Poisson Statistics for the Largest Eigenvalues in Random Matrix Ensemble

The paper studies the spectral properties of large Wigner, band and sample covariance random matrices with heavy tails of the marginal distributions of matrix entries.Comment: This is an extended version of my talk at the QMath 9 conference at Giens, France on September 13-17, 200

Supersymmetry approach to Wishart correlation matrices: Exact results

We calculate the `one-point function', meaning the marginal probability density function for any single eigenvalue, of real and complex Wishart correlation matrices. No explicit expression had been obtained for the real case so far. We succeed in doing so by using supersymmetry techniques to express the one-point function of real Wishart correlation matrices as a twofold integral. The result can be viewed as a resummation of a series of Jack polynomials in a non-trivial case. We illustrate our formula by numerical simulations. We also rederive a known expression for the one-point function of complex Wishart correlation matrices.Comment: 21 pages, 2 figure

Track E Implementation Science, Health Systems and Economics

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/138412/1/jia218443.pd

Economies of scale in the production of swine manure Economias de escala na produção de dejetos de suínos

Manure production on grower/finisher swine operations in the United States was examined using data from 184 grower/finisher swine operations that participated in the United States National Animal Health Monitoring System's 1995 National Swine Study. Two methods were used: one, assuming that pigs produced 8.4% of their body weight in manure each day; another using the difference between feed fed and weight gained as a proxy variable to study manure production. Using this latter approach, a production function was developed. The function exhibited diminishing returns to scale when food waste was not fed to pigs, but constant returns to scale when food waste was included in their diets. The difference between feed fed and weight gained was lower on operations that restricted entry to employees only.<br>A produção de dejetos em granjas de crescimento e terminação de suínos nos Estados Unidos foi avaliada utilizando dados de 184 granjas participantes de um estudo nacional de 1995 do "United States National Animal Health Monitoring System". Dois métodos foram usados: um considerando que suínos produzem 8,4% do seu peso corporal de dejetos por dia e o outro usando a diferença entre o alimento ingerido e o ganho de peso como um indicador para o estudo da produção de esterco. Através desse último procedimento, desenvolveu-se uma função de produção

Biallelic Variants in the Ectonucleotidase ENTPD1 Cause a Complex Neurodevelopmental Disorder with Intellectual Disability, Distinct White Matter Abnormalities, and Spastic Paraplegia

Objective Human genomics established that pathogenic variation in diverse genes can underlie a single disorder. For example, hereditary spastic paraplegia is associated with >80 genes, with frequently only few affected individuals described for each gene. Herein, we characterize a large cohort of individuals with biallelic variation in ENTPD1, a gene previously linked to spastic paraplegia 64 (Mendelian Inheritance in Man # 615683). Methods Individuals with biallelic ENTPD1 variants were recruited worldwide. Deep phenotyping and molecular characterization were performed. Results A total of 27 individuals from 17 unrelated families were studied; additional phenotypic information was collected from published cases. Twelve novel pathogenic ENTPD1 variants are described (NM 001776.6): c.398_399delinsAA; p.(Gly133Glu), c.540del; p.(Thr181Leufs*18), c.640del; p.(Gly216Glufs*75), c.185 T > G; p.(Leu62*), c.1531 T > C; p.(*511Glnext*100), c.967C > T; p.(Gln323*), c.414-2_414-1del, and c.146 A > G; p.(Tyr49Cys) including 4 recurrent variants c.1109 T > A; p.(Leu370*), c.574-6_574-3del, c.770_771del; p.(Gly257Glufs*18), and c.1041del; p.(Ile348Phefs*19). Shared disease traits include childhood onset, progressive spastic paraplegia, intellectual disability (ID), dysarthria, and white matter abnormalities. In vitro assays demonstrate that ENTPD1 expression and function are impaired and that c.574-6_574-3del causes exon skipping. Global metabolomics demonstrate ENTPD1 deficiency leads to impaired nucleotide, lipid, and energy metabolism. Interpretation The ENTPD1 locus trait consists of childhood disease onset, ID, progressive spastic paraparesis, dysarthria, dysmorphisms, and white matter abnormalities, with some individuals showing neurocognitive regression. Investigation of an allelic series of ENTPD1 (1) expands previously described features of ENTPD1-related neurological disease, (2) highlights the importance of genotype-driven deep phenotyping, (3) documents the need for global collaborative efforts to characterize rare autosomal recessive disease traits, and (4) provides insights into disease trait neurobiology. ANN NEUROL 202