A study of singularities on rational curves via syzygies

Consider a rational projective curve C of degree d over an algebraically closed field k. There are n homogeneous forms g_1,...,g_n of degree d in B=k[x,y] which parameterize C in a birational, base point free, manner. We study the singularities of C by studying a Hilbert-Burch matrix phi for the row vector [g_1,...,g_n]. In the "General Lemma" we use the generalized row ideals of phi to identify the singular points on C, their multiplicities, the number of branches at each singular point, and the multiplicity of each branch. Let p be a singular point on the parameterized planar curve C which corresponds to a generalized zero of phi. In the "Triple Lemma" we give a matrix phi' whose maximal minors parameterize the closure, in projective 2-space, of the blow-up at p of C in a neighborhood of p. We apply the General Lemma to phi' in order to learn about the singularities of C in the first neighborhood of p. If C has even degree d=2c and the multiplicity of C at p is equal to c, then we apply the Triple Lemma again to learn about the singularities of C in the second neighborhood of p. Consider rational plane curves C of even degree d=2c. We classify curves according to the configuration of multiplicity c singularities on or infinitely near C. There are 7 possible configurations of such singularities. We classify the Hilbert-Burch matrix which corresponds to each configuration. The study of multiplicity c singularities on, or infinitely near, a fixed rational plane curve C of degree 2c is equivalent to the study of the scheme of generalized zeros of the fixed balanced Hilbert-Burch matrix phi for a parameterization of C.Comment: Typos corrected and minor changes made. To appear in the Memoirs of the AM

A PSPACE Construction of a Hitting Set for the Closure of Small Algebraic Circuits

In this paper we study the complexity of constructing a hitting set for the closure of VP, the class of polynomials that can be infinitesimally approximated by polynomials that are computed by polynomial sized algebraic circuits, over the real or complex numbers. Specifically, we show that there is a PSPACE algorithm that given n,s,r in unary outputs a set of n-tuples over the rationals of size poly(n,s,r), with poly(n,s,r) bit complexity, that hits all n-variate polynomials of degree-r that are the limit of size-s algebraic circuits. Previously it was known that a random set of this size is a hitting set, but a construction that is certified to work was only known in EXPSPACE (or EXPH assuming the generalized Riemann hypothesis). As a corollary we get that a host of other algebraic problems such as Noether Normalization Lemma, can also be solved in PSPACE deterministically, where earlier only randomized algorithms and EXPSPACE algorithms (or EXPH assuming the generalized Riemann hypothesis) were known. The proof relies on the new notion of a robust hitting set which is a set of inputs such that any nonzero polynomial that can be computed by a polynomial size algebraic circuit, evaluates to a not too small value on at least one element of the set. Proving the existence of such a robust hitting set is the main technical difficulty in the proof. Our proof uses anti-concentration results for polynomials, basic tools from algebraic geometry and the existential theory of the reals

Lung transplantation and survival in children with cystic fibrosis

Journal ArticleThe effects of lung transplantation on the survival and quality of life in children with cystic fibrosis are uncertain. We used data from the U.S. Cystic Fibrosis Foundation Patient Registry and from the Organ Procurement and Transplantation Network to identify children with cystic fibrosis who were on the waiting list for lung transplantation during the period from 1992 through 2002. We performed proportional-hazards survival modeling, using multiple clinically relevant covariates that were available before the children were on the waiting list and the interactions of these covariates with lung transplantation as a time-dependent covariate. The data were insufficient in quality and quantity for a retrospective quality-of-life analysis

Functional Analysis of the Neurofibromatosis Type 2 Protein by Means of Disease-Causing Point Mutations

Despite intense study of the neurofibromatosis type 2 (NF2) tumor-suppressor protein merlin, the biological properties and tumor-suppressor functions of merlin are still largely unknown. In this study, we examined the molecular activities of NF2-causing mutant merlin proteins in transfected mammalian cells, to elucidate the merlin properties that are critical for tumor-suppressor function. Most important, we found that 80% of the merlin mutants studied significantly altered cell adhesion, causing cells to detach from the substratum. This finding implies a function for merlin in regulating cell-matrix attachment, and changes in cell adhesion caused by mutant protein expression may be an initial step in the pathogenesis of NF2. In addition, five different mutations in merlin caused a significant increase in detergent solubility of merlin compared to wild type, indicating a decreased ability to interact with the cytoskeleton. Although not correlated to the cell-adhesion phenotype, four missense mutations decreased the binding of merlin to the ERM-interacting protein EBP-50, implicating this interaction in merlin inhibition of cell growth. Last, we found that some NF2 point mutations in merlin most closely resembled gain-of-function alleles in their cellular phenotype, which suggests that mutant NF2 alleles may not always act in a loss-of-function manner, as had been assumed, but may include a spectrum of allelic types with different phenotypic effects on the function of the protein. In aggregate, these cellular phenotypes provide a useful assay for identifying the functional domains and molecular partners necessary for merlin tumor-suppressor activity

Occupational Component Analysis in Agricultural Mechanization: A Research Project of the Department of Agricultural Education

This item is part of the Agricultural Experiment Station archive. It was digitized from a physical copy provided by the University Libraries at the University of Arizona. For more information, please email CALS Publications at [email protected]

Downward shortwave surface irradiance from 17 sites for the FIRE/SRB Wisconsin experiment

A field experiment was conducted in Wisconsin during Oct. to Nov. 1986 for purposes of both intensive cirrus cloud measurments and SRB algorithm validation activities. The cirrus cloud measurements were part of the FIRE. Tables are presented which show data from 17 sites in the First ISCCP (International Satellite Cloud Climatology Project) Regional Experiment/Surface Radiation Budget (FIRE/SRB) Wisconsin experiment region. A discussion of intercomparison results and calibration inconsistencies is also included

Requested, Recommended and Allowed Returns to Equity: Serendipity or Substance

R. Charles Moyer is Professor of Finance and Chairman of the Area of Finance in the College of Business Administration. Texas Tech University. Raymond E. Spudeck is an Assistant Professor in the Department of Finance, College of Commerce and lndlustry at the University of Wyoming. David B. Cox is an Instructor in the Area of Finance in the College of Business Administration at Texas Tech University

Second-Hand Stress: Neurobiological Evidence for a Human Alarm Pheromone

Alarm pheromones are airborne chemical signals, released by an individual into the environment, which transmit warning of danger to conspecifics via olfaction. Using fMRI, we provide the first neurobiological evidence for a human alarm pheromone. Individuals showed activation of the amygdala in response to sweat produced by others during emotional stress, with exercise sweat as a control; behavioral data suggest facilitated evaluation of ambiguous threat