Ingredients of Consensus

Des Higham, Section Editor of SIAM Review gives an overview of the Survey and Review paper in the latest issue:

In this issue, Survey and Review readers are invited to “Meet the Flockers.” The article “Heterophilious Dynamics Enhances Consensus,” by Sebastien Motsch and Eitan Tadmor, considers models of flocking and opinion formation as prototypes for self-organized dynamics. The model classes surveyed are nonlinear ODE systems where each “agent” or “particle” in the system is summarized by a vector of state values that may represent geographical location, velocity, or some other time-dependent attribute such as an opinion. The rates of change of each agent’s coordinates are then assumed to be driven by that agent’s relative difference with each other agent; see equation (1.1). The key property of interest in this article is the emergence over long time intervals of a single cluster, or consensus, where all agents tend to a common state, as happens when a jury reaches a unanimous verdict or a collection of birds forms a single flock.

The authors distinguish between models with global and local connectivity, depending upon whether influence is felt between all agents or just those who are sufficiently close in coordinate space, respectively. The techniques of analysis used to establish the results include energy and spectral methods, and they involve concepts from graph theory to handle the time-dependent connectivity structure defined by the interactions. As indicated by the choice of title, the work emphasizes the counterintuitive phenomenon that, in appropriate circumstances, notably with local models, propensity for consensus is enhanced through heterophily—a preference for bonding more closely with far-neighbors than with near-neighbors in coordinate space. In this sense, it is birds of a very different feather that stick together. (more…)

Optimal Ball Placement in Rugby Conversions

Lou Rossi, Section Editor of SIAM Review gives an overview of the Education paper in the latest issue:

One of the great ironies in mathematics instruction is that typical instructional activities are bound to textbooks. Students expect mathematical structures, concepts, and techniques to begin and end in their texts when, in fact, they spend most of their days surrounded by great mathematical problems. In the fall, students learn about vector fields in calculus, but are never asked to give a thought to the leaves swirling outside the classroom window. The mathematical sciences are the sciences of abstraction, but observations of the world around us can inspire us to think about mathematical objects and problems in new and exciting ways. In this issue of SIAM Review, our Education section features two articles, the first of which is a perfect example of finding interesting mathematical problems in sports. In this case, the sport is rugby and asking a very simple question about the best approach to earning extra points reveals a very elaborate answer. The problem evolves into an expression that needs to be solved numerically, giving us a nice segue into our second paper, which explores fixed point iterations and Newton’s methods for solving nonlinear problems; so by coincidence our two Education papers follow a natural sequence. (more…)

Resolution of Steep Internal Layers in One-Dimensional Problems

Evelyn Sander, Section Editor of SIAM Review, recaps the Research Spotlights paper in the September 2014 issue of SIREV:

Accurately estimating solutions for models of physical systems with steep internal layers is an important but difficult numerical problem. For example, the formation of alloys—such as the creation of stainless steel—involves phase separation at the atomic level of its metallic components. This can be successfully modeled, but the delicate sharp interface structure makes computational methods for approximating solutions an ambitious problem. Sharp interface systems arise in the form of elliptic partial differential equations in an array of fluids problems, in semiconductor device simulations, and in microstructure evolution of materials. (more…)

My Lucky Break: A Visit to the White House

My Lucky Break: A Visit to the White House

Daniel Szyld (Temple University), SIAM Vice President at Large, writes:

I must admit that being SIAM Vice President at Large is a hard job.

The portfolio is broad (all activity groups, all sections, all SIAM prizes, membership, and more as detailed eloquently by my predecessor, Nick Higham).  Of course, one has plenty of good moments, and a lot of satisfaction in serving the membership and the community at large.

But last month, I had an unexpected perk: a visit to the White House.

SIAM President Irene Fonseca was invited to the ceremony at the White House in which the President (yes, “the” President of the United States) would present the National Medal of Science to this year’s recipients, but was unable to attend due to prior commitments.

Hence, the honor fell on me. It was my lucky break, and I was looking forward to being there.

This year’s recipients include two SIAM members: Alexandre Chorin (University of California, Berkeley) and Thomas Kailath (Stanford University) (more…)

CBMS Forum Addresses Math Curricula for College Transition 1

CBMS Forum Addresses Math Curricula for College Transition

Peter Turner (Clarkson University), SIAM’s Vice President for Education, writes:

The Conference Board of the Mathematical Sciences (CBMS) Forum on The First Two Years of College Math: Building Student Success held in Reston, VAlast month brought together approximately 150 mathematicians and educators to advance the discussions on the vital transitional first two years of college. Motivation for the meeting was drawn from criticisms raised in the PCAST Engage to Excel report and from SIAM’s initiative in Modeling across the Curriculum among others.

Plenary sessions covered a number of topics starting with Mark Green on the Mathematical Sciences in 2025 report. Evolving Mathematical Needs in Pathways for Students was an overarching theme for subsequent plenary sessions with varying foci: Needs, What is being done (largely based around a broad view of Modeling across the Curriculum), the Needs of the Users and Employers, and implications for high schools and the Common Core curriculum. (more…)

A Call for Better Indexes 7

A Call for Better Indexes

Nick Higham (University of Manchester) writes:

An index is an important component of a book. It provides a view with a much smaller granularity than a table of contents, reveals what is not present as well as what is, and by abstracting concepts can lead the reader to unexpected content.

Most academic books in mathematics are typeset in LaTeX, which has an excellent system for indexing. By inserting \index commands in the source code, and running the MakeIndex program as part of the LaTeXing sequence, an author can iteratively build up an index during the late stages of the writing process, safe in the knowledge that the automatically generated page locators will be correct.

One might expect that the quality of indexes would have improved since the pre-LaTeX days when indexes had to be generated by hand. But in my view they have not. Most indexes I see have obvious flaws. (more…)

Outreach in the Linear Algebra Community 1

Outreach in the Linear Algebra Community

David Bindel (Secretary of the SIAM Activity Group on Linear Algebra) writes: 

Since the start of 2012, postings to the SIAG-LA mailing list have been distributed in a SIAG-LA digest at the start of each month. These postings consist primarily of conference announcements and job listings, as is the case on most of the SIAG mailing lists. As a method of communication with SIAG members, this may be adequate, but it is hardly inspiring. In the October 2014 SIAG-LA digest, I wrote to request feedback from SIAG-LA members regarding ways in which SIAG-LA might better facilitate interactions between members or with the larger SIAM community (or beyond).

Beyond being the home of award-winning expository writers, our SIAG has several members who are promoting linear algebra to the world at large through blogs, Twitter, and other social media. And this is true of SIAM more broadly, as well! SIAM is broadly engaged in experimentation with different forms of outreach. SIAG-OPT is resurrecting its Views and News newsletter; SIAG-MA has started a Facebook page; and the SIAG-OPSF newsletter includes not only pointers to recent SIAM journal articles, but also to recent arXiV preprints. SIAM UKIE maintains a bimonthly newsletter. SIAM also solicits material for SIAM Blogs and for SIAM News. (more…)

Writing for Success: Applying for Funding 1

Writing for Success: Applying for Funding

Sven Leyffer (Argonne National Laboratory) writes: 

The following are some personal observations on how to write successful proposals. These thoughts are the fruit of half a career’s worth of (mostly unsuccessful!) proposals, observations from funding agency panels, and, most important, lessons learned from the panelists at SIAM’s professional development evening at the 2014 annual meeting in Chicago.

After describing the basic ingredients of a good proposal, I elaborate on the nuts and bolts of a proposal, including formatting and deadline aspects. Then I’ve attempted to include social aspects of proposal writing, offering suggestions on writing proposals with others; finally, I list lessons I learned from the SIAM professional development session.

Ingredients of a Good Proposal

Successful proposal writing starts long before you apply for funding. You might begin by writing white papers for program managers, describing new and challenging areas of research; by participating in special workshops organized by funding agencies that help draft the eventual call for proposals; by participating in forward-looking sessions at conferences; and by simply talking to program managers. Program managers have a wealth of experience and are usually happy to share their views, as long as it is not about one of their active calls for proposals. These activities often help shape calls for proposals, and being involved from the start with your ideas means that you already have a good story when it’s time to respond to the call. (more…)

Book Review Revisited: Overton’s Numerical Computing with IEEE Floating Point Arithmetic 1

Book Review Revisited: Overton's <em>Numerical Computing with IEEE Floating Point Arithmetic</em>

Nick Higham (University of Manchester) writes:

In the June 2002 issue of SIAM Review I reviewed Michael Overton’s 2001 SIAM book Numerical Computing with IEEE Floating Point Arithmetic: Including One Theorem, One Rule of Thumb, and One Hundred and One Exercises. In this post I reproduce the review and then discuss what has changed in the thirteen years since the book was published.

The Original Review

This very attractively produced hardback book of just over 100 pages describes IEEE standard floating point arithmetic and associated issues such as hardware implementations and language support, together with some basics of numerical analysis. Its main intended audience is computer science and mathematics students, where it can serve as a supplement to more general textbooks, and its motivation (stated in the preface) is that “15 years after its publication, the key ideas of the IEEE standard remain poorly understood by many students and computing professionals”. One could argue that the standard is so well designed that the average user does not need to understand it; many of the weaknesses that plagued earlier floating point arithmetics, such as \( x-y\) evaluating to zero when \( x\) and \( y\) are different floating point numbers, are not present in IEEE arithmetic, and so the unwary programmer is much less likely to be surprised by the results produced. Nevertheless, an appreciation of the standard is useful for anyone involved in scientific computation. A self-contained, accessible and easy to read treatment dedicated to IEEE arithmetic has been lacking, and this book admirably fills the gap. (more…)

Mathematics for Future Cities 1

Mathematics for Future Cities

Des Higham (University of Strathclyde) writes:

More than half of us live or work in a city. As our digital footprints become more visible, and machine-to-machine communication more commonplace, cities can become “Living Labs.”  Researchers, governments and commercial organisations interested in issues such as energy, transport, crime, wellbeing, marketing, privacy and ethics are beginning to map out this new territory, and Future Cities/Smart Cities/Digital Cities is high on the agenda of many research funding agencies.

Glasgow recently became the UK’s flagship Smart Demonstrator City, receiving £24M of government cash to “allow public, private and academic sectors to combine expertise and use cutting-edge technology to enhance day-to-day life in the city”. Within this project, the University of Strathclyde’s Institute for Future Cities will develop a City Observatory, where data streams will be collected, analysed, acted upon and made openly available. A temporary pop-up version of the City Observatory, opened to coincide with the 2014 Commonwealth Games, has attracted 8,000 visitors in two months. Members of the public have been particularly keen to interact with a set of maps (or a three-dimensional tensor for those of us with a linear algebra view of the world) that overlays city features such as house prices, drug misuse and population density. Refer to the figure below. (more…)