Multiscale and Heterogeneous Models for Traffic Flow and Crowd Dynamics - Benedetto Piccoli

We’ve all been stuck in traffic standstills at some point or another. How about using mathematics to ease vehicular traffic and congestion? That is precisely what Dr. Benedetto Piccoli (Rutgers University) described in his invited lecture, Multiscale and Heterogeneous Models for Traffic Flow and Crowd Dynamics. Piccoli began by explaining that vehicular traffic, networked robots, animal groups and crowd dynamics behave similarly because they consist of large groups of entities, where each individual agent can take decisions and influence the system. He discussed recent mixed models that involve continuous-discrete spaces and ODE-PDE systems to address such dynamics. Many previous traffic models have analyzed the issue by following the trajectory of a single car, he said. Such systems, however, are not completely coupled. A coupled system is achieved in Picolli’s model by the analysis of a moving bottleneck created by a large vehicle, such as a bus or truck. Here, the evolution of density depends on the position of the truck, and vice versa, thus resulting in complete coupling. This type of model can also be used to study other systems such as supply chains and data networks. And as someone in the audience suggested, such an integration of micro- and macroscopic models would also make a very appropriate platform for biological studies.

The Neuromechanics of Insect Locomotion: How Cockroaches Run Fast and Stably Without Much Thought, an invited lecture by Philip Holmes (Princeton University) described models for running insects that his team developed, especially for muscle-actuated hexapods like the common cockroach. Presenting models that include neuronal activation through realistic leg mechanics, he explained how insects can run in a straight line under various conditions, and execute turns. Drawing from work in dynamical systems theory, these models have been used to develop robotic devices that mimic the running behavior of these insects. Such models not only help to understand the biological systems, but can lead to improvements in self-guided robotic systems.

Low Mach Number Models in Computational Astrophysics - John Bell

In the invited lecture, Low Mach Number Models in Computational Astrophysics, John Bell
(Lawrence Berkeley National Laboratory) described several astrophysical problems that are characterized by low Mach number flows, such as convection phase in a supernova prior to ignition. Supernovae are important celestial objects in promoting our understanding of cosmology. A supernova accretes (gathers) material from a neighboring star, and as it grows, it heats to the point where it explodes. Adequate models exist for the period when ignition starts, but they rely on data that describes the state of the supernova at the point of ignition. The goal of models developed by Bell and his colleagues is to explain the phase leading up to ignition. Presenting a low-mach number model implemented on a supercomputer, he explained his team’s interpretation of the results.

Peter Fritzson (Linköping University) gave a comprehensive background of Modelica, “The Next Generation Scientific Programming and Mathematical Modeling Language,” a strongly typed, declarative, equation-based, object-oriented language that is used in modeling complex physical systems. “It’s a language, it’s not a tool,” Fritzson clarified to the audience, before going on to describe its many applications, which include aircraft simulations, automotive modeling and biomechanics. He also gave a brief overview of the open-source OpenModelica environment. In an interview following the lecture, Fritzson emphasized the importance of such opensource software, which allows others to “extend, improve and adapt” such languages, making them more versatile.

The Next Generation Scientific Programming and Mathematical Modeling Language - Peter Fritzson

In the invited lecture, Evolution of Masting — Synchronized and Intermittent Reproduction of Trees, Yoh Iwasa (Kyushu University), gave an overview of intermittent reproduction—or masting—that is seen in mature forests, a process that is synchronized among tree populations over long distances. “I like to show a little bit of mathematics,” Dr. Iwasa said, half-joking, before delving into the mathematical models behind various conditions that promote the evolution of masting, a concept which is important for ecological balance.

Pingwen Zhang (Peking University) provided an overview of phase behavior, including the thermodynamics and kinetics of phase transitions, in addition to describing the principles of self-assembly in complex fluids. Titled Phase Behavior of Complex Fluids, the invited lecture elegantly illustrated the role of each of these concepts with suitable examples.

Jed Brown, Large Scale Ice Sheet Modeling and Simulation minisymposium

The minisymposium on Large Scale Ice Sheet Modeling and Simulation presented a timely topic in a rapidly warming world. As one of the panelists, Omar Ghattas put it, “Ice sheets play an important role in mediating sea level rise.” The symposium addressed current advances in research that aims to create accurate, efficient, and scalable ice sheet models to characterize uncertainties, using state-of-the-art numerical and computational tools.

A minisymposium on Differential Equation Studies in Biomathematics Applications covered a wide range of applications in biomathematics, from cannibalism in tiger salamanders to stationary density of molecular constituent distributions in bacteria.  Dr. Kristin Swanson (University of Washington) illustrated the importance of patient-specific cancer modeling techniques, while explaining how classical approaches often ignore differential kinetics and patient-specific response metrics. In addition, she described how mathematical modeling can be used to predict imageable response to radiotherapy, in cases where techniques like MRI can fail to detect lesions.

Tim David, Patient Specific Modeling in Physiology minisymposium

In a minisymposium on Patient Specific Modeling in Physiology, panelists spoke about the dynamics within physiological systems and how they can be personalized for patient-specific treatments using modeling—arrived at by examining the underlying mechanistics. Topics spanned prediction of blood pressure regulation and effects of body composition on hemodialysis. Dynamic models for cerebral perfusions and cerebral autoregulation in the case of those affected by stroke, diabetes, epilepsy or traumatic brain injury—where normal regulation may be compensated–were discussed. This type of modeling allows for non-invasive treatments as opposed to invasive surgeries penetrating the brain with medical tools, as Dr. Mikio Aoi (North Carolina State University) explained.   

Before reliably estimating climate change patterns of the future, it is importance to reconstruct historical climate data to be able to make reasonable projections. The minisymposium on Mathematics and Statistics in Climate Data Reconstruction and Uncertainty Estimation did just that, illustrating mathematical and statistical methods that are used to reconstruct various climate parameters. Proxy-based reconstructions and pseudoproxy experiments are an important part of such projections. As one panelist, Jason Smerdon (Columbia University) aptly put it, pseudoproxies in climate research are similar to mouse models in medical and biological studies.

The minisymposium on Cloaking and Metamaterials organized by Graeme W. Milton described the mathematics behind the fascinating phenomenon which renders objects invisible to incoming waves and surrounding fields. Cloaking may be passive, active, interior or exterior—regardless of the type, the panelists proved that the mathematics involved is intriguing.

Understanding Complex Systems, a minisymposium organized by Christof Schuette (University of Berlin) gave a comprehensive view of the understanding of rare events, metastability and long-time behavior of complex dynamical systems.

Gabriel Nguetseng (University of Yaounde I) organized a minisymposium on Homogenization and its Applications, which gave an overview of theoretical and applied aspects of homogenization, which studies  multi-scale problems in quantum physics, mathematical biology and optimal design. The most recent advances in the field were discussed by the speakers.

The minisymposium on Mathematical Fluid Dynamics, organized by Andrei V. Fursikov (Moscow State University) described recent results in research into turbulent flows and their properties in addition to control problems connected with fluid flows.

Dr. Bjorn Engquist, (University of Texas) delivered his talk, Fast Algorithms for High Frequency Wave Propagation as the associated lecture for  the Peter Henrici Prize, a joint award of ETH Zurich and SIAM for original research contributions in applied and numerical analysis and their exposition.  Illustrating the large number of unknowns involved in the numerical simulation of high frequency electromagnetic wave propagation, Dr. Engquist went on to describe fast algorithms, such as the fast multipole method, for accurate solution to equations governing wave propagation.

The Marsden Memorial Lecture, delivered by Alan Weinstein (University of California, Berkeley) aptly captured the main areas of Dr. Jerry Marsden’s significant work in applied mathematics, giving an overview of his last study in geometric mechanics, and tracing back to his very first undergraduate paper. A reception to honor the great mathematician, who lost his battle to cancer last September, followed the lecture. “We are always inspired by what he did,” Weinstein said in an interview earlier in the day, emphasizing how much Marsden would be missed in the scientific world. “There are so many questions we now wish we’d asked Jerry.”

From the Twitterverse:

@nllspace: And the prize for most interesting #ICIAM2011 title this pm goes to: “Inter-morph Cannibalism amongst Tiger Salamanders” http://t.co/QYeKQl7

OUPMath_KM: The rest of Canada basks in hot air but #iciam2011 exists within its cool bubble. Clear mathematical thinking or a complex dynamical system?

Picture of the day:

Vancouver Convention Center West

Courtesy of PilotGirl

In his invited lecture on Metric Geometry in Action, Dr. Ron Kimmel (Technion Israel Institute of Technology) explained how similarities between surfaces, such as, faces under expressions, or bodies at different poses can be measured by treating geometric objects as metric spaces.

Metric Geometry in Action: Ron Kimmel

Applying the method of ‘multidimensional scaling’ to objects allows one to analyze targets numerically rather than analytically, he explained. Using the method to view an object as a surface of points, he demonstrated that it can be used to make very intricate distinctions, including distinguishing between identical twins. He further went on to explain how generalized multidimensional scaling can be used for texture mapping and for comparing intrinsic and external symmetries.

Dr. Andrea Bertozzi (University of California, Los Angeles) tackled a very timely topic this afternoon in her invited lecture, Particle Laden Viscous Fluids and the Gulf of Mexico Oilspill. The dynamics of particle matter in viscous fluids, which has always been a topic of great interest to scientists, has gathered more attention in the wake of the Deepwater Horizon oil spill, which washed ashore millions of gallons of oil along the Gulf Coast last year.

Particle-laden Viscous Fluids & the Gulf of Mexico Oil Spill: Andrea Bertozzi

“It’s a seemingly simple problem that’s actually quite difficult to understand,” she said, before going on to explain how fairly straightforward experiments in the lab can answer complex mathematical questions. Elegantly-designed experiments examine the influence of factors such as surface inclination, moisture content, and viscosity on fluid- particulate interactions that result from such spills. “It allows us to push the science ourselves rather than play a support role to scientists in other fields,” said Bertozzi. The Stokes Flow approximation is used to model the viscous flow problem as opposed to the elaborate Navier Stokes equation. Bertozzi went on to describe two-dimensional models that allow analysis of surface tension, effects of gravity, particle settling behavior, and pattern formation of the solutions. Future work would tackle dynamic models for the problem.

Dr. Alexander McNeil (Heriot-Watt University) took on another opportune topic earlier in the day in his invited lecture, Modelling Capital Adequacy and Solvency, which discussed the limits of the current regulatory framework in the banking and insurance sectors, as evidenced by the 2007 crash. Delving into the many stochastic modeling issues brought up by this problem, Dr. McNeil’s talk described various elements from interest rates and equities to credit risk, which should be considered when thinking of risk models and capital numbers that ensure solvency.

A workshop celebrating diversity spotlighted the diversity of applied mathematics, with such wide-ranging areas as fault detection by small parameter variations, mathematical models for photoreceptor interactions and dynamics in digital environments. Panel organizer Stephen Wirkus (Arizona State University) explained to us that often topics in applied math find solutions in other vastly divergent areas, and hence it is a good idea to bring them together to see the extent of the subject’s reach.

Tuesday saw another minisymposium on markets, with Financial Markets with Frictions, organized by Halil Mete Soner (ETH Zürich). The panel discussed recent research in financial markets that deviate from classical studies that involved more ideal markets. Risk factors and trading frictions can cause such market deviations. Better understanding the nonlinear parabolic differential equations and stochastic processes that underlie these systems can help us better comprehend them.

Mathematical Insights into Disease Dynamics - minisymposium

The minisymposium on Mathematical Insights into Disease Dynamics organized by Michael Reed (Duke University) shed light on the dynamical properties of various pathologies in human beings, which are manifest from the level of sub-cellular entities to whole organisms and entire populations. With an in-depth look at the dynamics of these systems, the panel left the audience with no doubt as to how a better understanding of mathematics can allow improved intervention, treatment and hence, better health.Jean-Pierre Puel (Universite de Versailles) organized a minisymposium on Controllability and Inverse Problems, which gave an overview of recent progress in the area in addition to important open problems, and links in the methods between these two domains. Controllability for Schrodinger equations, numerical approximation of controllability problems and Lagrangian control and the state of the art for the Calderon problem were specifically discussed.

Clovis Gonzaga (Universidade Federal de Santa Catarina) gave an engaging account of the influence of computational complexity on continuous optimization methods in the last four decades in his invited lecture, Complexity Based Methods for Convex Optimization. Presenting a geometrical description of techniques stimulated by a recent interest in very large scale problems, Dr. Gonzaga described the evolution of complexity results for descent methods into practical algorithms.

In his invited lecture, Communicating over Quantum Channels, Matthew Hastings (Microsoft Research) explained the basic problems encountered in such communication, including recent violations of additivity of capacity in these systems.

A minisymposium on Delayed Network Dynamics was organized by Gabor Stepan (Budapest University of Technology and Economics). The symposium discussed the emergent dynamics of complex physical and biological systems, which while usually well understood at the component level and at the level of the underlying networks, still present problems due to time evolution of system states. The session addressed the mathematical problems arising in such systems.

Modeling and Simulation in Biological Fluid Dynamics minisymposium

Modeling and Simulation in Biological Fluid Dynamics, a minisymposium on biological and medical models involving fluid dynamics covered fishlike swimming models, the dynamics behind jellyfish movement, continuum model for active suspensions, and optimization algorithms for locomotion of rigid bodies.

The poster session, featuring over 500 research posters presented by students, academics and industrial researchers spanned a wide range of areas in applied mathematics from drug discovery, wave propagation, nanoscience, imaging techniques to dynamical systems.

Poster Session

Olga Taussky-Todd Lecture: Boundary Value Problems & Integrability: Beatrice Pelloni

The eventful day culminated with the Olga Taussky-Todd Lecture by Dr. Beatrice Pelloni (University of Reading) recipient of the associated award, which is given to women researchers who have made outstanding contributions in applied mathematics and scientific computation. Her lecture, titled Boundary Value Problems & Integrability elucidated on a unified method for analyzing boundary value problems for integrable PDEs posed in a convex polygon.

From the Twitterverse:

@bluemarbl: All kinds of mathematical heavyweights walking around @ICIAM2011
 

Image of the day:

Vancouver Convention Center

Courtesy of Susan Whitehouse

ICIAM 2011, the largest meeting for the applied math and computational science community, opened today with nearly 3,000 attendees from over 70 countries around the world.

At the opening ceremony, ICIAM 2011 President Arvind Gupta and Congress Director Rolf Jeltsch emphasized the importance of Congress activities in spotlighting the relevance of applied math research. The ceremony was highlighted by ICIAM prize recipients Emmanuel Candès (Collatz Prize), Alexandre Chorin (Lagrange Prize), Vladimir Rokhlin (Maxwell Prize ), James Albert Sethian (Pioneer Prize ) and Edward Lungu (Su Buchin Prize).

The 40th Anniversary meeting of the Association of Women in Mathematics, an embedded meeting of the Congress, opened with a session featuring Women at the Forefront of Applied Mathematics, organized by Dr. Maeve McCarthy (Murray State University) and Dr. Gerda de Vries (University of Alberta).

As part of the panel, Professor Leah Edelstein-Keshet (University of British Columbia) described various Models for Cell Polarization and Crawling, illustrating simulations of moving cells, which are useful in the study of cell shape and behavior. She illustrated two-dimensional mechanical cells that allow detailed analysis of cell-signaling cascades, in addition to cell polarization and movement.

In her talk, Imaging Biomechanical Parameters for Disease Characterization, AWM President Joyce R. McLaughlin (Rensselaer Polytechnic Institute) described technologies for shear stiffness imaging, which allow characterization of diseases such as breast and prostate cancers– as part of the same panel. Dr. McLaughlin elegantly described the viscoelastic models that are used to identify such cancers, including mathematical challenges encountered in such diagnosis, such as uniqueness and stability results. Dr. McLaughlin is a 2009 Class of SIAM Fellow.

Dr. Jane Wang: How Do Insects Fly and Turn?

Dr. Jane Wang, in her talk, How Do Insects Fly and Turn? described just that with beautiful images and multimedia to complement math models. Using examples of the dragonfly and fruitfly, she illustrated the kinematics and aerodynamics behind insect flight and movement. Using mechanical models to illustrate the dynamics and control behind the processes, she also explained how they can be used to design optimal models, for example, in the case of efficient airplanes.

SIAM Fellow and Past President Margaret Wright (Courant Institute of Mathematical Sciences) concluded the session with an enlightening overview of Selected Developments in Non-derivative Optimization, retracing 50 years of solutions to real-world optimization problems in science, engineering, and medicine with the help of non-derivative methods. Discussing research in theoretical and computational aspects, she debated on the “most effective” methods, focusing on arguably one of the most popular of non-derivative methods, the Nelder–Mead simplex method.

Dr. Ingrid Daubechies (Duke University) delivered The John von Neumann Lecture this evening, joining a list of eminent mathematicians who have received this prestigious SIAM prize over the past five decades. Her lecture, Sparsity in Signal Analysis and in Computation, focused on the many ways in which mathematical insights can be applied to obtain sparse representations through the choice of wavelet and other bases, as well as the construction of such representations through mathematical tools and analysis. Applying various aspects of differential geometry and topology, such sparse representations are useful in analysis, storage and computation.

Dr. Susanne Brenner of Louisiana State University completed the lineup of distinguished women mathematicians for the evening with her talk on A Cautionary Tale in Numerical PDEs, fittingly in honor of the significant contributions of women to applied and computational mathematics. The Association for Women in Mathematics presents this annual award jointly with SIAM to recognize the contributions of women to the field. Dr. Brenner’s lecture examined the wrong solutions produced through the use of numerical methods for partial differential equations, which can nevertheless be confirmed by convergence and numerical experiments. With a wide range of examples, she discussed the ways in which such pitfalls can be avoided.

Earlier in the day, Mark Lewis (University of Alberta) elegantly described mathematical models to track expanding wave fronts of biological populations, using the help of parabolic PDEs and related integral formulations in his invited lecture, New Challenges in Modelling Biological Invasions.

Vicent Caselles (Universitat Pompeu-Fabra) gave an enlightening account of local and non-local methods employed in image inpainting and image recovery in video and cinema post-production in his invited talk Exemplar-Based Image Inpainting and Applications.

Alf Gerisch: Modelling and Simulation of Cellular Adhesion: the Impact on Spatio-temporal Patterns in Cancer Cell Invasion abstract

Mark Chaplain (University of Dundee) organized a minisymposium on the mathematics of cancer, which covered many mathematical models put forth to describe and study key processes contributing to the growth and spread of this debilitating disease: from tumor and tissue growth, cell lineages, and feedback control to functional shunting. Dr. Alf Gerisch (Technische Universität Darmstadt) described mathematical models of metastasis, a key process of tissue invasion by cancer cells. “Life is not always periodic,” Dr. Gerisch stated, before going on to describe nonperiodic boundary conditions for cancer modeling.

Michael Ferris (University of Wisconsin) outlined a mechanism to describe an extended mathematical program by means of annotating existing relationships that allow creation of models while illustrating the utility of this approach. Collections of optimization models and variational inequalities are used to form competitive equilibrium models.

In the minisymposiun on Numerical Solution of Stochastic PDEs organized by Roger Ghanem
(University of Southern California), recent advances in the topic were discussed, including modeling, reduction, approximation, adaptivity, algorithmic issues, multiphysics and multiscale physical behavior.
Eric Cances (Ecole des Ponts and INRIA) organized the minisympiosium on Quantum Modeling in Molecular Simulation, analyzing quantum models in addition to the simulation and control of molecular systems and applications of high-performance computing and optimal control theory.

Michael Ferris: Extended Mathematical Programming: Competition and Stochasticity

The minisymposium on Uncertainty Analysis of Dynamical Systems, which was organized by Igor Mezic (University of California), discussed the topic of uncertainty analysis in industrial scale problems, with special focus on the mechanical and aerospace industries. The symposium covered the concept of uncertainty before going into probabilistic design and scalable approaches to a wide range of industrial applications.

A minisymposium on The BP Gulf of Mexico Oil Discharge and Its Consequences, organized by Ben Fusaro (Florida State University) modeled the flow of effluents from oil spills using analytical and computational approaches. As part of the panel, Dr. Clint Dawson (University of Texas at Austin) examined the effects of weather conditions such as storms and ocean currents, which can further act to push the oil toward coastal regions.

Clint Dawson: Modeling Coastal and Near-Shore Processes such as the Deepwater Horizon Oil Spill

From the TwitterVerse: @oupmath_km: We feel like Will & Kate arriving in Canada & being treated to local traditional dancing. #iciam2011 opening ceremony

Poster Battle at ICIAM 2011 Courtesy of @L_ekiM