ACA 2016Kassel (Germany) August 1st - 4th
22nd Conference on Applications of Computer Algebra August 1st - 4th, 2016 Kassel University Germany
Computer Algebra Systems and the Lambert W Function
I have worked on many aspects of computer algebra systems, mostly in conjunction with either Soft Warehouse (Derive) or Maplesoft (Maple). One particular project has touched many of the challenges that system developers face: the implementation of the Lambert W function. In this talk, I shall present some of the interesting properties of W, and use them to discuss the various challenges that our favourite systems continue to grapple with. Some examples of such challenges are branch cuts, simplification, numerical evaluation, integration.
Exploring a Homotopy Approach to the Science of Data: Huge Scenarios, Topological Scintigraphy and Flagellate Structures
Given a cloud of points (or dataset) embedded in some high dimensional space, Topological Data Analysis focuses on recovering topological information of an unknow lower dimensional space within which the previous dataset is sampled. At present, this information is obtained mainly using algorithms for computing persistent homology. In this talk, we introduce some basic notions and algorithms for providing a more advanced topological analysis of the datasets, based on homotopy concepts and higher order (co)homological statistics. This theory generating asymmetric topological dynamics in a "huge" or "classifying" data scenario is presented here using the relevant and informative analogy of "breathing topological life to a digital image". The promising conclusions regarding not only the power of topological discrimination of this technique but also its potential feasibility of a parallel processing allow to be optimistic about opening a door to a new area of Data Analysis: Homotopy-based Data Analysis and Recognition.
Real Problems over the Reals: From Complete Elimination Procedures to Subtropical Decisions
Effective quantifier elimination procedures for first-order theories provide a powerful tool for generically solving a wide range of problems based on logical specifications. In contrast to general first-order provers, quantifier elimination procedures are based on a fixed set of admissible logical symbols with an implicitly fixed semantics. This admits the use of sub-algorithms from symbolic computation. We are going to focus on quantifier elimination for the reals and its applications giving examples from geometry and verification. Beyond quantifier elimination we are going to discuss recent results on an incomplete decision procedure for the existential fragment of the reals, which has been successfully applied to the analysis of reaction systems in chemistry and in the life sciences. We conclude with an overview on further quantifier-eliminable theories that have been realized in our open-source computer logic software Redlog (www.redlog.eu).
What's New in Maple 2016
We will present some of the new features in Maple 2016, in the areas of thermophysical computations, structured data manipulation, physics, series and limit computations, symbolic integration and summation, differential equations, statistics, graph theory, and others, and discuss some applications.