Algorithms and statistics for additive polynomials

24 June, 3.00pm AEST

Speaker's Name: Professor Mark Giesbrecht
Speaker's Institution: University of Waterloo
Title of Seminar: Algorithms and statistics for additive polynomials
Host Institution:

CARMA, University of Newcastle

Time and Date:

Tuesday 24 June, 3.00pm AEST

Seminar Abstract:

The additive or linearized polynomials were introduced by Ore in 1933 as an analogy over finite fields to his theory of difference and difference equations over function fields. The additive polynomials over a finite field field F=GF(q), where q=p^e for some p, are those of the form f = f_0x+f_1x^p + f_2x^{p^2} + ... + f_mx^{p^m} in F[x].
They form a non-commutative left-euclidean principal ideal domain under the usual addition and functional composition, and possess a rich structure in both their decomposition structures and root geometries. Additive polynomials have been employed in number theory and algebraic geometry, and applied to constructing error-correcting codes and cryptographic protocols. In this talk we will present fast algorithms for decomposing and factoring additive polynomials, and also for counting the number of decompositions with particular degree sequences.
Algebraically, we show how to reduce the problem of decomposing additive polynomials to decomposing a related associative algebra, the eigenring. We give computationally efficient versions of the Jordan-Holder and Krull-Schmidt theorems in this context to describe all possible factorization. Geometrically, we show how to compute a representation of the Frobenius operator on the space of roots, and show how its Jordan form can be used to count the number of decompositions. We also describe an inverse theory, from which we can construct and count the number of additive polynomials with specified factorization patterns.
Some of this is joint work with Joachim von zur Gathen (Bonn) and Konstantin-Ziegler (Bonn).

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M-stationarity Concept for a Class of Stochastic MPCC Problems

19 June, 12.00pm AEST

Speaker's Name: Arnab Sur
Speaker's Institution: Department of Mathematics and Statistics, Indian Institute of Technology Kanpur
Title of Seminar: M-stationarity Concept for a Class of Stochastic MPCC Problems
Host Institution:

CARMA, University of Newcastle

Time and Date:

Thursday 19 June, 12.00pm AEST

Seminar Abstract:

In this talk we are going to discuss the importance of M-stationary conditions for a special class of one-stage stochastic mathematical programming problem with complementarity constraints (SMPCC, for short). M-stationarity concept is well known for deterministic MPCC problems. Now using the results of deterministic MPCC problems we can easily derive the M-stationarity for SMPCC problems under some well known constraint qualifications. It is well observed that under MPCC-linear independence constraint qualification we obtain strong stationarity conditions at a local minimum, which is a stronger notion than M-stationarity. Same result cab be derived for SMPCC problems under SMPCC-LICQ. Then the question that will arise is: What is the importance to study M-stationarity under the assumption of SMPCC-LICQ. To answer this question we have to discuss sample average approximation (SAA) method, which is a common technique to solve stochastic optimization problems. Here one has to discretize the underlying probability space and then using the strong Law of Large Numbers one has to approximate the expectation functionals. Now the main result of this discussion as follows: If we consider a sequence of M-type Fritz John points of the SAA problems then any accumulation point of this sequence will be an M-stationarity point under SMPCC-LICQ. But this kind of result, in general, does not hold for strong stationarity conditions.

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AMSI/AustMS AGR National Seminar: The C*-algebras of right-angled Artin-Tits monoids

7 July, 3.00pm AEDT

Speaker's Name:

Professor Søren Eilers

Speaker's Institution:

The University of Copenhagen

Title of Seminar:

AMSI/AustMS AGR National Seminar: The C*-algebras of right-angled Artin-Tits monoids

Host Institution:

University of Wollongong

Time and Date:

Monday 7 July, 3.00pm AEST

Seminar Abstract:

The right-angled Artin groups and semigroups are defined from undirected graphs by associating a generator to each vertex, and imposing commutativity on a pair of generators exactly when they are connected by an edge. In a completely similar vein, one can study operators on Hilbert spaces which are required to commute according to data arising from the graph. Recent insight has clarified the sense in which this latter definition is founded on the former for semigroups.

Employing classification theory for non-simple C*-algebras, we have obtained a complete description of these right-angled Artin semigroup C*-algebras by their K-theory, which reflects the geometry of the graph through the Euler characteristic. Among many other things, this leads to surprisingly strong results on the stability of such operators, showing that if a familiy of operators satisfy the relevant relations up to a small error, then they can be perturbed a bit to obtain an exact match.

This is joint work with Xin Li and Efren Ruiz.

Speaker Bio:

Professor Søren Eilers received his PhD from the University of Copenhagen in 1995. He was appointed immediately to an assistant professorship at Copenhagen, and was promoted to full Professor in 2008. He has held numerous visiting positions at international institutions like the Fields Institute in Toronto, the Mittag-Leffler institute in Stockholm, and MSRI at Berkeley, and was the president of the Danish Mathematical Society from 2006 to 2008.

Søren’s research interests lie primarily in the areas of symbolic dynamics and of operator algebras. He has contributed to the study of invariants for symbolic-dynamical systems, to the theory of stability of relations for C*-algebras, and to C*-algebraic representation theory for various sorts of dynamical systems. In recent years, Søren has instigated a program of classification of non-simple C*-algebras by K-theoretic invariants. This program has taken great strides forward and is now a major international research focus which continues to grow apace.

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AMSI AGR National Seminar: Big data computing: Science and pseudoscience

11 July, 3.00pm AEDT

Speakers:

Prof David Bailey and Prof Jon Borwein

Speakers' Institutions:

Lawrence Berkeley Lab (retired) and U.C. Davis, USA; The University of Newcastle

Title of Seminar:

AMSI AGR National Seminar: Big data computing: Science and pseudoscience

Host Institution:

University of Newcastle (CARMA)

Time and Date:

Friday 11 July, 3.00pm AEST

Seminar Abstract:

The relentless advance of computer technology, a gift of Moore’s Law, and the data deluge available via the Internet and other sources, has been a gift to both scientific research and business/industry. Researchers in many fields are hard at work exploiting this data. The discipline of “machine learning,” for instance, attempts to automatically classify, interpret and find patterns in big data. It has applications as diverse as supernova astronomy, protein molecule analysis, cybersecurity, medicine and finance. However, with this opportunity comes the danger of “statistical overfitting,” namely attempting to find patterns in data beyond prudent limits, thus producing results that are statistically meaningless.
The problem of statistical overfitting has recently been highlighted in mathematical finance. A just-published paper by the present author, Jonathan Borwein, Marcos Lopez de Prado and Jim Zhu, entitled “Pseudo-Mathematics and Financial Charlatanism,” draws into question the present practice of using historical stock market data to “backtest" a new proposed investment strategy or exchange-traded fund. We demonstrate that in fact it is very easy to overfit stock market data, given powerful computer technology available, and, further, without disclosure of how many variations were tried in the design of a proposed investment strategy, it is impossible for potential investors to know if the strategy has been overfit. Hence, many published backtests are probably invalid, and this may explain why so many proposed investment strategies, which look great on paper, later fall flat when actually deployed.
In general, we argue that not only do those who directly deal with “big data” need to be better aware of the methodological and statistical pitfalls of analyzing this data, but those who observe these problems of this sort arising in their profession need to be more vocal about them. Otherwise, to quote our “Pseudo-Mathematics” paper, “Our silence is consent, making us accomplices in these abuses."

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Gap Functions, Error Bounds and Regularization of Variational Inequalities: Part 2

17 June, 3.00pm AEST

Speaker's Name: Professor Joydeep Dutta
Speaker's Institution: Department of Mathematics and Statistics, Indian Institute of Technology Kanpur
Title of Seminar: Gap Functions, Error Bounds and Regularization of Variational Inequalities: Part 2
Host Institution:

CARMA, University of Newcastle

Time and Date:

Tuesday 17 June, 3.00pm AEST

Seminar Abstract:

Our aim in this talk is to show that D-gap function can play a pivotal role in developing inexact descent methods to solve monotone variational inequality problem where the feasible set of the variational inequality is a closed convex set rather than just the non-negative orthant. We also focus on the issue of regularization of variational inequality. Freidlander and Tseng has shown in 2007 that by the regularizing the convex objective function by using another convex function which in practice is chosen correctly can make the solution of the problem simpler. Tseng and Freiedlander has provided a criteria for exact regularization of convex optimization problems. In this section we ask the question as to what extent one can extend the idea of exact regularization in the context of variational inequalities. We study this in this talk and we show the central role played by the dual gap function in this analysis.

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