**News & Events**

**Computing Seminar**

The computing seminar usually takes place in the Science Center in Room McNulty 106 on Fridays at 1-2pm. Exceptions are noted below.

**Spring 2010**

**3/26/2010: S. A. Robila **

Montclair State University

Department of Computer Science

Hyperspectral Data - New Techniques and New Applications Hyperspectral data are remotely sensed image sets obtained by measuring the light reflected from a scene within hundreds of narrow contiguous spectral wavelength intervals. Due to its richness in information, hyperspectral imagery allows for detection of targets covering areas smaller than a pixel or separation of objects and shapes otherwise undistinguishable in regular images. The talk will provide an overview of hyperspectral images, current sensor technology and applications. Next it will discuss new results generated by the author and his collaborators, focusing on improving efficiency in processing. Most of the hyperspectral image processing techniques have complexity that depends directly on the number of spectral bands in the acquired data. Since this is usually a large number, it is of interest to find methods that transform the data cube into one with reduced dimensionality while, at the same time, maintaining as much information content as possible. Several techniques will be discussed, including Principal Component Analysis, Independent Component Analysis, Nonnegative Matrix Factorization, as well as efforts to improve computational times through parallel computing.

**Fall 2009**

**9/11/09: M. Minimair**

Seton Hall University

Department of Mathematics and Computer Science

**Maximal-Rank Minors of the Macaulay Matrix**

joint work with

Deepak Kapur

University of New Mexico

Department of Computer Science

Albuquerque, New Mexico

We study under which conditions the maximal-rank minors of a (possibly singular) Macaulay matrix vanish. The Macaulay matrix is a matrix whose entries are the coefficients of a system of multivariate polynomial equations. Macaulay matrices have applications in many areas of computing, such as computer aided geometric design, robotics, computational chemistry, etc. It is shown that the vanishing of the maximal-rank minors of the Macaulay matrix of a parametric system of polynomials under specialization is a necessary condition for the specialized polynomials to have an additional common root even when the parametric system has common roots without any specialization of parameters. This result has applications where conditions for additional common roots of polynomial systems with generic roots are needed, such as in implicitization of surfaces with base points and in various other areas of computational geometry. We discuss such applications.

**Spring 2009**

**4/24/09: P. Turner, J. Oyola, G. Riggi, A. Minarik, S. Bontempo, B. White, V. James, M. Minimair**

Department of Mathematics and Computer Science, Seton Hall University, South Orange,

**Numerical Division of Polynomials in Bernstein Basis**

The numberical accuracy if dividing univariate polynomials presented in Bernstein basis is investigated. A strategy for dynamically adjusting the floating point precision in order to improve Dr. Minimair's division algorithm is proposed.

**3/20/09: Rex Page**

Department of Computer Science, University of Oklahoma, Norman, OK

**Hard-Core Software Engineering**

Software design is a form of engineering when it applies principles of science and mathematics to the creation of software artifacts. In practice software design has generally fallen short of this standard. However, a computer program is a formal, mathematical object, which makes it amenable to the full power of symbolic reasoning. Modern tools of mechanized logic now make this power accessible to software developers. To make use of it, the application of logic and mechanized logic engines must be a standard element of computing education at the baccalaureate level.

With the support of the U.S. National Science Foundation, we have developed three courses centered around the idea of applying formal logic to software development. The first of these courses, which is required of second-year computer science students at the University of Oklahoma, covers the traditional material of symbolic logic: propositions, predicates, and rules of inference, including induction. Instead of traditional examples that reason about the mortality of men or sums of integers, all of the examples in this course reason about, and verify properties of, software components and digital circuits. The other two courses, which are required of fourth-year students, apply mechanized logic in software development projects that scale gradually from small components with tens of lines of code, to medium scale systems with thousands of lines of code.

The presentation describes the content of these courses, with a few examples for clarification, discuss the reception of the material by students and by advisers from industry who regularly review our computer science program, and speculate about potential, longer term effects of integrating symbolic logic, and especially mechanized logic, into computer science education.

**1/16/09: Manfred Minimair**

Department of Mathematics and Computer Science, Seton Hall University

**Polynomial Division in Lagrange and Bernstein Basis**

Division algorithms for univariate polynomials represented with respect

to Lagrange and Bernstein basis are developed. These algorithms are obtained by

abstracting from the classical polynomial division algorithm for polynomials

represented with respect to the usual power basis. It is shown that these

algorithms are quadratic in the degrees of their inputs, as in the power basis case

**Selected past presentations**

**9/16/08: Olivier Danvy**

University of Aarhus, Denmark

**Functional Languages and Programming**

Defunctionalization is a program transformation introduced by John Reynolds 25 years ago to "firstify" an interpreter. The goal of this work is to illustrate how defunctionalization is useful in other areas of functional programming than writing interpreters, and to present its left inverse, refunctionalization. Together, defunctionalization and refunctionalization connect the usual first-order style of writing programs and the seemingly more complex higher-order style of writing functional programs. This talk will be illustrated by simple and (one hopes) telling examples. This presentation is based on joint work with Lasse R. Nielsen and Kevin Millikin.

**4/18/08: Sarah Smith, Manfred Minimair**

Department of Mathematics and Computer Science, Seton Hall University

**Determinants of Modular Macauley Matrices **

We present ongoing work on an optimized C++ software developed for computing determinants of modular Macaulay matrices. By modular matrices we mean matrices whose entries are integer remainders modulo a given prime number. Macaulay matrices are particular matrices that arise in many applications of science and engineering when solving systems of polynomial equations. The algorithm for computing determinants is based on Gaussian elimination. This work is part of the NSF project CCF-0430741 under direction of M. Minimair