Algebraic Statistics and the Study of Multistate Models: Theory and Applications, April 1-4, 2025, Aalto and U. Helsinki
Group testing is a branch of the mathematics of communications and coding theory that is almost as old as Shannon's information theory itself. It arose from the need to screen populations of potentially infected individuals for an infectious disease with as few tests as possible, since testing was expensive or otherwise cumbersome. Current developments in the field assume that tests may be considerably cheaper but are often affected by false positives and false negatives. This reopens the line of research known as error-correcting group testing. In this talk, we revisit several old and new ideas in the language of residuation theory and show how this framework mitigates some of the awkwardness of earlier approaches to modelling the problem. We conclude the presentation with results on the error tolerance and test efficiency of various examples of error-correcting group testing schemes based on finite geometries, partial linear spaces, and other appealing combinatorial designs. Remark: This talk is dedicated to my late wife, Cornelia Roessing, who encouraged me to take up this awarding field within the mathematics of communications. It includes joint work with Oliver Gnilke (Aalborg), Johan Dinesen (Aalto), and David Forbes (UCD).
We discuss two algebraic constructions of lattices with special geometric properties. First, we consider free Z-modules spanned by algebraic conjugates of some algebraic numbers under Minkowski embedding into a Euclidean space. We are interested in conditions on the corresponding algebraic numbers that results in well-rounded nearly-orthogonal lattices with large automorophism groups. Second, we consider lattices generated by orbits of a single vector under permutation by a fixed element of the symmetric group. We show that such lattices have a great deal of structure and posess some interesting properties. One example of such lattices comes from free Z-modules in number fields and is related to the first construction.
Group testing is a branch of the mathematics of communications and coding theory that is almost as old as Shannon's information theory itself. It arose from the need to screen populations of potentially infected individuals for an infectious disease with as few tests as possible, since testing was expensive or otherwise cumbersome. Current developments in the field assume that tests may be considerably cheaper but are often affected by false positives and false negatives. This reopens the line of research known as error-correcting group testing. In this talk, we revisit several old and new ideas in the language of residuation theory and show how this framework mitigates some of the awkwardness of earlier approaches to modelling the problem. We conclude the presentation with results on the error tolerance and test efficiency of various examples of error-correcting group testing schemes based on finite geometries, partial linear spaces, and other appealing combinatorial designs. Remark: This talk is dedicated to my late wife, Cornelia Roessing, who encouraged me to take up this awarding field within the mathematics of communications. It includes joint work with Oliver Gnilke (Aalborg), Johan Dinesen (Aalto), and David Forbes (UCD).
Group testing is a branch of the mathematics of communications and coding theory that is almost as old as Shannon's information theory itself. It arose from the need to screen populations of potentially infected individuals for an infectious disease with as few tests as possible, since testing was expensive or otherwise cumbersome. Current developments in the field assume that tests may be considerably cheaper but are often affected by false positives and false negatives. This reopens the line of research known as error-correcting group testing. In this talk, we revisit several old and new ideas in the language of residuation theory and show how this framework mitigates some of the awkwardness of earlier approaches to modelling the problem. We conclude the presentation with results on the error tolerance and test efficiency of various examples of error-correcting group testing schemes based on finite geometries, partial linear spaces, and other appealing combinatorial designs. Remark: This talk is dedicated to my late wife, Cornelia Roessing, who encouraged me to take up this awarding field within the mathematics of communications. It includes joint work with Oliver Gnilke (Aalborg), Johan Dinesen (Aalto), and David Forbes (UCD).
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