Stein's Method and Characters of Compact Lie Groups

Stein's method is used to study the trace of a random element from a compact Lie group or symmetric space. Central limit theorems are proved using very little information: character values on a single element and the decomposition of the square of the trace into irreducible components. This is illustrated for Lie groups of classical type and Dyson's circular ensembles. The approach in this paper will be useful for the study of higher dimensional characters, where normal approximations need not hold.Comment: 22 pages; same results, but more efficient exposition in Section 3.

From Quantum Systems to L-Functions: Pair Correlation Statistics and Beyond

The discovery of connections between the distribution of energy levels of heavy nuclei and spacings between prime numbers has been one of the most surprising and fruitful observations in the twentieth century. The connection between the two areas was first observed through Montgomery's work on the pair correlation of zeros of the Riemann zeta function. As its generalizations and consequences have motivated much of the following work, and to this day remains one of the most important outstanding conjectures in the field, it occupies a central role in our discussion below. We describe some of the many techniques and results from the past sixty years, especially the important roles played by numerical and experimental investigations, that led to the discovery of the connections and progress towards understanding the behaviors. In our survey of these two areas, we describe the common mathematics that explains the remarkable universality. We conclude with some thoughts on what might lie ahead in the pair correlation of zeros of the zeta function, and other similar quantities.Comment: Version 1.1, 50 pages, 6 figures. To appear in "Open Problems in Mathematics", Editors John Nash and Michael Th. Rassias. arXiv admin note: text overlap with arXiv:0909.491

The lowest eigenvalue of Jacobi random matrix ensembles and Painlev\'e VI

We present two complementary methods, each applicable in a different range, to evaluate the distribution of the lowest eigenvalue of random matrices in a Jacobi ensemble. The first method solves an associated Painleve VI nonlinear differential equation numerically, with suitable initial conditions that we determine. The second method proceeds via constructing the power-series expansion of the Painleve VI function. Our results are applied in a forthcoming paper in which we model the distribution of the first zero above the central point of elliptic curve L-function families of finite conductor and of conjecturally orthogonal symmetry.Comment: 30 pages, 2 figure

Increasing subsequences and the hard-to-soft edge transition in matrix ensembles

Our interest is in the cumulative probabilities Pr(L(t) \le l) for the maximum length of increasing subsequences in Poissonized ensembles of random permutations, random fixed point free involutions and reversed random fixed point free involutions. It is shown that these probabilities are equal to the hard edge gap probability for matrix ensembles with unitary, orthogonal and symplectic symmetry respectively. The gap probabilities can be written as a sum over correlations for certain determinantal point processes. From these expressions a proof can be given that the limiting form of Pr(L(t) \le l) in the three cases is equal to the soft edge gap probability for matrix ensembles with unitary, orthogonal and symplectic symmetry respectively, thereby reclaiming theorems due to Baik-Deift-Johansson and Baik-Rains.Comment: LaTeX, 19 page

A Random Matrix Model for Elliptic Curve L-Functions of Finite Conductor

We propose a random matrix model for families of elliptic curve L-functions of finite conductor. A repulsion of the critical zeros of these L-functions away from the center of the critical strip was observed numerically by S. J. Miller in 2006; such behaviour deviates qualitatively from the conjectural limiting distribution of the zeros (for large conductors this distribution is expected to approach the one-level density of eigenvalues of orthogonal matrices after appropriate rescaling).Our purpose here is to provide a random matrix model for Miller's surprising discovery. We consider the family of even quadratic twists of a given elliptic curve. The main ingredient in our model is a calculation of the eigenvalue distribution of random orthogonal matrices whose characteristic polynomials are larger than some given value at the symmetry point in the spectra. We call this sub-ensemble of SO(2N) the excised orthogonal ensemble. The sieving-off of matrices with small values of the characteristic polynomial is akin to the discretization of the central values of L-functions implied by the formula of Waldspurger and Kohnen-Zagier.The cut-off scale appropriate to modeling elliptic curve L-functions is exponentially small relative to the matrix size N. The one-level density of the excised ensemble can be expressed in terms of that of the well-known Jacobi ensemble, enabling the former to be explicitly calculated. It exhibits an exponentially small (on the scale of the mean spacing) hard gap determined by the cut-off value, followed by soft repulsion on a much larger scale. Neither of these features is present in the one-level density of SO(2N). When N tends to infinity we recover the limiting orthogonal behaviour. Our results agree qualitatively with Miller's discrepancy. Choosing the cut-off appropriately gives a model in good quantitative agreement with the number-theoretical data.Comment: 38 pages, version 2 (added some plots

Canonical moments and random spectral measures

We study some connections between the random moment problem and the random matrix theory. A uniform draw in a space of moments can be lifted into the spectral probability measure of the pair (A,e) where A is a random matrix from a classical ensemble and e is a fixed unit vector. This random measure is a weighted sampling among the eigenvalues of A. We also study the large deviations properties of this random measure when the dimension of the matrix grows. The rate function for these large deviations involves the reversed Kullback information.Comment: 32 pages. Revised version accepted for publication in Journal of Theoretical Probabilit

Impact of 25 years of grazing exclusion and shrub removal on plant community structure and soil characteristics in a xerophytic rangeland

Aim of study: We tested the hypothesis that long periods of grazing exclusion in areas with a history of high grazing intensity will have a positive impact on soil nutrient conditions and favor soil infiltration, increase biomass and lead to a recovery in vegetation.Area of study: Noria de Guadalupe, Zacatecas, Mexico.Material and methods: We analyzed the impact of grazing exclusion on biomass, species richness, evenness, soil nutrient content and soil water infiltration after 25 years of exclusion during each of the four seasons by  excluding two 15 × 15 m plots of grazing and compared with two control plots.Main results: Exclusion management did not lead to biomass increases; however, it did lead to an important recovery in the plant community. Moreover, soil nutrient content was more affected by the seasonality of rainfall in the study site than by 25 years of exclusion. The elimination of dominant shrubs in the excluded area led to a faster recovery in palatable shrubs and shortgrass vegetation, which was improved by better infiltration values during the end of spring and summer explaining some of the differences in nutrient avaibility.Research highlights: In our study, exclusion management can lead to an important recovery in vegetation without affecting the growth of Atriplex canescens, a valuable source of fodder. Although biomass presented a higher dependence on seasonality and was not related to the treatment, the impact on the forage quality is evident by the different plant communities established after 25 years of exclusion

Caracterização de confiscos de vísceras vermelhas num frigorífico de exportação em Santander – Colômbia

Red viscera confiscation represents a significant cause of economic loss for the meat products’ trade. This study was aimed at determining the causes and epidemiological variables associated with red viscera confiscation in a slaughterhouse (FRIGORÍFICO RÍO FRÍO (FRF)) located in Floridablanca, in Colombia’s Santander department, and estimating the value of the economic losses associated with such confiscation. A cross-sectional study was carried out between November and December 2018 based on epidemiological information regarding all animals slaughtered at the FRF recorded after routine health inspection by Colombian Food and Drug Surveillance Institute (INVIMA) officials. Frequency analysis was used for estimating the main causes of and the epidemiological variables associated with red viscera confiscation whilst economic losses were estimated by national market analysis. It was found that red viscera were confiscated in 15.8% of 8,671 sacrificed cattle compared to 26.5% for 226 buffaloes. The lungs (87.4%), liver (11.1%) and spleen (0.6%) were the main organs seized for cattle and lungs (88.3%), liver (8.3%) and kidneys (1.7%) for buffaloes. Bronchoaspiration (86.6%) and emphysema (9.4%) were the main causes of confiscation regarding the lungs in both species while for the liver these were abscesses (40.5%) and hepatic dystomatosis (28.8%) in cattle and fatty liver (80.0%) and cirrhosis (20.0%) in buffaloes. There were significant differences regarding the percentage of cattle having hepatic dystomatosis amongst municipalities in the Santander department (χ²=50.03, p<0.05). Lung (4,886 USD) and liver confiscation (2,639 USD) led to the greatest economic losses; the lungs were the main organ confiscated in both species, mainly being associated with bronchoaspiration. Future intervention strategies are needed to reduce the livestock industry’s financial losses, aimed at reducing bronchoaspiration in animals in the slaughterhouse and interrupting Fasciola hepatica’s life-cycle in some municipalities in the Santander department.A nivel mundial el decomiso de vísceras rojas es una de las principales causas de pérdidas económicas en la comercialización de productos cárnicos. El objetivo del presente estudio fue determinar las principales causas y variables epidemiológicas asociadas al decomiso de vísceras rojas en el FRIGORÍFICO RÍO FRÍO (FRF), del municipio de Floridablanca, Santander y estimar el valor de las pérdidas económicas asociadas a esta actividad. Entre 9 de noviembre al 9 de diciembre de 2018, se realizó un estudio transversal en el total de animales sacrificados en el FRF, a los cuales se les recolectó información epidemiológica posterior a la inspección sanitaria realizada por funcionarios del INVIMA. Las principales causas y variables epidemiológicas asociadas al decomiso de vísceras rojas se estimaron a partir de análisis de frecuencias, mientras el valor de las pérdidas económicas, a través de un análisis económico en el mercado nacional. Se sacrificaron un total de 8671 bovinos, y 226 búfalos, en los cuales se realizó el decomiso de vísceras rojas en el 15,8% y 26,5% de los animales, respectivamente. En los bovinos los principales órganos decomisados fueron pulmón, hígado y bazo con porcentajes del 87,4%, 11,1% y 0,6%, respectivamente. Mientras que, en los búfalos, fueron el pulmón, hígado y riñón con porcentajes del 88,3%, 8,3% y 1,7%, respectivamente. Las principales causas de decomiso de pulmón en ambas especies fueron la broncoaspiración (86,6%) y enfisema (9,4%), mientras para el hígado fueron los abscesos (40,5%) y la distomatosis hepática (28,8%) en los bovinos, hígado graso (80,0%) y cirrosis (20,0%) en los búfalos. Para el caso de los bovinos, hubo diferencias significativas en la proporción de animales con distomatosis hepática entre los diferentes municipios de Santander (χ² = 50.03, P < 0.05). Las mayores pérdidas económicas durante el periodo de estudio se deben al decomiso de pulmón e hígado con valores de 4886 y 2639 USD. En conclusión, el pulmón fue el órgano decomisado con mayor frecuencia en ambas especies, principalmente asociado a la broncoaspiración. Futuras estrategias de intervención, con el fin de reducir la broncoaspiración en los animales que ingresan a la planta de beneficio, e interrumpir el ciclo de vida de Fasciola hepatica en algunos municipios de Santander, son necesarios para disminuir el nivel de pérdidas económicas a lo largo de la cadena productiva.Globalmente, os confiscos de órgãos e vísceras vermelhas é uma das principais causas de perdas econômicas na comercialização de produtos à base de carne. O objetivo deste estudo foi determinar as principais causas e variáveis epidemiológicas associadas aos confiscos de vísceras vermelhas num frigorífico (FRIGORÍFICO RÍO FRÍO (FRF)), do município de Floridablanca, Santander, e estimar o valor das perdas econômicas associadas a esta atividade. Entre 9 de novembro e 9 de dezembro do 2018, foi realizado um estudo transversal sobre o total de animais abatidos no FRF, nos quais a informação epidemiológica era diligenciada depois da inspeção sanitária realizada pelos funcionários do INVIMA. As principais causas e variáveis epidemiológicas associadas ao confisco de vísceras vermelhas foram estimadas a partir da análise de freqüência, e o valor de perdas econômicas, através de uma análise no mercado nacional. Foram abatidos 8.671 bovinos e 226 búfalos, nos quais 15,8% e 26,5% tiveram confiscos de vísceras vermelhas, respectivamente. Em bovinos, as principais vísceras confiscadas, foram pulmões, fígado e baço com percentagens de 87,4%, 11,1% e 0,6%, respectivamente. Nos búfalos, foram pulmões, fígado e rim com porcentagens de 88,3%, 8,3% e 1,7%, respectivamente. Para as duas espécies, broncoaspiração (86,6%) e enfisema (9,4%) foram as principais causas de confiscos dos pulmões. Para o fígado, foram os abcessos (40,5%) e fasciolose (28,8%) em bois, esteatose hepática (80,0%) e cirrose (20,0%) em búfalos. No caso dos bois, houve diferenças significativas na proporção de animais com fasciolose nos diferentes municípios do Santander (χ² = 50,03, P <0,05). As maiores perdas econômicas durante o período de estudo correspondem ao confisco de pulmão e fígado com valores de 4886 e 2639 USD. Em conclusão, o pulmão foi a principal víscera confiscada em ambas espécies, principalmente associados a broncoaspiração. Estratégias futuras de intervenção, com o objetivo de reduzir a broncoaspiração, e interromper o ciclo de vida da Fasciola hepatica em alguns municípios do Santander são necessários para reduzir as perdas econômicas na cadeia de produção

Characterising red viscera confiscation in an export slaughterhouse in Santander, Colombia

A nivel mundial el decomiso de vísceras rojas es una de las principales causas de pérdidas económicas en la comercialización de productos cárnicos. El objetivo del presente estudio fue determinar las principales causas y variables epidemiológicas asociadas al decomiso de vísceras rojas en el FRIGORÍFICO RÍO FRÍO (FRF), del municipio de Floridablanca, Santander y estimar el valor de las pérdidas económicas asociadas a esta actividad. Entre 9 de noviembre al 9 de diciembre de 2018, se realizó un estudio transversal en el total de animales sacrificados en el FRF, a los cuales se les recolectó información epidemiológica posterior a la inspección sanitaria realizada por funcionarios del INVIMA. Las principales causas y variables epidemiológicas asociadas al decomiso de vísceras rojas se estimaron a partir de análisis de frecuencias, mientras el valor de las pérdidas económicas, a través de un análisis económico en el mercado nacional. Se sacrificaron un total de 8671 bovinos, y 226 búfalos, en los cuales se realizó el decomiso de vísceras rojas en el 15,8% y 26,5% de los animales, respectivamente. En los bovinos los principales órganos decomisados fueron pulmón, hígado y bazo con porcentajes del 87,4%, 11,1% y 0,6%, respectivamente. Mientras que, en los búfalos, fueron el pulmón, hígado y riñón con porcentajes del 88,3%, 8,3% y 1,7%, respectivamente. Las principales causas de decomiso de pulmón en ambas especies fueron la broncoaspiración (86,6%) y enfisema (9,4%), mientras para el hígado fueron los abscesos (40,5%) y la distomatosis hepática (28,8%) en los bovinos, hígado graso (80,0%) y cirrosis (20,0%) en los búfalos. Para el caso de los bovinos, hubo diferencias significativas en la proporción de animales con distomatosis hepática entre los diferentes municipios de Santander (χ² = 50.03, P < 0.05). Las mayores pérdidas económicas durante el periodo de estudio se deben al decomiso de pulmón e hígado con valores de 4886 y 2639 USD. En conclusión, el pulmón fue el órgano decomisado con mayor frecuencia en ambas especies, principalmente asociado a la broncoaspiración. Futuras estrategias de intervención, con el fin de reducir la broncoaspiración en los animales que ingresan a la planta de beneficio, e interrumpir el ciclo de vida de Fasciola hepatica en algunos municipios de Santander, son necesarios para disminuir el nivel de pérdidas económicas a lo largo de la cadena productiva.Red viscera confiscation represents a significant cause of economic loss for the meat products’ trade. This study was aimed at determining the causes and epidemiological variables associated with red viscera confiscation in a slaughterhouse (FRIGORÍFICO RÍO FRÍO (FRF)) located in Floridablanca, in Colombia’s Santander department, and estimating the value of the economic losses associated with such confiscation. A cross-sectional study was carried out between November and December 2018 based on epidemiological information regarding all animals slaughtered at the FRF recorded after routine health inspection by Colombian Food and Drug Surveillance Institute (INVIMA) officials. Frequency analysis was used for estimating the main causes of and the epidemiological variables associated with red viscera confiscation whilst economic losses were estimated by national market analysis. It was found that red viscera were confiscated in 15.8% of 8,671 sacrificed cattle compared to 26.5% for 226 buffaloes. The lungs (87.4%), liver (11.1%) and spleen (0.6%) were the main organs seized for cattle and lungs (88.3%), liver (8.3%) and kidneys (1.7%) for buffaloes. Bronchoaspiration (86.6%) and emphysema (9.4%) were the main causes of confiscation regarding the lungs in both species while for the liver these were abscesses (40.5%) and hepatic dystomatosis (28.8%) in cattle and fatty liver (80.0%) and cirrhosis (20.0%) in buffaloes. There were significant differences regarding the percentage of cattle having hepatic dystomatosis amongst municipalities in the Santander department (χ²=50.03, p<0.05). Lung (4,886 USD) and liver confiscation (2,639 USD) led to the greatest economic losses; the lungs were the main organ confiscated in both species, mainly being associated with bronchoaspiration. Future intervention strategies are needed to reduce the livestock industry’s financial losses, aimed at reducing bronchoaspiration in animals in the slaughterhouse and interrupting Fasciola hepatica’s life-cycle in some municipalities in the Santander department