Almost Periodic Solutions to Some Singular Systems of Differential Equations
Martin Arienmughare, Department of Mathematics, Howard University
The main objective of this Thesis is two-fold. We first study properties of almost periodic functions using trigonometric polynomials. In particular, some properties of almost periodic functions are expressed in terms of the coefficients of the associated trigonometric polynomials. Next, we make extensive use of the so-called Drazin inverse of a matrix to study and obtain the existence of C(k)-almost periodic solutions to the first-order singular differential equations
where A, B are singular n x n-square matrix with complex coefficients, the function f: R -> Cn is C(2k-1)-almost periodic with k = ind(A) >= 1. To illustrate our abstract results, several examples are discussed.
Blackwell's Impact on a Young African Student of Statistical Genetics
George Bonney, National Human Genome Center and the Department of Community and Family Medicine, Howard University
My first encounter with David Blackwell was through the well-known Rao-Blackwell Theorem. I was then a college student in the Bachelor of Science Honors Program in Mathematics at the University of Ghana. That a formal mathematical theory for improving a statistical estimator can be constructed as he did was interesting. Six of my contemporaries at the University of Ghana continued on to graduate schools and became statisticians. All of them still remember their first encounter with the Rao-Blackwell Theorem. My second encounter with David Blackwell occurred when I was in Graduate School at the University of North Carolina, Chapel Hill. David Blackwell came to give a talk in 1979. When I saw him and heard him I said quietly to myself, "So a black person too can do these things!" These two encounters deeply affected my thinking and gave me confidence. In this brief presentation I will give examples from my own work of when I have asked myself, "Can the statistical procedure be improved?" and a summary of some of the results.
A u'(t) + Bu(t) = f(t), t in R
David Blackwell: A Lesson in History for the Mathematical Community
Carlos Castillo-Chavez, Mathematical, Computational and Modeling Sciences Center, Arizona State University
On the recently updated version of the history of the Blackwell-Tapia Prize and Conference kept at the Math Institutes site, it is stated that: "Mathematical and Theoretical Biology Institute Director Carlos-Castillo Chavez, a member of MSRI’s Human Resources Advisory Committee (HRAC) from 1997-2000 and a faculty member at Cornell University at the time, broached the idea during an HRAC meeting of a conference honoring David Blackwell and Richard Tapia. He then implemented that vision by securing funding from Cornell for the first Blackwell-Tapia Conference, held at Cornell in 2000 and attended by both Blackwell and Tapia. MSRI Director David Eisenbud then suggested the establishment of the David Blackwell and Richard Tapia Award as a joint enterprise between Cornell and MSRI, to extend the honoring of these two eminent mathematical scientists to those who have followed in their footsteps. That award was first presented in 2002 at the second Blackwell-Tapia Conference, held at MSRI. Starting in 2004, the Blackwell-Tapia Conference has been hosted by other North American mathematical sciences institutes every two years, including the Institute for Pure and Applied Mathematics in 2004, the Institute for Mathematics and its Applications in 2006, the Statistical and Applied Mathematical Sciences Institute in 2008, and the Mathematical Biosciences Institute in 2010. The 2012 conference and prize will be hosted by the Institute for Computational and Experimental Research in Mathematics. The National Blackwell-Tapia Committee selects the prize recipient. Primary funding for the conference comes from the host institute, while funding for the prize itself continues to be provided by a generous contribution from Cornell University." In this presentation, I will revisit the events of the 2000 event and some of the history of the B-T even from a rather personal perspective.
David Blackwell's Impact on Mathematics at Howard University
James Donaldson, Dean of the College of Arts and Sciences, Howard University
IIn the early 1940s the Mathematics Department at Howard University, like many such departments in America, devoted most of its attention to providing mathematical instruction to undergraduate students and to offering a small Master of Science degree program. Much of this changed with the arrival of David Blackwell whose teaching, scholarship, leadership and vision transformed the mathematical atmosphere at Howard profoundly. This paper, drawing upon College and University documents and other sources, discusses some aspects of this transformation and their ramifications.
Malaria in Irrigated and Non-Irrigated Villages of Mali
Moussa Doumbia, Department of Mathematics, Howard University
In this paper, we extend the mathematical model framework of Dembele et. al. and used it to determine the disease administration protocols of a generic malaria drug that lead to fewest episodes of malaria in both irrigated and adjacent non-irrigated villages of Niono in Mali during the wet season. We show that there are more malaria cases in non-irrigated villages of Niono than the adjacent irrigated villages whereas the mosquito density in the irrigated villages in much higher than that of the adjacent non-irrigated villages of Niono.
A Moment Series Approach to Bayesian Statistics and Inference
Adebukola Gbade-Oyelakin, Department of Mathematics, Howard University
A moment series approach to the Bayesian inference is proposed. This approach has two principal features: The development of the computation of the Bayesian estimator using a moment series with any loss function and for the special case of the quadratic loss function. This addresses some of the computational concerns faced in Bayesian statistics. Secondly, the use of a non-pdf form prior: the moment sequence of a distribution, in particular, Bonney’s moment sequence. We show how to compute the proposed estimator and give examples of the estimators for commonly used distributions, such as, the binomial, poisson, exponential and normal distributions. Finally, the implementation of this method is illustrated using the binomial model with application to familiar data on sarcoma cancer in nuclear families.
David Blackwell, A Member of the Community of Scholars
Nancy L. Geller, Office of Biostatistics Research, National Heart, Lung, and Blood Institute, National Institute of Health
I will review David Blackwell's personal history and some of his many contributions to the statistics and mathematics communities and the recognition he received.
David Blackwell's Gift to the National Association of Mathematicians, Inspiration for Generations
William Hawkins, Department of Mathematics, University of District of Columbia
The many accomplishments of Dr. David H. Blackwell are especially inspiring to minority mathematicians. The talk will focus on less well-known details of his biography and their impact on his work.
Minimal Hales-Jewett Sets
Henry Jordan, Department of Mathematics, Howard University
A structure is Ramseyian if whenever it is divided into r classes, one of the classes exhibits properties similar to the whole structure. The Hales-Jewett Theorem is one of the major results of Ramsey Theory. In this work, we shall establish the existence of minimal Hales-Jewett sets, and specifically identify one.
Blackwell's Impact on the Theory of Queues
William Massey, Department of Operations Research and Financial Engineering, Princeton University
David Blackwell's impact on probability and statistics is far reaching. From the celebrated Rao-Blackwell theorem, to careful work with stochastic processes and urn schemes, Blackwell's work is characterized by results that go directly to the heart of a problem. In this talk, we show the influence of his work on the theory of queues. We can describe the stochastic dynamics of infinite-server queues with non-homogenous Poisson arrivals and general service times in an elegant manner by using renewal theory concepts.
Blackwell's Legacy to a Community for African-American Researchers in the Mathematical Sciences
William Massey, Department of Operations Research and Financial Engineering, Princeton University
During the decade of the 1940's there were no more than 10 African Americans who received a Ph.D. in mathematics from American institutions. Two of them are well known to attendees of the Conference for African American Researchers in the Mathematical Sciences. They are David Blackwell and J. Ernest Wilkins, who both attended the first CAARMS conference in 1995. In the first decade of the 21st century, there were over 300 Ph.D.'s in the mathematical sciences given by American institutions to members of the African diaspora. This talk will discuss the lasting impact of David Blackwell on the research community in general, minority students, minority researchers, and the CAARMS conferences.
Contributions of Blackwell to the Martingale Dilation Stochastic Order
Isaac Meilijson, Department of Statistics and Operations Research, Tel Aviv University
Blackwell contributed in "Comparison of Experiments" to the integral characterization of what is known in various circles as
Second-degree stochastic dominance, Mean-preserving Increase in Risk, Convex inequality and Martingale dilation. The talk will review the Hardy &
Littlewood origin, Blackwell's contribution above, and Blackwell & Dubins'
identification (in "A converse to the dominated convergence theorem") of the
least upper stochastic bound to Martingale dilation. Stricter forms of
Martingale dilation will be surveyed, Bickel & Lehmann's dispersive order in
particular, the subject of my last conversation with Blackwell.
Pseudo-Almost Automorphic Solutions to Some Second Order Differential Equations
Ahmed Mohamed, Department of Mathematics, Howard University
In this poster we present and obtain the existence of pseudo-almost automorphic solutions to some classes of second order abstract differential equations on a Hilbert space. To illustrate our abstract results, we present the existence of pseudo almost automorphic solutions to the N-dimensional Sine-Gordon boundary value problem.
Fluid Model of the Dynamics of Patients and Physicians in Emergency
Rooms: Optimal Control Staffing Policy and Workshift Schedules
Jerome Ndayishimiye, Department of Systems Science and Industrial Engineering, Binghamton University
Hospital emergency rooms are increasingly crowded and increasingly difficult to manage because of the complexity of allocating physicians in light of inhomogeneous and stochastic service demand. We propose a fluid model using ordinary differential equations to approximate inhomogeneous service demand and corresponding complex dynamics of patients and physicians. We then use the Pontryagin’s Maximum Principle to determine the optimal physicians staffing policy that minimizes crowding and controls the marginal costs of physicians. We use the first-hour scheduling principle to determine workshift schedules.
C^(n)-Pseudo Almost Automorphy and its Applications to Some Higher-Order Differential Equations
Valerie Nelson, Department of Mathematics, Howard University
Differential equations play a major role in modeling natural phenomena such as heat conduction, population growth, and the spread of disease. However, it is often difficult, if not impossible, to find solutions to complex models. Despite this fact, it is sometimes possible to prove the existence of solutions to some differential equations and to classify them. The study of C(n)-almost periodic (and more generally, C(n)-almost automorphic) solutions to differential equations is one of the most interesting topics in qualitative theory of differential equations due to their applications. Almost automorphy generalizes almost periodicity, which generalizes periodic functions. Extensions of these areas include the study of existence of such solutions to some of differential equations in abstract spaces such as Banach and Hilbert spaces. In this presentation, we introduce and examine a new concept called C(n)-pseudo-almost automorphy, which generalizes both the notions of C(n)-almost periodicity and that of C(n)-almost automorphy. Properties of such a new concept will be presented. We then prove the existence of C(n)-pseudo-almost automorphic solutions to some n-order differential equations. These results represent joint work with Toka Diagana, PhD.
Blackwell's Impact on Statistics: Bayesian
Giovanni Parmigiani, Department of Biostatistics and Computational Biology, Dana-Farber Cancer Institute
This presentation will provide a brief overview of David Blackwell's perspective of Bayesian statistics; a synopsis of his contributions to Bayesian decision theory; and a commentary on the long term impact of the Rao-Blackwell theorem on Bayesian analysis.
Gaussian Skewness Approximation for Dynamic Rate Queues
Jamol Pender, Department of Operations Research and Financial Engineering, Princeton University
The multi-server queue with non-homogeneous Poisson arrivals and customer abandonment is a fundamental dynamic rate queueing model for large scale service systems such as call centers and hospitals. Scaling the arrival rates and number of servers arises naturally as staffing issues for these systems in response to predictable increasing demand. Mathematically, this gives us the fluid and diffusion limits as found in Mandelbaum, Massey, and Reiman . The general rate asymptotics used here for Markovian service networks reduce to the Halfin-Whitt  scaling for these multi-server queues.
The diffusion limit suggests a Gaussian approximation to the stochastic behavior of this queueing process. The mean and variance are easily computed from a two-dimensional dynamical system from the fluid and diffusion limiting processes. Recent work by Ko and Gautum  found that a modified version of these differential equations can be used to obtain better Gaussian estimates of the original queueing system distribution. In this paper, we introduce a new three-dimensional dynamical system that improves on both of these approaches by constructing a non-Gaussian estimation of the mean, variance, and third cumulative moment.
David Blackwell and Dynamic Programming
William Sudderth, Department of Statistics, University of Minnesota
David Blackwell and his students made many fundamental contributions to the mathematics of dynamic programming, which is also known as Markov decision theory. I will give a brief explanation of what dynamic programming is, and then describe a few of Blackwell's contributions.
Mulitpotent Stem Cells Bifurcating Dynamics from Gene Transcription Factor Interactions
Ilyssa Summer, Department of Mathematics, Arizona State University
Multipotent progenitor cells have appealing characteristics such that they can self divide or develop into virtually any given cell type depending on environmental factors. Lineage affiliated transcription factors govern the specification of a given cell lineage. A concern is how lineage determining transcription factors lead to the stability of progenitor cells, committing to a specific cell line Binary cell fate decisions can be governed mathematically by circuits that generate attractors corresponding to specified lineages. Bifurcations represent cell divisions and stage differentiation from lineage specific attractors. The findings of the constructed model represent that stages of stem cell differentiation through auto-regulation, inhibition and degradation factors can be analyzed mathematically by the stability of the stochastic and deterministic features within the system.
Remembering a Mentor: David Blackwell at Berkeley
Daphne L. Smith, CVS Caremark, Northbrook, Illinois
David Blackwell was a distinguished statistician. But he was also a masterful teacher. His style of teaching (lively and powerfully persuasive) left an indelible impression on those who had the benefit of learning from him.
He was a role model who was willing to take the time to encourage young scholars to make thoughtful career choices. The speaker will reflect on her memories of this great scholar and teacher.
NIR Spectroscopy Data Pre-Processing Using SAS
Anna Sun, Department of Mathematics and Statistics, University of Maryland Baltimore County
NIR spectroscopy is one of the most popular analytical methods, especially for many practical and industrial applications. In pharmaceutical company, NIR is used by analytical and formulation scientists and chemometricians. Since it is fast, non-destructive, does not require chemical reagents, and it is easy to extend to on-line
analysis. So how to use statistical methods to deal with NIR data and use the efficient software to do the data analysis is crucial.
My topic will cover: different Pre-processing methods for spectroscopic data; use of different software to do the analysis of the NIR spectroscopy data; the efficient of using SAS to deal with the spectroscopy data; and application to other research.
David Blackwell: King of the Precious Few
Richard Tapia, Computational and Applied Mathematics, Rice University
By the precious few we mean those underrepresented minorities who successfully navigated the United State's educational system to rise to the
level of professional in a stem discipline at a research university or other research facility. These are indeed a precious few. Today extreme growth in the minority population, primarily Hispanic, is forcing educational
challenges at a crisis level for the nation. Race and ethnicity should not dictate educational destiny. Unfortunately, today they do. Our faculty representation in STEM areas is critically low. The rate at which the minority population is growing outpaces the rate at which we are improving our effectiveness in educating this segment of the population. Because the economic health of the nation is based in large measure upon technical advances, we must find a way to incorporate more individuals from this
population, not just a precious few, into the mainstream of scientific and
technical endeavors. The speaker's remarks will focus on the steps needed
to motivate and expand the pool of the precious few in order to improve the
representation situation and will be made in the context of David
Blackwell's path to success.
David Blackwell's Impact on Information Theory
Sergio Verdu, Department of Electrical Engineering, Princeton University
One of the first American probabilists to work on Shannon's information theory, David Blackwell pioneered the use of randomization in combating certain types of channel uncertainties, introduced the trapdoor channel and other channels with memory, and the Blackwell deterministic broadcast channel. He also proposed what is known as the "Blackwell measure" for the analysis of the entropy rate of hidden Markov chains.