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Report 2018-04 from the Department of Mathematics and Statistics, McGill University, Montréal

Rapport 2018-04 du Département de mathématiques et de statistique, Université McGill, Montréal, ISSN 0824-4944

Programme and abstracts booklet for talks at the

26th International Workshop on Matrices and Statistics (IWMS-2018)

edited & prepared by:

Ka Lok Chu, Dawson College, Westmount/Montréal (Québec), Canada: gchu@dawsoncollege.qc.ca Simo Puntanen, University of Tampere, Tampere, Finland: simo.puntanen@uta.fi

& George P. H. Styan, McGill University, Montréal (Québec), Canada: geostyan@gmail.com

0.1. IWMS/57 June 2018: Introduction. The International Scientic and Organizing Committees of the 26th International Workshop on Matrices and Statistics (IWMS-2018) is delighted to have you join us at IWMS-2018 in Montréal (57 June 2018) to be held in the Multimedia Centre Rooms 3F.37, 3F.38 and 3F.43 (third oor) at Dawson College, 3040 rue Sherbrooke ouest, Westmount/Montréal.

On Tuesday 5 June 2018 we will hold a mini-symposium celebrating the 100th birth anniversary of Theodore Wilbur Anderson, Jr. (19182016). On Wednesday 6 June 2018 several talks by invited speakers will be presented, as well as some contributed talks. On Thursday 7 June 2018 we will hold the Third mini-symposium on Magic squares, prime numbers and postage stamps (IWMS-2018/M3). The rst two mini-symposia were held in Madeira, Portugal (2016) and in Westmount/Montréal (2017). For more about the IWMS-2018 Workshop please visit our IWMS-2018 website https://profchu.wixsite.com/mysite

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Our IWMS-2018 logo comprisesh= 92philatelic-friendly most-perfect pandiagonal4×4fully-magic matri- ces with equal magic sumsm92= 2946and entries then92 = 1472consecutive integers from1−1472. Our logo follows up on the logo withh= 53, m53= 1698, n53 = 848entitled ?Happy 2018? Equal Sums Magic Squares of Order 4, published by Inder J. Taneja, Numbers Magic: Magic Squares, Sele Numbers and Information Measures online at https://inderjtaneja.com/2017/12/29/2018-equal-sums-magic-squares-of-order-4/

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Contents

0.1. IWMS/57 June 2018: Introduction 1

0.2. Multimedia Centre Rooms 3F.37 and 3F.38 (third oor) at Dawson College 3

0.3. International Scientic Committee 4

0.4. International Organizing Committee 4

0.5. Participants 4

0.6. Acknowledgements 4

1. Timetable & Programme 4

1.1. Tuesday, 5 June 2018 (11:00 am/11h00): Registration with pre-lunch coee break in room 3F.43 and lunch break 4 1.2. Tuesday, 5 June 2018 (2:00 pm/14h00): Mini-symposium celebrating the 100th birth anniversary of Theodore

Wilbur Anderson, Jr. (19182016) on 5 June 1918. 4

1.3. Theodore Anderson, 98; Paved Way for Modern Data Analysis, by Regina Nuzzo: The New York Times,

vol. CLXVI, no. 57,381, page B5 (Monday, October 10, 2016) 5

1.4. Wednesday, 6 June 2018: Timetable for IWMS-2018 Invited & Contributed Talks [all talks to be held in the Multimedia Centre Rooms 3F.37 and/or 3F.38 (third oor) at Dawson College, 3040 rue Sherbrooke ouest,

Westmount/Montréal]. 6

2. Third mini-symposium on magic squares, prime numbers & postage stamps 7 2.1. Philatelic magic square for Götz Trenkler in celebration of his 75th birthday: 14 July 2018 7 2.2. Thursday, 7 June 2018: Timetable for three talks in the IWMS-2018/M3 Mini-Symposium on Magic squares, prime

numbers and postage stamps 8

2.3. Poster presentation by Richard William Farebrother 8

2.4. Poster presentations by Ka Lok Chu, Simo Puntanen & George P. H. Styan 8 2.5. Thursday, 7 June 2018: After-lunch excursion possibility Dawson College Garden of Peace 8

3. Abstracts for IWMS-2018 invited talks 9

3.1. S. Ejaz Ahmed: Post selection, estimation and prediction in sparse regression models 9 3.2. Oskar Maria Baksalary & Götz Trenkler: Representations of the MoorePenrose inverses of matrices 9

3.3. Adi Ben-Israel: Matrix volume and its applications 9

3.4. Dennis S. Bernstein: Input estimation for linear discrete-time dynamical systems 10

3.5. S. W. Drury: Some old conjectures of Bapat and Sunder 10

3.6. Yonghui Liu: Estimation and inuence diagnostics for an autoregressive model under skew-normal distributions 10

3.7. Mika Mattila: The arithmetic Jacobian matrix and determinant 10

3.8. Christopher C. Paige: The eects of loss of orthogonality on large sparse matrix computations 10 3.9. Yongge Tian: Multilevel statistical models, least-squares estimators, and reverse-order laws for generalized inverses 11

4. Abstracts for IWMS-2018 contributed talks 11

4.1. Jorge Delgado Gracia, Guillermo Peña & Juan Manuel Peña: SchoenmakersCoey matrices 11 4.2. Simo Puntanen & Augustyn Markiewicz: Linear prediction suciency in the misspecied linear model 11 5. Abstracts for the 3rd international mini-symposium on Magic squares, prime numbers & postage stamps

(IWMS-2018/M3) 12

5.1. Richard William Farebrother: Symmetric and nonsymmetric square matrices with common row and column totals expressed as weighted sums of permutation matrices, illustrated philatelically: Poster P1 12

6. Presentations by Ka Lok Chu, Simo Puntanen & George P. H. Styan 12

6.1. Poster Q4: A philatelic introduction to Dawson College, McGill University and Lord Strathcona (18201914) 12 6.2. Poster Q5: A philatelic introduction to Mersenne primes and perfect numbers 13

6.3. Poster Q6: Magic square-friendly 19 13

6.4. Talk M3a & Poster Q1: A philatelic magic square for the chemical-friendly 4×4 TrenklerTrenkler most-perfect

pandiagonal prime-magic square 14

6.5. Talk M3b & Poster Q2: Two logos and some related curiosity- and philatelic-friendly numbers 15 6.6. Talk M3c/Poster Q3: Selected new mathematical postage stamps from USA, Italy, Croatia 16

7. Updated timetable: Tuesday, 5 June 2018 17

8. Updated timetable: Wednesday, 6 June 2018 17

9. Updated timetable: Thursday, 7 June 2018 17

10. Group Photos 18

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The nal version for private circulation only. IWMS-2018/June 15, 2018: page 3

https://mail.google.com/mail/h/u0ifoo5hnjj3/?&th=16397e6ce26af311&d=u&n=3&v=c#m_16397e0342084e41 1/3

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  George Styan Fri, May 25, 2018 at 10:24 AM

  Simo Puntanen Fri, May 25, 2018 at 11:01 AM

  Garry and Michelle<garrymichellechu@yahoo.com> Fri, May 25, 2018 at 11:16 AM To: George Styan <geostyan@gmail.com>, Simo Puntanen <simo.puntanen@uta.fi>

Reply | Reply to all | Forward | Print | Delete | Show original

Hi all,

Maybe these campus maps can help. 5/25/2018 Gmail - MiniFinal-25red

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- Show quoted text -

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  George Styan<geostyan@gmail.com> Fri, May 25, 2018 at 11:24 AM

To: Simo Puntanen <simo.puntanen@uta.fi>

Reply | Reply to all | Forward | Print | Delete | Show original All looks fine, good!

***Thanks      

 Though Bertie could be out of expected participants for he is not coming.

***Indeed      

Pse confirm: I understand that you're the only speaker on Tuesday's TWA­100 Symposium. You have your slides 10 years back and they work  out nicely. Participants are certainly eager to hear about your  

connections to and history with TWA.  

***I think it would be nice if you would chair the session and then  maybe after my beamer files you would say a few words, e.g., about TWA 

& Madeira/quinta & PunSty bib file. OK?  

   

Do we have a video of Ted's talk in Tampere? 1987 I guess, 31 years ago.

    HG   =======

­ Show quoted text ­ 

0.2. Multimedia Centre Rooms 3F.37 and 3F.38 (third oor) at Dawson College. All invited and contributed talks at IWMS-2018 in Westmount/Montréal (57 June 2018) will be held in the Multimedia Cen- tre Rooms 3F.37 and 3F.38 (third oor) at Dawson College, 3040 rue Sherbrooke ouest, Westmount/Montréal.

We have requested a special password for wi internet access at Dawson College from 57 June 2018: username guestmathws with password Dawson2018

For parking at Dawson College use the south entrance at 4001 boulevard de Maisonneuve ouest (see right panel above: lower left between H and Wood Avenue). Other parking options include metered parking near the campus on the street. Indoor parking at the Alexis-Nihon shopping mall just opposite Dawson College;

the entrance to Alexis-Nihon is on rue Ste-Catherine ouest. Or park at the Pepsi Forum de Montréal (see right panel: P lower right). The Métro station for Dawson and Alexis-Nihon is Atwater. The photo (below) of Dawson College is of the main north entrance at 3040 rue Sherbrooke ouest.

4/13/2018 About Dawson – Dawson College

https://www.dawsoncollege.qc.ca/about-dawson 1/4

THIS IS THE PLACE

Dawson College is a large, long-established educational institution within Quebec’s network of CEGEPs that is woven into the fabric of academic life in Montreal. Dawson students, faculty and sta� embody a broad spectrum of languages and ethnic origins re�ective of the multicultural character of Montreal itself. This diversity greatly enriches all members of the College community by providing a welcoming and stimulating environment in which to learn and work, and where students are prepared to assume their role as

productive and responsible citizens of the world.

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0.3. International Scientic Committee. S. Ejaz Ahmed (co-chair), Hans Joachim Werner (co-chair), George P. H. Styan (honorary chair), Francisco Carvalho, Katarzyna Filipiak, Jerey J. Hunter, Daniel Klein, Augustyn Markiewicz, Simo Puntanen, Dietrich von Rosen, Júlia Volaufová.

0.4. International Organizing Committee. Ka Lok Chu (chair), Simo Puntanen, George P. H. Styan.

0.5. Participants. Joanna Baksalary, Oskar Maria Baksalary, Adi Ben-Israel, Dennis S. Bernstein, Ka Lok Chu, S. W. Drury, J. P. David Dufour, Jorge Delgado Gracia, Alexander Hariton, Joshua Hum, Michelle Kuan,

Yonghui Liu, Mika Mattila, Christopher C. Paige, Juan Manuel Peña, Simo Puntanen, Soile Puntanen,

Evelyn Matheson Styan, George P. H. Styan, Yongge Tian, Hans Joachim Werner, Magdala Werner, Douglas P. Wiens, Marilyn Wiens.

0.6. Acknowledgements. We are most grateful to Karina D'Elmo and Myriam Dimanche for their help with local arrangements at Dawson College.

1. Timetable & Programme

1.1. Tuesday, 5 June 2018 (11:00 am/11h00): Registration with pre-lunch coee break in room 3F.43 and lunch break.

1.2. Tuesday, 5 June 2018 (2:00 pm/14h00): Mini-symposium celebrating the 100th birth anniversary of Theodore Wilbur Anderson, Jr. (19182016) on 5 June 1918. rooms 3F.37, 3F.38 & 3F.43.

Abstract

This document is a handout for a special invited talk at The 17th International Workshop on Matrices and Statis- tics in Honour of Prof. T. W. Anderson’s 90thbirthday, Tomar, Portugal, 23–26 July 2008; see also [41]. We iden- tify books, edited books (and other collections including journal special issues), and book reviews by Theodore Wilbur Anderson (b. 1918). Hyperlinks are provided to reviews of these publications that are available online with JSTOR; excerpts from some of these reviews are also included. Biographical articles and one videorecord- ing about T. W. Anderson are identified. For items listed by (open-access) WorldCat First Search OCLC, a hyperlink is given with the number (as given by OCLC) of libraries worldwide that own the item (in parenthe- ses). Our presentation is illustrated with photographs of several of Anderson’s collaborators; some pictures of other well-known statisticians are also included. A soft-copy pdf file of this handout is available from the second author. This file compiled on July 13, 20081.

T. W. Anderson (June 2008) The first edition (1958)

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Tuesday, 5 June 2018 (2:00 pm/14h00): Mini-symposium celebrating the 100th birth anniversary of Theodore Wilbur Anderson, Jr. (19182016) on 5 June 1918. rooms 3F.37, 3F.38 & 3F.43.

Presentations will include (updated versions) of

• Some comments on T. W. Anderson's publications, by George P. H. Styan, with updates for George Boole, Donald A. Darling & Milton Friedman:

• An annotated and illustrated bibliography with hyperlinks for T. W. Anderson in celebration of his 90th birthday, by Simo Puntanen & George P. H. Styan,

based on presentations at the 17th International Workshop on Matrices and Statistics in Honour of Professor T. W.

Anderson's 90th Birthday (IWMS-2008), Tomar, Portugal, 2326 July 2008.

1.3. Theodore Anderson, 98; Paved Way for Modern Data Analysis, by Regina Nuzzo: The New York Times, vol. CLXVI, no. 57,381, page B5 (Monday, October 10, 2016).

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1.4. Wednesday, 6 June 2018: Timetable for IWMS-2018 Invited & Contributed Talks [all talks to be held in the Multimedia Centre Rooms 3F.37 and/or 3F.38 (third oor) at Dawson College, 3040 rue Sherbrooke ouest, Westmount/Montréal].

• 09:30 am/09h30: S. Ejaz Ahmed: Post selection, estimation and prediction in sparse regression models (abstract 3.1)

• 10:00 am/10h00: Oskar Maria Baksalary & Götz Trenkler: Representations of the MoorePenrose inverses of matrices (abstract 3.2)

• 10:30 am/10h30: Adi Ben-Israel: Matrix volume and its applications (abstract 3.3)

• 11:00 am/11h00: Coee break: room 3F.43

• 11:30 am/11h30: Dennis S. Bernstein: Input estimation for linear discrete-time dynamical systems (abstract 3.4)

• 12:00 noon/12h00: S. W. Drury: Some old conjectures of Bapat and Sunder (abstract 3.5)

• 12:30 noon/12h30: Yonghui Liu: Estimation and inuence diagnostics for an autoregressive model under skew-normal distributions (abstract 3.6)

• 1:00 pm/13h00: Lunch break

• 2:30 pm/14h30: Mika Mattila: The arithmetic Jacobian matrix and determinant (abstract 3.7)

• 3:00 pm/15h00: Christopher C. Paige: The eects of loss of orthogonality on large sparse matrix computations (abstract 3.8)

• 3:30 pm/15h30: Coee break: room 3F.43

• 4:00 pm/16h00: Yongge Tian: Multilevel statistical models, least-squares estimators, and reverse-order laws for generalized inverses (abstract 3.9)

Wednesday, 6 June 2018: Timetable for IWMS-2018 Contributed Talks

• 4:30 pm/16h30: Jorge Delgado Gracia, Guillermo Peña & Juan Manuel Peña: SchoenmakersCoey matrices (abstract 4.1)

• 5:00 pm/17h00: Simo Puntanen & Augustyn Markiewicz: Linear prediction suciency in the misspecied linear model (abstract 4.2)

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2. Third mini-symposium on magic squares, prime numbers & postage stamps organized by Ka Lok Chu, Simo Puntanen & George P. H. Styan

2.1. Philatelic magic square for Götz Trenkler in celebration of his 75th birthday: 14 July 2018.

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2.2. Thursday, 7 June 2018: Timetable for three talks in the IWMS-2018/M3 Mini-Symposium on Magic squares, prime numbers and postage stamps.

Three talks M3a, M3b, M3c by Ka Lok Chu, Simo Puntanen & George P. H. Styan:

• 10:00 am/10h00: Talk M3a: Some comments on a philatelic magic square for the TrenklerTrenkler MPPD prime-magic matrix (abstract 6.3)

• 10:30 am/10h30: Talk M3b: Some comments on two logos and on some related curiosity- and philatelic-friendly numbers (abstract 6.4)

• 11:00 am/11h00: Talk M3c: Some comments on selected new mathematical postage stamps from USA, Italy and Croatia (abstract 6.5)

2.3. Poster presentation by Richard William Farebrother.

Poster P1: Symmetric and nonsymmetric square matrices with common row and column totals expressed as weighted sums of permutation matrices, illustrated philatelically (abstract 5.1)

2.4. Poster presentations by Ka Lok Chu, Simo Puntanen & George P. H. Styan.

Poster Q1: A philatelic magic square (with details) for Götz Trenkler celebrating his 75th birthday: 14 July 2018 (abstract 6.4 for Poster Q1 and talk M3a)

Poster Q2: Some comments on philatelic stued cheese (keshi yena): bon appétit! (abstract 6.5 for Poster Q2 and talk M3b)

Poster Q3: Some more comments on Wells's ve most beautiful theorems (abstract 6.6 for Poster Q3 and talk M3c) Poster Q4: A philatelic introduction to Dawson College, McGill University & Lord Strathcona (abstract 6.1) Poster Q5: A philatelic introduction to Mersenne primes and perfect numbers (abstract 6.2)

Poster Q6: Magic square-friendly 19 (The nal report). (abstract 6.3)

2.5. Thursday, 7 June 2018: After-lunch excursion possibility Dawson College Garden of Peace.

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3. Abstracts for IWMS-2018 invited talks

3.1. S. Ejaz Ahmed: Post selection, estimation and prediction in sparse regression models. Nowadays a huge amount of data is available, and the need for novel statistical strategies to analyze such data sets is pressing. This talk focuses on the development of statistical and computational strategies for a sparse regression model in the presence of mixed signals. The search for such signals, sometimes called networks or pathways, is for instance an important topic for those working on personalized medicine. We propose a new and unique post selection shrinkage estimation strategy that takes into account the joint impact of both strong and weak signals to improve the prediction accuracy, and opens pathways for further research in such scenarios. E-mail address: sahmed5@brocku.ca

3.2. Oskar Maria Baksalary & Götz Trenkler: Representations of the MoorePenrose inverses of ma- trices. During the talk we will recall various results concerned with dierent representations of the MoorePenrose inverses of matrices. We will look at the representations from dierent perspectives demonstrating diversity of possible approaches to the subject. Among the topics discussed will be the MoorePenrose inverses of: matrices modied by matrices of rank-one, partitioned matrices, functions of a pair of Hermitian idempotent matrices, and functions of a square matrix represented by the HartwigSpindelböck decomposition. Furthermore, some of the results will shed light on the links between the MoorePenrose inverse and other generalized inverses, such as BottDun or core inverses. A number of examples dealing with applications of the MoorePenrose inverse in various areas of research (e.g., physics) will be discussed as well. E-mail address: obaksalary@gmail.com

3.3. Adi Ben-Israel: Matrix volume and its applications. E-mail address: adi.benisrael@gmail.com

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3.4. Dennis S. Bernstein: Input estimation for linear discrete-time dynamical systems. Given the output of a system, can we nd the input? For static maps, we need only construct a left inverse. This talk will focus on challenges that arise when the system has dynamics. These challenges include the stability and causality of the left inverse, knowledge of the initial condition, the achievable estimation delay, and the need to avoid unstable pole-zero cancellation. It will be shown that, for linear discrete-time systems, the answers to these questions depend on the analysis of a block-Toeplitz matrix. Finite-time and asymptotic input estimation will be shown for various classes of systems. E-mail address: dsbaero@umich.edu

3.5. S. W. Drury: Some old conjectures of Bapat and Sunder. In the mid 1980s, Bapat and Sunder made two conjectures concerning the permanents of positive semidenite matrices. Recently both of these conjectures have been shown to be false. We will present the counterexamples, place them in context and discuss some of the open proble ms in this area. E-mail address: <swdrury@hotmail.ca>

3.6. Yonghui Liu: Estimation and inuence diagnostics for an autoregressive model under skew-normal distributions. Autoregressive models have played an important role in time series. In this paper, an autoregressive model under skew-normal distributions is considered. The estimation of parameters in the model is studied based on the EM algorithm and the local inuence method is used to conduct statistical diagnostics. The normal curvature diagnostics for the model under four perturbation schemes for identifying possible inuential observations are estab- lished. After a simulation study is conducted and the performance of the proposed method is evaluated, an example of real-data analysis is presented and discussed. Our model is used to analyse weekly log-return data for Chevron shares with our local inuence analysis conducted to improve the model t. E-mail address: liuyh@lsec.cc.ac.cn

3.7. Mika Mattila: The arithmetic Jacobian matrix and determinant. Let a1, . . . , am be such real numbers that can be expressed as a nite product of prime powers with rational exponents. Using arithmetic partial derivatives, we dene the arithmetic Jacobian matrixJa of the vectora= (a1, . . . , am) analogously to the Jacobian matrixJf of a vector functionf. We introduce the concept of multiplicative independence of{a1, . . . , am} and show thatJa plays in it a similar role as Jf does in functional independence. We also present a kind of arithmetic implicit function theorem and show that Ja applies to it somewhat analogously asJf applies to the ordinary implicit function theorem. E-mail address: mika.mattila@tut.fi

3.8. Christopher C. Paige: The eects of loss of orthogonality on large sparse matrix computations. Many useful large sparse matrix algorithms are based on orthogonality, but for eciency this orthogonality is often obtained via short term recurrences. This can lead to both loss of orthogonality and loss of linear independence of computed vectors, yet with well designed algorithms high accuracy can still be obtained. Here we discuss a nice theoretical indicator of loss of orthogonality and linear independence and show how it leads to a related higher dimensional orthogonality that can be used to analyze and prove the eectiveness of such algorithms. We illustrate advantages and shortcomings of such algorithms with Cornelius Lanczos' symmetric matrix tridiagonalization process. This is the basis for several very useful large sparse matrix algorithms, and is itself very eective for solving the eigenproblem and solution of equations problems for large sparse symmetric matrices. The talk is expository, summarizing other work, and avoiding detailed error analyses. Key words & phrases: orthogonality, large sparse matrices, Lanczos process.

E-mail address: chris@cs.math.mcgill

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