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Past Events2019: Lunch Seminars
April 24, 2019
Heather Zinn-Brooks ▦ Influence of media on opinion dynamics in social networks ▦ Many people rely on online social networks as sources for news and information, and the spread of media content with ideologies across the political spectrum both influences online discussions and impacts actions offline. To examine such phenomena, we generalize bounded-confidence models of opinion dynamics on a social network by incorporating media accounts as influencers. We quantify partisanship of content as a continuous parameter on an interval, and we present higher-dimensional generalizations to incorporate content quality and increasingly nuanced political positions. We simulate our model with one and two ideological dimensions, and we use the results of our simulations to quantify the ``entrainment'' of non-media account content to the ideologies of media accounts in networks. We maximize media impact over a social network by tuning the number of media accounts that promote the content and the number of followers of the accounts. Through our numerical computations, we find that the entrainment of the non-media content's ideology to the media ideology depends on structural features of networks such as size, mean number of followers, and the receptiveness of nodes to different opinions. We then introduce content quality --- a key novel contribution of our work --- into our model. We incorporate multiple media sources with ideological biases and qualities that we draw from real media sources and demonstrate that our model can produce distinct communities (``echo chambers") that are polarized in both ideology and quality. Our model provides a step toward understanding content quality in spreading dynamics, with important ramifications for how to mitigate the spread of undesired content and promote the spread of desired content.
April 17, 2019
Thomas Anderson ▦ "Fast hybrid" frequency/time techniques for efficient and parallelizable high-order transient wave scattering simulation ▦ We propose a frequency/time hybrid integral-equation (though other frequency-domain methods are readily usable) method for the time-dependent wave equation in two and three-dimensional spatial domains. Relying on Fourier transformation in time, the method utilizes a fixed (time-independent) number of frequency-domain integral-equation solutions to evaluate time domain solutions for arbitrarily long times. The approach relies on two main elements, namely, 1) A smooth time-windowing methodology that enables accurate band-limited representations for arbitrary long time signals, and 2) A novel Fourier transform approach which, in a time-parallel manner and without causing spurious periodicity effects, delivers numerically-dispersionless spectrally-accurate solutions. The algorithm can tackle complex physical structures, it enables parallelization in time in a straightforward manner, and it allows for time leaping--that is, solution sampling at any given time T at O(1)-bounded sampling cost. The proposed frequency/time hybridization strategy, which generalizes to any linear partial differential equation in the time domain for which frequency-domain solutions can be obtained (including e.g. the time-domain Maxwell equations or time domain problems posed with dispersive media), provides significant advantages over other available alternatives such as volumetric discretization and convolution-quadrature approaches.
February 27, 2019
Tapio Schneider ▦ Clouds, Climate Predictions, and Possible Surprises in Warm Climates ▦ While climate change is certain, precisely how climate will change is less clear. Uncertainties arise from the representation of small-scale processes such as clouds and turbulence. Moreover, these uncertainties are poorly quantified; the ensemble of existing climate models may not span the range of possible climate outcomes. I will illustrate this with an example from the dynamics of stratocumulus clouds, which are crucial for Earth’s energy balance. Large-eddy simulations of stratocumulus clouds show that they can exhibit an instability that leads to dramatic global warming under high greenhouse gas concentrations—an instability that does not seem to be captured by current climate models and whose probability of occurrence cannot be assessed with current models. Breakthroughs in the accuracy of climate projections and in the quantification of their uncertainties are now within reach, thanks to advances in the computational and data sciences and in the availability of Earth observations from space and from the ground. To achieve a step change in accuracy of climate projections, we are developing a new Earth system modeling platform. Developed by a university consortium dubbed the Climate Modeling Alliance (CliMA), it will fuse an Earth system model (ESM) with global observations and targeted local high-resolution simulations of clouds and other elements of the Earth system. CliMA capitalizes on advances in data assimilation and machine learning to develop an ESM that automatically learns from diverse data sources, be they observations from space or data generated computationally in high-resolution simulations.
February 20, 2019
Oscar Bruno ▦ Fast spectral time-domain PDE solvers for complex structures: the Fourier-Continuation method ▦ We present fast spectral solvers for time-domain Partial Differential Equations. Based on a novel Fourier-Continuation (FC) method for the resolution of the Gibbs phenomenon, these methodologies give rise to time-domain solvers for PDEs for general engineering problems and structures. The methods enjoy a number of desirable properties, including spectral time evolution essentially free of pollution or dispersion errors for general PDEs in the time domain, with conditional/unconditional stability for explicit/alternating-direction methods and high order of temporal accuracy. A variety of applications to linear and nonlinear PDE problems will be presented, including the diffusion and wave equations, the Navier-Stokes equations and the elastic wave equation, demonstrating the significant improvements the new algorithms can provide over the accuracy and speed resulting from other approaches.
January 23, 2019
Lior Pachter ▦ Computational and algorithmic challenges of biological sequence alignment ▦ I will briefly review the history of biological sequence alignment, and introduce some of the fundamental challenges that emerge from biological, technical and computational considerations. I will then discuss current state-of-the-art methods, which are based on a variety of computational ideas, with a view towards forthcoming opportunities. 2019: Other Seminars
April 11, 2019
• CMX Special Seminar • Annenberg 213 4:00pm Richard Nickl ▦ Statistical Guarantees for the Bayesian Approach to Inverse Problems ▦ Bayes methods for inverse problems have become very popular in applied mathematics in the last decade. They provide reconstruction algorithms as well as in-built `uncertainty quantification’ via Bayesian credible sets, and particularly for Gaussian priors can be efficiently implemented by MCMC methodology. For linear inverse problems, they are closely related to classical penalised least squares methods and thus not fundamentally new, but for non-linear and non-convex problems, they give genuinely distinct and computable algorithmic alternatives that cannot be studied by variational analysis or convex optimisation techniques. In this talk we will discuss recent progress in Bayesian Non-Parametric statistics that allows to give rigorous statistical guarantees for posterior mean reconstructions in non-linear non-convex inverse problems arising in some elliptic PDE models and in non-Abelian (`neutronspin’) X-ray tomography.
January 28, 2019
• CMX Special Seminar • Annenberg 213 12:00pm Camille Carvalho ▦ Accurate evaluation of near-fields in plasmonic structures ▦ Plasmonic structures are commonly made of dielectrics and metals. At optical frequencies metals exhibit unusual electromagnetic properties like a dielectric permittivity with a negative real part whereas dielectrics have a positive one. This configuration allows the propagation of electromagnetic surface waves strongly oscillating at the metal-dielectric interface, and hyper-oscillating if the interface presents corners. Standard numerical methods to study surface plasmons excitation do not always take into account the multiple scales inherent in electromagnetic problems which may lead to inaccurate predictions. In this presentation we present some techniques (using Finite Element method, or Boundary Integral Equation methods) to accurately compute and efficiently take into account the multiple scales of 2D light scattering problems in plasmonic structures.
January 31, 2019
• CMX Seminar Series: Optimal Transport • Location tba 2:30pm Wuchen Li ▦ Learning via Wasserstein information geometry ▦ In this talk, I review several differential structures from optimal transport (Wasserstein metric). Based on it, I will introduce the Wasserstein natural gradient in parametric models. The L2-Wasserstein metric tensor in probability density space is pulled back to the one on parameter space, under which the parameter space forms a Riemannian manifold. The Wasserstein gradient flows and proximal operator in parameter space are derived. We demonstrate that the Wasserstein natural gradient works efficiently in several machine learning examples, including Boltzmann machine, generative adversary models (GANs) and variational Bayesian statistics.
February 28, 2019
• CMX Seminar Series: Optimal Transport • Location tba 2:30pm Chenchen Mou ▦ Mean field games on graphs ▦ Mean field game theory is the study of the limit of Nash equilibria of differential games when the number of players tends to infinity. It was introduced by J.-M. Lasry and P.-L. Lions, and independently by P. Caines, M. Huang and R. Malhame. A fundamental object in the theory is the master equation, which fully characterizes the limit equilibrium. In this talk, we will introduce Mean field game and master equations on graphs. We will construct solutions to both equations and link them to the solution to a Hamilton-Jacobi equation on graphs.
March 7, 2019
• CMX Special Seminar • Annenberg 213 12:00pm Gitta Kutyniok ▦ Deep Learning and Modeling: Taking the Best out of Both Worlds ▦ Inverse problems in imaging such as denoising, recovery of missing data, or the inverse scattering problem appear in numerous applications. However, due to their increasing complexity, model-based methods are often today not sufficient anymore. At the same time, we witness the tremendous success of data-based methodologies, in particular, deep neural networks for such problems. However, at the same time, pure deep learning approaches often neglect known and valuable information from the modeling world. In this talk, we will provide an introduction to this problem complex and then focus on the inverse problem of computed tomography, where one of the key issues is the limited angle problem. For this problem, we will demonstrate the success of hybrid approaches. We will develop a solver for this severely ill-posed inverse problem by combining the model-based method of sparse regularization by shearlets with the data-driven method of deep learning. Our approach is faithful in the sense that we only learn the part which cannot be handled by model-based methods, while applying the theoretically controllable sparse regularization technique to all other parts. We further show that our algorithm significantly outperforms previous methodologies, including methods entirely based on deep learning.
March 7, 2019
• CMX Special Seminar • Annenberg 314 4:00pm Zbigniew J. Jurek ▦ Selfdecomposability and S-Selfdecomposability: A view towards simulations? ▦ Click here for abstract
March 14, 2019
• CMX Seminar Series: Optimal Transport • Annenberg 314 2:30pm Flavien Leger ▦ The Schrödinger bridge problem ▦ We present the Schrödinger bridge problem and discuss its connections with optimal transport, mean field games and stochastic optimal control. 2019: Meetings & Workshops |