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Volume 52/ Issue 1 January/February 2019

Life Sciences Special Issue Understanding Knowledge In this special issue, explore the application of mathematics and computational science to numerous topics in the life sciences. Networks in the Brain By Matthew R. Francis be tested experimentally. Fundamental research on brain networks can potentially ne strength of the human mind is facilitate the understanding and treatment O its ability to find patterns and draw of conditions as diverse as schizophrenia connections between disparate concepts, and Parkinson’s disease. a trait that often enables science, poetry, In mathematical terms, a network is a visual art, and a myriad of other human type of graph: a set of points connected by endeavors. In a more concrete sense, the lines. The particular model for knowledge brain assembles acquired knowledge and networks is based on the assumption that links pieces of information into a network. humans essentially experience phenomena Knowledge networks also seem to have as discrete events or concepts arranged a physical aspect in the form of intercon- sequentially in time. Each of these is mod- nected neuron pathways in the brain. eled as a node in a graph, with lines called During her invited address at the 2018 “edges” linking them together. The edges SIAM Annual Meeting, held in Portland represent possible transitions between the Ore., last July, Danielle Bassett of the events or concepts; a particular graph thus University of Pennsylvania illustrated how describes how knowledge networks inter- brains construct knowledge networks. Citing connect ideas. The first big question for this early 20th century progressive educational model is whether optimal pathways of con- reformer John Dewey, she explained that the nectivity that maximize learning exist. goal of a talk—and learning in general—is to map concepts from the speaker/teacher’s Hot Thoughts and Modular Thinking Figure 2. Scout bees apply a head-butt stop signal to dancers promoting alterna- mind to those of his or her listeners. When To address this problem, Bassett and tive nest sites. Image courtesy of James Nieh. the presenter is successful, the audience her collaborators constructed a knowledge In an article titled “Multi-Agent Decision-Making in Design” on gains new conceptual networks. network consisting of nodes that represent page 6, Paul Davis reports on Naomi Leonard’s use of nonlinear More generally, Bassett explored how random stimuli. Each node was connected dynamics to design multi-agent control systems, taking cues from humans acquire knowledge networks, to the same number of other nodes—cre- collective animal behavior. whether that process can be modeled math- ematically, and how such models may See Knowledge Networks on page 4 Mathematical Models of Cell Invasion Track Spatial Position and

Progression through the Cell Cycle

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Bellmawr, NJ Bellmawr, By Matthew J. Simpson Nonprofit Org Nonprofit Pe Fisher-Kolmogorov equation [3, 4, 6]. We imental methodology called the Fluorescent patial spreading of cell populations is can write this equation in one dimension as Ubiquitination-based Cell Cycle Indicator S crucial for embryonic development, (FUCCI) [5] enabled real-time analysis of tissue repair, and malignant invasion. 2   the cell cycle. FUCCI provides spatial and ∂s ∂ s  s  During embryonic development, various = D +−ls 1 , (1) temporal information about the cell cycle’s ∂t 2  K  types of tissues and organs with different ∂x   progression through fluorescent probes that functions evolve from an initially homoge- glow red when the cell is in the first gap neous population of cells in the very early where sx(,t)> 0 represents cell density, (G1) phase of the cycle and green when embryo. Normal development requires that D> 0 is cell diffusivity, l > 0 signifies the in the synthesis (S), second gap (G2), or these structures arise with the correct cell cell proliferation rate, and K > 0 denotes mitotic/cell division (M) phases [5, 9]. types in the appropriate three-dimensional the environment’s carrying capacity den- Figure 1a depicts still images from a time- geometry, a process that necessitates simul- sity. This simple mathematical model sup- lapse movie of a FUCCI-transduced mela- taneous migration and growth of cell popu- poses that cells undergo an unbiased ran- noma cell that illustrate these colour changes lations. Abnormal cell migration during dom walk and proliferate logistically so that during the cell cycle. A visual comparison of adulthood is associated with pathological some initial density will evolve—through the phase contrast image of a C8161 melano- conditions like cancer invasion and metas- a combination of diffusion and carrying- ma spheroid (see Figure 1b) and a correspond- tasis. While motility of individual cells is capacity limited growth—to produce mov- ing FUCCI-transduced spheroid (see Figure crucial for population-level spreading, cell ing fronts. Such fronts lead to the coloni- 1c) confirms that the FUCCI system reveals a proliferation plays an important and some- zation of initially-vacant regions that will great deal about the relationship between spa- times overlooked role in driving spatial eventually reach carrying capacity density tial location and the cell cycle. For example, expansion of cell populations [4]. K. For certain initial and boundary condi- freely cycling cells—indicated by the mixture Previous researchers have employed both tions, (1) can yield travelling wave solutions of red and green fluorescence—are visible on continuum differential-equation models and [4]. This type of modelling framework has the FUCCI spheroid’s outer shell. Upon look- discrete models that use lattice-based random successfully described a range of phenom- ing deeper into the spheroid, we observe cells walks, lattice-free random walks, and cellu- ena related to collective cell spreading and that are largely arrested in the G1 (red) phase, lar automata to mathematically model spatial cell invasion, from the study of simple in presumably due to a lack of nutrients such as spreading in cell populations. Continuum vitro scratch assays to in vivo malignant mathematical models of combined cell motil- brain tumour progression. See Cell Cycle on page 2

Figure 1. Experimental images and conceptual model for the cell cycle as revealed by FUCCI labelling. 1a. Time-lapse images depicting the progression of three generations of FUCCI-transduced C8161 melanoma cells through the cell cycle. The numbers in each subfigure indicate the time in hours. 1b. Phase contrast image of a C8161 melanoma spheroid with an approximate diameter of 0.5 millimeters. 1c. Image of a slice of a C8161 melanoma spheroid of similar size to 1b where the cells are transduced with FUCCI. 1d. Conceptual model of FUCCI technology. 1e. Experimental data presenting quantification of the rate of red-to-green and green-to-red transitions for the C8161 melanoma cell line. 1a courtesy of [2], 1b and 1c courtesy of [1], 1d and 1e courtesy of [8]. SOCIETY for INDUSTRIAL and APPLIED MATHEMATICS 3600 Market Street, 6th Floor Philadelphia, PA 19104-2688 USA 2 • January/February 2019 SIAM NEWS

Cell Cycle Continued from page 1 Volume 52/ Issue 1/ January/February 2019 oxygen. The spheroid’s centre completely 5 Politics, Policy, lacks fluorescence; this indicates the presence Science, and Risk of a necrotic core. Unsurprisingly, FUCCI Paul Davis reviews Michael technology has revolutionized the analysis Lewis’s The Fifth Risk, which of cell proliferation and has applications in describes politics’ impact experimental models of cancer, stem cell, and on federal science, specifi- developmental biology [9]. cally at the Departments of We have recently sought to develop and Energy, Agriculture, and validate continuum models of cell invasion Commerce. Lewis interviews for use with FUCCI technology [7, 8]. We experts in the field who employ FUCCI-transduced C8161 mela- describe potential risks in noma cells and perform a series of scratch the electric grid and radioac- assays to observe cell migration; these tive waste storage, as well as disappearing data on climate assays involve creating a “scratch” in a cell change and natural disasters. monolayer and capturing images close to the scratch at regular intervals. Next we attempt 6 Forward-Looking Panel to quantitatively describe these experiments at MPE18 Examines the with a new continuum model — a generali- Intersection of Mathematics sation of the Fisher-Kolmogorov equation. and Environmental Science Figure 2a shows a population of FUCCI- How do mathematicians con- transduced C8161 melanoma cells on a two- duct successful interdisciplinary dimensional substrate following the creation work and foster collaborations of a 0.5 millimeter artificial scratch in the within various areas of climate population. Figure 2d displays the same science? What are some of the experiment after 18 hours; now we see that future’s biggest challenges? the cells have moved into the initially-vacant Climate scientists pondered these and other questions dur- region while continuing to progress through ing a forward-looking panel at the cell cycle. To model these experiments, we last year’s SIAM Conference suppose that the cell population—with total on Mathematics of Planet density sx(,t)—consists of two subpopula- Figure 2. Comparison of experiential images, experiential data, and solutions of the new

Earth. Hans Engler and Emil tions, yielding sx(,tv)(=+rgxt,) vx(,t). mathematical model for scratch assays with FUCCI-transduced melanoma cells. 2a-2c. Initial Constantinescu offer a recap. Here vx(,t) is the red cell density in the G1 condition for experimental modelling comparison th= 0. 2d-2f. Comparison of experimental r observation and modelling prediction th= 18 . 2a and 2d display images of a scratch assay phase and vx(,t) is the green cell density in g with C8161 melanoma cells where the scratch’s initial width is approximately 0.5 millimeters. the S/G2/M phases. Assuming that both sub- We extract density profiles at th= 0 from 2a and plot them in 2b and 2c, where the red populations undergo diffusive migration and profile corresponds to cell density in the G1 phase, the green profile corresponds to cells in proceed through the cell cycle, we encode the S/G2/M phases, and the black profile corresponds to total density. We also extract density profiles at th= 18 from 2d and plot them in 2e. Solutions of (2) and (3) in 2f—obtained with this information into a generalisation of the 2 D = 400uhm/2 , D = 400uhm/2 , k = 0./ 084 h, k = 0./ 079 h, and K = 0 004. cells/um — Fisher-Kolmogorov equation given by r g r g compare very well with experimental profiles in 2e. Figure courtesy of [8].

2 9 Trump Administration ∂v ∂ v Kolmogorov equation existing as a linearly anticipate further refinements in these math- r =  r Releases Update to STEM ∂t r ∂x 2 decreasing function of total density. ematical modelling tools to keep pace with Strategic Plan (2) To determine whether (2) and (3) can new advances in experimental cell biology.  s  The National Science and   predict the spatial and temporal dynamics of −+kkrrvv21gg − , Technology Council has released  K  the scratch assay in Figure 2a, we divide each References the federal government’s five- image of the assay into a series of equally- [1] Beaumont, K.A., Anfosso, A., Ahmed, year strategic plan for science, 2 spaced columns. Counting the number of F., Weninger, W., & Haass, N.K. (2015). technology, engineering, and ∂v ∂ v g =  g red and green cells per column and dividing Imaging- and flow cytometry-based analysis mathematics education. Planned g 2 ∂t ∂x by the column area estimates the total cell of cell position and the cell cycle in 3D mel- objectives that are relevant to (3) anoma spheroids. J Vis. Exp., 106, e53486.  s  density and the density for both the red and the SIAM community include −−kkv 1, + v [2] Haass, N.K, Beaumont, K.A., Hill, gg  rr green subpopulations (see Figure 2b). The contextual integration of math-  K  D.S., Anfosso, A., Mrass, P., Munoz ematics across disciplines and density profile in 2e portrays the system’s state after 18 hours. Two main outcomes are M.A.,…Weninger, W. (2014). Real-time incorporation of computational where  > 0 is the diffusivity of cells in the r apparent: the initially-vacant region is now cell cycle imaging during melanoma thinking in higher education. G1 phase,  > 0 is the diffusivity of cells in growth, invasion, and drug response. Pig. g occupied, and the cell cycle continues as the the S/G2/M phases, k > 0 is the rate of cell Cell Melan. Res., 27, 764-776. 10 SIAM Announces r density of cells away from the initially-vacant [3] Jin, W., Shah, E.T., Penington, C.J., Major CS&E Prizes transition from the G1 phase to the S/G2/M region approximately doubles. Solving (2) McCue, S.W., Chopin, L.K., & Simpson, Jack Dongarra of the University phases, and k > 0 is the rate of cell transi- g and (3) for the initial condition in Figures 2b M.J. (2016). Reproducibility of scratch of Tennessee is the 2019 recipi- tion from the S/G2/M phases to the G1 phase. and 2c generates the prediction in Figure 2f, assays is affected by the initial degree of con- ent of the SIAM/ACM Prize Terms proportional to k model the red- r which matches the experimental observation fluence: experiments, modelling and model in Computational Science to-green transition. This transition is con- in Figures 2d and 2e remarkably well. selection. J. Theor. Biol., 390, 136-145. and Engineering, while Julia servative because the positive term in (3) In summary, the continuum modelling [4] Maini, P.K., McElwain, D.L.S., & Computing’s Jeff Bezanson, balances the negative term in (2). Terms framework in (2) and (3) shows promise Leavesley, D.I. (2004) Traveling wave Stefan Karpinski, and Viral proportional to model the green-to-red kg model to interpret a wound-healing cell Shah will receive the James H. in quantifying experimental investigations transition, which is not conservative due to migration assay for human peritoneal meso- Wilkinson Prize for Numerical with FUCCI technology. Researchers can the factor of two in (2) that reflects this tran- thelial cells. Tissue Eng., 10, 475-482. Software. Both prizes will be extend this type of modelling platform in sition’s association with cell division. This [5] Sakaue-Sawano, A., Kurokawa, H., awarded at the upcoming SIAM multiple ways, such as in the context of dif- also explains why we include the nonlinear Morimura T., Hanyu, A., Hama, H., Osawa, Conference on Computational ferent geometries and coordinate systems. logistic parameter in terms proportional to H.,…Miyawaki, A. (2008). Visualizing spa- Science and Engineering. One could also develop an analogous set k , since this event would require suf- tiotemporal dynamics of multicellular cell- g of modelling tools based on a discrete ran- 11 Professional Opportunities ficient space to accommodate the daughter cycle progression. Cell, 132, 487-498. dom walk with exclusion and subsequently [6] Sherratt, J.A., & Murray, J.D. (1990). and Announcements agent. Our result is directly analogous to the apply these tools to reveal both population- per capita proliferation rate in the Fisher- Models of epidermal wound healing. Proc. level and individual-level properties [7]. We R. Soc. Lond. B., 249, 29-36. [7] Simpson, M.J., Jin, W., Vittadello, Editorial Board Geosciences T. Mayo, University of Central Florida, USA S.T., Tambyah, T.A., Ryan, J.M., Gunasingh, H. Kaper, Editor-in-Chief, Georgetown University, USA Imaging Science K. Burke, University of California, Davis, USA G., …McCue, S.W. (2018). Stochastic mod- G. Kutyniok, Technische Universität Berlin, Germany els of cell invasion with fluorescent cell ISSN 1557–9573. Copyright 2019, all rights A.S. El-Bakry, ExxonMobil Production Co., USA Linear Algebra reserved, by the Society for Industrial and Applied J.M. Hyman, Tulane University, USA R. Renaut, Arizona State University, USA cycle indicators. Physica A, 510, 375-386. L.C. McInnes, Argonne National Laboratory, USA Mathematics, SIAM, 3600 Market Street, 6th Floor, Mathematical Aspects of Materials Science [8] Vittadello, S.T., McCue, S.W., Philadelphia, PA 19104-2688; (215) 382-9800; siam@ S. Minkoff, University of Texas at Dallas, USA Q. Du, Columbia University , USA N. Nigam, Simon Fraser University, Canada Mathematics of Planet Earth Gunasingh, G., Haass, N.K., & Simpson, siam.org. To be published 10 times in 2017: January/ H. Kaper, Georgetown University, USA February, March, April, May, June, July/August, A. Pinar, Sandia National Laboratories, USA M.J. (2018). Mathematical models for cell R.A. Renaut, Arizona State University, USA Nonlinear Waves and Coherent Structures September, October, November, and December. K. Oliveras, Seattle University, USA migration with real-time cell cycle dynam- The material published herein is not endorsed by Optimization SIAM, nor is it intended to reflect SIAM’s opinion. A. Wächter, Northwestern University, USA ics. Biophys J., 114, 1241-1253. The editors reserve the right to select and edit all Orthogonal Polynomials and Special Functions [9] Zielke, N., & Edgar, B.A. (2015). material submitted for publication. Representatives, SIAM Activity Groups P. Clarkson, University of Kent, UK FUCCI sensors: powerful new tools for Uncertainty Quantification Algebraic Geometry E. Spiller, Marquette University, USA analysis of cell proliferation. WIREs Dev T. Crick, Universidad de Buenos Aires, Argentina Advertisers: For display advertising rates and Applied Mathematics Education Biol., 4, 469487. information, contact Kristin O’Neill at P. Seshaiyer, George Mason University, USA [email protected]. Computational Science and Engineering P. Constantine, Colorado School of Mines, USA SIAM News Staff Matthew J. Simpson is a professor of One-year subscription (nonmembers): Electronic- Control and Systems Theory J.M. Crowley, editorial director, [email protected] applied mathematics at Queensland only subscription is free. $73.00 subscription rate F. Dufour, INRIA Bordeaux Sud-Ouest, France K.S. Cohen, managing editor, [email protected] worldwide for print copies. SIAM members and Discrete Mathematics L.I. Sorg, associate editor, [email protected] University of Technology in Australia. His subscribers should allow eight weeks for an address D. Hochbaum, University of California, Berkeley, USA research interest is broadly in the area of change to be effected. Change of address notice Dynamical Systems should include old and new addresses with zip codes. K. Burke, University of California, Davis, USA mathematical biology, with specific atten- Printed in the USA. Please request address change only if it will last six Geometric Design tion to stochastic modelling, computational J. Peters, University of Florida, USA months or more. is a registered trademark. mathematics, and experimental cell biology. January/February 2019 SIAM NEWS • 3 New Results in Stochastic Analysis Using Dynamical Systems Theory By Lora Billings probability of observing a given number tence. We use a Monte Carlo algorithm to leading order of a Taylor series expansion and Eric Forgoston of individuals in a population at a cer- evolve the population in time [5]. In Figure 1, of the scaled master equation results in a tain time. As the master equation gener- the population persists near what appears to Hamilton-Jacobi equation with an effective ith its long history in a variety of ally cannot be solved analytically, we use be an oscillating steady state and eventually Hamiltonian, for which we analyze the zero- W fields, stochastic analysis contin- a Wentzel-Kramers-Brillouin-Jeffreys drops to zero via spontaneous extinction. Our energy solutions. The WKBJ approximation ues to challenge modelers. Noise plays an (WKBJ), or eikonal, approximation to the goal is to develop a method to analytically introduces a conjugate momentum vari- important functional role in changing a master equation. This ansatz approximates predict the average time of occurrence for able pi=∂(,ti)/∂ , which doubles the system’s dynamics in applications across the probability density function for the sys- an extinction event. Numerous simulations system’s dimension but reveals additional mathematical finance, physics, and biology tem dynamics and leads to the development reveal the existence of many possible escape dynamics that stem from stochasticity. [7]. Researchers in multiple disciplines have of a Hamiltonian system. The Hamiltonian’s paths, with extinction taking place at differ- The advantage of recasting the prob- developed numerous approaches and nota- dimensions are twice the dimensions of the ent times. Aggregation of simulation data lem in terms of the conjugate momen- tions to understand the dynamics beyond original system’s mean-field equation due demonstrates a path along which extinction is tum is that it reveals a higher-dimensional numerical simulation. Adding to the com- to the conjugate momenta variables, which most likely to occur. This optimal path coin- Hamiltonian system with steady states clas- plexity, one can model noise as an external capture the effects of noise. The benefit is cides with the manifold connecting steady sified as saddles and centers. This allows a source or a collection of random internal that the transformed system is deterministic states in the corresponding Hamiltonian sys- trajectory to escape from the deterministi- processes, and few have considered incor- and lends itself to dynamical systems theory. tem. Identifying the action along the optimal cally stable endemic limit cycle through the porating either concept into models with For instance, standard methods can identify path lets researchers determine the mean expanded p space (see Figure 2, on page time-dependent forcing. Inspired by the work steady states, which correspond to the meta- time of escape from a steady state or the 5). Specifically, there exists a heteroclinic in [2, 4], we find that classical tools from stable states in the original stochastic system. average time to an extinction event. trajectory connecting it to the fluctuational As an example, consider a time-depen- The analytical approach uses the WKBJ extinction state for which i = 0 and p ¹ 0. dynamical systems and perturbation theory −Ni(,t) provide an intuitive way to analyze stochastic dent susceptible-infected-susceptible (SIS) approximation r =e for the prob- If one rewrites the Hamiltonian using epidemiological models with seasonal forc- model consisting of a finite population of ability distribution in the master equation, a linear expansion in d, the Poincaré- ing and predict noise-induced rare events. N individuals divided into two groups: sus- for which  is the action and the state vari- Birkhoff fixed point theorem guarantees ceptibles and infectives. The flux terms for able i is the scaled infective population. The Seasonal forcing is important in epidemic See Stochastic Analysis on page 5 modeling because contact rates and other these groups are as follows. An individual parameters may vary in time in diseases like is born susceptible, assuming a constant measles, mumps, and chickenpox. This is birth rate. Through contact modeled by a evident from the periodic and aperiodic recur- mass action approximation, he/she may rence of such conditions, as observed in pre- become ill and be classified as infectious. vaccine United States data and English and We suppose that the contact rate varies Welsh data [1]. Our recent work considers a throughout the year in a periodic fashion, general class of dynamical models with inter- approximated by the time-dependent func- tion ()tt=+(c12os( )), where t nal noise that symbolizes demographic sto- ββ0 δπ is time, is the average contact rate, and chasticity, or random interactions of individu- b0 als [3]. Our model can represent any group d is a small parameter. Assuming an aver- of well-mixed individuals from the nano- to age recovery rate, the individual recovers macro-scale. We study disease dynamics in a and returns to the susceptible group. While human population that requires seasonality to removal by natural death is possible from accurately capture the force of infection, and both groups, we presume the absence of focus on internal random dynamics that can disease-related deaths in this model. induce a rare, spontaneous disease eradication. Figure 1 offers a numerical realization of Figure 1. A realization of the stochastic SIS model with seasonality exhibiting an extinction event. We plot the number of infectives ()I in time ()t in blue. Note how the graph follows To understand random dynamics, one can this stochastic time-dependent SIS model for parameters that support the disease’s persis- the red curve, which represents the endemic limit cycle given by the solution to the mean field use a master equation that describes the equation (p = 0, no noise). Image courtesy of [3]. Updates from the December SIAM Board Meeting By James Crowley deployment of algorithms for combinatorial Tondeur Donation Looking Ahead problems formulated from applications. It SIAM leadership wishes to thank Philippe Through a set of ad hoc committees, the t its December meeting, the SIAM complements—but does not replace—the Tondeur (University of Illinois at Urbana- Board has started further discussion on a A Board of Trustees took many signifi- SIAG on Discrete Mathematics, which will Champaign) for his very generous donation variety of issues, motivated in part by SIAM’s cant actions of interest to members, includ- continue operation according to its approved to SIAM. Philippe contributed $100,000 to deficits over the past few years. SIAM News ing changes in membership options and charter. A biennial SIAM conference will be SIAM—and a similar amount to its sister readers will hear more about the results from approval of a new SIAM activity group organized by the SIAG. Further details about societies, the American Mathematical Society these committees in future updates. (SIAG), conference, and section. SIAG/ACDA will be forthcoming. and the Mathematical Association of America January 1 was a date of many transitions, Besides this new SIAG, the Board (MAA)—to support the mission of the BIG as newly-elected members of the Board and Going Green recently authorized the creation of the Math Network,3 a joint collaboration among Council assumed office and new committee Of note is the move towards a greener SIAM Conference on Mathematics of Data several organizations to raise awareness and memberships took effect. We would like to option with cost savings. SIAM member- Science. The inaugural meeting will occur promote opportunities for mathematics stu- thank all outgoing committee members for ship has always included a print copy of in the spring of 2020 and be co-locat- dents’ employment in business, industry, their service. Two particular transitions are of SIAM Review. In its desire to reduce SIAM’s ed with—but independent of—the SIAM and government. The BIG Math Network— note: Lisa Fauci (Tulane University), elected carbon footprint and save money, the Board Conference on Data Mining. The dates formerly chaired by Rachel Levy (MAA), in the fall of 2017, takes over as SIAM agreed to make receipt of the print copy of and location are still being finalized at the then SIAM Vice President for Education—is President after one year as President-Elect. SIAM Review an opt-in selection. Members time of this writing. Like a standard SIAM currently led by Fadil Santosa (University of Nick Higham (University of Manchester) who do not actively indicate their preference conference, the data science conference Minnesota). SIAM is developing programs, becomes Past President for 2019. to continue to receive the print copy in their will feature minisymposia and invited talks. in coordination with the BIG Math Network, We also welcome Richard Moore to next renewal will not receive it. Of course, Its topical coverage will be similar to areas to carry out Philippe’s wishes. SIAM as the new Director of Programs and served by the new SIAM Journal on the Services. Richard is replacing Linda Thiel, all members will retain access to the online 1 version as part of their membership. Mathematics of Data Science, which began Changes to the Fellows Program who retired in late 2018. Along the same lines, the Board moved accepting papers in 2018. The SIAM Fellows Program has been In the fall of 2018, the Board also approved Suggestions? to eliminate paper copies of full programs 2 very popular in recent years in terms of from conferences whenever practical the SIAM Northern States Section — a nomination submissions. The large number SIAM is happy to receive suggestions (except for the Program-at-a-Glance, which new SIAM section that covers a region of of nominations necessitated several modi- from its members. You can do this through will still be available in print). The online the U.S. including the Dakotas, Montana, fications, including an earlier nomination the footer of any page of the SIAM website,5 program and the mobile app (for those Utah, and Wyoming. As is standard prac- submission deadline to provide the Fellows where an item labeled “Suggestions” links conferences that provide apps) will allow tice, members of SIAM living in the des- Selection Committee with more review to a form that states, “Whether you want to attendees to find information on sessions ignated region are considered members of time. This year’s nominations will close on recommend a member to a leadership posi- and talks at future SIAM meetings. the section. Sections hold regional meet- Wednesday, October 16. To simplify the tion, add your company to our list of career ings, workshops, and conferences. The first selection process and ensure fairness, some resources, weigh in on our new website, ask Activity Groups and Sections meeting of the Northern States Section will standardization of nomination packages will a question, or anything else, we want to hear take place in the fall of 2019. Additional The Board also approved creation of also be enforced. See the Fellows website4 from you.” Let us know if you have a ques- conversation about regional sections—their the SIAM Activity Group on Applied and for details pertaining to specifications on tion or suggestion. Suggestions made on the purpose, funding, and governance—will Computational Discrete Algorithms (SIAG/ page length, font size, etc. SIAM thanks site go to me, the executive director, and I occur at a later date. ACDA). This SIAG grew in part out of a those involved for their hard work in making ensure that the appropriate person or com- this a successful program. mittee receives and reacts to each message. series of SIAM workshops on Combinatorial 1 Scientific Computing but has expanded cov- https://www.siam.org/Publications/ Journals/SIAM-Journal-on-Mathematics-of- James Crowley is the executive director erage to include more subjects. SIAG/ACDA Data-Science-SIMODS 3 https://bigmathnetwork.org/ of SIAM. fosters research on the design, theoretical 2 https://www.siam.org/Membership/ 4 https://www.siam.org/Prizes-Recognition/ analysis, computational evaluation, and Sections/Detail/siam-northern-states-section Fellows-Program 5 https://www.siam.org 4 • January/February 2019 SIAM NEWS

Knowledge Networks Continuing with the phys- Continued from page 1 ics metaphor, this model is akin to the difference ating a k-regular graph, in graph theory between materials at vari- terms—to ensure equal transition prob- ous temperatures. Solids are abilities between nodes. often highly ordered at low The researchers tested human reactions, temperatures, with atoms assigning key presses or abstract “avatars” arranged in predictable pat- to every node. Test subjects “learned” terns; raising temperatures the graph by performing set tasks, and destroys the order, giving Bassett’s team quantified these perfor- rise to random and time-vari- mances based on the amount of time the able fluid arrangements. subjects spent responding to each task. The experiments involved two types of graphs: Networks and Learning graphs in which nodes clustered together in Bassett then presented a groups and graphs with evenly-connected larger question: Is it possible nodes in a more lattice-like structure. For to design optimal knowledge example, consider a four-regular graph of networks that help people 15 nodes where each node is connected learn? As is moderately obvi- Figure 2. Recall of tasks can be modeled using statistical mechanics, where the inverse “temperature” b param- to four others. The modular graph could ous, there is much individual eterizes the probability of recall over time. High temperature or low b produces a messy graph recall, while lower simply cluster the nodes into three linked variation among humanity in temperatures represent increased accuracy. The darkness of the graphs’ edges indicates how well subjects remember the transitions between tasks on the graph topology from Figure 1. Figure courtesy of [4]. groups of five (see Figure 1), while the terms of cognitive function. lattice-like graph lacks modules [3]. At the same time, the mind’s Ultimately, network models facilitate one’s Bassett, D.S. (2015). Controllability of struc- Although both graphs were k-regular, ability to reconstruct modular patterns understanding of how the mind, and possibly tural brain networks. Nat. Comm., 6, 8414. subjects learned the modular graphs more seems to indicate a general, shared means the brain itself, functions. Thus, research- [3] Kahn, A., Karuza, E.A., Vettel, J.M., efficiently and performed faster on transi- of operation. Bassett posed the question ers could extend many areas of applied & Bassett, D.S. (2018). Network constraints tions between nodes within a module than as follows: Are the actual, physical neural mathematics—currently used in information on learnability of probabilistic motor transitions between modules themselves, networks in a brain modular? theory, network control, and thermodynam- sequences. Nat. Hum. Behav., 2, 936-947. regardless of the nature of the task. Edges To explore this hypothesis, she and ics—to the study of the mind. Such connec- [4] Lynn, C.W., Kahn, A.E., & Bassett, D.S. (2018). Structure from noise: Mental between clusters are called “cross-cluster her collaborators tested subjects while tions satisfy the human impulse to find and errors yield abstract representations of surprisal” because they had slower reaction they were inside a magnetic resonance transform patterns into something new. events. Preprint, arXiv:1805.12491. times than those within modules. imaging (MRI) machine. They found that [5] Medaglia, J.D., Zurn, P., Sinnott- These results suggest that human minds real brain networks are multilayered and Bassett’s presentation is available from Armstrong, W., & Bassett, D.S. (2017). “lump” concepts together, a premise that dynamic, as opposed (for example) to one SIAM either as slides with synchronized Mind control as a guide for the mind. Nat. 1 is borne out by other psychological tests. static group of cells that routinely corre- audio or a PDF of slides only. Hum. Behav., 1, 0119. Despite having equal transition probabilities sponds to learning. for all graph edges, the brain evidently dis- More to the point, the flexibility of References Further Reading tinguishes between topological “distances” physical brain networks apparently linked [1] Braun, U., Schäfer, A., Walter, H., Kim, J.Z., Soffer, J.M., Kahn, A.E., Vettel, by the type of transition performed in the to individual cognitive capabilities. Low Erk, S., Romanczuk-Seiferth, N., Haddad, J.M., Pasqualetti, F., & Bassett, D.S. (2018). graph. This indicates that humans implicitly flexibility limited subjects’ ability to L,…Bassett, D.S. (2015). Dynamic recon- Role of graph architecture in controlling recognize the graph’s topology. learn and retain information, but Bassett’s figuration of frontal brain networks dur- dynamical networks with applications to To quantify how well test subjects team noted that certain test subjects with ing executive cognition in humans. PNAS, neural systems. Nat. Phys., 14, 91-98. recalled the learned material, Bassett and schizophrenia exhibited very high flex- 112(37), 11678-83. her colleagues assigned a probability to ibility along with other deficits in func- [2] Gu, S., Pasqualetti, F., Cieslak, M., Matthew R. Francis is a physicist, sci- time interval Dt between when the event tion, leading the group to hypothesize an Telesford, Q.K., Yu, A.B., Kahn, A.E.,… ence writer, public speaker, educator, and frequent wearer of jaunty hats. His website actually happened and when the subjects optimal range for flexibility to support 1 https://www.pathlms.com/siam/courses/ is BowlerHatScience.org. thought it occurred. Drawing on thermal cognitive performance [1]. 8264/sections/11794 physics, the team associated Dt with the Bassett and her colleagues were interest- concept of cognitive “free energy,” which ed in connecting their mathematical model the brain minimizes to reduce computa- with the MRI results to examine a possible tional resources and recall errors [4]. correlation between cognitive control and In this language, the probability P of brain dynamics. MRI studies indicate that recall for a given time interval Dt after network control increases as children devel- an event is op, approaching an asymptotic maximum roughly at age 20 in healthy brains [2]. 1 When discussing cognitive abilities and Pt()∆ = e−b∆t , Z mental health, researchers must always be cautious about ethical complications. where Z is the partition function Bassett and her collaborators are prudent to argue that one should handle issues involv- − ∆t ing brain control with caution in order to Z = e b ∑ prevent misuse [5]. Understanding the way ∆t the mind works leads to questions of how and b is the parameter that sets the and when mind control modification is pos- distribution scale. Bassett suggested that sible or advisable. While control structures humans operate at a particular “temper- can be beneficial in treating some cognitive ature” T ~ 1/b that changes over the conditions resulting from lack of internal course of their lives (this is similar to how control, they can give rise to possible misus- temperature is defined in information the- es as well (and not just science-fiction-style ory). High “temperatures” (limit as b ® 0) whole-brain hijacking scenarios). result in a flat probability distribution, Bassett presented a therapeutic argument which means poor graph recall. Low “tem- for this avenue of research: if human brains peratures” (b →∞) ensure that the prob- control their network functions in particu- ability drops precipitously for nonzero Dt lar ways, introducing external controls to values, thus corresponding to an accurate change or enhance certain behaviors might memory. For moderate “temperatures,” the be possible. For conditions like epilepsy or subjects reproduce the basic graph — but Parkinson’s disease, these modifications with some errors (see Figure 2). could be extremely helpful.

Figure 1. Test subjects had better reaction times (RTs) for switching tasks arranged on nodes within clusters on a graph than for tasks across clusters (left). The graph topology also affected performance, with better behavior on clustered nodes than nodes with a lattice-like topology (right), even when both graphs had the same number of edges per node. Figure adapted from [4]. January/February 2019 SIAM NEWS • 5 Politics, Policy, Science, and Risk The Fifth Risk. By Michael Lewis. W.W. cial risks using his experience in law and that managing risks is an act of the imagi- shocked by the possibilities that lurked Norton & Company, New York, NY, October investment banking. MacWilliams’s remit nation.” Humans can respond to a real-time in the raw piles of information the gov- 2018. 256 pages, $26.95. quickly expanded to encompass all risks crisis better than they can conceive of one ernment had acquired.” Lewis writes. “‘I facing the DOE, including nuclear weap- that is forthcoming. “There is another way didn’t grasp the scope at first,’ he said.” ichael Lewis’s 2010 best-seller, The ons, nuclear power generation, spent fuel to think of John MacWilliams’s fifth risk: “After Trump took office,” Lewis M Big Short, describes the global econ- disposal, the electric power grid, and more. the risk a society runs when it falls into reports, “DJ Patil watched with wonder omy’s catastrophic fall onto the sharpened Sitting across from MacWilliams at his the habit of responding to long-term risks as the data disappeared across the gov- stakes in the pit of subprime mortgages. He kitchen table, Lewis sought to emulate the with short-term solutions,” Lewis writes. ernment.” Links to climate change data tells the tale through the eyes of prescient— transition briefing that never “‘Program management’ is evaporated, along with reports of consum- if sometimes idiosyncratic—players who happened. “Just give me the not just program manage- er complaints about businesses. Statistics were “in the room where it happened,” as top five risks I need to worry BOOK REVIEW ment…It is what you never on access to drinking water in Puerto Aaron Burr raps to Alexander Hamilton in about right away,” he brusque- By Paul Davis learned that might have saved Rico vanished two weeks after Hurricane Lin-Manuel Miranda’s eponymous musical. ly demanded of MacWilliams. you.” It is the best kind of sci- Maria. Nearly three-quarters of the data Lewis’s latest book, The Fifth Risk, tells “Start at the top.” MacWilliams want- ence — conceiving the inconceivable. tables in the annual FBI crime report dis- its story of politics, policy, and science ed to describe an accident with nuclear With that sobering warning in mind, the appeared. Links to weather forecasts on with similar energy and an analogous set weapons, but Lewis—like the phantom remaining chapters on the Departments of the NOAA site moved from prominence of engaged and engaging characters. But transition team—lacked a security clear- Agriculture and Commerce are distress- to obscurity. All sorts of data that could unlike the widespread economic devastation ance. Generalities had to suffice. The same ing yet engrossing. Admiration for the fuel discovery, insight, and understanding described in The Big Short, politics has not constraint limited MacWilliams’s descrip- work of Lewis’s heroes competes with fell from public reach. quite pushed the entirety of federal science tion of his second concern over what You might wonder what awful things into the pit. The dazed victim is merely tee- proposed risk to two could happen with- could arise from neglecting the Department tering on the edge, punctured and bleeding words: North Korea. out such stalwarts at of Agriculture, Lewis’s third subject. When but not yet fully lacerated. Despite the secu- the ramparts; most of Lewis asked one recently retired senior The Fifth Risk is a quick and grip- rity restrictions, Lewis’s sources are official to identify his primary concern, he ping read. A prologue describes the will- MacWilliams and reporting after leav- replied, “Wildfires.” Yet we have heard fully determined ignorance underlying the his former col- ing Washington. little about them in the news recently! Trump administration’s neglectful transi- leagues from the The final section The entirety of The Fifth Risk, brief tion. Three subsequent chapters tell tales DOE said enough to on the Department as it is, offers compelling accounts of of the aftermath, one each for the U.S. frighten Lewis. They of Commerce will scientists, engineers, and science-savvy Departments of Energy, Agriculture, and spoke of precarious draw many SIAM government employees struggling to keep Commerce. For scientists who have spent scenarios involv- readers through its the lights on in their hard-won corners of time in Washington, D.C., reading Lewis’s ing—but not limited focus on the National expertise. Lewis’s intense account of poli- account is likely akin to sitting down with a to—technical fail- Oceanographic tics’ heavy hand falling on government John le Carré thriller set in a familiar place. ures in the electric and Atmospheric science should draw more civic-minded Caught up in the fast-paced plot, they are grid or storage of Administration scientists into government. The SIAM transported back to locations they know, radioactive waste. (NOAA). This agen- members and their colleagues who heed brain-numbing corridors in monolithic gov- Of course, more than cy consumes more Lewis’s call are unlikely to become central ernment offices, ideas, policy debates, and a few SIAM mem- than half of the characters in his next book. Nonetheless, talking points. They see skeletons that rattle bers have studied Commerce budget they will have a memorable opportunity like ones they might have hauled through aspects of both pos- to generate and ana- to learn and serve during a critical time in those same buildings, even if the flesh that sibilities in depth. lyze big data—really our shared professions. falls from the bones in Lewis’s narrative Compared to these The Fifth Risk. By Michael Lewis. Courtesy big data—to predict of W.W. Norton & Company. differs from their own experiences. Hollywood-style the weather. Lewis Paul Davis is professor emeritus of math- The first chapter’s setting in the disaster situations, MacWilliams’s “fifth reminds readers that the Department of ematical sciences at Worcester Polytechnic Department of Energy (DOE) is most likely risk,” which lends the book its title, seems Commerce also houses the U.S. Patent and Institute. He served as an assistant pro- to produce a le-Carré-esque response among anticlimactic. He identifies this titular risk Trademark Office and the National Institute gram manager in applied mathematics at mathematicians. The DOE’s national labs as “project management.” But where is of Standards and Technology, home to other the Army Research Office from 1974 to are central to applied and computational the risk in project management? Are the active SIAM members. 1975, where his duties included managing mathematics. Many SIAM members have scientists managing research programs— DJ Patil appears frequently in this proposal evaluations and advocating for worked in or visited these labs, while others whether as rotators or permanent staff at chapter. Patil began his career study- the Mathematics Research Program. As have served as rotators in the department’s DOE laboratories, the National Science ing dynamical systems and hacking into a Jefferson Science Fellow from 2007 to research program offices. Foundation, Office of Naval Research, the National Weather Service to grab 2008, Davis was a Senior Science Advisor Lewis found DOE alumnus John Army Research Office, Air Force Office of weather data for his doctoral research. in the Bureau of East Asian and Pacific Affairs of the U.S. Department of State. MacWilliams at home five months after he Scientific Research, Department of Defense, He was appointed Chief Data Scientist His primary responsibility was establishing had left the department, his briefing books etc.—really engaged in perilous work? Was in President Barack Obama’s Office of the structure of an agreement for scien- untouched by the Trump transition team. MacWilliams making a bad joke about paper Science and Technology Policy. Despite tific cooperation between the United States In 2013, then-Secretary-of-Energy Ernest shufflers’ exposure to paper cuts? Patil’s high-level view of government and the 10 nations of the Association of Moniz (a physicist, not a politician) invited Certainly not. Lewis explains that data, some things still caught him off Southeast Asian Nations. MacWilliams to assess the DOE’s finan- MacWilliams’s “more general point was guard. “In the end, even DJ Patil was

Stochastic Analysis analyze the extinction event in Figure 1 (on [2] Assaf, M., Kamenev, page 3). Additional detail for this example is A., & Meerson, B. (2008). Continued from page 3 available in our published work [3]. Population extinction in a existence of the perturbed hyperbolic Much work remains pertaining to the time-modulated environ- points. The presence of a corresponding het- analysis of rare noise-induced transition ment. Phys. Rev. E, 78(4), eroclinic trajectory depends on the optimal events in time-dependent models. For epi- 041123. correction to the action, or the minimization demic models, such as the aforementioned [3] Billings, L., & Forgoston, E. (2018). of  with respect to initial time t . Finding SIS model, knowledge of the optimal path 0 Seasonal forcing in stochas- the zeros of the derivative of  yields an enables discovery of the mean time to tic epidemiology models. integral of a Poisson bracket of the unper- extinction from the endemic state, which Ricerc. Mat., 67(1), 27-47. turbed Hamiltonian and the time-dependent is verifiable by stochastic realizations. [4] Dykman, M.I., Rabitz, Hamiltonian evaluated on the unperturbed Determining the mean time to extinction H., Smelyanskiy, V.N., & optimal path; this integral is the perturbed allows researchers to quantify the effect of Vugmeister, B.E. (1997). problem’s Melnikov function. A sufficient various control schemes—including vacci- Resonant directed diffusion condition for the perturbed optimal path’s nation pulses and treatment—on infectious in nonadiabatically driven Figure 2. The phase space for Hamilton’s equations with forcing, existence is the Melnikov function’s pos- disease. More generally, one can use classi- systems. Phys. Rev. Lett., which corresponds to the stochastic SIS model with seasonal- session of simple zeros. We can numerically cal dynamical systems theory to understand 79, 118-1181. ity. Note the location of the endemic and fluctuational extinc- evaluate this equation to identify a periodic noise-induced transitions in a wide variety [5] Gillespie, D.T. tion states and the connecting manifold. Approximation of the set of zeros, which determines the phase for of stochastic problems, from biology to (1976). A general method optimal path found with the iterative action minimizing method for numerically simulating numerical scheme appears in red. The implicit ordinary differen- the optimal correction to the action. physics. Some examples include genetic tial equation solution is plotted in black. Image courtesy of [3]. While we cannot explicitly solve the time- switching, pest eradication, and bit error the stochastic time evolu- dependent Hamilton’s equations, we can rate in communication systems. As scien- tion of coupled chemical deterministic and stochastic dynamical sys- reactions. J. Comput. Phys., 22(4), 403-434. numerically approximate the heteroclinic tists increasingly discover more systems tems that model applications in epidemiol- [6] Lindley, B.S., & Schwartz, I.B. ogy, physics, and ecology. Eric Forgoston manifold via the optimal correction — or that exhibit rare events, we look forward (2013). An iterative action minimizing is an associate professor of applied math- appropriate phase defined by initial time t . to the implementation of old and new tech- 0 method for computing optimal paths in ematics at Montclair State University. His One can use the implicit MATLAB solver niques to understand the effect of stochas- stochastic dynamical systems. Phys. D: research involves the study of complex ode15i to do so. We compared the results ticity and control measures. Nonlin. Phenom., 255, 22-30. physical and biological phenomena, includ- with those from the iterative action minimiz- [7] Tsimring, L.S. (2014). Noise in biol- ing material transport in the ocean, the out- ing method [6], a numerical scheme based on References ogy. Rep. Prog. Phys., 77(2), 026601. break and extinction of infectious diseases, Newton’s Method. Figure 2 depicts agree- [1] Anderson, R.M., May, R.M., & behavior of biological and robotic swarms, ment of the time-dependent optimal paths Anderson, B. (1992). Infectious Diseases Lora Billings is dean of the College of food web dynamics in ecological systems, resulting from the two different numerical of Humans: Dynamics and Control. New Science and Mathematics at Montclair State and the stability of fluid flows. methods. One can now use the paths to York, NY: Oxford University Press. University. Her research focuses on applied 6 • January/February 2019 SIAM NEWS Multi-Agent Decision-Making in Design By Paul Davis decision-making dynamical system (see such as that of house-hunting honeybees. the remaining few either committed to A Figure 1a). The handle of a stable pitch- After the birth of a new queen, the old queen or undecided U —when site B is more aomi Ehrich Leonard of Princeton fork bifurcation diagram represents dead- and about half of her fellow bees abandon valuable than A. In both the model and in N University and her colleagues employ lock; the twin forks that spring from it their hive in search of a new nest. Scout bees nature, the swarm chooses the better site. a bold approach when designing controls as the decision parameter changes sig- set off to investigate suitable nest sites. They There are three possible outcomes in for multi-agent systems. “[We use] the tools nify the choices competing to attract con- report the direction and distance of sites case of a tie in the value v of two sites: a of nonlinear dynamics to connect collective sensus. The tools of singularity theory that they find, promoting the sites’ qualities lasting tie or a choice between one of the decision-making in animal groups with the allow designers to “translate from nature with a sophisticated “waggle-dance” while two locations (see Figure 4, on page 7). design of collective decision-making in robot- to design and back again,” Leonard says. competitors try to stop them with head butts The difference between a tie and a deci- ic groups,” she says. For example, she asks She adds that the systematic translation of (see Figure 2, on page 1). The house-hunting sion depends on the strength of the scouts’ if capturing such collective behavior could the physical mechanisms that explain animal swarm reacts efficiently to the scouts when commitment to their preferred sites. A frame the development of a control system behavior to a “bio-inspired design meth- choosing the best site; the swarm can even tie’s steady-state, which occurs when an enabling turbines in a wind farm to respond odology” is difficult. This is because most reliably break ties between sites of near- equal number of scouts vote for A as for collectively, similarly to a flock of birds. animal behavior studies are empirical rather equal value, in contrast to the befuddled B, changes from stable to unstable when Could they react to changes in wind direction, than model-based, use simulation models house hunters on reality television. the bifurcation parameter s—the strength given the constraints of their limited sensing, that are not easily generalized, or rely on To begin quantifying these ideas, Leonard of the stop signal, in this case the head communication, and computation? mean-field behavior that fails to reveal the explores a pair of differential equations for butts—delivered to a scout for the other site Instead of attempting to capture the effects of heterogeneity or system structure. the fraction of the swarm preferring either increases from 0.2 to 5. system’s essential physical properties, Despite these challenges, Leonard and her site A or B. Figure 3 (on page 7) illus- Figure 5 (on page 7) summarizes the Leonard and her collaborators aim for team have identified the fundamentals of trates the transitions in this dynamic mixing honeybees’ value-sensitive decision-mak- a pitchfork bifurcation: the fundamental bio-inspired design for some remarkable model that lead to one possible steady-state ing when a classic pitchfork bifurcation mathematical property of a multi-party examples of collective decision-making, outcome—a quorum committed to B with governs the stop signal’s response. If the shared value of the two sites is relatively small, the scouts may wait for a third, better option or send a more intense stop signal s and make a stronger commitment to render a tie unstable and force a stable decision for one site or the other. This value-sensitive decision-making is also robust to perturbations in system parameters. Figure 1a shows the original pitchfork bifurcation for sites of equal value as the stop signal increases; 1b por- trays the qualitatively similar diagram with saddle node bifurcation for sites of fixed, slightly different values; and 1c depicts the Figure 1. Value-sensitive decision-making persists when a system is perturbed. 1a. The original pitchfork bifurcation for sites of equal value as behavior as the difference in the values of the stop signal increases. 1b. The qualitatively similar diagram with a saddle node bifurcation for sites of fixed, slightly different values (unfolding). 1c. Decision behavior with variation in the difference of the sites’ values for a fixed stop signal. Image courtesy of [1]. See Decision-Making on page 7 Forward-Looking Panel at MPE18 Examines the Intersection of Mathematics and Environmental Science By Hans Engler and involving mathematical scientists. Hobbs Emil Constantinescu talked about the science team working with NASA’s Orbiting Carbon Observatory 2 he second SIAM Conference on satellite—which collects spatiotemporal T Mathematics of Planet Earth, information related to environmental sci- sponsored by the Activity Group on ence—and Rousseau acknowledged high- Mathematics of Planet Earth (SIAG/MPE), level institutional collaborations through took place last fall in Philadelphia, Pa. the International Science Council, which During the meeting, a forward-looking was founded in July 2018. The council’s panel on emerging topics—in the style of first president is a mathematician. a well-attended panel from the inaugural A question from the audience sug- SIAG/MPE conference two years earlier— gested that some MPE themes, such as attracted a sizable crowd. “Planet Earth as a physical system” and Panelists included Beth Wingate “Planet Earth as a system at risk,” might (University of Exeter), Mihai Anitescu be more amenable to interdisciplinary (Argonne National Laboratory and The collaboration than others, like “Planet University of Chicago), Hans G. Kaper Earth as a system supporting life” and (Georgetown University), Christiane “Planet Earth as a system organized by humans.” Reluctant to agree with this Panelists discuss present and future research at the 2018 SIAM Conference on Mathematics Rousseau (Université de Montréal), and of Planet Earth, which took place in September 2018 in Philadelphia, Pa. From left: mod- Jon Hobbs (Jet Propulsion Laboratory). assessment, panelists utilized the question erator Emil Constantinescu (Argonne National Laboratory), Mihai Anitescu (Argonne National Emil Constantinescu (Argonne National to comment on expectations, rewards, and Laboratory and The University of Chicago), Christiane Rousseau (Université de Montréal), Hans Laboratory) moderated the discussion. obstacles associated with interdisciplinary G. Kaper (Georgetown University), Beth Wingate (University of Exeter), and Jon Hobbs (Jet The panel’s themes were derived from research. The typically long timeframes of Propulsion Laboratory). Photo credit: Katie Kavanagh. MPE-related work by mathematical scien- such work make it challenging for junior sciences in the next decade. The report 1958) and the Intergovernmental Panel on tists, and conversation covered the success- researchers to get involved. Academic highlights the concept of Earth information Climate Change. A similar effort within ful execution of such work and its potential reward culture also tends to recognize and calls attention to major mathematical mathematics was the MPE2013 initiative— focus areas in the future. Constantinescu contributions within the discipline, and implications. Other panelists considered supported by many international mathemat- opened the discussion by asking panelists our current training system may not ade- climate and environmental change and the ical institutions and organizations—that led about their particular success stories in quately prepare students for interdisciplin- pressing need to assess their inevitable to the founding of SIAG/MPE. accomplishing interdisciplinary work per- ary work on changing topics. effects, communicate relevant findings to The panel concluded after an hour of taining to MPE. He also conjectured how Constantinescu’s second question to the the public, and develop and evaluate adap- lively conversation. It provided a wel- to best foster collaborations between math- group pondered a big MPE-related sci- tion strategies. They also emphasized the come opportunity for SIAG/MPE mem- ematicians and domain experts. entific challenge in need of resolution obligation to understand extreme environ- bers with very different application areas All five panelists had interesting stories over the next five to 20 years, and how mental events, possibly in nonstationary to identify common scientific themes. We to tell and spoke about scientific efforts mathematics can play an influential role. situations, and devise tools for interpreting look forward to a similar panel at the next that involved substantial mathematics. Most panelists interpreted this question small probability phenomena. SIAM Conference on Mathematics of Wingate explained how numerical analysts somewhat broadly and examined conse- Another audience question broached Planet Earth in 2020. can aid and advance ocean flow model- quences stemming from global change. ideas to improve effective interac- ing projects. Anitescu pointed to recent Hobbs specifically referred to a recent tion between academics and practitio- Hans Engler is a professor of mathemat- successes in high-quality forecasting (of report entitled Thriving on Our Changing ners. Wingate remarked that the bound- ics at Georgetown University. He previ- Planet: A Decadal Strategy for Earth ously chaired the SIAM Activity Group weather, energy demand, etc.) that depend 1 ary between academic and nonacademic on mathematical contributions, while Observation from Space (published by the researchers is already blurring, at least in on Mathematics of Planet Earth. Emil Kaper reported on a classical superconduc- National Academies Press), which articu- the United Kingdom. Rousseau pointed to Constantinescu is a computational math- tivity modeling success where experiments lates a vision of scientific tasks for Earth past successful interdisciplinary and inter- ematician at Argonne National Laboratory confirmed mathematical predictions. national research efforts that have had last- and scientist-at-large of the Consortium for 1 https://www.nap.edu/catalog/24938/ Advanced Science and Engineering at The Hobbs and Rousseau turned their atten- ing scientific and political impact, including thriving-on-our-changing-planet-a-decadal- University of Chicago. tion to sustained interdisciplinary research strategy-for-earth the International Geophysical Year (1957- January/February 2019 SIAM NEWS • 7 Inside Out: A Value-Based Approach to Industry Job Hunting By Vrushali A. Bokil ing and one-on-one coaching to clients a support network. For reference, attendees tify the people in their network, pinpoint from various institutions, including Boeing, received a booklet entitled Industry Job missing categories, and brainstorm ways tudents looking for jobs in industry are Microsoft, and the Massachusetts Institute Hunting Bootcamp: How to Stand out in the to engage and expand their connections. S often advised to develop soft skills, of Technology. During a three-and-a-half- Industry Job Hunting Process and Optimize Some attendees expressed discomfort in effective communication abilities, cross- hour gathering, Ye—who has industry expe- your Career Potential. categorizing people this way, noting that disciplinary collaborative techniques, and rience working at a variety of different To begin, Ye asked participants to clarify it made friendships feel business-like. Ye interdisciplinary and transdisciplinary train- firms—led the eager participants in a profes- their core values—such as “authenticity” assured them that this would not be the ing. What jobseekers do not typically hear sional coaching session that comprised top- and “creativity”—and record a few of their case, provided they approach networking about is the need to understand who they ics like “self-discovery and self-awareness,” most important principles along with a brief with respect, authenticity, and a mindset are, what they want, and their core values, “clarifying your core values,” and “strategic, description of their personal significance. that includes genuine intention and grati- strengths, and passions. In other words, the authentic, and disciplined networking.” The She emphasized that people must know tude when building meaningful connec- most efficient method of career prepara- session also covered familiar subjects, such who they are, what they want, and what tions. This technique helps set the right tion is the inside-out approach. Roughly 50 as writing a resume, developing and deliver- their contributions are worth to confidently expectation about the kinds of support to young SIAM members received this mes- ing an elevator speech, and preparing for a communicate and negotiate job offers with seek from each person in one’s network. sage during the Professional Development job interview. Ye explained the differences prospective employers. Effective communi- Everyone wants to find their dream job Evening at the 2018 SIAM Annual Meeting, between industry and academia, the value of cation is a crucial soft skill, and an elevator — employment that is fulfilling, avoids held in Portland, Ore., last July. networking and referrals, and the realities speech that employs powerful, concise state- undesirable tasks, and involves an ideal During the event, graduate students and of the job market. She discussed ways to ments and clear language helps one articu- location. But is this always possible? One postdoctoral researchers received advice determine goodness-of-fit for specific jobs late his/her hiring potential. Participants participant noted that applicants must face and training from Di Ye, a professional and institutions, and articulated a big-picture had the opportunity to test what they had realities, such as paying bills. Ye reassured trainer and certified coach at Zhennovate view of the process of landing a satisfying learned and practice their elevator pitches attendees that while their first job may not [3]. Ye provides high-performance train- “dream” job and fulfilling career, aided by with volunteers from companies including be their dream job, and they may have to Microsoft, NASA, 3M, and Nokia Bell Labs work their way through several positions at a networking reception during the session. acting as stepping stones, they can even- The inside-out approach requires outside tually attain their ideal career. She also help in the form of a support network. Did affirmed that realistically optimizing and you know that more than 70 percent of strategizing one’s job search is far more jobs on the market are not published [2]? important than the quantity of applications Ouch! On average, every posted opening he/she sends out. First salary does matter receives over 100 applications [2]. The as a benchmark for future pay. realities of the job market require that In summary, an inside-out approach that applicants not only know who they are and accounts for authenticity, curiosity, motiva- what they want, but also have a network tion to learn and contribute, willingness to of people familiar with their values and build meaningful relationships, and constant passions to promote them to prospective adaptation to the job market will keep people job hunters. Ye classified members of moving towards their objectives and goals this support network into four categories: and hopefully lead to that ideal dream job. people who provide emotional support, The Professional Development Evening challenge one to grow, help expand one’s received positive feedback, and SIAM possibilities, and share power. Participants plans to offer similar career development Di Ye of Zhennovate (left) interacts with attendees of the Professional Development Evening at the 2018 SIAM Annual Meeting, held in Portland, Ore., last July. SIAM photo. then performed a short activity to iden- See Industry Job Hunting on page 8

Leonard delivered an invited lecture Decision-Making on this topic at the 2017 SIAM Annual Continued from page 6 Meeting. The presentation is available from the sites varies for a fixed stop signal. Note SIAM either as slides with synchronized 1 the hysteresis in Figure 1c (on page 6) as the audio or a PDF of slides only. difference between the sites’ values passes through zero. Instead of a sudden flip, the References original choice persists until the difference [1] Pais, D., Hogan, P.M., Schlegel, T., in value becomes too large to ignore. Franks, N.R., Leonard, N.E., & Marshall, How might these ideas extend to increas- J.A.R. (2013). A Mechanism for Value- ingly realistic multi-agent systems with Sensitive Decision-Making. PLoS ONE, Figure 4. The three possible outcomes when two sufficiently valuable nest sites have equal 8(9), e73216. more heterogeneous agents and intercon- value v are either a tie or a choice between the sites. The difference between a tie and a nections? For example, some agents may decision is the strength s of the scouts’ commitment to their preferred sites. The tied steady- Further Reading have pre-existing preferences or access state—an equal number of the scouts voting for A as for B—changes from stable to unstable to other external information. Or perhaps when the bifurcation parameter s increases from 0.2 to 5. Image courtesy of [1]. Gray, R., Franci, A., Srivastava, V., & some bees are unable to see the waggle Leonard, N.E. (2018). Multiagent Decision- To formulate a model, suppose agent outcome—in which no agent has an opin- Making Dynamics Inspired by Honeybees. dance. Can the stop signal serve as a control i 's opinion xi changes in response to exter- ion—is destabilized. As the control variable IEEE Trans. Cont. Net. Syst., 5(2), 793-806. input? Can such agents choose unanimously nal information (positive, negative, or increases, a decision is taken. Furthermore, and robustly between competing choices? zero); negative self-feedback; and positive, because “the center manifold is tangent to Paul Davis is professor emeritus of Classic singularity theory for dynami- weighted, saturating “social” feedback from the consensus manifold, we get unanimity mathematical sciences at Worcester cal systems offers an answer through the agents with whom it communicates. The by design,” Leonard explains. Polytechnic Institute. pitchfork bifurcation’s deadlock-or-deci- social feedback is weighted by a control Additional analysis reveals the effects sion property in Figure 1a (on page 6). variable — a generalization of the stop sig- of information and network asymmetry, An agent’s decision is positive for choice nal. Critically, the (negative) sum of other explores value-sensitive decision-making, 1 A and negative for B; at consensus, all https://www.pathlms.com/siam/courses/ agents’ influence weights on a given agent and builds a framework for feedback con- 4988/sections/7408 agents’ decision variables are equal. The is the latter’s self-feedback factor; that is, trol of the bifurcation sum of the individuals’ decision variables an individual bee’s opinion is influenced by parameter (i.e., avoid- yields the collective decision. a weighted sum of the differences between ing a deadlock among its opinion and a scaling—according to the bees if they reach no control variable—of the saturating opinions consensus on a good of its neighbors in the network. potential nesting site). When the control variable is unity How can humans and the system is linearized about zero design multi-agent (no agent has an opinion), the system control systems that reduces to xL =− x, where L is the match the perfor- social network’s rank-deficient Laplacian mance of Mother (or admittance) matrix. Network types Nature’s networks might regard an agent’s opinion as the among animals?

potential xi at its node. They might also Leonard’s answer conclude that the linearized system has is to design a net- Figure 3. Trajectories to the one steady- a zero eigenvalue because a version of work using singular- state outcome—a quorum committed to Kirchhoff’s Voltage Law holds. ity theory to organize site B, and the remaining few either unde- cided U or committed to site A—for a “We can create bifurcation by design,” the agents’ decision- swarm of honeybees deciding between Leonard says. If the control variable is making — bifurca- Figure 5. Value-sensitive decision-making; a pitchfork bifurcation nest sites A and B when B is of higher slightly bigger than unity, the first eigenval- tion by design. separates a tied vote between two sites of lesser but equal value value than A and both are sufficiently valu- ue is positive and the steady-state undecided (lower left) from a stable choice in favor of a particular site (upper able. Image courtesy of [1]. right). Image courtesy of [1]. 8 • January/February 2019 SIAM NEWS Brown University’s TRIPODS Institute Furthers Research and Education in Data Science By Jeffrey Brock, Alden (Department of Computer Science)—to Bumstead, and Björn Sandstede apply for a TRIPODS grant. Our institute’s research is organized rown University’s Data Science around three themes: geometric and topo- B Initiative1 is in its second year of logical methods for complex data, new running a TRIPODS institute. TRIPODS— tools for causal and model-based inference, Transdisciplinary Research in Principles of and data analysis on massive graphs and Data Science—is a program established and networks. A concrete example of our ongo- funded by the National Science Foundation ing work is an effort by Geman’s team to (NSF) to “bring together the mathemat- improve collective understanding of deep ics, statistics, and theoretical computer sci- neural networks: This research is based on ence communities to develop the theo- the belief that one cannot substantially close retical foundations of data science through the gap between human and machine per- integrated research and training activities.” formance with regard to interpretation (as Brown’s institute, entitled “Foundations of opposed to classification) without architec- Model Driven Discovery from Massive tures that support stronger representations. Data,”2 is one of 12 TRIPODS institutes3 The group has developed a mechanism for across the United States. embedding spatial and abstract relation- ships that bind parts and objects and define The Data Science Initiative serves as a Lunch discussion during the TRIPODS Workshop on “Geometry and Topology of Data,” held at hub for research and education in the foun- context within deep neural networks; cur- rently the resulting dynamics considerably the Institute for Computational and Experimental Research in Mathematics in December 2017. dational methodologies, domain applica- Photo credit: Alden Bumstead. tions, and societal impacts of data science complicate both inference and estimation, the NSF-funded Institute for Computational from different organizations; and supporting at Brown. A collaborative effort of Brown’s although smaller experiments have been and Experimental Research in Mathematics5 students and postdoctoral researchers capa- Departments of Biostatistics, Computer encouraging. A second project focuses on and brought together 36 attendees from 20 ble of bridging multiple institutions. Science, and Mathematics, as well as the the development of algorithms that reveal institutions, ranging from undergraduate and We are excited about our three Division of Applied Mathematics, the ini- differential genetic architecture between graduate students to faculty and scientists TRIPODS+X projects7 that connect our tiative was established in 2015 to foster traits in sizeable genome data sets. The from national laboratories. The bootcamp TRIPODS institute at Brown with research- methodological and domain-driven data goal of this work is to use large genome- used tutorial lectures and hands-on labs to ers from Duke University, Montana State science research and support educational wide association studies that combine medi- provide an in-depth introduction to topo- University, Rutgers University, Smith and training activities in data science that cal records with genome data from over logical data analysis, machine learning, and College, Valparaiso University, and Yale intersect these disciplines. Thus, it was 300,000 individuals to detect genes that their intersection. At the end of the week, University. One project aims to develop com- natural for our team—consisting of Jeffrey share mutations across disease groups. invited speakers presented their research in putational tools to identify gene regulatory Brock (Department of Mathematics), Stuart Training and community building have these areas and connected bootcamp topics networks from genome-wide expression data Geman and Björn Sandstede (Division been major focal points of the institute over to concrete research projects. sets, another seeks to build methodological of Applied Mathematics), Joseph Hogan the past 18 months. Two activities were par- The second noteworthy event was a and theoretical bridges between neurosci- (Department of Biostatistics), and Eli Upfal ticularly successful: the first was an exciting weeklong summer bootcamp on “Topology two-day informal networking workshop on ence and data science, and a third attempts 4 1 and Machine Learning” in August 2018, a “Building Community in the Foundations of to improve data science education for under- https://www.brown.edu/initiatives/data- Data Science,”6 which took place that same graduates by recognizing student miscon- science/ feat that would not have been possible with- 2 https://www.brown.edu/initiatives/data- out TRIPODS. This program was hosted at month. The workshop involved a series of ceptions about data science concepts and science/research/tripods short talks and brainstorming sessions dedi- mismatches between core curricular elements 3 https://nsf-tripods.org/institutes/ 4 https://icerm.brown.edu/tripods/tri18-2-tml/ cated to strengthening data science activity and daily work of early-career practitioners. in the Northeastern U.S. A mix of partici- More information about the 12 TRIPODS pants from a range of research universities institutes and corresponding events is avail- and liberal arts colleges made the workshop able at the TRIPODS website.8 informative, inspiring, and forward-looking. Discussions focused on research, education, Jeffrey Brock is a professor of mathemat- and the need for accessible data-fluency cur- ics and the inaugural Dean of Science in the ricula. Among the outcomes was a concrete Faculty of Arts and Sciences at Yale University. list of suggestions for how TRIPODS could Alden Bumstead is associate director of the further research and educational activities in Data Science Initiative at Brown University. the Northeast, i.e., by developing listings of Björn Sandstede is a professor of applied mathematics, a Royce Family Professor of researchers, their expertise, and methods to Teaching Excellence, and director of the Data encourage collaboration; organizing smaller Science Initiative at Brown. working groups around specific topics; fos- tering the co-design of courses by instructors 7 https://www.brown.edu/initiatives/data- 5 https://icerm.brown.edu/ science/news/2018/10/tripodsx-brown-university 6 https://icerm.brown.edu/tripods/tri18-1-bcds/ 8 https://nsf-tripods.org/institutes/

Industry Job Hunting at the University of Minnesota, and Continued from page 7 Richard Laugesen of the Department of Mathematics at the University of Illinois workshops at future meetings. Stay tuned at Urbana-Champaign for feedback that for announcements about these upcoming greatly enhanced this article. workshops from SIAM. In the meantime, online workshops about soft skills develop- References 1 ment are available through Zhennovate. All [1] Levy, R., Laugesen, R., & Santosa, F. job seekers in mathematics, statistics, and (2018). BIG Jobs Guide: Business, Industry, operations research would highly benefit and Government Careers for Mathematical from perusing BIG Jobs Guide by Rachel Scientists, Statisticians, and Operations Levy, Richard Laugesen, and Fadil Santosa, Researchers (1st Ed.) Philadelphia, PA: Society now available for online purchase at the for Industrial and Applied Mathematics. SIAM bookstore [1]. Jobs in these areas are [2] Smith, J. (2013, April 17). 7 Things projected to grow by 30 percent over the You Probably Didn’t Know About Your next decade. The guide provides practical Job Search. Forbes – Leadership. Retrieved steps for finding that dream job in business, from https://www.forbes.com/sites/ industry, or government (BIG), and includes jacquelynsmith/2013/04/17/7-things-you- probably-didnt-know-about-your-job-search/. information on the types of available jobs as [3] Ye, D. (2018, June). Stand Out in the well as tips for writing high-impact resumes Industry Job-Hunting Process and Optimize and securing rewarding internships. BIG Your Career Potential. SIAM News, 51(5), p. 10. Jobs Guide also offers insights to mentors and advisors on building institutional rela- Vrushali A. Bokil is a professor in the tionships and enabling math departments Department of Mathematics at Oregon to aid students in finding BIG employment. State University. She is a computational mathematician whose interests lie in math- Acknowledgments: The author would ematical modeling and numerical analysis, like to thank Di Ye from Zhennovate, with applications in mathematical biology, Fadil Santosa of the School of Mathematics epidemiology, and computational electro- magnetics. Bokil is a member of the SIAM 1 www.zhennovate.com/events Career Opportunities Committee. January/February 2019 SIAM NEWS • 9 Trump Administration Releases Update to STEM Strategic Plan he National Science and Technology core academic and applied technical cur- T Council recently released the federal ricula in preparation for higher education.” government’s five-year strategic plan for 2. Engage Students where Disciplines science, technology, engineering, and math- Converge. In this pathway, students are ematics (STEM) education. The report, encouraged to engage with “real-world prob- Charting a Course for Success: America’s lems…using knowledge and methods from Strategy for STEM Education,1 represents a across disciplines.” This path also issues a plan for STEM education programs, invest- call to address the barrier that mathematics ments, and activities that are implemented often creates in STEM career accessibility. by federal agencies. The 2018 plan is a 3. Build Computational Literacy. This five-year update of the initial 2013 plan pathway acknowledges the importance released under the Obama administration. of digital literacy while calling for the In addition to guiding federal activities and advancement of CT, which “means solving investments, the strategic plan notes its complex problems with data.” It also calls intention to serve as a “North Star” for the for expanded use of digital platforms for broader STEM community. The finalized teaching and learning. plan includes several objectives that are 4. Operate with Transparency and relevant to this population: Accountability. This pathway urges the Make Mathematics a Magnet: The federal government and stakeholders to plan notes that mathematics continues to utilize “open, evidence-based practices and serve as a gateway to higher-income jobs decision-making” in monitoring progress for STEM majors. Our comments were towards the strategic plan’s goals. very supportive of mathematics’ contextual Each pathway has associated objectives for integration across disciplines to improve federal agencies and departments with STEM mathematical literacy among students. This programs. These objectives are as follows: goal was ultimately incorporated, and the • Foster STEM ecosystems that unite plan specifically emphasizes the importance communities, increase work-based learn- of education in data science and model- ing and training through educator-employer ing. Federal actions that the plan seeks to partnerships, and blend successful practices prioritize include support for programs and from across the learning landscape. partnerships that integrate mathematics and • Advance innovation and entrepreneur- statistics education in applied contexts, and ship education, make mathematics a magnet, education practices that demonstrate reten- and encourage transdisciplinary learning. tion of diverse learners. • Promote digital literacy and cyber safe- Make Computational Thinking ty, make computational thinking an integral an Integral Element of All Education: element of all education, and expand digital Consistent with our comments, the plan platforms for teaching and learning. defines computational thinking (CT) broad- • Leverage and scale evidence-based prac- ly. The language specifically frames CT as tices across STEM communities, report par- “a set of broadly valuable thinking skills that ticipation rates of underrepresented groups, helps people solve problems, design systems, use common metrics to measure progress, and understand human behavior” and notes make program performance and outcomes the strong linkage between CT and computer publicly available, and develop a federal science. Policymakers and individuals in implementation plan and track progress. higher education are urged to integrate and SIAM leadership, particularly the SIAM standardize CT into learning materials and Committee on Science Policy, will be plan- teacher preparation programs, while employ- ning its strategy to engage with agencies in ers are encouraged to engage educational 2019 in the context of this new plan. institutions to support CT instruction. The plan’s vision is that “All Americans Encourage Transdisciplinary Learning: will have lifelong access to high-quality The strategic plan calls for further support of STEM education and the United States will research, development, and dissemination of be the global leader in STEM literacy, inno- effective transdisciplinary STEM education vation, and employment.” This vision—and practices, programs, and policies, as well as the details set forth in the plan—are in the expansion of support for STEM learners line with themes that many policymakers studying transdisciplinary problems through have been sounding, including a global internships, fellowships, scholarships, and competition for scientific and technical tal- other training opportunities. It also promotes ent as well as the relationship between federal activities in support of the recruit- STEM, economic prosperity, and national ment, preparation, retention, and upskill- security. The plan recognizes education ing of STEM educators in transdisciplinary and research organizations as stakehold- approaches that integrate local and global ers that will engage federal agencies in community questions. supporting STEM education. It notes that The strategic plan states the federal gov- “The United States has a higher education ernment’s key role in working with stake- system that is the envy of the world, pro- holders to further STEM education and viding undergraduate and graduate degrees supports three overarching goals: Build in STEM and conducting research that is Strong Foundations for STEM Literacy; an engine for American prosperity and Increase Diversity, Equity, and Inclusion security.” Specifically-mentioned areas in STEM; and Prepare the STEM where further STEM education is needed Workforce for the Future. to support the training of future researchers The plan identifies the following four include national security, artificial intelli- pathways for achieving these goals: gence, cybersecurity, quantum information 1. Develop and Enrich Strategic science, and advanced manufacturing. Partnerships. This pathway is focused on strengthening and creating relationships Next Steps between educational institutions, employ- Federal agencies involved in STEM edu- ers, and communities. For institutions of cation will collaborate to develop a consoli- higher education, this involves contributing dated implementation method that includes to STEM ecosystems that engage students in additional necessary actions to meet the work-based learning, including internships, strategic plan’s goals and objectives. Some apprenticeships, and research experiences. agencies have already announced commit- The plan notes that “Having strategic part- ments related to the strategic plan’s release. nerships also means exploring opportunities The National Science Foundation (NSF) within the education community to blend stated that it will be working with other fed- formal and informal learning, and to blend eral agencies in support of the NSF Inclusion curricula to enable students to complete both across the Nation of Communities of Learners of Underrepresented Discoverers 1 https://www.whitehouse.gov/wp- in Engineering and Science (INCLUDES) content/uploads/2018/12/STEM-Education- Strategic-Plan-2018.pdf See STEM Strategic Plan on page 10 10 • January/February 2019 SIAM NEWS SIAM Announces Major CS&E Prizes he following prizes will be awarded at Science Foundation and the U.S. Department libraries in Julia. The past winners of this products,” they continued. “Our commu- T the SIAM Conference on Computational of Energy. Dongarra’s software is freely prize have been a huge inspiration to us.” nity does research related to many of the Science and Engineering (CSE19), to be held available to the community. Bezanson, Karpinski, and Shah conveyed grand challenges identified by the National February 25-March 1 in Spokane, Wash. their gratitude to Alan Edelman, who— Academy of Engineering, including climate James H. Wilkinson Prize while not eligible for the prize—is the fourth change, affordable healthcare, clean energy, SIAM/ACM Prize in Computational for Numerical Software co-founder of the Julia Project. “Without personalized medicine and education, and Science and Engineering Jeff Bezanson, Stefan Karpinski, and Alan’s support and mentorship, Julia would more. We stay attuned to our commu- Jack Dongarra of the University of Viral B. Shah of Julia Computing are the have been extremely difficult to pull off,” nity and focus on building abstractions and Tennessee (UT) will receive the SIAM/ 2019 recipients of the James H. Wilkinson they said. “And it was already a long shot.” capabilities in Julia that will help research- ACM Prize in Computational Science and Prize for Numerical Software. The trio also outlined Julia’s offerings ers achieve these greater goals. Enabling Engineering. SIAM awards this prize joint- This prize recognizes innovative soft- to society at large. “Julia brings down them and seeing the amazing things that ly with the Association for Computing ware in scientific computing developed by the time and cost for trying new ideas, they do with it gets us excited to work on Machinery (ACM) every two years for researchers in the earlier stages of their inventing new algorithms, and creating new Julia every morning!” outstanding contributions to the develop- careers. To be eligible for the award, can- ment and use of mathematical and compu- didates must have worked in mathematics tational tools and methods for the solution or science for no more than 12 years after of science and engineering problems. With receiving their Ph.D., allowing for breaks this award, SIAM and the ACM recognize in continuity. The prize was established by Dongarra for his key role in the devel- Argonne National Laboratory, the National opment of software, software standards, Physical Laboratory, and the Numerical software repositories, and performance and Algorithms Group Ltd. in honor of James benchmarking software, as well as his com- H. Wilkinson’s outstanding contributions to munity efforts to prepare for the challenges the field of numerical software. of exascale computing, especially in the The award recognizes Bezanson, adaptation of linear algebra infrastructure to Karpinski, and Shah for the development emerging architectures. of Julia,1 an innovative environment for Dongarra holds appointments as the creation of high-performance tools that University Distinguished Professor enable the analysis and solution of com- From left to right: Jeff Bezanson, Stefan Karpinski, and Viral B. Shah of Julia Computing. of Computer Science in the Electrical putational science problems. Julia allows Engineering and Computer Science researchers to write high-level code in an extension projects, increased participation Department, and director of both the STEM Strategic Plan intuitive syntax and produce code with the Continued from page 9 by women and underrepresented minori- Innovative Computing Laboratory and speed of production programming languag- ties, digital platforms, and work-based the Center for Information Technology es. The scientific computing community National Network, a program focused on learning will remain priorities for agen- Research at UT. He is also a Distinguished has widely adopted it for application areas diversifying the STEM workforce. Progress cies engaged in STEM education. Lewis- Research Staff member in the Computer that include astronomy, economics, deep tracking is a major component of the strate- Burke Associates, SIAM’s Washington, Science and Mathematics Division at Oak learning, energy optimization, and medi- gic plan and will entail ongoing review of D.C., liaison, will continue to monitor Ridge National Laboratory, a Turing Fellow cine. In particular, the Federal Aviation evidence from current programs, an annual opportunities to shape the strategic plan’s at Manchester University, Administration has chosen inventory of STEM programs, and publica- implementation. and an adjunct professor Julia as the language for the tion of participation rates by women, under- in the Computer Science next-generation airborne represented minorities, and persons in rural Further Reading Department at Rice collision avoidance system. areas in programs and activities. To support [1] Committee on STEM Education University. Bezanson conducted the use of evidence-based STEM processes, of the National Science and Technology “The list of people who his Ph.D. thesis work on agencies are encouraged to identify and Council. (2018, December). Charting a have been awarded this Julia, after which he co- share effective STEM education programs, Course for Success: America’s Strategy prize is truly amazing, and founded Julia Computing practices, and policies, including those at for STEM Education. Washington, D.C.: to be included on that list is with Karpinski to contin- the postsecondary level and in lifelong National Science and Technology Council. humbling and a great honor, ue pushing the ideas and learning. The plan urges institutions of Retrieved from https://www.whitehouse. as it validates the work we abstractions behind the higher education to use “the objectives as gov/wp-content/uploads/2018/12/STEM- have been doing in a major software into new domains fruitful lines of scholarship, useful guide- Education-Strategic-Plan-2018.pdf. way,” Dongarra said. “The and bring the benefits of lines for course design, and touchpoints for [2] Lewis-Burke Associates, LLC. (2018). Agency Support for the 2018 work helps form the basic Julia to industry and aca- teacher preparation programs.” Federal STEM Education Strategic Plan. part of the fabric of compu- demic users worldwide. The strategic plan notes that “There tational science and high- Jack Dongarra of the University Washington, D.C.: Office of Science and of Tennessee. Julia began as a hobby for can be no doubt that STEM education performance computing. It Technology Policy. Retrieved from http:// Shah but has grown into a continues to be a significant priority for www.lewis-burke.com/sites/default/files/ can be directly integrated with many impor- full-time preoccupation. He is currently the the United States.” It remains to be seen federal_agency_statements.pdf. tant technologies, which have uses in large- chief executive officer of Julia Computing. whether this sentiment will translate into [3] Office of Science and Technology scale computations in medical and health The recipients expressed their delight increased funding and support for fed- Policy. (2018, December 4). President sciences, high-performance computing for upon winning the award. “We are very eral programs. Research organizations and Donald J. Trump is Working to Ensure biomedical and biomechanical engineering, excited on a personal level to receive institutions of higher education should use All Americans Have Access to STEM parallel computing in bioinformation and the 2019 James H. Wilkinson Prize for the plan’s goals, pathways, and objectives Education. Washington, D.C.: Office of computational biology, modeling and simu- Numerical Software, but even more so for to identify areas of strengths and expertise, Science and Technology Policy. Retrieved lation of materials sciences and process- the Julia community as a whole,” they said. and leverage those in recognizing and from https://www.whitehouse.gov/brief- ing controls, environmental sciences and “The prize is really a recognition of the shaping future federal STEM opportuni- ings-statements/president-donald-j-trump- physics, chemical and biochemical systems community and accomplishments of the ties. One should incorporate the language is-working-to-ensure-all-americans-have- simulations, and other areas.” people developing amazing projects and and themes employed in this plan when access-to-stem-education/. The research that won the prize was interfacing and engaging with policymak- — Lewis-Burke Associates LLC developed with support from the National 1 https://julialang.org/ ers. Efforts around rural communities, January/February 2019 SIAM NEWS • 11 Lie Brackets and Bulletproof Vests

bullet punctures a wall made of two ′′ x 1 ′ 2 course or a faculty lounge: if dv/( dt =fv), vv21−=()gf−+fghk Fv=+vfxf++fx …. 2 00 v A thin layers A and B of different (2) 2 then K = satisfies dK/( dx = fv). Thus, materials (see Figure 1). Does the exit …=[,gf],hk +… 2 I omit further details. dv// dt= dK dx. Velocity changes with velocity change if we turn the two-layered respect to time exactly like kinetic energy “vest” inside out, as in the figure? It for small and Here, 22 h k. …=oh()+ k . An example changes with respect to distance. turns out that it does, and the difference The Lie bracket [,gf] can be the If fv()=−vgαβ,(vv), =− then we As a special case of this remark, the vv- of exit velocities is given by a difference between life and αβ+−1 21 get [,fg](=−βα),v kinetic energy decays exponentially with death (although this differ- certain Lie bracket. Let us assume, per- and so only for αβ= is the the distance for the commonly-assumed haps unrealistically, that the bullet’s decel- ence is small). MATHEMATICAL “vest” reversible. quadratic drag fc=− v2. Indeed, we have eration is a given function of its velocity, I conclude with a trivial but dK/( dx ==fv).−2cK Proof CURIOSITIES dv/( dt =av); for example, one could take curious observation, worth 2 x By Mark Levi av()=−kv . The velocity considered as Let F denote the flow mentioning in an ordinary dif- Mark Levi ([email protected]) is a pro- a function of the position x (rather than of the vector field f. In ferential equation or mechanics fessor of mathematics at the Pennsylvania the time) satisfies the differential equation x State University. other words, v0 becomes Fv0 after the dv/( dx =fv) with fv()=av ()/.v Indeed, bullet travels distance x in material A; the flow G x is defined similarly for mate- dv dv dt av() rial B. Then === fv(). (1) dx dt dx v kh hk vG==Fv,,vFGv 1020 Similarly, for the second material we and have dv/( dx =gv) for some other function hk kh g. We thus have two vector fields, f and g, vv21−=FGvG00− Fv, in the one-dimensional velocity space; the position x plays the role of time, since we This difference is given by the right side eliminated t in (1). of (2), as verified by a Taylor expansion I claim that the effect of swapping A and x x of Gv0 and Fv0 to second order; for B is given by the Lie bracket: example, Figure 1. Does the exit velocity change if the two layers are permuted? Figure credit: Mark Levi. Professional Opportunities and Announcements

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The 3x + 1 Function is Not “Chaotic”! For details on the simpler structure, see “The Anyone who makes trial calculations with Remarkably Simple Structure of the 31x + the 31x + function is struck by its seemingly Function” on occampress.com. For details on chaotic behavior. Yet a very simple—and I dare- three possible solutions to the 31x + Problem say elegant—structure underlies the function. that follow quite readily from the structure, It is based on a seldom-used definition of the see “A Solution to the 31x + Problem” on function that is equivalent to the original defini- occampress.com. tion. The 31x + Problem research community, (There is a formal definition of “chaotic” however, is tied to the original definition, which that applies to the 31x + function, but that is yields the far more complicated Collatz graphs not the one that people typically have in mind as the structure of the function (examples of when using the word to describe the behavior these can be seen in the papers resulting from a of the function.) Google search on “Collatz graphs”). 12 • January/February 2019 SIAM NEWS Students Tackle Bayesian Inverse Problems in the Colorado Rockies Reflections on the 2018 Gene Golub Summer School By Omar Ghattas, Youssef The Bayesian inversion theme was very Marzouk, Matt Parno, Noemi Petra, popular, as evidenced by the 257 applications we received from students around the world. Georg Stadler, and Umberto Villa The two-week summer school was spon- sored by SIAM through a generous endow- ecent years have seen rapid growth ment from the estate of mathematician Gene R in the volumes of observational and Golub. The National Science Foundation’s experimental data acquired from natural (NSF) Division of Mathematical Sciences or engineered systems. How do we extract provided additional support for U.S.-based knowledge and insight about these systems students. Together these funds allowed 44 from all of this data? This learning-from- students to attend. However, limitations on data problem is at its core a mathematical available funding and meeting space meant inverse problem. That is, given (possibly that many excellent applicants were turned noisy) data and a (possibly uncertain) “for- down. Participants formed a highly diverse ward” model that maps parameters to data, group with respect to gender, geography, we seek to infer parameters that character- and research interests. They hailed from ize the model. Inverse problems abound in five continents with a wide range of back- all areas of science, engineering, medicine, grounds spanning applied math, statistics, and beyond. Examples include inference of engineering, and natural sciences. The entire 2018 Gene Golub SIAM Summer School team poses in the shape of a Gaussian curve in Breckenridge, Colo. Photo credit: Georg Stadler. internal defects from scattered ultrasonic The summer school lectures offered an wave measurements, anatomical struc- integrated presentation of deterministic realistic and challenging inverse problems estate, SIAM, and the NSF for making this tures from X-ray computed tomography and Bayesian inverse theory and algo- of their choice. The 11 teams presented year’s school possible. The students’ enthu- data, coalescence of binary systems from rithms that first introduced ill-posedness their projects—ranging in areas such as siasm and positive feedback has encouraged detected gravitational waves, ocean state and regularization; developed the ideas photoacoustic tomography, incompressible us to offer a similar event in the future. from surface temperature observations, and and tools for deterministic inversion via flows, seismic imaging, elastography, heat subsurface contaminant plume spread from adjoint-based first- and second-order sensi- conduction, and wave scattering—on the Omar Ghattas is a professor in the crosswell electromagnetic measurements. tivity analysis and numerical optimization; last day of the program. Departments of Geological Sciences and Inverse problems are often ill-posed, i.e., acquainted students with the Bayesian sta- The secluded mountain environment Mechanical Engineering and the Institute their solutions may not exist or be unique or tistical framework for finite- and infinite- of Breckenridge provided a relaxed and for Computational Engineering and Sciences stable to perturbations in the data. Simply dimensional inverse problems; and finally inspiring atmosphere highly conducive to at the University of Texas at Austin. Youssef put, the data—even when large-scale— explored linearized and sampling-based learning, collaboration, and idea exchange. Marzouk is a professor in the Department does not provide sufficient information to of Aeronautics and Astronautics at the statistical solution methods, which built on Additionally, the Rocky Mountains created fully determine the model parameters. Non- several deterministic tools. Massachusetts Institute of Technology. Matt many opportunities for recreational activi- Parno is a researcher at the U.S. Army ties like hiking, whitewater rafting, and Cold Regions Research and Engineering mountain biking. Laboratory. Noemi Petra is a professor of Seven of Gene Golub’s eight most-cited applied mathematics at the University of papers treat methods that are important California, Merced. Georg Stadler is a profes- components of inverse problems (least sor at New York University’s Courant Institute squares optimization, saddle point solvers, of Mathematical Sciences. Umberto Villa singular values, and cross-validation). We is a research professor in the Department think he would have approved of the theme of Electrical and Systems Engineering at of the 2018 G2S3! We thank Gene Golub’s Washington University in St. Louis. Congratulations to the 2017 and 2018 SIGEST Authors Each issue of SIAM Review (SIREV) contains the SIGEST section, which spotlights an outstanding paper of general interest that has previously appeared in one of SIAM’s specialized research journals. SIGEST’s purpose is to make the 13,000+ readers of SIREV aware of exceptional papers published in SIAM’s various journals. We would like to congratulate the following authors of the SIGEST selections that A group of students and instructors hike to the summit of Quandary Peak, one of the appeared in the 2017 and 2018 editions of SIREV: 14,000-foot mountains near Breckenridge, Colo., during the 2018 Gene Golub SIAM Summer School. Photo credit: Georg Stadler. Vol. 59, Issue 1 Full Waveform Inversion and the Truncated Newton Method Concepts discussed in the morning lec- uniqueness can stem from noise in the data By Ludovic Métivier, Romain Brossier, Stéphane Operto, and Jean Virieux tures were put into practice and examined Originally published in the SIAM Journal on Scientific Computing or model, sparsity or redundancy in the more thoroughly during hands-on laborato- data, or smoothing properties of the map Vol. 59, Issue 2 ry sessions in the afternoon. These sessions The Foucault Pendulum (with a Twist) from model parameters to observables. In utilized powerful open-source software that such cases, uncertainty is a fundamental By Richard Moeckel implemented state-of-the-art deterministic Originally published in the SIAM Journal on Applied Dynamical Systems feature of the inverse problem; we wish to and Bayesian inversion methods (hIPPYlib, both infer the parameters and quantify the Vol. 59, Issue 3 MUQ) and finite element solution of PDEs Core-Periphery Structure in Networks (Revisited) uncertainty associated with this inference. (FEniCS). The laboratory components fea- The ability to do the latter opens the door By Puck Rombach, Mason A. Porter, James H. Fowler, and Peter J. Mucha tured cloud-based interactive tutorials via Originally published in the SIAM Journal on Applied Mathematics to powerful capabilities for model-based Jupyter notebooks, which mixed instruction decision-making under uncertainty. Vol. 59, Issue 4 and theory with editable and runnable code. Interactive Information Complexity Bayesian inference provides a powerful The notebooks enabled students to run and framework for solution of inverse problems By Mark Braverman modify sample codes through their web Originally published in the SIAM Journal on Computing under uncertainty. However, when the for- browsers, permitting rapid experimentation ward model is expensive (as for partial dif- with different inverse problem formulations, Vol. 60, Issue 1 ferential equations (PDEs)) and the param- discretizations, and solution algorithms. An Second-Order Necessary Conditions for Stochastic Optimal Control Problems eter dimension is large (as with discretized NSF XSEDE cloud system called Jetstream By Haisen Zhang and Xu Zhang fields), Bayesian inversion becomes prohib- deployed the software libraries via Docker Originally published in the SIAM Journal on Control and Optimization itive with standard statistical methods. The containers, simplifying their installation Vol. 60, Issue 2 last few years have seen the development of and use. To broaden the summer school’s On the Metric s–t Path Traveling Salesman Problem advanced mathematical and computational impact and availability beyond just attend- By Zhihan Gao methods for Bayesian inverse problems ees, all lab material—including 16 tutorials Originally published in the SIAM Journal on Discrete Mathematics governed by complex, high-dimensional and associated code—is freely available on Vol. 60, Issue 3 forward models. To introduce graduate stu- the G2S3 website.1 Algorithmic Trading, Stochastic Control, and Mutually Exciting Processes dents to these recent advances, we orga- The school culminated with team- By Álvaro Cartea, Sebastian Jaimungal, and Jason Ricci nized the 2018 Gene Golub SIAM Summer based research projects in which partici- Originally published in the SIAM Journal on Financial Mathematics School (G2S3) last June in Breckenridge, pants employed the theory, algorithms, Vol. 60, Issue 4 Colo., with the theme of Inverse Problems: and software they had learned to tackle Semidual Regularized Optimal Transport Systematic Integration of Data with Models By Marco Cuturi and Gabriel Peyré under Uncertainty. Originally published in the SIAM Journal on Imaging Sciences 1 http://g2s3.com/labs/index.html