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Articles 1 - 6 of 6
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Common Cyclic Vectors For Unitary Operators, William T. Ross, Warren R. Wogen
Common Cyclic Vectors For Unitary Operators, William T. Ross, Warren R. Wogen
Department of Math & Statistics Faculty Publications
In this paper, we determine whether or not certain natural classes of unitary multiplication operators on L2(dƟ) have common cyclic vectors. For some classes which have common cyclic vectors, we obtain a classification of these vectors.
A Nonlinear Extremal Problem On The Hardy Space, William T. Ross, Stephan Ramon Garcia
A Nonlinear Extremal Problem On The Hardy Space, William T. Ross, Stephan Ramon Garcia
Department of Math & Statistics Faculty Publications
We relate some classical extremal problems on the Hardy space to norms of truncated Toeplitz operators and complex symmetric operators
Complementary Responses To Mean And Variance Modulations In The Perfect Integrate-And-Fire Model, Joanna R. Wares, Todd W. Troyer
Complementary Responses To Mean And Variance Modulations In The Perfect Integrate-And-Fire Model, Joanna R. Wares, Todd W. Troyer
Department of Math & Statistics Faculty Publications
In the perfect integrate-and-fire model (PIF), the membrane voltage is proportional to the integral of the input current since the time of the previous spike. It has been shown that the firing rate within a noise free ensemble of PIF neurons responds instantaneously to dynamic changes in the input current, whereas in the presence of white noise, model neurons preferentially pass low frequency modulations of the mean current. Here, we prove that when the input variance is perturbed while holding the mean current constant, the PIF responds preferentially to high frequency modulations. Moreover, the linear filters for mean and variance …
Biology In Mathematics At The University Of Richmond, Lester Caudill
Biology In Mathematics At The University Of Richmond, Lester Caudill
Department of Math & Statistics Faculty Publications
In an effort to meet the needs of science students for modeling skills, three new courses have been created at the University of Richmond: Scientific Calculus I and II, and Mathematical Models in Biology and Medicine. The courses are described, and lessons learned and future directions are discussed.
Extending The Skill Test For Disease Diagnosis, Shu-Chuan Lin, Paul H. Kvam, Jye-Chyi Lu
Extending The Skill Test For Disease Diagnosis, Shu-Chuan Lin, Paul H. Kvam, Jye-Chyi Lu
Department of Math & Statistics Faculty Publications
For diagnostic tests, we present an extension to the skill plot introduced by Briggs and Zaretski (Biometrics 2008; 64:250–261). The method is motivated by diagnostic measures for osteopetrosis in a study summarized by Hans et al. (The Lancet 1996; 348:511–514). Diagnostic test accuracy is typically defined using the area (or partial area) under the receiver operator characteristic (ROC) curve. If partial area is used, the resulting statistic can be highly subjective because the focus region of the ROC curve corresponds to a set of low false‐positive rates that are chosen by the experimenter. This paper introduces a more …
[Introduction To] The Hardy Space Of A Slit Domain, William T. Ross, Alexandra Aleman, Nathan S. Feldman
[Introduction To] The Hardy Space Of A Slit Domain, William T. Ross, Alexandra Aleman, Nathan S. Feldman
Bookshelf
If H is a Hilbert space and T : H ? H is a continous linear operator, a natural question to ask is: What are the closed subspaces M of H for which T M ? M? Of course the famous invariant subspace problem asks whether or not T has any non-trivial invariant subspaces. This monograph is part of a long line of study of the invariant subspaces of the operator T = M (multiplication by the independent variable z, i. e. , M f = zf ) on a z z Hilbert space of analytic functions on a bounded …