Borcherds Forms and Generalizations of Singular Moduli

We give a factorization of averages of Borcherds forms over CM points associated to a quadratic form of signature (n,2). As a consequence of this result, we are able to state a theorem like that of Gross and Zagier about which primes can occur in this factorization. One remarkable phenomenon we observe is that the regularized theta lift of a weakly holomorphic modular form is always finite

Variational Optimal-Control Problems with Delayed Arguments on Time Scales

This article deals with variational optimal-control problems on time scales in the presence of delay in the state variables. The problem is considered on a time scale unifying the discrete, the continuous and the quantum cases. Two examples in the discrete and quantum cases are analyzed to illustrate our results.Comment: To apear in Advances in Difference Equation

Massively parallel approximate Gaussian process regression

We explore how the big-three computing paradigms -- symmetric multi-processor (SMC), graphical processing units (GPUs), and cluster computing -- can together be brought to bare on large-data Gaussian processes (GP) regression problems via a careful implementation of a newly developed local approximation scheme. Our methodological contribution focuses primarily on GPU computation, as this requires the most care and also provides the largest performance boost. However, in our empirical work we study the relative merits of all three paradigms to determine how best to combine them. The paper concludes with two case studies. One is a real data fluid-dynamics computer experiment which benefits from the local nature of our approximation; the second is a synthetic data example designed to find the largest design for which (accurate) GP emulation can performed on a commensurate predictive set under an hour.Comment: 24 pages, 6 figures, 1 tabl

Lincoln, Civil War national traveling exhibit on display in Booth Library

https://thekeep.eiu.edu/lincoln_2015_news/1004/thumbnail.jp

Treatment of Subacromial Impingement Syndrome in a 53-Year-Old Female: A Case Study

Background and Purpose. Subacromial impingement syndrome (SAIS) is a common shoulder pathology. The purpose of this case report is to discuss the outcomes of subsequent physical therapy after operative treatment for SAIS and the clinical decision making involved in seeking surgical intervention. Case Description. This case report describes a 54 y/o female who participated in eight weeks of physical therapy after undergoing shoulder decompression surgery while failing conservative physical therapy prior to surgical intervention. Intervention. Physical therapy interventions were designed to strengthen the rotator cuff and shoulder, increase range of motion, decrease pain, and improve functional activity. Outcomes. The patient increased strength, and range of motion to near normal limits, and had decreased pain and functional limitations. Discussion. Physical therapy intervention after shoulder decompression surgery can improve strength, range of motion, pain, and functional activity. The patient would have benefitted from continued therapy for further improvements of strength and range of motion, but opted to continue therapy with a home exercise program. Further research is needed to determine early diagnostics to provide the most appropriate plan of care