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

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

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

Allele-Specific KRT1 Expression Is a Complex Trait

The differential expression of alleles occurs commonly in humans and is likely an important genetic factor underlying heritable differences in phenotypic traits. Understanding the molecular basis of allelic expression differences is thus an important challenge. Although many genes have been shown to display differential allelic expression, this is the first study to examine in detail the cumulative effects of multiple cis-regulatory polymorphisms responsible for allele-specific expression differences. We have used a variety of experimental approaches to identify and characterize cis-regulatory polymorphisms responsible for the extreme allele-specific expression differences of keratin-1 (KRT1) in human white blood cells. The combined data from our analyses provide strong evidence that the KRT1 allelic expression differences result from the haplotypic combinations and interactions of five cis-regulatory single nucleotide polymorphisms (SNPs) whose alleles differ in their affinity to bind transcription factors and modulate KRT1 promoter activity. Two of these cis-regulatory SNPs bind transcriptional activators with the alleles on the high-expressing KRT1 haplotype pattern having a higher affinity than the alleles on the low-expressing haplotype pattern. In contrast, the other three cis-regulatory SNPs bind transcriptional inhibitors with the alleles on the low-expressing haplotype pattern having a higher affinity than the alleles on the high-expressing haplotype pattern. Our study provides important new insights into the degree of complexity that the cis-regulatory sequences responsible for allele-specific transcriptional regulation have. These data suggest that allelic expression differences result from the cumulative contribution of multiple DNA sequence polymorphisms, with each having a small effect, and that allele-specific expression can thus be viewed as a complex trait