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2017 Applied Dynamics Seminar Archives

February 9, 2017

Integrability of Matrix Riccati Equations that Arise in Hydrodynamics

David Levermore

University of Maryland | Department of Mathematics

Abstract: TBA


February 16, 2017

Plasmon Resonances in Nanoparticles and the Reimann Hypothesis

Isaac Mayorgoyz

University of Maryland | Department of Electrical and Computer Engineering

Abstract: TBA


February 23, 2017

Observation of Localizad Stress Fluctuations that Drive Shear Thinning in Dense Suspensions

Jeff Urbach

Georgetown University | Department of Physics

Abstract: TBA


March 2, 2017

Helicity Dynamics

Dan Lathrop 

University of Maryland | Department of Physics

Abstract: Helicity is a conserved quantity that arises in ideal fluid flows and ideal magnetohydrodynamic magnetic fields. I will first review the background theory of Helicity in those two cases, a famous paper by Finn and Antonsen, and another by Keith Moffatt. I will follow by covering some basic phenomenology of quantized vortices, reconnection, and Kelvin waves, and background of our visualization studies in superfluid helium. These topics lead into a discussion of what has been done, what we know, and what is predicted about Helicity dynamics. Some observations about the untangling of vortices via reconnection lead to predictions regarding the Helicity we are exploring experimentally. Some puzzles and questions about the role of invariants like the Helicity in the Gross-Pitaevskii (nonlinear Schrodinger) equation play a role in thinking about this phenomenon.


March 9, 2017

Toward a theory of reservoir computing prediction

Brian Hunt and Zhixin Lu

University of Maryland | Department of Mathematics and University of Maryland | IREAP

Abstract: We consider the problem of predicting a chaotic time series from a system whose equations of motion are unknown. We use a machine-learning technique called reservoir computing, which we find is often able to learn the dynamics of the system that generated the time series, in the following sense. In addition to making accurate short-term predictions, the reservoir predictor can generate a long-term "climate" forecast that stays close to the attractor of the actual system. We give examples, and we discuss a preliminary theory relating reservoir predictor performance to Lyapunov exponents and generalized synchronization in an associated dynamical system.


March 16, 2017

Flames, Fire Whirls, and Blue Whirls: What more can there be?

Elaine Oran

University of Maryland | Department of Aerospace Engineering

Abstract: As we were investigating the efficiency of fire-whirl burning on water, we observed the usual transformation of a pool fire to a fire whirl, and then suddenly, we saw the fire undergo a third transition. A blue cup appeared around the base of the fire whirl, surrounding the yellow flame, the yellow flame receded into the cup and finally disappeared. What remained was a small, rapidly spinning blue flame that burned until the fuel on the water was consumed. The blue whirl was shaped like a spinning cup, closed at the bottom near the water surface, and spreading in radius moving upwards towards the rim. Above the blue cup lip, there was a purple cone-shaped mist. The fuel initially used was n-heptane, but now it has been varied and includes crude oil, and still the blue whirl formed naturally. The height of the fire whirl on the laboratory pan was larger than a half meter, and this evolved into a blue whirl about 4–8 cm high. Occasionally the blue whirl would become “unstable” and revert to a transitional state of blue cup holding a yellow flame. When the blue whirl formed, turbulence seemed to disappear, and the flame became quiet. Videos of the experiments are used to show how this happened and discuss the evolution of the fire whirl to the blue whirl in vortex-breakdown concepts.


March 23, 2017 

Spring Break - No Seminar 


March 30, 2017 

Some Adjoint Methods in Physics and Engineering or How the solution to not my problem just might be the answer to your problem 

Thomas Antonsen

University of Maryland | Department of Physics

Abstract: Physicists and engineers frequently encounter situations where calculations of the governing equations of a system of interest appear to need to be repeated many times to describe or optimize the system. It is often the case that only a particular state dependent quantity or metric needs to be determined. In this case a computational savings can be achieved if an “adjoint problem” can be found that produces the desired information without requiring multiple computations. A simple example is the design of a receiving antenna. One wishes to know and optimize the signal received as a function of the incident angle and polarization of incoming waves. It might appear that solution of Maxwell’s field equations would have to be repeated for each possible incident direction and polarization. However, due to the reciprocal property of the governing equations, the desired information is obtained by treating the antenna as a transmitter and calculating the far field radiation pattern. Thus, one computation replaces many. In this talk I will review some problems from the area of charged particle dynamics where adjoint methods have proven useful. A new example is the optimization of electron beam optics in beam sources used in microwave and millimeter wave amplifiers.


April 6, 2017 

Why Have Network Modulation of Sensory Cortex that Causes Variability to Sensory Processing? 

Daniel Butts

University of Maryland | Department of Biology

Abstract: A fundamental goal in brain research is to understand how electrical activity of individual neurons represents information relevant for brain function. This is most often studied in sensory systems, where neural activity can be directly related to sensory stimuli that can be experimentally controlled. However, recordings in awake animals can reveal an enormous amount to variability — that is, different responses to the same stimuli. Such variability has traditionally been characterized as noise that imposes limits on sensory processing. However, with experimental technology allowing for access to large amounts of simultaneously recorded neurons, it is becoming clear that this noise is shared and purposeful, and likely relates to a larger view of the function of sensory cortex. My lab has been developing new methods for analyzing population activity (and its dynamics) to infer what information is being represented by this variability, and how it relates to the larger functions of sensory cortex. This points to a picture where sensory processing does not occur in a vacuum, but is implicitly tied to the behavioral and motivational context of the animal.


April 13, 2017 

Chaotic Dynamics in the Physical Sciences

Edward Ott

University of Maryland | Department of Electrical Engineering and Department of Physics

Ed Ott will be the recipient of the 2017 Lewis Fry Richardson Medal from The European Geosciences Union (E.G.U.). In connection with this award, he will give a lecture at the annual E.G.U. Assembly in Vienna, Austria, later this month. This Applied Dynamics Seminar will be a preview of his talk in Vienna.

Abstract: Chaos was discovered at the end of the 19th century by Poincare in his famous work on the motion of N>2 celestial bodies interacting through gravitational attraction. Although steady progress was made by mathematicians following Poincare's work, the widespread impact and development of chaos in the physical sciences is comparatively recent, i.e., approximately starting in the 1970's. This talk will review and comment on this history and will give some examples illustrating the types of questions, problems and results arising from perspectives resulting from the widespread participation of physical scientists in chaos research.


April 20, 2017 

Multi Chaos: A low dimensional Paradigm for higher-dimensional chaos

James Yorke

University of Maryland | Department of Mathematics

Abstract: The most frequently studied dynamical systems are low dimensional and all the periodic orbits in a chaotic set have the same number of unstable dimensions, but this property seems to fail in high dimensional systems. In this paper, we define a property called ``multi-chaos'', in which, along with the usual properties of chaos, there is a dense set of k-dimensionally unstable periodic orbits, and this holds for more than one k. We provide examples including a piecewise linear generalized Baker map. 


April 27, 2017 

Dynamics of Granular Clogging 

Doug Durian

University of Pennsylvania | Department of Physics

Abstract: The gravity-driven flow of grains from a hole in a hopper is an iconic granular phenomenon. It’s different from a fluid in that the rate is constant also in that it can suddenly and unexpectedly clog. How does the the susceptibility to clogging decrease with increasing hole size, and is there a well-defined clogging transition above which the system never clogs? This problem is distinct from jamming due to presence of boundaries and gradients. We show how the fraction F of flow configurations that cause a clog may be deduced from the average mass discharged between clogs. We construct a simple model to account for the observation that F decays exponentially in hole width to the power of dimensionality. Thus the clogging transition is not sharp but rather is defined by observation limits similar to the glass transition. When the system is immersed in water, F barely changes. Therefore, the crucial microscopic variables are the grain positions; grain momenta play only a secondary role in destabilizing weak incipient arches. There is also a surprising effect whereby the discharge causes water to be pumped downwards, faster than the grains. 


May 4, 2017 

Nonlinear Dynamics, Chaos and Complex Systems: a Historical Perspective

Miguel Sanjuán

Universidad Rey Juan Carlos | Department of Physics

Abstract: "When we talk about dynamics, we do not only understand the motion of celestial bodies and solid mechanical systems, but any changes with respect to time of one or more variables. From that point of view, we can find dynamics everywhere, in any field of science. Thus, now we have a more general vision, including stock market movements and economic variables, concentration changes in chemical reactions, changes in physiological, biological and medical variables, action potentials of neurons, etc ... providing a more interdisciplinary perspective. The various interactions between the constituent parts of a physical system and their feedback mechanisms, are a source of nonlinearity and complexity, which added to the sensitivity dependence to initial conditions which is a hallmark of chaotic behavior, constitutes a change of perspective in dynamical systems with important consequences for the understanding of science. I will give a historical perspective of Nonlinear Dynamics, Chaos Theory and Complex Systems, including some of the different sources that have contributed to the construction of the discipline as we know it today. Among them, the three-body problem in celestial mechanics, turbulence in fluid dynamics, irreversibility and fundamentals of statistical physics and the logistic map and population dynamics in biology. Many schools of mathematics and physics have played an essential role in the historical development of the subject, including the French, Russian, Japanese and American school. The knowledge of this historical perspective allows us to understand the breadth of the discipline itself and the multiple interdisciplinary applications to various fields of science. " 


May 11, 2017 

Non-Monotonic Aging and Memory Retention in Disordered Mechanical Systems

Yoav Lahini

Harvard University | Harvard John A. Paulson School of Engineering and Applied Sciences

Abstract: From materials such as polymers and glass to properties of interfaces leading to friction and even earthquakes, many disordered systems exhibit a similar repertoire of far-from-equilibrium behaviors such as non-exponential relaxations, aging and memory effects. Yet, in spite of numerous studies of these recurring motifs, identifying the mechanisms underlying the unusual dynamics of disordered systems remains a challenge. I will describe the observation of slow relaxations, aging and memory effects - hallmarks of glassy dynamics – in two disordered mechanical systems: crumpled thin sheets and elastic foams. In particular, I’ll report the observation of a non-monotonic aging response that can last many hours. I will then describe ongoing experiments that exploit the macroscopic nature of these systems to try and uncover the underlying mechanisms. The experimental results are in good agreement with a theoretical model recently used to describe observations of monotonic aging in several glassy systems. This suggests not only a general mechanism, but also that the non-monotonic behavior we observe may be generic and that a-thermal systems can show genuine glassy behavior. 


Special Seminar - Tuesday May 16 at 11am (ERF 1027), 2017 

Dynamics of Rewired Networks

Sudeshna Sinha

Indian Institute of Science Education and Research

Abstract: We will show how spatio-temporal chaos in networks with strongly chaotic nodal dynamics can be tamed by dynamically changing links. Specifically, we will illustrate the results in examples ranging from neuronal networks to disease spreading models. Further we will show how random links can prevent blow-ups in coupled nonlinear systems suffering from unbounded growth.


Special Seminar - May 18, 2017 

Topological methods for analyzing two dimensional flows

Tomoo Yokoyama

Kyoto University of Education | Department of Mathematics

Abstract: We introduce tree representations of two dimensional flows. Applying the topological methods to an evolution of an incompressible and viscid flow around an inclined flat plate placed in a uniform flow, we can estimate when the lift-to-drag ratios of the plate are maximal and can determine transient streamline patterns between structurally stable streamline patterns. Moreover, we state the possibilities of analyzing ocean phenomena and medical phenomena. Finally, we discuss low-dimensional dynamical systems which are theoretical backgrounds of the methods.


September 7, 2017

Ultrafast Large-scale Neural Network Processor on a Chip

Daniel Lathrop and Itamar Shani

University of Maryland | Department of Physics / IREAP

Abstract: Neural networks allow machines to imitate the way in which human intelligence solves problems by inferring from past experience. These networks are composed of large arrays of communicating neurons, each one performing a simple non-linear operation. When combined and trained by variation of connection weights, the network can perform complex perceptive computational tasks such as image and voice recognition and complex pattern predictions. When implementing neural networks on conventional digital processing hardware such as those at the core of our PCs, an immense inefficiency stands out: neural network computations are inherently parallel, while computers were designed to perform computations serially. This leads to slow computation times and a high toll of energy consumption. Here we report a way to overcome this challenge. We implement a silicon chip with thousands, and potentially millions, of processing interconnected ‘neurons’, each one operating at 200ps rates. The chip is, thus, capable of performing fully parallel, highly efficient computation. For the design of our network, we follow the well-established machine learning algorithms in which interconnections are described by a random sparse directed graph. We show preliminary laboratory measurements of the network dynamics on a chip and discuss its software variations.


September 14, 2017

Synchronization of Quantum Dipoles

Juan Restrepo

University of Colorado Boulder | Department of Applied Mathematics

Abstract: In this talk we discuss the emergence of synchronization in arrays of quantum radiating dipoles coupled only via anisotropic and long-range dipolar interactions. It is found that in the presence of an incoherent energy source, dipolar interactions can lead to a resilient synchronized steady-state. A classical mean-field description of the model results in equations similar to the classical Kuramoto model for synchronization of phase oscillators. Using the mean-field formulation for the all-to-all coupled case, the synchronized state can be studied, and it is found that it exists only for a finite range of the external energy source rates. Results obtained from the mean-field model are compared with numerical simulations of the quantum system and it is found that synchronization is robust to quantum fluctuations and spatially decaying coupling. Additional nonstationary synchronization patterns and bistability are discussed.


September 21, 2017

Basin Entropy: A Measure of the Final State Unpredictability and Applications to Some Physical Systems

Miguel Sanjuán

King Juan Carlos University | Department of Physics

Abstract: In nonlinear dynamics, basins of attraction link a given set of initial conditions to its corresponding final states. This notion appears in a broad range of applications where several outcomes are possible, which is a common situation in neuroscience, economy, astronomy, ecology and many other disciplines. Depending on the nature of the basins, prediction can be difficult even in systems that evolve under deterministic rules. From this respect, a proper classification of this unpredictability is clearly required. To address this issue, we introduce the basin entropy, a measure to quantify this uncertainty. Its application is illustrated with several paradigmatic examples that allow us to identify the ingredients that hinder the prediction of the final state. The basin entropy provides an efficient method to probe the behavior of a system when different parameters are varied.Additionally, we provide a sufficient condition for the existence of fractal basin boundaries: when the basin entropy of the boundaries is larger than log 2, the basin is fractal. These ideas have been applied to some physical systems such as experiments of chaotic scattering of cold atoms, models of shadows of binary black holes, and classical and relativistic chaotic scattering associated to the Hénon-Heiles Hamiltonian system in astrophysics.


September 28, 2017

A Model-Free Machine Learning Technique for Studying High Dimensional Spatiotemporal Chaos

Jaideep Pathak

University of Maryland | IREAP

Abstract: Networks of nonlinearly interacting neuron-like units have the capacity to approximately reproduce the dynamical behavior of a wide variety of dynamical systems. We demonstrate the use of such neural networks for reconstruction of chaotic attractors from limited time series data using a machine learning technique known as reservoir computing. The orbits of the reconstructed attractor can be used to obtain approximate estimates of the ergodic properties of the original system. As a specific example, we focus on the task of determining the Lyapunov exponents of a system from limited time series data. Using the example of the Kuramoto-Sivashinsky system, we show that this technique offers a robust estimate of a large number of Lyapunov exponents of a high dimensional spatiotemporal chaotic system. We further develop an effective, computationally parallelizable technique for model-free prediction of spatiotemporal chaotic systems of arbitrarily large spatial extent and dimension purely from observations of the system's past evolution.


October 5, 2017

Complexity and Self Organization in Superconducting Metamaterials

George Tsironis

University of Crete | Department of Physics

Abstract: Macroscopic quantum devices are becoming reality not only for computational purposes but also as sensors and for other general applications In this talk we will focus on superconducting technology and analyze the emergence of coherence in coupled networks of meta-atoms made of units such as SQUIDS and Josephson junctions. These networks may operate classically in a negative permeability regime[1], induce intrinsic nonlinear localized modes and partial coherence in the form of chimeras[2], tame disorder through hysteretic loops or transmit through nonlinear frequency bands. In the quantum regime, on the other hand, meta-atoms may interact through injected electromagnetic fields and form propagating “quantum breathers”, i.e. compound semi-classical propagating modes induced by the nonlinearity of the qubit-field interaction [3]. These coherent modes generate self-induced transparency in the medium and in certain cases may also induce super-radiance. [1] N. Lazarides and G. P. Tsironis, rf SQUID metamaterials, Appl. Phys. Lett. 90, 163501 (2007). [2] N. Lazarides, G. Neofotistos, and G. P. Tsironis, Chimeras in SQUID metamaterials, Physical Review B 91, 054303 (2015). [3] Z. Ivic, N. Lazarides, and G. P. Tsironis, Qubit lattice coherence induced by electromagnetic pulses in superconducting metamaterials, Scientific Reports 6, 29374(2016).


October 12, 2017

Granular Dynamics in Low Gravity

Derek Richardson

University of Maryland | Department of Astronomy

Abstract: Small solar system bodies are generally covered in layers of particulate "regolith" with largely unknown properties. The effective gravities on these bodies can sometimes tend to zero at the equator, and have been measured to be negative in a few cases. Space agencies and commercial enterprises show increasing interest in visiting, landing on, and sampling from such bodies, so it is important to understand how the regolith will respond to intrusion. Due to the difficulty and expense of carrying out experiments in low gravity, we turn to computer simulations of granular dynamics to provide insight into the conditions that missions to other worlds may encounter and to help interpret observations of these bodies. As high-end computing resources become more readily available, granular dynamics simulations have become more sophisticated, treating particle collisions as finite-duration, multi-contact events with explicit friction forces between irregularly shaped grains subject to external forces, boundary conditions, and cohesion. It is imperative that such simulation methods be calibrated and validated at laboratory scales to give confidence in their application to other environments. Here I review our group's approach to simulating granular dynamics in low gravity, with examples that include impacts into granular materials, vibration-induced segregation, landslides, models of samplers and landers, and, on larger scales, simulations of entire granular bodies (rubble piles) and planetary rings.


Special Seminar: FRIDAY October 13, 2017 at 3:00pm

Statistical Description of Mixed Systems (Chaotic and Regular), Correlations and "Thermalization"

Shmuel Fishman

Technion | Department of Physics

Abstract: We discuss a statistical theory for Hamiltonian dynamics with a mixed phase space, where in some parts of phase space the dynamics is chaotic while in other parts it is regular. Transport in phase space is dominated by sticking to complicated structures and its distribution is universal. The survival probability in the vicinity of the initial point is a power law in time with a universal exponent. We calculate this exponent in the framework of the Markov Tree model proposed by Meiss and Ott in 1986. It turns out that, inspite of many approximations, it predicts important results quantitatively. The calculations are extended to the quantum regime where correlation functions and observables are studied. The seminar will be very informal and some work still in progress will be reported. The work reported is in collaboration with Or Alus, James Meiss and Mark Srednicki.


October 19, 2017 

Ultra-High Intensity Laser Physics and Applications

Phillip Sprangle

University of Maryland | Department of Electrical and Computer Engineering / Department of Physics

Abstract: This talk will cover ultra-high field physics phenomena and interactions associated with high intensity short pulse lasers. The operating parameter regime of these lasers covers a wide range, e.g., peak powers of ~ 1012 - 1015 W, pulse lengths of ~ 10-12 – 10-14 sec, and intensities of ~ 1014 - 1023 W/cm2. These lasers are used in high-field physics research and have a number of unique applications. The physical processes associated with USPL interactions and propagation include: photo ionization, Kerr and Raman effects, self-phase modulation, optical and plasma filamentation, optical shocks, frequency chirping, propagation through atmospheric turbulence, etc. This talk will discuss these interrelated physical processes and some unique applications, such as: laser driven acceleration, UV/X-ray generation, underwater acoustic sources, atmospheric spark formation, detection of radioactive materials and atmospheric lasing.


October 26, 2017 

Neural Representation of Speech in Human Auditory Cortex

Jonathan Simon

University of Maryland | Department of Electrical and Computer Engineering

Abstract: We investigate how continuous speech is represented in human auditory cortex. We use magnetoencephalography (MEG) to record the neural responses of listeners to natural, continuous speech, in a variety of auditory scenes. Systems analysis, which quantitatively compares a speech signal to its evoked cortical responses, allows us to determine the cortical representations of the speech. Interestingly, the cortical representation allows the time-varying envelope of the speech to be reconstructed from the observed neural response to the speech. We find that cortical representations of continuous speech are very robust to interference from competing speakers, and many other kinds of noise, consistent with our ability to understand speech even in a noisy room (the "Cocktail Party" problem). Indeed, individual neural representations of the speech of both the foreground and background speaker are observed, with each being selectively time-locked to the rhythm of the corresponding speech, but the with the foreground speech represented more faithfully than the background.


November 2, 2017 

Modeling the Network Dynamics of Pulse-Coupled Neurons

Sarthak Chandra

University of Maryland | IREAP

Abstract: Computer modeling of neural dynamics is an important component of the long-term goal of understanding the brain. A barrier to such modeling is the practical limit on computer resources given the enormous number of neurons in the human brain (about 10^11.) Our work addresses this problem by developing a method for obtaining low dimensional macroscopic descriptions for functional groups consisting of many neurons. Specifically, we formulate a mean-field approximation to investigate macroscopic network effects on the dynamics of large systems of pulse-coupled neurons and derive a reduced system of ordinary differential equations describing the dynamics. We find that solutions of the reduced system agree with those of the full network. This dimensional reduction allows for more efficient characterization of system phase transitions and attractors. Our results show the utility of these dimensional reduction techniques for analyzing the effects of network topology on macroscopic behavior in neuronal networks.


November 9, 2017 

Optimal Bounds and Extremal Trajectories for Time Averages in Dynamical Systems

Charles Doering

University of Michigan | Mathematics / Center for the Study of Complex Systems

Abstract: For any quantity of interest in a dynamical system governed by ordinary differential equations it is natural to seek the largest (or smallest) long-time average among solution trajectories. Upper bounds can be proved a priori using auxiliary functions, the optimal choice of which is a convex optimization. The problems of finding maximal trajectories and minimal auxiliary functions are in fact strongly dual so auxiliary functions can produce arbitrarily sharp upper bounds on maximal time averages. They also define volumes in phase space where maximal trajectories must lie. For polynomial equations of motion auxiliary functions can be constructed by semidefinite programming, which we illustrate using the Lorenz system. This is joint work with Ian Tobasco and David Goluskin.


Special Seminar: TUESDAY November 14, 2017 at 11:00am

Sturm-Liouville Framework for Dynamical Reconstruction by Delay Embedding

Naoto Nakano

Kyoto University | Department of Mathematics

Abstract: Delay embedding is well-known for non-linear time-series analysis, and it is used in several research fields such as physics, informatics, neuroscience and so on. The celebrated theorem of Takens ensures validity of the delay embedding analysis: embedded data preserves topological properties, which the original dynamics possesses, if one embeds into some phase space with sufficiently high dimension. This means that, for example, an attractor can be reconstructed by the delay coordinate system topologically. However, configuration of an embedded dataset may easily vary with the delay width and the delay dimension, namely, ``the way of embedding". In a practical sense, this sensitivity may cause degradation of reliability of the method, therefore it is natural to require robustness of the result obtained by the embedding method in certain sense. In this study, we investigate the mathematical structure of the framework of delay-embedding analysis to provide Ansatz to choose the appropriate way of embedding, in order to utilize for time-series prediction. In short, mathematical theories of the Hilbert-Schmidt integral operator and the corresponding Sturm-Liouville eigenvalue problem underlie the framework. Using these mathematical theories, one can derive error estimates of mode decomposition obtained by the present method and can obtain the phase-space reconstruction by using the leading modes of the decomposition. In this talk, we will show some results for some numerical and experimental datasets to validate the present method.


November 16, 2017 

Adaptive Coding for Sensory Inference in Dynamic Environments

Ann Hermundstad

HHMI Janelia Research Campus

Abstract: Making reliable inferences about the environment is crucial for survival. In order to escape a hawk, for example, a mouse might need to infer the hawk’s position and velocity from patterns of light that fall on its retina. Such inferences require large ensembles of sensory neurons whose activity is metabolically expensive. A growing body of evidence suggests that sensory systems reduce metabolic costs by limiting the fidelity with which some stimuli are encoded in neural responses. Limited coding fidelity, however, can lead to inaccuracies in inference. Here, we derive a framework for dynamically balancing the cost of encoding with the error that encoding can induce in inference. We model a system that must use minimal metabolic resources to maintain an accurate estimate of a nonstationary environment, and we show that the optimal system should adapt the fidelity with which stimuli are encoded in neural responses based on a changing estimate of the environment. We use this framework to illustrate how a range of neuronal and behavioral phenomena can be understood as signatures of adaptive encoding for accurate inference.


November 23, 2017 

Thanksgiving Break - No Seminar 


November 30, 2017 

No Equations, No Variables, No Parameters, No Space, No Time: Data and the Modeling of Complex Systems

Yannis Kevrekidis

Johns Hopkins Univeristy | Department Chemical and Biomolecular Engineering / Department of Applied Mathematics and Statistics

Abstract: Obtaining predictive dynamical equations from data lies at the heart of science and engineering modeling, and is the linchpin of our technology. In mathematical modeling one typically progresses from observations of the world (and some serious thinking!) first to equations for a model, and then to the analysis of the model to make predictions. Good mathematical models give good predictions (and inaccurate ones do not) - but the computational tools for analyzing them are the same: algorithms that are typically based on closed form equations. While the skeleton of the process remains the same, today we witness the development of mathematical techniques that operate directly on observations -data-, and appear to circumvent the serious thinking that goes into selecting variables and parameters and deriving accurate equations. The process then may appear to the user a little like making predictions by "looking in a crystal ball". Yet the "serious thinking" is still there and uses the same -and some new- mathematics: it goes into building algorithms that "jump directly" from data to the analysis of the model (which is now not available in closed form) so as to make predictions. Our work here presents a couple of efforts that illustrate this ``new” path from data to predictions. It really is the same old path, but it is travelled by new means.


December 7, 2017 

Optical Control of Excitation Waves in A Biological Excitable Medium

Gil Bub

McGill University | Department of Physiology

Abstract: Macroscopic excitation waves are found in a diverse range of settings including chemical reactions and the heart and brain. In the case of living biological tissue, the spatiotemporal patterns formed by these excitation waves are different in healthy and diseased states. Current electrical and pharmacological methods for wave modulation lack the spatiotemporal precision needed to control these patterns. Optical methods have the potential to overcome these limitations, but until recently have only been demonstrated in simple systems. Here I discuss results using a new dye-free optical imaging modality with optogenetic actuation to achieve dynamic control of cardiac excitation waves. Illumination with patterned light is demonstrated to optically control the direction, speed, and spiral chirality of such waves in cardiac tissue. This all-optical approach offers a new experimental platform for the study and control of pattern formation in complex biological excitable systems.


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