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 âneuronsâ, 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.
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.
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.
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.
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.
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 â 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.
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.
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.
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.
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.
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 hawkâs 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.
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 ``newâ path from data to predictions. It really is the same old path, but it is travelled by new means.
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.
Abstract: Complex networks of coupled oscillators have proven to be systems that can display incredibly rich dynamical behaviors. Despite great theoretical advances in our understanding of coupled oscillator networks, it has proven difficult to design experiments that permit the study of dynamics on large networks with arbitrary topology. Here we present a new experimental approach that allows for the investigation of large networks of truly identical nodes with arbitrary topology. Our approach relies upon the space-time interpretation of systems with time delay in order to construct a network of coupled maps using a single nonlinear, time-delayed feedback loop. This system has many advantages: the network nodes are truly identical, the network is easily reconfigurable, and the network dynamics occur at high speeds. We use this system to study cluster synchronization and chimera states in both small and large networks of different topologies.
Abstract: The spherical Couette system consists of two concentric spheres rotating differentially about a common axis. The space in between the spheres is filled with a conducting fluid. It is a relatively simple system without any thermal or density stratification and and has potential applications to planetary and stellar interiors. In addition, it is also an extremely interesting fluid dynamical system displaying a host of complex instabilities and other fluid dynamics phenomena. In the first part of the talk, I shall introduce the system and explore the generic regimes of different instabilities. This will be followed by some results using hydrodynamic simulations of this system with two pseudo-spectral codes MagIC and XSHELLS while comparing them with experimental data. Focus will be on the origin of special wave instabilities called 'inertial modes' and the transition to turbulence. In the next part, I will present magnetohydrodynamic simulations exploring the effect of an external magnetic field on inertial modes. In the final part of the talk, I will present simulations of self-consistent dynamo action in this system and the parameter dependence of the same.
Abstract: One of the most intriguing phenomena in the studies of classical chaos is the butterfly effect, which manifests itself in that small changes in initial conditions lead to drastically different trajectories. It is characterized by a Lyapunov exponent that measures divergence of the classical trajectories. The question how/if this prototypical effect of classical chaos theory generalizes to quantum systems (where the notion of a trajectory is undefined) has been of interest for decades, but became more popular recently, when it was realized that there exist intriguing connections to string theory and general relativity in some quantum chaotic models. At the center of this activity is the so-called out-of-time-ordered correlator (OTOC) - a quantity that in the classical limit seems to approximate the classical Lyapunov correlator. In this talk, I will discuss the connection between the standard Wigner-Dyson approach to "quantum chaos" and that based on the OTOC on the example of a chaotic billiard and a disordered interacting electron system (i.e., a metal). I will also consider the standard model of quantum and classical chaos - kicked rotor - and calculate the correlator and Lyapunov exponents. The focus will be on how classical chaos and Lyapunov divergence develop in the OTOC and cross-over to the quantum regime. We will see that the quantum out-of-time-ordered correlator exhibits a clear singularity at the Ehrenfest time, when quantum interference effects sharply kick in: transitioning from a time-independent value to its monotonous decrease with time. In conclusion, I will discuss many-body generalizations of such quantum chaotic models.
Abstract: Inequality is an important and seemingly inevitable aspect of the human society. Various manifestations of inequality can be derived from the concept of entropy in statistical physics. In a stylized model of monetary economy, with a constrained money supply implicitly reflecting constrained resources, the probability distribution of money among the agents converges to the exponential Boltzmann-Gibbs law due to entropy maximization. Our empirical data analysis  shows that income distributions in the USA, European Union, and other countries exhibit a well-defined two-class structure. The majority of the population (about 97%) belongs to the lower class characterized by the exponential ("thermal") distribution. The upper class (about 3% of the population) is characterized by the Pareto power-law ("superthermal") distribution, and its share of the total income expands and contracts dramatically during booms and busts in financial markets. Interestingly, the same equations can be also applied to heavy-ion collisions . Globally, energy consumption (and CO2 emissions) per capita around the world shows decreasing inequality in the last 30 years and convergence toward the exponential probability distribution, as expected from the maximal entropy principle. In agreement with our prediction , a saturation of the global Gini coefficient for energy consumption at 0.5 is observed for the most recent years. All papers are available at http://physics.umd.edu/~yakovenk/econophysics/.
 Yong Tao et al., "Exponential structure of income inequality: evidence from 67 countries", Journal of Economic Interaction and Coordination (2017) http://doi.org/10.1007/s11403-017-0211-6 http://arxiv.org/abs/1612.01624
 Xuejiao Yin et al., "A new two-component model for hadron production in heavy-ion collisions", Advances in High Energy Physics (2017) 6708581, http://doi.org/10.1155/2017/6708581
 S. Lawrence, Q. Liu, and V. M. Yakovenko, "Global inequality in energy consumption from 1980 to 2010", Entropy 15, 5565 (2013), http://dx.doi.org/10.3390/e15125565
Abstract: Recent years have witnessed increased interest from the scientific community regarding the control of complex dynamical networks. Some common types of networks examined throughout the literature are power grids, communication networks, gene regulatory networks, neuronal systems, food webs, and social systems. Optimal control studies strategies to control a system that minimize a cost function, for example the energy that is required by the control action.We show that by controlling the states of a subset of the nodes of a network, rather than the state of every node, the required energy to control a portion of the network can be reduced substantially. The energy requirements exponentially decay with the number of target nodes, suggesting that large networks can be controlled by a relatively small number of inputs, as long as the target set is appropriately sized. An important observation is that the minimum energy solution of the control problem for a linear system produces a control trajectory that is nonlocal. However, when the network dynamics is linearized, the linearization is only valid in a local region of the state space and hence the question arises whether optimal control can be used. We provide a solution to this problem by determining the region of state space where the trajectory does remain local and so minimum energy control can still be applied to linearized approximations of nonlinear systems. We apply our results to develop an algorithm that determines a piecewise open-loop control signal for nonlinear systems. Applications include controlling power grid dynamics and the regulatory dynamics of the intracellular circadian clock. This work is in collaboration with Isaac Klickstein and Afroza Shirin (UNM).
Abstract: In many plasmas in nature magnetic reconnection is the primary process whereby energy stored in the magnetic field is transformed into kinetic and thermal energy. It lies at the heart of such phenomena as disruptions in fusion experiments, auroras, and solar flares. In addition, it is strongly suspected that reconnection plays a significant role in generating energetic particles (i.e., non-thermal power laws) in these and other systems. I will discuss the basic physics of magnetic reconnection as well as some of the numerical tools (e.g., particle-in-cell simulations) used to study its complex interplay of scales. Finally, I will discuss recent advances in quantifying how and under what conditions reconnection accelerates particles to non-thermal energies.
Abstract: Neural networks mediate human cognitive functions, such as sensory processing, memory, attention, etc. Computational modeling has proved to be a powerful tool to test hypotheses of network mechanisms underlying cognitive functions, and to better understand human neuroimaging data. Here we present a large-scale neural network modeling study of human brain visual/auditory processing and how this process interacts with memory and attention. We show how our modeling and simulation can relate phenomena across different scales from the neuronal level to the whole-brain network level. The model can perform a number of cognitive tasks utilizing different cognitive functions by only changing a task-specification parameter. Based on the performance and simulated imaging results of these tasks, we proposed hypothesis for the neural mechanisms underlying several important cognitive phenomena, which could be tested experimentally in the future.
Abstract: The Kuramoto model, originally motivated by the dynamics of many interacting oscillators, has been used and generalized for a wide range of applications involving the collective behavior of large heterogenous groups of dynamical units whose states are characterized by a scalar angle variable. One such application in which we are interested is the alignment of velocity vectors among members of a swarm. Despite being commonly used for this purpose, the Kuramoto model can only describe swarms in 2 dimensions, and hence the results obtained do not apply to the often relevant situation of swarms in 3 dimensions. Partly based on this motivation, we study the Kuramoto model generalized to D dimensions, focusing on the 3-dimensional case. We show that in 3 dimensions, as well as for all odd dimensionality, the generalized Kuramoto model for heterogenous units has dynamics that are remarkably different from the dynamics in 2 dimensions. In particular, for odd D the transition of the time asymptotic equilibrium state to coherence occurs discontinuously as the coupling constant K is increased through zero, as opposed to the D=2 case (and, as we will show, also the case of even D) for which the transition to coherence occurs as K increases through a postitive critical value Kc. We observe that the odd-dimensional Kuramoto models with a large number of swarm elements is not low dimensional in the sense of Ott & Antonsen (2008). However, application of our generalized form of the Ott-Antonsen ansatz does reduce the complexity of the problem when compared with the full system of equations. We generalize our results beyond the Kuramoto model to a wider class of swarm dynamics in high dimensions, and we show that the Ott-Antonsen ansatz can be appropriately generalized for this class of systems. We expect that our results will hence be useful for solving questions involving coupled systems on a sphere in high dimensions, beyond just the Kuramoto model.
Abstract: First-principles turbulence simulations are expensive but very useful in many contexts. One approach to improving one's ability to predict experimental or observational data is to design algorithms for ever more processors, allowing ever higher (and more realistic) resolution. But one can also try to work in the opposite direction, developing closures to reduce the resource demands of computations. In a typical high-resolution turbulence simulation that I undertake, there are O(10**9) spectral amplitudes. Only a tiny percentage of these modes are excited to any appreciable level. I will discuss (and seek advice from the audience!) approaches we are pursuing to develop algorithms that solve a closed (or somewhat reduced) first-principles system with as little resolution as should be required.
Abstract: A reservoir computer is an approach to machine learning that appears to be ideally suited for classifying time varying signals or as a black-box system for forecasting the behavior of a dynamical system. It consists of a recurrent artificial neural network that serves as a âuniversalâ dynamical system into which data are input, where the connections on the input layer and recurrent links within the network are chosen randomly and held fixed. Only the weights of network output layer are adjusted during the training period, which greatly reduces the training time. I will discuss our recent progress on realizing high-speed prediction of the Mackey-Glass chaotic system (>10^8 predictions per second) using a reservoir computer based on a time-delay autonomous Boolean network realized on a field programmable gate array. I will also touch on our efforts to control a dynamical system with a reservoir computer and some recent results on methods to identify the optimum size of the reservoir computer network for a given task.
Abstract: There is a saying: "there are two kinds of people in the worldâthe simple-minded and the muddle-headed."
I prefer the former. But much of the investigation of chaotic attractors uses models that are sometimes overly simplistic at least for studying high dimensional chaotic attractors. Our goal is to produce more models that are still simplistic but better reflect typical high dimensional chaotic attractors and permit a better but still simple-minded understanding of chaos in high dimensions.
This is a report on joint work with Miguel Sanjuan and Yoshi Saiki.
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