MacMahon's sum-of-divisors functions, Chebyshev polynomials, and Quasi-modular forms

We investigate a relationship between MacMahon's generalized sum-of-divisors functions and Chebyshev polynomials of the first kind. This determines a recurrence relation to compute these functions, as well as proving a conjecture of MacMahon about their general form by relating them to quasi-modular forms. These functions arise as solutions to a curve-counting problem on Abelian surfaces.Comment: 6 Page

Wind tunnel performance results of an aeroelastically scaled 2/9 model of the PTA flight test prop-fan

High speed wind tunnel aerodynamic performance tests of the SR-7A advanced prop-fan have been completed in support of the Prop-Fan Test Assessment (PTA) flight test program. The test showed that the SR-7A model performed aerodynamically very well. At the cruise design condition, the SR-7A prop fan had a high measured net efficiency of 79.3 percent

Toxic metal enrichment and boating intensity: sediment records of antifoulant copper in shallow lakes of eastern England

Tributyltin (TBT), an aqueous biocide derived from antifouling paint pollution, is known to have impacted coastal marine ecosystems, and has been reported in the sediment of the Norfolk and Suffolk Broads, a network of rivers and shallow lakes in eastern England. In the marine environment, the 1987 TBT ban has resulted in expanded use of alternative biocides, raising the question of whether these products too have impacted the Broads ecosystem and freshwaters in general. Here we examine the lake sediment record in the Norfolk and Suffolk Broads for contamination by copper (Cu) (as an active biocide agent) and zinc (Zn) (as a component of booster biocides), to assess their occurrence and potential for causing environmental harm in freshwater ecosystems. We find that, after the introduction of leisure boating, there is a statistically significant difference in Cu enrichment between heavily and lightly boated sites, while no such difference exists prior to this time. At the heavily boated sites the onset of Cu enrichment coincides with a period of rapid increase in leisure boating. Such enrichment is maintained to the present day, with some evidence of continued increase. We conclude that Cu-based antifouling has measurably contaminated lakes exposed to boating, at concentrations high enough to cause ecological harm. Similar findings can be expected at other boated freshwater ecosystems elsewhere in the world

Education, income, occupation, and the 34-year incidence (1965–99) of Type 2 diabetes in the Alameda County Study

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/51500/1/Maty SC, Education, Income, Occupation, and the 34-year Incidence, 2005.pd

A Pilot Study of Neuroplasticity Based Cognitive Remediation in Early Onset Psychosis

Introduction – Neuroplasticity based auditory and visual training programs appear to improve neurocognitive function in adults with schizophrenia, but use in younger individuals has not been determined. We hypothesized that adolescents might play more often and respond better than adults to training using a game-like laptop in their home environment. Methods -- Youth 10-19 years with Early Onset Psychosis (EOP) were provided a laptop and randomly assigned to play games to enhance basic auditory, visual and social processing neuroplasticity games (NPG) or assigned to control games with cognitive components, such as Sudoku or hangman or (CG). All received neurocognitive assessments at baseline, intervention completion and 4 months post treatment. Results — 12 youth (15.5 +3.2 yrs) were assigned to NPG and 10 participants (16.2 +2.1 years) were assigned to CG. More NPG than CG participants completed the prescribed hours of game play (block 1 - 92% vs. 70% over the first 40 hours), with both groups engaged less over time. Although most neurocognitive functions did not change, the NPG group did show improvements in WRAML Visual Learning, WISC Digit Span Forward, Spatial Span Backwards and CPT omission errors. Surprisingly, satisfaction was lower for NPG than CG. Conclusions — Groups were well matched for baseline illness characteristics. On the global measures of cognition, both EOP groups showed improvement over time but those improvements were generally greater in the CG than in the NPG group, with potentially significant differences favoring the CG evident in the neurocognitive composite score (p=0.072) and BRIEF metacognition (p=.117). Youth did not play as frequently or as long as requested despite providing a laptop for their home use and stipends for playing

Physician decision making in selection of second-line treatments in immune thrombocytopenia in children.

Immune thrombocytopenia (ITP) is an acquired autoimmune bleeding disorder which presents with isolated thrombocytopenia and risk of hemorrhage. While most children with ITP promptly recover with or without drug therapy, ITP is persistent or chronic in others. When needed, how to select second-line therapies is not clear. ICON1, conducted within the Pediatric ITP Consortium of North America (ICON), is a prospective, observational, longitudinal cohort study of 120 children from 21 centers starting second-line treatments for ITP which examined treatment decisions. Treating physicians reported reasons for selecting therapies, ranking the top three. In a propensity weighted model, the most important factors were patient/parental preference (53%) and treatment-related factors: side effect profile (58%), long-term toxicity (54%), ease of administration (46%), possibility of remission (45%), and perceived efficacy (30%). Physician, health system, and clinical factors rarely influenced decision-making. Patient/parent preferences were selected as reasons more often in chronic ITP (85.7%) than in newly diagnosed (0%) or persistent ITP (14.3%, P = .003). Splenectomy and rituximab were chosen for the possibility of inducing long-term remission (P < .001). Oral agents, such as eltrombopag and immunosuppressants, were chosen for ease of administration and expected adherence (P < .001). Physicians chose rituximab in patients with lower expected adherence (P = .017). Treatment choice showed some physician and treatment center bias. This study illustrates the complexity and many factors involved in decision-making in selecting second-line ITP treatments, given the absence of comparative trials. It highlights shared decision-making and the need for well-conducted, comparative effectiveness studies to allow for informed discussion between patients and clinicians