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News Article | May 22, 2017

Tamás Terlaky, chair of Lehigh University's Industrial and Systems Engineering department, along with fellow editors Miguel F. Anjos of Polytechnique Montréal and Shabbir Ahmed of Georgia Institute of Technology, has released a new textbook to "provide a solid foundation for engineers and mathematical optimizers alike who want to understand the importance of optimization methods to engineering, and the capabilities of these methods." Advances and Trends in Optimization with Engineering Applications, as published by the Mathematical Optimization Society and the Society for Industrial and Applied Mathematics (SIAM) is volume 24 of a prestigious MOS-SIAM series on optimization. This series, published jointly by the two organizations, includes research monographs, textbooks at all levels, books on applications, and tutorials. Topics covered by the series explore the theory and practice of optimization, discussing theory, algorithms, software, computational practice, applications, and the links among these subjects. Advances reviews 10 major areas of optimization and related engineering applications, providing a broad summary of state-of-the-art optimization techniques that are of crucial importance to engineering practice. "In recent years," reads the book's description, "the theory and methodology of optimization have seen revolutionary improvement. Moreover, the exponential growth in computational power, along with the availability of multicore computing with virtually unlimited memory and storage capacity, has fundamentally changed what engineers can do to optimize their designs." "From idea to product this was a 4-year-long project," Tamás explains. "The book includes 40 chapters, and covers all major areas of optimization and includes applications of modern optimization methodology in virtually all areas of engineering. Just designing its scope, content and structure took more than a year. Then, recruiting its 70 authors, among the most renowned experts in their respective fields, and working to unify terminology and notation across the content, was itself a major operation." Terlaky's research interests include high-performance optimization methods, optimization models, algorithms and software, and solving optimization problems in engineering sciences. Through his work, he harnesses algorithms to optimize the core refueling process of nuclear reactors, the radiation effectiveness of cancer treatment, the maintenance of oil refineries, the management of correctional facilities, and more. Over the course of his academic career, Terlaky has published 4 books and more than 160 scholarly papers. The topics of his publications include the theoretical and algorithmic foundations of Operations Research, and numerous engineering applications. He is founding editor-in-chief of the journal Optimization and Engineering and has served as associate editor of seven journals. He is a Fellow of the Toronto-based Fields Institute for Research in Mathematical Sciences, and has received the Canada's Mitacs Mentorship Award for his distinguished graduate student supervisory record. The book is available via SIAM's online bookstore, and will soon be available as an eBook in the SIAM digital library package for Universities and other venues.

Zarkoob H.,University of Waterloo | Taube J.H.,University of Houston | Singh S.K.,McMaster Stem Cell and Cancer Research Institute | Singh S.K.,McMaster University | And 3 more authors.
PLoS ONE | Year: 2013

In this manuscript, we use genetic data to provide a three-faceted analysis on the links between molecular subclasses of glioblastoma, epithelial-to-mesenchymal transition (EMT) and CD133 cell surface protein. The contribution of this paper is three-fold: First, we use a newly identified signature for epithelial-to-mesenchymal transition in human mammary epithelial cells, and demonstrate that genes in this signature have significant overlap with genes differentially expressed in all known GBM subtypes. However, the overlap between genes up regulated in the mesenchymal subtype of GBM and in the EMT signature was more significant than other GBM subtypes. Second, we provide evidence that there is a negative correlation between the genetic signature of EMT and that of CD133 cell surface protein, a putative marker for neural stem cells. Third, we study the correlation between GBM molecular subtypes and the genetic signature of CD133 cell surface protein. We demonstrate that the mesenchymal and neural subtypes of GBM have the strongest correlations with the CD133 genetic signature. While the mesenchymal subtype of GBM displays similarity with the signatures of both EMT and CD133, it also exhibits some differences with each of these signatures that are partly due to the fact that the signatures of EMT and CD133 are inversely related to each other. Taken together these data shed light on the role of the mesenchymal transition and neural stem cells, and their mutual interaction, in molecular subtypes of glioblastoma multiforme. © 2013 Zarkoob et al.

News Article | November 30, 2016

John Friedlander of the University of Toronto and Henryk Iwaniec of Rutgers University will receive the 2017 AMS Joseph L. Doob Prize. The two are honored for their book Opera de Cribro (AMS, 2010). The prime numbers, the building blocks of the whole numbers, have fascinated humankind for millennia. While it has been known since the time of Euclid that the number of primes is infinite, exactly how they are distributed among the whole numbers is still not understood. The Latin title of the prizewinning book by Friedlander and Iwaniec could be translated as A Laborious Work Around the Sieve, where in this context a "sieve" is a mathematical tool for sifting prime numbers out of sets of whole numbers. The Sieve of Eratosthenes, dating from the third century BC, is a simple, efficient method to produce a table of prime numbers. For a long time, it was the only way to study the mysterious sequence of the primes. In the early 20th century, improvements came through the work of Norwegian mathematician Viggo Brun, who combined the Sieve of Eratosthenes with ideas from combinatorics. Tools from another branch of mathematics, complex analysis, came into play through the work of English mathematicians G.H. Hardy and J.E. Littlewood, and of the iconic Indian mathematician Srinivasa Ramanujan (protagonist of the 2016 film The Man Who Knew Infinity). For 30 years, Brun's method and its refinements were the main tools in sieve theory. Then, in 1950, another Norwegian mathematician, Atle Selberg, put forward a new, simple, and elegant method. As his method was independent of that of Brun, the combination of the two gave rise to deep new results. The latter part of the 20th century saw the proof of many profound results on classical prime-number questions that had previously been considered inaccessible. Among these was a formula for the number of primes representable as the sum of a square and of a fourth power, obtained by Friedlander and Iwaniec in 1998. With these developments, the time was ripe for a new book dealing with prime-number sieves and the techniques needed for their applications. Written by two of the top masters of the subject, Opera de Cribro is an insightful and comprehensive presentation of the theory and application of sieves. In addition to providing the latest technical background and results, the book looks to the future by raising new questions, giving partial answers, and indicating new ways of approaching the problems. With high-quality writing, clear explanations, and numerous examples, the book helps readers understand the subject in depth. "These features distinguish this unique monograph from anything that had been written before on the subject and lift it to the level of a true masterpiece," the prize citation says. The two prizewinners collaborated on an expository article on number sieves, "What is the Parity Phenomenon?", which appeared in the August 2009 issue of the AMS Notices. Born in Toronto, John Friedlander received his BSc from the University of Toronto and his MA from the University of Waterloo. In 1972, he earned his PhD at Pennsylvania State University under the supervision of S. Chowla. His first position was that of assistant to Atle Selberg at the Institute for Advanced Study. After further positions at IAS, the Massachusetts Institute of Technology, the Scuola Normale Superiore in Pisa, and the University of Illinois at Urbana-Champaign, he returned to the University of Toronto as a faculty member in 1980. He was Mathematics Department Chair from 1987 to 1991 and since 2002 has been University Professor of Mathematics. He was awarded the Jeffery-Williams Prize of the Canadian Mathematical Society (1999) and the CRM-Fields (currently CRM-Fields-PIMS) Prize of the Canadian Mathematical Institutes (2002). He gave an invited lecture at the International Congress of Mathematicians in Zurich in 1994. He is a Fellow of the Royal Society of Canada, a Founding Fellow of the Fields Institute, and a Fellow of the AMS. Born in Elblag, Poland, Henryk Iwaniec graduated from Warsaw University in 1971 and received his PhD in 1972. In 1976 he defended his habilitation thesis at the Institute of Mathematics of the Polish Academy of Sciences and was elected to member correspondent. He left Poland in 1983 to take visiting positions in the USA, including long stays at the Institute for Advanced Study in Princeton. In 1987, he was appointed to his present position as New Jersey State Professor of Mathematics at Rutgers University. He was elected to the American Academy of Arts and Sciences (1995), the US National Academy of Sciences (2006), and the Polska Akademia Umiejetnosci (2006, foreign member). He has received numerous prizes including the Sierpinski Medal (1996), the Ostrowski Prize (2001, shared with Richard Taylor and Peter Sarnak), the AMS Cole Prize in Number Theory (2002, shared with Richard Taylor), the AMS Steele Prize for Mathematical Exposition (2011), the Banach Medal of the Polish Academy of Sciences (2015), and the Shaw Prize in Mathematical Sciences (2015, shared with Gerd Faltings). He was an invited speaker at the International Congress of Mathematicians in Helsinki (1978), Berkeley (1986), and Madrid (2006). Presented every three years, the AMS Doob Prize recognizes a single, relatively recent, outstanding research book that makes a seminal contribution to the research literature, reflects the highest standards of research exposition, and promises to have a deep and long-term impact in its area. The prize will be awarded Thursday, January 5, 2017, at the Joint Mathematics Meetings in Atlanta. Find out more about AMS prizes and awards at http://www. . Founded in 1888 to further mathematical research and scholarship, today the American Mathematical Society fulfills its mission through programs and services that promote mathematical research and its uses, strengthen mathematical education, and foster awareness and appreciation of mathematics and its connections to other disciplines and to everyday life.

Turner C.,University of Waterloo | Kohandel M.,University of Waterloo | Kohandel M.,Fields Institute
Journal of Theoretical Biology | Year: 2010

Under the cancer stem cell (CSC) hypothesis, sustained metastatic growth requires the dissemination of a CSC from the primary tumour followed by its re-establishment in a secondary site. The epithelial-mesenchymal transition (EMT), a differentiation process crucial to normal development, has been implicated in conferring metastatic ability on carcinomas. Balancing these two concepts has led researchers to investigate a possible link between EMT and the CSC phenotype-indeed, recent evidence indicates that, following induction of EMT in human breast cancer and related cell lines, stem cell activity increased, as judged by the presence of cells displaying the CD44high/CD24low phenotype and an increase in the ability of cells to form mammospheres. We mathematically investigate the nature of this increase in stem cell activity. A stochastic model is used when small number of cells are under consideration, namely in simulating the mammosphere assay, while a related continuous model is used to probe the dynamics of larger cell populations. Two scenarios of EMT-mediated CSC enrichment are considered. In the first, differentiated cells re-acquire a CSC phenotype-this model implicates fully mature cells as key subjects of de-differentiation and entails a delay period of several days before de-differentiation occurs. In the second, pre-existing CSCs experience accelerated division and increased proportion of self-renewing divisions; a lack of perfect CSC biomarkers and cell sorting techniques requires that this model be considered, further emphasizing the need for better characterization of the mammary (cancer) stem cell hierarchy. Additionally, we suggest the utility of comparing mammosphere data to computational mammosphere simulations in elucidating the growth characteristics of mammary (cancer) stem cells. © 2010 Elsevier Ltd.

Turner C.,Dalhousie University | Kohandel M.,University of Waterloo | Kohandel M.,Fields Institute
Seminars in Cancer Biology | Year: 2012

The last decade has witnessed significant advances in the application of mathematical and computational models to biological systems, especially to cancer biology. Here, we present stochastic and deterministic models describing tumour growth based on the cancer stem cell hypothesis, and discuss the application of these models to the epithelial-mesenchymal transition. In particular, we discuss how such quantitative approaches can be used to validate different possible scenarios that can lead to an increase in stem cell activity following induction of epithelial-mesenchymal transition, observed in recent experimental studies on human breast cancer and related cell lines. The utility of comparing mammosphere data to computational mammosphere simulations in elucidating the growth characteristics of mammary (cancer) stem cells is discussed as well. © 2012 Elsevier Ltd.

Rose S.C.F.,Queen's University | Rose S.C.F.,Fields Institute
Communications in Number Theory and Physics | Year: 2014

In this paper, we produce a generating function for the number of hyperelliptic curves (up to translation) on a polarized Abelian surface using the crepant resolution conjecture and the Yau-Zaslow formula. We present a formula to compute these in terms of MacMahon's generalized sum-of-divisors functions, and prove that they are quasi-modular forms.

Tiglay F.,Ecole Polytechnique Federale de Lausanne | Tiglay F.,Fields Institute | Vizman C.,West University of Timișoara
Letters in Mathematical Physics | Year: 2011

We develop the necessary tools, including a notion of logarithmic derivative for curves in homogeneous spaces, for deriving a general class of equations including Euler-Poincaré equations on Lie groups and homogeneous spaces. Orbit invariants play an important role in this context and we use these invariants to prove global existence and uniqueness results for a class of PDE. This class includes Euler-Poincaré equations that have not yet been considered in the literature as well as integrable equations like Camassa-Holm, Degasperis-Procesi, μCH and μDP equations, and the geodesic equations with respect to right-invariant Sobolev metrics on the group of diffeomorphisms of the circle. © 2011 Springer.

Lyaghfouri A.,Fields Institute
Advanced Nonlinear Studies | Year: 2011

In this paper we consider the problem of minimizing the functional J(u) = ∫Ω(1/p(x)|∇u|p(x) + Q(x)Χ[u≥0])dx. We prove Lipschitz continuity for each minimizer u and establish the nondegeneracy at the free boundary (∂[u ≥ 0]) ∩ Ω and the locally uniform positive density of the sets [u ≥ 0] and [u = 0]. In particular we obtain that the Lebesgue measure of the free boundary is zero.

Berg C.,Fields Institute
Electronic Journal of Combinatorics | Year: 2010

In this paper I introduce a new description of the crystal B(Λ0) of sie. As in the Misra-Miwa model of B(Λ0), the nodes of this crystal are indexed by partitions and the i-arrows correspond to adding a box of residue i. I then show that the two models are equivalent by interpreting the operation of regularization introduced by James as a crystal isomorphism.

Berg C.,Fields Institute
Electronic Journal of Combinatorics | Year: 2010

Vazirani and the author [Electron. J. Combin., 15 (1) (2008), R130] gave a new interpretation of what we called ℓ-partitions, also known as (ℓ, 0)-Carter partitions. The primary interpretation of such a partition λ is that it corresponds to a Specht module Sλ which remains irreducible over the finite Hecke algebra Hn(q) when q is specialized to a primitive ℓth root of unity. To accomplish this we relied heavily on the description of such a partition in terms of its hook lengths, a condition provided by James and Mathas. In this paper, I use a new description of the crystal regℓ which helps extend previous results to all (ℓ, 0)-JM partitions (similar to (ℓ, 0)- Carter partitions, but not necessarily ℓ-regular), by using an analogous condition for hook lengths which was proven by work of Lyle and Fayers.

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