. One consequence of the sparse universality principle is that the circular law holds for sparse random matrices so long as the entries have zero mean and unit variance, which is the most general result for sparse random matrices to date.Comment: Published in at http://dx.doi.org/10.1214/11-AAP789 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Nitrogen, Phosphorus, and Suspended Solids Concentrations in Tributaries to the Great Bay Estuary Watershed in 2013

Nitrogen, phosphorus, and sediment loads to the Great Bay Estuary are a growing concern. The Piscataqua Region Estuaries Partnership (PREP) calculates the nitrogen load from tributaries to the Great Bay Estuary for its State of Our Estuaries reports. Therefore, the purpose of this study was to collect representative data on nitrogen, phosphorus, and suspended sediment concentrations in tributaries to the Great Bay Estuary in 2013. The study design followed the tributary sampling design which was implemented by the New Hampshire Department of Environmental Services between 2001 and 2007 and by the University of New Hampshire between 2008 and 2012, so as to provide comparable data to the previous loading estimates

Limiting empirical spectral distribution for the non-backtracking matrix of an Erd\H{o}s-R\'enyi random graph

In this note, we give a precise description of the limiting empirical spectral distribution (ESD) for the non-backtracking matrices for an Erd\H{o}s-R\'{e}nyi graph assuming $np/\log n$ tends to infinity. We show that derandomizing part of the non-backtracking random matrix simplifies the spectrum considerably, and then we use Tao and Vu's replacement principle and the Bauer-Fike theorem to show that the partly derandomized spectrum is, in fact, very close to the original spectrum.Comment: 19 pages, 1 figure. Adjusted the figure in the new versio

Shellfish Tissue Monitoring in Piscataqua Region Estuaries 2010 and 2011

Conducted by a committee of Canadian and US government and university scientists, Gulfwatch examines the effects of decades of development and industrialization on the water quality of the Gulf as it relates to human health primarily through assessing contaminant exposure of marine organisms. Gulfwatch scientists collect blue mussels at over 60 US and Canadian sites Gulfwide, and analyze the organisms’ tissue for potentially harmful levels and concentrations of toxins including heavy metals, chlorinated pesticides, polychlorinated biphenyls (PCBs), and polycyclic aromatic hydrocarbons (PAHs)

Shellfish Tissue Monitoring in Piscataqua Region Estuaries 2012

Originally conducted by a committee of Canadian and US governments and university scientists, Gulfwatch examined the effects of decades of development and industrialization on the water quality of the Gulf of Maine as it relates to human health primarily through assessing contaminant exposure of marine organisms from 1993 to 2010. The NH Gulfwatch Program continues these efforts by collecting blue mussels at two sites in the Great Bay Estuary and one in the Hampron-Seabrook Estuary, and analyzes the organisms’ tissue for potentially harmful levels and concentrations of toxins including heavy metals, chlorinated pesticides, polychlorinated biphenyls (PCBs), and polycyclic aromatic hydrocarbons (PAHs). During the 2012 sampling season, mussels were collected at three sampling locations in New Hampshire and Maine (MECC, NHHS and NHDP)

Shellfish Tissue Monitoring in Piscataqua Region Estuaries 2013

Originally conducted by the Gulf of Maine Council on the Marine Environment from 1993 to 2011, the Gulfwatch Program examined trends in the water quality of the Gulf of Maine by monitoring toxic contaminant concentrations in the tissues of shellfish. Starting in 2012 the Piscataqua Region Estuaries Partnership (PREP) continued this program in the Piscataqua Region. Each year, PREP collects blue mussels at three sites: Dover Point, NH (NHDP), Clark Cove on Seavey Island, ME (MECC), and Hampton-Seabrook Harbor (NHHS). The mussel tissue is analyzed to determine the concentrations of toxic contaminantss including heavy metals, chlorinated pesticides, polychlorinated biphenyls (PCBs), and polycyclic aromatic hydrocarbons (PAHs)

Shellfish Tissue Monitoring in Piscataqua Region Estuaries 2010: Final Report

Gulfwatch examines the effects of decades of development and industrialization on the water quality of the Gulf as it relates to human health primarily through assessing contaminant exposure of marine organisms. Gulfwatch scientists collect blue mussels at over 60 US and Canadian sites Gulfwide, and analyze the organisms’ tissue for potentially harmful levels and concentrations of toxins including heavy metals, chlorinated pesticides, polychlorinated biphenyls (PCBs), and polycyclic aromatic hydrocarbons (PAHs). New Hampshire increased the number of Gulfwatch sampling locations from two sites per year in 1997 to an average of five sites per year from 1998-2010. The increased spatial coverage provides comprehensive information for contaminant concentrations throughout the New Hampshire estuarine waters. All samples collected for the Gulfwatch monitoring program, from the Canadian provinces as well as the New England states involved, have been sent to the same laboratories for analysis. All of the samples have been analyzed at the same time in the same laboratories in an effort to reduce error and variability. This practice has ensured the consistency that was necessary to allow a region-wide assessment of the health of the Gulf. During the 2010 sampling season, mussels were collected at six sampling locations in New Hampshire and Maine (MECC, NHHS, NHDP, NHRH, NHPI and NHLH). Project Goals and Objectives The goal of this project was to provide data for two PREP indicators of estuarine condition: TOX1 and TOX3. These two indicators report on “Shellfish tissue concentrations relative to FDA standards” and “Trends in shellfish tissue contaminant concentrations”, respectively. Both of these indicators depend on data from the Gulfwatch Program. In particular, TOX3 requires annual data at benchmark sites to assess trends. In 2010, PREP supported the collection and analysis of tissue samples from benchmark mussel sites in Hampton-Seabrook Harbor and Dover Point