Abstracts of Recent Doctoral Dissertations in Computer Algebra

Each quarter we are pleased to present abstracts of recent doctoral dissertations in Computer Algebra and Symbolic Computation. We encourage all recent Ph.D. graduates who have defended in the past two years (and their supervisors), to submit their abstracts for publication in CCA.

Each quarter we are pleased to present abstracts of recent doctoral dissertations in Computer Algebra and Symbolic Computation. We encourage all recent Ph.D. graduates who have defended in the past two years (and their supervisors), to submit their abstracts for publication in CCA.

Dynamic approaches for real-time LVCSR(Abstracts of Recent Doctoral Dissertations on Acoustics)

Abstracts of recent doctoral dissertations of interest to specialists in comparative communism

The International Symposium on Symbolic and Algebraic Computation (ISSAC) is the premier conference for research in symbolic computation and computer algebra. ISSAC 2012 is the 37th meeting in the series, started in 1966 and held annually since 1981, in North America, Europe and Asia. The conference presents a range of invited speakers, tutorials, poster sessions, software demonstrations and vendor exhibits with a centerpiece of contributed research papers.

The Canny–Emiris formula (Canny and Emiris in International symposium on applied algebra, algebraic algorithms, and error-correcting codes, 1993) gives the sparse resultant as the ratio of the determinant of a Sylvester-type matrix over a minor of it, both obtained via a mixed subdivision algorithm. In Checa and Emiris (Proceedings of the 2022 international symposium on symbolic and algebraic computation, 2022), the same authors gave an explicit class of mixed subdivisions for the greedy approach so that the formula holds, and the dimension of the constructed matrices is smaller than that of the subdivision algorithm, following the approach of Canny and Pedersen (An algorithm for the Newton resultant, 1993). Our method improves upon the dimensions of the matrices when the Newton polytopes are zonotopes and the systems are multihomogeneous. In this text, we provide more such cases, and we conjecture which might be the liftings providing minimal size of the resultant matrices. We also describe two applications of this formula, namely in computer vision and in the implicitization of surfaces, while offering the corresponding JULIA code. We finally introduce a novel tropical approach that leads to an alternative proof of a result in Checa and Emiris (Proceedings of the 2022 international symposium on symbolic and algebraic computation, 2022).

The 40th International Symposium on Symbolic and Algebraic Computation (ISSAC 2015) was held at The University of Bath, Bath, UK from 6 - 9 July 2015. It featured: • 43 Contributed Paper talks selected by the ISSAC 2015 Program Committee; • 3 Invited Speakers; • 3 Tutorial Sessions; • 12 Poster Presentations; • 6 Software Demonstrations.

During the past decade, symbolic computation has become an important problem solving tool for many algebraic calculations in physics and engineering. In this paper, we describe the nature of the field along with some of the characteristics of presently available symbolic computation systems. Some typical applications to physical problems are then considered. Analytic integration by computer is also discussed. We conclude with some considerations about the future of the field.

The aim of SNC 2009 is to offer a forum for researchers in symbolic and numeric computation to present their work, interact, exchange ideas and identify important problems in this research area. SNC 2009 continues a successful tradition of previous highly successful workshops in the area of symbolic and numeric computation: SNAP 96, held July 15-17, 1996 in Sophia Antipolis, FranceSNC 2005, held July 19-21, 2005 in Xi'an, ChinaSNC 2007, held July 25-27, 2007 in London Ontario, Canada A warm thank you goes to all those that worked hard to make SNC 2009 happen and in particular the local organizers, the program committee members, the anonymous referees, the invited speakers and the participants. The SNC 2009 Call For Papers solicited submissions in several topics: Hybrid symbolic-numeric algorithmsApproximate polynomial GCD and factorizationSymbolic-numeric methods for solving polynomial systemsResultants and structured matrices for symbolic-numeric computationDifferential equations for symbolic-numeric computationSymbolic-numeric methods for geometric computationSymbolic-numeric algorithms in algebraic geometrySymbolic-numeric algorithms for nonlinear optimizationNumeric computation of characteristic sets and Groebner basesImplementation of symbolic-numeric algorithmsApproximate algebraic algorithmsApplications of symbolic-numeric computation SNC 2009 is sponsored by the University of Tsukuba (http://www.tsukuba.ac.jp/english/). SNC 2009 is in cooperation with ACM SIGSAM (http://www.sigsam.org/) and we wish to thank the Chair of SIGSAM, Dr. Mark Giesbrecht, for his continuous help and support. SNC 2009 is also in cooperation with JSSAC, the Japan Society for Symbolic and Algebraic Computation (http://www.jssac.org/). We hope that the current book of proceedings of SNC 2009 will become a useful resource for researchers in Symbolic-Numeric Computation and other related research areas. We also hope that it will become another testament of the liveliness and vibrancy of this research area and a precursor of the future developments that await us ahead.

We present the design of a user interface program that can be used with Maple and other symbolic algebra packages. Through the use of a standard communications protocol to such a program, symbolic algebra packages can shed the bulk of code not directly ...

This thesis proposes a rigorous object-oriented methodology, supported by computer algebra software, to generate and relate features in a mathematical model. Evidence shows that there is little heuristic or theoretical research into this problem from any of the three principal modelling methodologies: 'case study’, ‘scenario’ and ‘generic’. This thesis comprises two other major strands: applications of computer algebra software and the efficacy of symbolic computation in teaching and learning. Developing the principal algorithms in computer algebra has sometimes been done at the expense of ease of use. Developers have also not concentrated on integrating an algebra engine into other software. A thorough review of quantitative studies in teaching and learning mathematics highlights a serious difficulty in measuring the effect of using computer algebra. This arises because of the disparate nature of learning with and without a computer. This research tackles relationship formulation by casting the problem domain into object-oriented terms and building an appropriate class hierarchy. This capitalises on the fact that specific problems are instances of generic problems involving prototype physical objects. The computer algebra facilitates calculus operations and algebraic manipulation. In conjunction, I develop an object-oriented design methodology applicable to small-scale mathematical modelling. An object model modifies the generic modelling cycle. This allows relationships between features in the mathematical model to be generated automatically. The software is validated by quantifying the benefits of using the object-oriented techniques, and the results are statistically significant. The principal problem domain considered is Newtonian particle mechanics. Although the Newtonian axioms form a firm basis for a mathematical description of interactions between physical objects, applying them within a particular modelling context can cause problems. The goal is to produce an equation of motion. Applications to other contexts are also demonstrated. This research is significant because it formalises feature and equation-generation in a novel way. A new modelling methodology ensures that this crucial stage in the modelling cycle is given priority and automated.

Mathematical models of biochemical reaction networks involve nonlinear differential equations with a number of parameters whose values are generally not known a priori. Analysis of such networks includes both analytical and numerical work. The analytical part of such analysis often requires manipulation with massive algebraic expressions that may become challenging due to the inherent nonlinearities and unknown parameters in the model. Computer algebra systems (CASs), which are also capable of performing calculations with symbols and to generate ready‐to‐use computer codes for numerical computations, are excellent tools in such analysis. The present work gives a brief description of how we can benefit from computer algebra to overcome such difficulties and combine symbolic and numeric computation techniques in such analysis with several illustrative biochemical reaction networks. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006

We like to fix the starting point of the research activities in Symbolic and Algebraic Computation (SAC) in Italy at the IFIP Working Conference on Symbol Manipulation Languages and Techniques held in Pisa in September 1966. This event in fact, stimulated early research conducted for several years by single researchers cooperating more with foreign colleagues than each other.

This paper describes a symbolic method for robust stability analysis of which the stability margin (k/sub M/) problem can be formulated by solving polynomial systems using symbolic computation. Once the solutions are found, the stability margin problem can be easily solved. For the complex k/sub M/ problem, no matter how many uncertainties, there is only one polynomial system which needs to be solved in order to find all singularities to determine whether the boundary of Horowitz template intercepts the origin or not. In addition, the corresponding polynomial systems can be transformed into several zero-dimensional polynomial systems which are considered as easy problems by many mathematicians and computer scientists. Therefore, we can compute exact the complex /spl mu/ efficiently by this method.

The paper describes a pilot study on the use of computer algebra at upper secondary level. A symbolic calculator was introduced in a pre-examination class studying for advanced pre-university mathematics. With the theoretical framework of Realistic Mathematics Education and Developmental Research as a background, the study focused on the identification of obstacles that students encountered while using computer algebra. Five obstacles were identified that have both a technical and a mathematical character. It is the author's belief that taking these barriers seriously is important in developing useful pedagogical strategies.