Random matrices: Universality of ESDs and the circular law

Given an n x n complex matrix A, let mu(A)(x, y) := 1/n vertical bar{1 <= i <= n, Re lambda(i) <= x, Im lambda(i) <= y}vertical bar be the empirical spectral distribution (ESD) of its eigenvalues lambda(i) is an element of C, i = l, ... , n. We consider the limiting distribution (both in probability and in the almost sure convergence sense) of the normalized ESD mu(1/root n An) of a random matrix A(n) = (a(ij))(1 <= i, j <= n), where the random variables a(ij) - E(a(ij)) are i.i.d. copies of a fixed random variable x with unit variance. We prove a universality principle for such ensembles, namely, that the limit distribution in question is independent of the actual choice of x. In particular, in order to compute this distribution, one can assume that x is real or complex Gaussian. As a related result, we show how laws for this ESD follow from laws for the singular value distribution of 1/root n A(n) - zI for complex z. As a corollary, we establish the circular law conjecture (both almost surely and in probability), which asserts that mu(1/root n An) converges to the uniform measure on the unit disc when the a(ij) have zero mean.

Sensitive high-resolution ion microprobe U-Pb dating of prograde and retrograde ultrahigh-temperature metamorphism as exemplified by Sri Lankan granulites

Ultrahigh-temperature (UHT) granulites of the central Highland Complex, Sri Lanka, underwent some of the highest known peak temperatures of crustal metamorphism. Zircon and monazite U-Pb systems in granulites near Kandy, the highest grade region (similar to 1050 degrees C; 0.9 GPa), preserve both a record of the timing of prograde and retrograde phases of UHT metamorphism and evidence for the ages of older protolith components. Zircon grains from a quartz-saturated granulite containing relics of the peak UHT assemblage have remnant detrital cores with dates of ca. 2.5-0.83 Ga. Date clusters of ca. 1.7 and 1.04-0.83 Ga record episodes of zircon growth in the source region of the protolith sediment. Two generations of overgrowths with contrasting Th/U record metamorphic zircon growth at 569 +/- 5 and 551 +/- 7 Ma, probably in the absence and presence of monazite, respectively. The age of coexisting metamorphic monazite (547 +/- 7 Ma) is indistinguishable from that of the younger, low-Th/U zircon overgrowths. Zircon from a quartz-undersaturated monazite-absent UHT granulite with a mainly retrograde assemblage is mostly metamorphic (551 +/- 5 Ma). The ca. 570 Ma zircon overgrowths in the quartz-saturated granulite probably record partial melting just before or at the metamorphic peak. The ca. 550 Ma zircon in both rocks, and the ca. 550 Ma monazite in the quartz-saturated sample, record post-peak isothermal decompression. A possible model for this pressure-temperature-time evolution is ultrahot collisional orogeny during the assembly of Gondwana, locally superheated by basaltic underplating, followed by fast extensional exhumation.

Electron transfer statistics and thermal fluctuations in molecular junctions

We derive analytical expressions for probability distribution function (PDF) for electron transport in a simple model of quantum junction in presence of thermal fluctuations. Our approach is based on the large deviation theory combined with the generating function method. For large number of electrons transferred, the PDF is found to decay exponentially in the tails with different rates due to applied bias. This asymmetry in the PDF is related to the fluctuation theorem. Statistics of fluctuations are analyzed in terms of the Fano factor. Thermal fluctuations play a quantitative role in determining the statistics of electron transfer; they tend to suppress the average current while enhancing the fluctuations in particle transfer. This gives rise to both bunching and antibunching phenomena as determined by the Fano factor. The thermal fluctuations and shot noise compete with each other and determine the net (effective) statistics of particle transfer. Exact analytical expression is obtained for delay time distribution. The optimal values of the delay time between successive electron transfers can be lowered below the corresponding shot noise values by tuning the thermal effects. (C) 2015 AIP Publishing LLC.

Spatial distribution of Chlorpyrifos and Endosulfan in USA coastal waters and the Great Lakes

Between 1994 and 1997, 258 tissue and 178 sediment samples were analyzed for chlorpyrifos throughout the coastal United States and the Great Lakes. Subsequently, 95 of the 1997 tissue samples were reanalyzed for endosulfan. Tissue chlorpyrifos concentrations, which exceeded the 90th percentile, were found in coastal regions known to have high agricultural use rates but also strongly correlated with sites near high population. The highest concentrations of endosulfans in contrast, were generally limited to agricultural regions of the country. Detections of chlorpyrifos at several Alaskan sites suggest an atmospheric transport mechanism. Many Great Lakes sites had chlorpyrifos tissue concentrations above the 90th percentile which decreased with increasing distance from the Corn Belt region (Iowa, Indiana, Illinois, and Wisconsin) where most agriculturally applied chlorpyrifos is used. Correlation analysis suggests that fluvial discharge is the primary transport pathway on the Atlantic and Gulf of Mexico coasts for chlorpyrifos but not necessarily for endosulfans. (PDF contains 28 pages)

Exploratory survey of Malian and Ndururu traps in River Rima, north western Nigeria

The fabrication and operational techniques of Malian and Ndurutu traps mostly used by the fishermen in River Rima in north western Nigeria were evaluated through structured questionnaire and measurement of samples of the Data collected were analyzed using descriptive statistics. There was no standard in the dimensions of either of the traps. The traps were made of locally sourced materials, except the synthetic net of the Malian trap. About 81 and 80% of the respondents fabricated their Malian and Ndurutu traps, respectively. The major problems encountered in the structure and operation of the Malian trap included projection above water, stealing of catches and trap, and trapping of small sized fishes as indicated by 61.9, 47.6 and 28.6% of the respondents, respectively. In the case of the Ndurutu trap, 72.0, 48.0, 12.0 and 8.0% of the respondents respectively indicated poor durability, single entrance valve, destruction by cattle and instability in water, as the major problems encountered. As improvement measures for the Malian trap, the respondents suggested increase in number and size of valve (81.0%), horizontal positioning (57.1%) and square shape (47.6%) while 52.0% each suggested increase in number of entrance valve and netting of Ndurutu trap. The fishermen demonstrated ingenuity in the fabrication and operation of the traps, but they failed to initiate the required improvement. It is important to critically examine the designs, materials, costs and limitations of the traps and the suggestions of the fishermen, as basis for improvement on the technology of the traps

A theory of strong and weak scintillations with applications to astrophysics

The propagation of waves in an extended, irregular medium is studied under the "quasi-optics" and the "Markov random process" approximations. Under these assumptions, a Fokker-Planck equation satisfied by the characteristic functional of the random wave field is derived. A complete set of the moment equations with different transverse coordinates and different wavenumbers is then obtained from the characteristic functional. The derivation does not require Gaussian statistics of the random medium and the result can be applied to the time-dependent problem. We then solve the moment equations for the phase correlation function, angular broadening, temporal pulse smearing, intensity correlation function, and the probability distribution of the random waves. The necessary and sufficient conditions for strong scintillation are also given.

We also consider the problem of diffraction of waves by a random, phase-changing screen. The intensity correlation function is solved in the whole Fresnel diffraction region and the temporal pulse broadening function is derived rigorously from the wave equation.

The method of smooth perturbations is applied to interplanetary scintillations. We formulate and calculate the effects of the solar-wind velocity fluctuations on the observed intensity power spectrum and on the ratio of the observed "pattern" velocity and the true velocity of the solar wind in the three-dimensional spherical model. The r.m.s. solar-wind velocity fluctuations are found to be ~200 km/sec in the region about 20 solar radii from the Sun.

We then interpret the observed interstellar scintillation data using the theories derived under the Markov approximation, which are also valid for the strong scintillation. We find that the Kolmogorov power-law spectrum with an outer scale of 10 to 100 pc fits the scintillation data and that the ambient averaged electron density in the interstellar medium is about 0.025 cm^-3. It is also found that there exists a region of strong electron density fluctuation with thickness ~10 pc and mean electron density ~7 cm^-3 between the PSR 0833-45 pulsar and the earth.

History of Whaling and Estimated Kill of Right Whales, Balaena glacialis, in the Northeastern United States, 1620–1924

This study, part of a broader investigation of the history of exploitation of right whales, Balaena glacialis, in the western North Atlantic, emphasizes U.S. shore whaling from Maine to Delaware (from lat. 45°N to 38°30'N) in the period 1620–1924. Our broader study of the entire catch history is intended to provide an empirical basis for assessing past distribution and abundance of this whale population. Shore whaling may have begun at Cape Cod, Mass., in the 1620’s or 1630’s; it was certainly underway there by 1668. Right whale catches in New England waters peaked before 1725, and shore whaling at Cape Cod, Martha’s Vineyard, and Nantucket continued to decline through the rest of the 18th century. Right whales continued to be taken opportunistically in Massachusetts, however, until the early 20th century. They were hunted in Narragansett Bay, R.I., as early as 1662, and desultory whaling continued in Rhode Island until at least 1828. Shore whaling in Connecticut may have begun in the middle 1600’s, continuing there until at least 1718. Long Island shore whaling spanned the period 1650–1924. From its Dutch origins in the 1630’s, a persistent shore whaling enterprise developed in Delaware Bay and along the New Jersey shore. Although this activity was most profi table in New Jersey in the early 1700’s, it continued there until at least the 1820’s. Whaling in all areas of the northeastern United States was seasonal, with most catches in the winter and spring. Historically, right whales appear to have been essentially absent from coastal waters south of Maine during the summer and autumn. Based on documented references to specific whale kills, about 750–950 right whales were taken between Maine and Delaware, from 1620 to 1924. Using production statistics in British customs records, the estimated total secured catch of right whales in New England, New York, and Pennsylvania between 1696 and 1734 was 3,839 whales based on oil and 2,049 based on baleen. After adjusting these totals for hunting loss (loss-rate correction factor = 1.2), we estimate that 4,607 (oil) or 2,459 (baleen) right whales were removed from the stock in this region during the 38-year period 1696–1734. A cumulative catch estimate of the stock’s size in 1724 is 1,100–1,200. Although recent evidence of occurrence and movements suggests that right whales continue to use their traditional migratory corridor along the U.S. east coast, the catch history indicates that this stock was much larger in the 1600’s and early 1700’s than it is today. Right whale hunting in the eastern United States ended by the early 1900’s, and the species has been protected throughout the North Atlantic since the mid 1930’s. Among the possible reasons for the relatively slow stock recovery are: the very small number of whales that survived the whaling era to become founders, a decline in environmental carrying capacity, and, especially in recent decades, mortality from ship strikes and entanglement in fishing gear.

The Atlantic and Gulf Menhaden Purse Seine Fisheries: Origins, Harvesting Technologies, Biostatistical Monitoring, Recent Trends in Fisheries Statistics, and Forecasting

With its genesis in New England during the 1800's, the purse seine fishery for Atlantic menhaden, Brevoortia tyrannus, expanded south and by the early 1900's ranged the length of the eastern seaboard. The purse seine fishery for Gulf menhaden. B. patronus, is of relatively recent development, exploitation of the stock beginning in the late 1940's. Landings from both fisheries annually comprise 35-40% of the total U. S. fisheries landings, ranking menhaden first in terms of volume landed. Technological advances in harvesting methods, fish-spotting capabilities, and vessel designs accelerated after World War II, resulting in larger, faster, and wider-ranging carrier vessels, improved speed and efficiency of the harvest, and reduction in labor requirements. Chief products of the menhaden industry are fish meal, fish oil, and solubles, but research into new product lines is underway. Since 1955 on the Atlantic coast and 1964 on the Gulf coast, the NMFS has monitored the fisheries for biostatistical data. Annual data summaries of numbers-of-fish-at-age harvested, catch tonnage, and fishing effort of the fleet form the basis of routine stock assessments and annual catch forecasts to industry for the upcoming fishing season. After landings declined in the 1960's, the Atlantic menhaden stock has recovered through the 1970's and 1980's. Exceptional year classes of Gulf menhaden in recent years account for record landings during the 1980's.

Effects of water quality in Bassenthwaite Lake on anglers' catches of salmon and sea-trout in the River Derwent

This is the report on the Effects of Water Quality in the Bassenthwaite Lake on Anglers Catches of Salmon and Sea-trout in the River Derwent April 1993 by the Institute of Freshwater Ecology. An analysis of the catch statistics for salmon and sea-trout in the Rivers Derwent and Cocker was undertaken in relation to available information on the algal water quality in Bassenthwaite Lake to test the hypothesis that poor catch returns were associated with a deterioration of water quality within the lake. Analysis of the catch statistics failed to reveal any correlation between water quality and catch returns for either species of fish and it is concluded that any water deterioration in Bassenthwaite Lake has not caused any major damage to the salmon and sea trout fisheries of the Derwent/Cocker system. This conclusion is supported by the analysis of the Windermere/Leven and Crake system, where no correlation could be found between lake water quality and downstream catches of migratory salmonid fish. However, the possibility still exists and such an effect might be detected by further field work on the macroinvertebrates and on the composition of potential salmonid spawning in the area.

Scientific statistics and graphics on the Macintosh

The personal computer has become commonplace on the desk of most scientists. As hardware costs have plummeted, software capabilities have expanded enormously, permitting the scientist to examine extremely large datasets in novel ways. Advances in networking now permit rapid transfer of large datasets, which can often be used unchanged from one machine to the next. In spite of these significant advances, many scientists still use their personal computers only for word processing or e-mail, or as "dumb terminals". Many are simply unaware of the richness of software now available to statistically analyze and display scientific data in highly innovative ways. This paper presents several examples drawn from actual climate data analysis that illustrate some novel and practical features of several widely-used software packages for Macintosh computers.

Techno-economic analysis of production and marketing of marine by-products in India

Marine by-products coming under the ancillary products group found many applications in pharmaceutical and industrial sectors. Although many of these products are fetching very high price at the export market, adequate statistics regarding their current production, marketing and utilisation is lacking. The present analysis deals with the production potential, level of exploitation, uses, export growth rate and potential for the future of some of these marine by-products. The analysis revealed that an estimated quantity of 205 t. of shells, 10 t. of gastropod operculum, 4,932 t. of shark liver oil and 4,384 t. of shark cartilage could be produced annually in India with the current landings. The production potential of chitin is estimated as 3,560 t. from shrimp shell wastes and 1,354 t. from crab shell wastes. The high unit value of different products clearly indicates the scope for their development by evolving appropriate utilisation and marketing strategies.

Identification of biodiversity and distribution pattern of benthic Foraminifera and Ostracoda in continental shelf sediments of the Oman Sea

Biodiversity and distribution of benthic Foraminifera and Ostracoda in the continental shelf sediments of the Omman Sea was studied in order to indicating of the composition of benthic foraminiferal and ostracodal communities and determining of their relationship with the environmental factors of the Omman Sea. Sediment samples were gathered in winter 2006 from twelve stations ranging in depth from 30 to 103 meters. Environmental factors including depth, temperature, salinity, dissolved Oxygen and pH were measured with a CTD system during sampling time and grain size and total organic matter were measured in laboratory. From the overall 57 benthic foram species, there were 52 identified species belong to 25 genera of 16 families. The cosmopolitan foraminifer, Ammonia beccarii, was common in all sampling stations. The composition of benthic foram communities had a highly positive correlation with depth, salinity and total organic matter. From the overall 30 ostracod species, there were 26 identified species belong to 22 genera of 13 families. Diversity and aboundance of ostracoda of the Oman Sea decreased from east to west and from south to north but increased slightly in the northwest (near the Strait of Hormoz). Ostracoda of the genus Propontocypris were common in all sampling stations but the genera Cyprideis, Paradoxostom and Hemicytheridea were rare in the Oman Sea. Diversity and aboundance of ostracoda in northern regions were less than southern and were less than foraminifera too. The composition of ostracodal communities had a highly positive correlation with dept, salinity and grain size. Biodiversity and distribution pattern of benthic foraminifera and ostracoda were being different in various sampling stations, especially between northern and southern regions. Water depth, salinity and structure of the sediments were the most important abiotic factors controlling the distribution pattern of benthic foraminifera and ostracoda in the Omman Sea. None existence or rare observation of structural abnormalities and oil polluted individuals in the vicinity of all sampling stations, resulted to the "clean" benthic environment of the Omman Sea.