Richard A. Alo

Non-destructive testing of aerospace structures: granularity and data mining approach

For large aerospace structures, it is extremely important to detect faults, and nondestructive testing is the only practical way to do it. Based on measurements of ultrasonic waves, Eddy currents, magnetic resonance, etc., we reconstruct the locations of the faults. The best (most efficient) known statistical methods for fault reconstruction are not perfect. We show that the use of expert knowledge-based granulation improves the quality of fault reconstruction.

Decision making mechanisms and stopping times in a generalized information system

Abstract A mechanism for a decision maker ethically bound to pursue the best available course of action is studied. The model allows for feedback information to be input for each cycle of decision making. This type of information-feedback loop is relevant to many real decision making situations. Equations describing the updated expected utility in terms of the learning factor are given and a discussion follows as to when learning takes place. It is then shown that these estimates converge to the appropriate values. Moreover these estimators form a martingale or a submartingale, thus allowing the analysis of when and how the decision makers can terminate the feedback decision making loop. Several strategies are discussed as well as the corresponding probabilities of ending the loop in a finite amount of time.

The Computing Alliance of Hispanic-Serving Institutions: Supporting Hispanics at Critical Transition Points

Hispanics have the highest growth rates among all groups in the U.S., yet they remain considerably underrepresented in computing careers and in the numbers who obtain advanced degrees. Hispanics constituted about 7% of undergraduate computer science and computer engineering graduates and 1% of doctoral graduates in 2007--2008. The small number of Hispanic faculty, combined with the lack of Hispanic role models and mentors, perpetuates a troublesome cycle of underrepresentation in STEM fields. In 2004, seven Hispanic-Serving Institutions (HSIs) formed the Computing Alliance of Hispanic-Serving Institutions (CAHSI) to consolidate their strengths, resources, and concerns with the aim of increasing the number of Hispanics who pursue and complete baccalaureate and advanced degrees in computing areas. To address barriers that hinder students from advancing, CAHSI defined a number of initiatives, based on programs that produced promising results at one or more institutions. These included the following: a CS-0 course that focuses on adoption of a three-unit pre-CS course that uses graphics and animation to engage and prepare students who have no prior experience in computing; a peer mentoring strategy that provides an active, collaborative learning experience for students while creating leadership roles for undergraduates; an undergraduate and graduate student research model that emphasizes the deliberate and intentional development of technical, team, and professional skills and knowledge required for research and cooperative work; and a mentoring framework for engaging undergraduates in experiences and activities that prepare them for graduate studies and onto the professoriate. CAHSI plays a critical role in evaluating, documenting, and disseminating effective practices that achieve its mission. This paper provides an overview of CAHSI initiatives and describes how each addresses causes of underrepresentation of Hispanics in computing. In addition, it describes the evaluation and assessment of the initiatives and presents the results that support CAHSI’s claim of their effectiveness.

Work in progress - peer-led team learning implementation in computer science

The Computing Alliance of Hispanic Serving Institutions (CA-HSI) is a consortium of eight institutions that is committed to increasing the number of Hispanics who earn baccalaureate and advanced degrees in computing. CA-HSI is implementing and promoting the development of peer-led team learning (PLTL) in the computing curriculum as one of its interventions to increase the number of students who succeed in computing gatekeeper courses. PLTL is a proven strategy for retention and motivation of students having already shown its effectiveness in other disciplines. It utilizes student-driven focus groups to confront issues of lack of academic and social support. CA-HSI is creating a repository for support materials for PLTL implementation and it is also promoting implementation within the Alliance as well as other institutions. This paper discusses the materials and mechanisms for implementations, and it presents initial results of the intervention. At least 2,000 computing students have used these materials to date.

Emergence of a dominant course of action in a general feedback loop when goal uncertainty is present

A decision maker is confronted with a finite set of possible courses of action, each of which can generate one of several possible outcomes. The decision maker must make a (possibly infinite) sequence of such decisions, the consequence of each decision being fed back to him so that the estimated averages can be updated before the next course of action is selected. Furthermore, suppose that initially the decision maker is uncertain of precisely how to assess the utilities associated with each action-outcome pair (goal uncertainty), but that as he proceeds through the decision-information feedback loop he is gradually able to sharpen his perception of these utilities (goal shaping). In this article a mathematical model of a decision maker subject to goal uncertainty is given. Conditions are established which guarantee that the decision makers ranges of expected utilities stabilize as he cycles through the decision-feedback loop. It is also shown that a single dominant course of action will always emerge. A specific example involving a decision maker functioning in the type of environment described above provides insight as to how this procedure works in practice.

Non-linear operators on sets of measures

SummaryIf M[ℬ, U(C, C)] is the collection of U(C, C)-valued (non-linear) set functions defined on the Borel subsetsℬ of the compact Hausdorff space S, one may define operators on M[ℬ, U(C, C)] which are « of the Hammerstein type ». We initiate a study of a concept analogous to the second dual of a space of continuous functions by inquiring as to what representation theorems one may obtain for these operators. A « Lebesgue type » decomposition theorem for elements of M[ℬ, U(C, C)] is obtained. A « density » theorem is also obtained for the space M[ℬ, U(C, C)].

Nonlinear integration on measures

THE MAIN purpose of the present paper is to study Hammerstein operators on vector valued measures, generalizing the work contained in [l], [2], [3] and [4]. Since operators will be represented as integrals. a systematic study of the integration of measures relative to convex set functions will also be initiated. Elementary properties of vector measures will be found in [S]. Before stating our main results, we wish to set our results in the proper perspective. A long standing problem is to characterize the bidual of C[O, 11, the space of continuous functions defined on the real interval [0, l] with the sup norm topology. A possible approach is taken in the interesting paper of Mauldin [4]. If M[O, I] denotes the space of measure representing the dual space of CEO, 11, then Mauldin shows that if T is a continuous linear functional on M[O, l] then T(p) = i p dK. Here 1 p dK is defined as

p-integrable selectors of multimeasures

The present work is a study of multivalued functions and measures which have many applications to mathematical economics and control problems. Both have received considerable attention in recent years. We study the set of selectors of the space of all p- integrable, X- valued additive set functions. This space contains an isometrically imbedded copy of Lp(X).

Integration theory for Hammerstein operators

Abstract We develop in this article a strong nonlinear integral and obtain a Riesz-type theorem (utilizing this integral) for the class of (nonlinear) Hammerstein operators. The integral is extended to the class M E( B ) of E-valued totally B -measurable functions and convergence theorems are studied. Then an exchange of information is carried out between the operators and the corresponding set functions; for example, the implication of the operator being compact or unconditionally summing is drawn. In the latter case it is shown that the representing set function is analogous to strongly bounded set functions. A vast body of literature exists for both of these concepts.

SOME DYNAMICAL PROPERTIES OF SEQUENTIALLY ACQUIRED INFORMATION

Abstract In this article we obtain two closely related theorems that essentially say that, no matter what information metric is used, on the average the value of the accumulated information at stopping time is bounded by a multiple of the expected stopping time. These results are also independent of the particular stopping strategy employed, although they do require that the expected stopping time be finite. These results, along with a general type of stopping strategy based on incremental information, are given. Later we apply our general theorem to a specific stopping strategy associated with the GIS model. Although we concentrate on the problem of stopping, the information function on which this stopping decision is based can also be used to choose the COA for the next cycle of the feedback loop. We will apply our results to an estimation problem involving the well-known Shannon-Wiener measure of information. Since our theorems require that the expected stopping times be finite, some time is devoted to a discussion of necessary and sufficient conditions for finite expected stopping times.