Umbral Calculus, Discretization, and Quantum Mechanics on a Lattice

`Umbral calculus' deals with representations of the canonical commutation relations. We present a short exposition of it and discuss how this calculus can be used to discretize continuum models and to construct representations of Lie algebras on a lattice. Related ideas appeared in recent publications and we show that the examples treated there are special cases of umbral calculus. This observation then suggests various generalizations of these examples. A special umbral representation of the canonical commutation relations given in terms of the position and momentum operator on a lattice is investigated in detail.Comment: 19 pages, Late

Seismic imaging in Long Valley, California, by surface and borehole techniques: An investigation of active tectonics

The search for silicic magma in the upper crust is converging on the Long Valley Caldera of eastern California, where several lines of geophysical evidence show that an active magma chamber exists at mid‐to lower‐crustal depths. There are also other strong indications that magma may be present at depths no greater than about 5 km below the surface. In this paper, we review the history of the search for magma at Long Valley. We also present the preliminary results from a coordinated suite of seismic experiments, conducted by a consortium of institutions in the summer and fall of 1984, that were designed to refine our knowledge of the upper extent of the magma chamber. Major funding for the experiments was provided by the Geothermal Research Program of the U.S. Geological Survey (USGS) and by the Magma Energy Technology Program of the U.S. Department of Energy (DOE), a program to develop the technology necessary to extract energy directly from crustal magma. Additional funding came from DOE's Office of Basic Energy Sciences and the National Science Foundation (NSF). Also, because extensive use was made of a 0.9‐km‐deep well lent to us by Santa Fe Geothermal, Inc., the project was conducted partly under the auspices of the Continental Scientific Drilling Program (CSDP). As an integrated seismic study of the crust within the caldera that involved the close cooperation of a large number of institutions, the project was moreover viewed as a prototype for future scientific experiments to be conducted under the Program for Array Seismic Studies of the Continental Lithosphere (PASSCAL). The experiment thus represented a unique blend of CSDP and PASSCAL methods, and achieved goals consistent with both programs

Seismic imaging in Long Valley, California, by surface and borehole techniques: An investigation of active tectonics

The search for silicic magma in the upper crust is converging on the Long Valley Caldera of eastern California, where several lines of geophysical evidence show that an active magma chamber exists at mid‐to lower‐crustal depths. There are also other strong indications that magma may be present at depths no greater than about 5 km below the surface. In this paper, we review the history of the search for magma at Long Valley. We also present the preliminary results from a coordinated suite of seismic experiments, conducted by a consortium of institutions in the summer and fall of 1984, that were designed to refine our knowledge of the upper extent of the magma chamber. Major funding for the experiments was provided by the Geothermal Research Program of the U.S. Geological Survey (USGS) and by the Magma Energy Technology Program of the U.S. Department of Energy (DOE), a program to develop the technology necessary to extract energy directly from crustal magma. Additional funding came from DOE's Office of Basic Energy Sciences and the National Science Foundation (NSF). Also, because extensive use was made of a 0.9‐km‐deep well lent to us by Santa Fe Geothermal, Inc., the project was conducted partly under the auspices of the Continental Scientific Drilling Program (CSDP). As an integrated seismic study of the crust within the caldera that involved the close cooperation of a large number of institutions, the project was moreover viewed as a prototype for future scientific experiments to be conducted under the Program for Array Seismic Studies of the Continental Lithosphere (PASSCAL). The experiment thus represented a unique blend of CSDP and PASSCAL methods, and achieved goals consistent with both programs

A Molecular Signature of Proteinuria in Glomerulonephritis

Proteinuria is the most important predictor of outcome in glomerulonephritis and experimental data suggest that the tubular cell response to proteinuria is an important determinant of progressive fibrosis in the kidney. However, it is unclear whether proteinuria is a marker of disease severity or has a direct effect on tubular cells in the kidneys of patients with glomerulonephritis. Accordingly we studied an in vitro model of proteinuria, and identified 231 “albumin-regulated genes” differentially expressed by primary human kidney tubular epithelial cells exposed to albumin. We translated these findings to human disease by studying mRNA levels of these genes in the tubulo-interstitial compartment of kidney biopsies from patients with IgA nephropathy using microarrays. Biopsies from patients with IgAN (n = 25) could be distinguished from those of control subjects (n = 6) based solely upon the expression of these 231 “albumin-regulated genes.” The expression of an 11-transcript subset related to the degree of proteinuria, and this 11-mRNA subset was also sufficient to distinguish biopsies of subjects with IgAN from control biopsies. We tested if these findings could be extrapolated to other proteinuric diseases beyond IgAN and found that all forms of primary glomerulonephritis (n = 33) can be distinguished from controls (n = 21) based solely on the expression levels of these 11 genes derived from our in vitro proteinuria model. Pathway analysis suggests common regulatory elements shared by these 11 transcripts. In conclusion, we have identified an albumin-regulated 11-gene signature shared between all forms of primary glomerulonephritis. Our findings support the hypothesis that albuminuria may directly promote injury in the tubulo-interstitial compartment of the kidney in patients with glomerulonephritis

Dissecting the Shared Genetic Architecture of Suicide Attempt, Psychiatric Disorders, and Known Risk Factors

Background Suicide is a leading cause of death worldwide, and nonfatal suicide attempts, which occur far more frequently, are a major source of disability and social and economic burden. Both have substantial genetic etiology, which is partially shared and partially distinct from that of related psychiatric disorders. Methods We conducted a genome-wide association study (GWAS) of 29,782 suicide attempt (SA) cases and 519,961 controls in the International Suicide Genetics Consortium (ISGC). The GWAS of SA was conditioned on psychiatric disorders using GWAS summary statistics via multitrait-based conditional and joint analysis, to remove genetic effects on SA mediated by psychiatric disorders. We investigated the shared and divergent genetic architectures of SA, psychiatric disorders, and other known risk factors. Results Two loci reached genome-wide significance for SA: the major histocompatibility complex and an intergenic locus on chromosome 7, the latter of which remained associated with SA after conditioning on psychiatric disorders and replicated in an independent cohort from the Million Veteran Program. This locus has been implicated in risk-taking behavior, smoking, and insomnia. SA showed strong genetic correlation with psychiatric disorders, particularly major depression, and also with smoking, pain, risk-taking behavior, sleep disturbances, lower educational attainment, reproductive traits, lower socioeconomic status, and poorer general health. After conditioning on psychiatric disorders, the genetic correlations between SA and psychiatric disorders decreased, whereas those with nonpsychiatric traits remained largely unchanged. Conclusions Our results identify a risk locus that contributes more strongly to SA than other phenotypes and suggest a shared underlying biology between SA and known risk factors that is not mediated by psychiatric disorders.Peer reviewe