Artin Group Presentations Arising from Cluster Algebras

In 2003, Fomin and Zelevinsky proved that finite type cluster algebras can be classified by Dynkin diagrams. Then in 2013, Barot and Marsh defined the presentation of a reflection group associated to a Dynkin diagram in terms of an edge-weighted, oriented graph, and proved that this group is invariant (up to isomorphism) under diagram mutations. In this paper, we extend Barot and Marsh's results to Artin group presentations, defining new generator relations and showing mutation-invariance for these presentations.Comment: 26 pages, 7 figures, comments are welcom

Interpretation of CT studies: single-screen workstation versus film alternator

A prototype single-screen workstation with a 2,048 x 2,560-pixel high-brightness monitor, 0.11-second image display time, and simple ergonomic design was compared to a conventional horizontal film alternator in diagnostic interpretation of chest computed tomography (CT) studies. Four radiologists used either the workstation or film alternator in interpretation of studies obtained in 10 patients. A counterbalanced within-subject repeated measures experimental design was used. Response times were analyzed for both methods of interpretation. Grades of excellent, acceptable, and unacceptable were assigned by a blinded "grader" to reports of the radiologists. The average time needed for an interpretation at the workstation was 5.65 minutes. No interpretations were graded unacceptable. Retrospective power analysis showed that 16 observers rather than four would have been required to show that use of the workstation was faster than the alternator. With this 95% confidence interval, the workstation interpretation time is clinically equivalent to that with the alternator. These data show that this type of workstation has practical application in interpretation of CT, magnetic resonance imaging, and ultrasound studies

Interpretation time of serial chest CT examinations with stacked-metaphor workstation versus film alternator

PURPOSE: Interpretation time of serial staging chest CT cases, which each contained current and previous examinations, with a simple prototype workstation called filmstack was experimentally compared with interpretation time with a film alternator. MATERIALS AND METHODS: The filmstack displayed a "stack" of sections for each examination; user controls allowed rapid selection of preset attenuation windows and both synchronized and unsynchronized scrolling. Eight radiologists were timed as they used the filmstack and the film alternator to interpret four ergonomically complex serial CT cases. RESULTS: All reports dictated on the basis of findings with filmstack and film were of acceptable clinical accuracy. The time to examine a case with filmstack was significantly faster than the time with film, including the time to load and unload the alternator (99% confidence [P = .01]). There was no statistically significant difference in interpretation time between filmstack and prehung film. CONCLUSION: Use of a low-cost stacked CT workstation with a single 1,024 x 1,024 monitor is an effective means of interpreting cases that require comparison of multiple CT examinations

Association Analysis of 94 Candidate Genes and Schizophrenia-Related Endophenotypes

While it is clear that schizophrenia is highly heritable, the genetic basis of this heritability is complex. Human genetic, brain imaging, and model organism studies have met with only modest gains. A complementary research tactic is to evaluate the genetic substrates of quantitative endophenotypes with demonstrated deficits in schizophrenia patients. We used an Illumina custom 1,536-SNP array to interrogate 94 functionally relevant candidate genes for schizophrenia and evaluate association with both the qualitative diagnosis of schizophrenia and quantitative endophenotypes for schizophrenia. Subjects included 219 schizophrenia patients and normal comparison subjects of European ancestry and 76 schizophrenia patients and normal comparison subjects of African ancestry, all ascertained by the UCSD Schizophrenia Research Program. Six neurophysiological and neurocognitive endophenotype test paradigms were assessed: prepulse inhibition (PPI), P50 suppression, the antisaccade oculomotor task, the Letter-Number Span Test, the California Verbal Learning Test-II, and the Wisconsin Card Sorting Test-64 Card Version. These endophenotype test paradigms yielded six primary endophenotypes with prior evidence of heritability and demonstrated schizophrenia-related impairments, as well as eight secondary measures investigated as candidate endophenotypes. Schizophrenia patients showed significant deficits on ten of the endophenotypic measures, replicating prior studies and facilitating genetic analyses of these phenotypes. A total of 38 genes were found to be associated with at least one endophenotypic measure or schizophrenia with an empirical p-value<0.01. Many of these genes have been shown to interact on a molecular level, and eleven genes displayed evidence for pleiotropy, revealing associations with three or more endophenotypic measures. Among these genes were ERBB4 and NRG1, providing further support for a role of these genes in schizophrenia susceptibility. The observation of extensive pleiotropy for some genes and singular associations for others in our data may suggest both converging and independent genetic (and neural) pathways mediating schizophrenia risk and pathogenesis

Lannes's T-functor, equivariant Chow rings, and motivic homology

This dissertation takes place in three parts, all themed around motivic cohomology and Voevodsky's derived category of motives. In Chapter 1, we use Lannes's T-functor to study equivariant Chow rings. In Chapter 2, we explicitly compute certain equivariant Chow rings, namely Chow rings of classifying spaces of finite groups of order 32. In Chapter 3, we prove that isomorphisms in Voevodsky's derived category of motives are detected by a certain family of motivic homology group

Lannes's T-functor, equivariant Chow rings, and motivic homology

This dissertation takes place in three parts, all themed around motivic cohomology and Voevodsky's derived category of motives. In Chapter 1, we use Lannes's T-functor to study equivariant Chow rings. In Chapter 2, we explicitly compute certain equivariant Chow rings, namely Chow rings of classifying spaces of finite groups of order 32. In Chapter 3, we prove that isomorphisms in Voevodsky's derived category of motives are detected by a certain family of motivic homology group

Augmentation Rank of Satellites with Braid Pattern

Given a knot $K$ in $S^3$, a question raised by Cappell and Shaneson asks if the meridional rank of $K$ equals the bridge number of $K$. Using augmentations in knot contact homology we consider the persistence of equality between these two invariants under satellite operations on $K$ with a braid pattern. In particular, we answer the question in the affirmative for a large class of iterated torus knots.Honors thesi