New Orthogonal Polynomials and their Applications

We propose development and validation of novel mathematical tools which can be

used for information processing for object and/or model identification and detection within

decision support systems (DSS) in various decision frameworks such as situation

assessment and analysis, genetic modeling and analysis, medical imaging, etc. The project

will have two main novel contributions: (1) introducing new families of polynomials and (2) the

discretization of old and new polynomials. Specifically, in the proposed research, symmetries

of n dimensional lattices for defining families of orthogonal functions and orthogonal

polynomials will be exploited in order to be used in n dimensional Fourier analysis in digital

and analog signal processing, as well as in object and pattern recognition methods. The

aforementioned symmetries have been recently linked to knot symmetries and to DNA

properties, [BPP]. The project aims at better in-depth understanding the of these relations which will further lead to fundamental contributions in knot theory and group theory and their

various practical applications……………….

Faculty Supervisor:

Jiri Patera

Student:

Partner:

OODA Technologies Inc

Discipline:

Mathematics

Sector:

Professional, scientific and technical services

University:

Université de Montréal

Program:

Accelerate

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