Colloquia
The Applied Mathematics and Statistics Colloquium takes place at 3 p.m. on Fridays. The format for the seminars this semester is a 30 minute talk + interview via Zoom. Please contact Jennifer Ryan at jkryan@mines.edu for further information and the Zoom link and password.
View colloquium videos on YouTube.
Spring 2021
Book Club (See schedule and discussed chapters below): As part of our colloquia this semester, we will share a discussion of:
The summary provided from the wikipedia page describes the book in the following manner:
“Rosling suggests the vast majority of human beings are wrong about the state of the world. He demonstrates that his test subjects believe the world is poorer, less healthy, and more dangerous than it actually is, attributing this not to random chance but to misinformation.
Rosling recommends thinking about the world as divided into four levels based on income brackets (rather than the prototypical developed/developing framework) and suggests ten instincts that prevent us from seeing real progress in the world “
| January 29 | Book Club "Factfulness: 10 Reasons We’re Wrong about the World – and Why Things are Getting Better" (2018), Hans Rosling Chapters 1-3 |
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| February 5 | Michelle McCarthy Boston University Title: Mathematical modeling of neuronal rhythms: from physiology to function Abstract: Brain rhythms are a ubiquitous feature of brain dynamics, tightly correlated with neuronal activity underlying such basic functions as cognition, emotions, movement, and sleep. Moreover, abnormal rhythmic activity is associated with brain disfunction and altered brain states. Identifying the neuronal units and network structures that create, sustain and modulate brain rhythms is fundamental to identifying both their function and dysfunction in mediating behavioral output. Experimental studies of brain rhythms are limited by the inability to isolate large ensembles of neurons and their interconnections during active brain states. However, mathematical models have been used extensively to study network dynamics of the brain and to give insight into the determinants and functions of brain oscillations during various cognitive and behavioral states. Here I will give a brief introduction to the field of study of rhythmic brain activity and the mathematical formulations underlying biophysical neuronal network models. Existing mathematical models of brain development, sleep and neurodegenerative disease will be used to demonstrate how neuronal models of rhythmic dynamics can be used to explore the link between the brain physiology and functional network dynamics. |
| February 12 | Daniel Nordman Iowa State Title: Within-sample prediction of a number of future events Abstract: The talk overviews a prediction problem encountered in reliability engineering, where a need arises to predict the number of future events (e.g., failures) among a cohort of units associated with a time-to-event process. Examples include the prediction of warranty returns or the prediction of the number of future product failures that could cause serious harm. Important decisions, such as a product recall, are often based on such predictions. Data, typically right-censored, are used to estimate the parameters of a time-to-event distribution. This distribution can then be used to predict the number of events over future periods of time. Because all units belong to the same data set, either by providing information (i.e., observed event times) or by becoming the subject of prediction (i.e., censored event times), such predictions are called within-sample predictions and differ from other prediction problems considered in most literature. A standard plug-in (also known as estimative) prediction approach is shown to be invalid for this problem (i.e., for even large amounts of data, the method fails to have correct coverage probability). However, a commonly used prediction calibration method is shown to be asymptotically correct for within-sample predictions, and two alternative predictive-distribution-based methods are presented that perform better than the calibration method. |
| February 19 Special Time of 1:00 PM | Olivia Prosper University of Tennessee Title: Modeling malaria parasite dynamics within the mosquito Abstract: The malaria parasite Plasmodium falciparum requires a vertebrate host and a female Anopheles mosquito to complete a full life cycle, with sexual reproduction occurring in the mosquito. While parasite dynamics within the vertebrate host, such as humans, has been extensively studied, less is understood about dynamics within the mosquito, a critical component of malaria transmission dynamics. This sexual stage of the parasite life cycle allows for the production of genetically novel parasites. In the meantime, a mosquito’s biology creates bottlenecks in the infecting parasites’ development. We developed a two-stage stochastic model of the generation of parasite diversity within a mosquito and were able to demonstrate the importance of heterogeneity amongst parasite dynamics across a population of mosquitoes on estimates of parasite diversity. A key epidemiological parameter related to the timing of onward transmission from mosquito to vertebrate host is the extrinsic incubation period (EIP). Using simple models of within-mosquito parasite dynamics fitted to empirical data, we investigated factors influencing the EIP. |
| February 26 | Book Club "Factfulness: 10 Reasons We’re Wrong about the World – and Why Things are Getting Better" (2018), Hans Rosling Chapters 4-6 |
| March 12 | Lise-Marie Imbert-Gerard University of Arizona Title: Wave propagation in inhomogeneous media: An introduction to Generalized Plane Waves Abstract: Trefftz methods rely, in broad terms, on the idea of approximating solutions to Partial Differential Equation (PDEs) using basis functions which are exact solutions of the PDE, making explicit use of information about the ambient medium. But wave propagation problems in inhomogeneous media is modeled by PDEs with variable coefficients, and in general no exact solutions are available. Generalized Plane Waves (GPWs) are functions that have been introduced, in the case of the Helmholtz equation with variable coefficients, to address this problem: they are not exact solutions to the PDE but are instead constructed locally as high order approximate solutions. We will discuss the origin, the construction, and the properties of GPWs. The construction process introduces a consistency error, requiring a specific analysis. |
| March 19 | Ethan Anderes UCDavis Title: Gravitational wave and lensing inference from the CMB polarization Abstract: In the last decade cosmologists have spent a considerable amount of effort mapping the radially-projected large-scale mass distribution in the universe by measuring the distortion it imprints on the CMB. Indeed, all the major surveys of the CMB produce estimated maps of the projected gravitational potential generated by mass density fluctuations over the sky. These maps contain a wealth of cosmological information and, as such, are an important data product of CMB experiments. However, the most profound impact from CMB lensing studies may not come from measuring the lensing effect, per se, but rather from our ability to remove it, a process called delensing. This is due to the fact that lensing, along with emission of millimeter wavelength radiation from the interstellar medium in our own galaxy, are the two dominant sources of foreground contaminants for primordial gravitational wave signals in the CMB polarization. As such delensing, i.e. the process of removing the lensing contaminants, and our ability to either model or remove galactic foreground emission sets the noise floor on upcoming gravitational wave science. In this talk we will present a complete Bayesian solution for simultaneous inference of lensing, delensing and gravitational wave signals in the CMB polarization as characterized by the tensor-to-scalar ratio r parameter. Our solution relies crucially on a physically motivated re-parameterization of the CMB polarization which is designed specifically, along with the design of the Gibbs Markov chain itself, to result in an efficient Gibbs sampler---in terms of mixing time and the computational cost of each step---of the Bayesian posterior. This re-parameterization also takes advantage of a newly developed lensing algorithm, which we term LenseFlow, that lenses a map by solving a system of ordinary differential equations. This description has conceptual advantages, such as allowing us to give a simple non-perturbative proof that the lensing determinant is equal to unity in the weak-lensing regime. The algorithm itself maintains this property even on pixelized maps, which is crucial for our purposes and unique to LenseFlow as compared to other lensing algorithms we have tested. It also has other useful properties such as that it can be trivially inverted (i.e. delensing) for the same computational cost as the forward operation, and can be used for fast and exact likelihood gradients with respect to the lensing potential. Incidentally, the ODEs for calculating these derivatives are exactly analogous to the backpropagation techniques used in deep neural networks but are derived in this case completely from ODE theory. |
| March 26 | Book Club "Factfulness: 10 Reasons We’re Wrong about the World – and Why Things are Getting Better" (2018), Hans Rosling Chapters 7-9 |
| April 9 | Andrew Zammit Mangion University of Wollongong Title: Statistical Machine Learning for Spatio-Temporal Forecasting Abstract: Conventional spatio-temporal statistical models are well-suited for modelling and forecasting using data collected over short time horizons. However, they are generally time-consuming to fit, and often do not realistically encapsulate temporally-varying dynamics. Here, we tackle these two issues by using a deep convolution neural network (CNN) in a hierarchical statistical framework, where the CNN is designed to extract process dynamics from the process' most recent behaviour. Once the CNN is fitted, probabilistic forecasting can be done extremely quickly online using an ensemble Kalman filter with no requirement for repeated parameter estimation. We conduct an experiment where we train the model using 13 years of daily sea-surface temperature data in the North Atlantic Ocean. Forecasts are seen to be accurate and calibrated. We show the versatility of the approach by successfully producing 10-minute nowcasts of weather radar reflectivities in Sydney using the same model that was trained on daily sea-surface temperature data in the North Atlantic Ocean. This is joint work with Christopher Wikle, University of Missouri. |
| April 16 | Diogo Bolster University of Notre Dame Title: Incomplete mixing in reactive systems - from Lab to Field scale Abstract: In order for two items to react they must physically come into contact with one another. In the lab we often measure reaction rates by forcing two species to continuously mix together. However, in real systems such forced mixing mechanisms may often not exist and so a natural question arises: How do we take measurements from our well mixed laboratory experiments and use them to make meaningful predictions at scales of interest? In this talk we propose a novel modeling framework that aims precisely to do this. To show its applicability we will discuss it as related to a few examples: (i) mixing driven reactions in a quasi-well-mixed systems (ii) mixing driven reactions in a porous column experiment and (iii) mixing in a highly heterogeneous aquifer with a broad range of velocity and spatial scales. While this work was originally motivated by chemical reactions in porous media, the modeling framework is much more general than this and should be applicable to a broad range of problems. Also, the term reaction, as defined within our framework, can loosely be defined as an event where two items come together to produce something else; it is not in any way limited to purely chemical reactions. |
| April 23 | Kiona Ogle Northern Arizon Title: A Bayesian approach to quantifying time-scales of influence and ecological memory Abstract: Many time-varying ecological processes are influenced by both concurrent and antecedent (past) conditions; in some cases, antecedent conditions may outweigh concurrent influences. The time-scales over which environmental conditions influence processes of interest (e.g., photosynthesis, carbon and water fluxes, tree growth, ecosystem productivity) are not well understood, motivating our development and application of the stochastic antecedent modeling (SAM) approach. The SAM approach is applied to ecological time-series data within a Bayesian statistical framework to quantify ecological memory. We use “memory” to broadly describe time-scales of influence, including the importance of antecedent conditions experienced at different times into the past, potentially revealing lagged responses. The coupled Bayesian-SAM approach, however, can lead to computational inefficiencies, and we describe reparameterization “solutions” to address such issues. To illustrate, we apply the approach to responses operating at distinctly different time-scales: annual tree growth (e.g., tree-rings widths) and sub-daily plant physiological responses (e.g., indices of stomatal behavior). Our Bayesian-SAM applications to tree growth in arid and semi-arid regions has identified particular seasons or months during which climatic conditions (e.g., precipitation or temperature) are most influential to subsequent tree growth; in many cases, conditions experienced 2-4 years ago continue to influence growth. The analysis has also revealed novel, multi-day lagged responses of plant physiological behavior to soil and atmospheric moisture conditions. In general, the Bayesian-SAM approach has demonstrated that ecological memory is an important process governing plant and ecosystem responses to environmental perturbations. |
| April 30 | Book Club "Factfulness: 10 Reasons We’re Wrong about the World – and Why Things are Getting Better" (2018), Hans Rosling Chapter 9-10 + Factfulness Rules of Thumb |
Book Club (See schedule and discussed chapters below): As part of our colloquia this semester, we will share a discussion of:
“Weapons of Math Destruction” by Cathy O’Neil
https://weaponsofmathdestructionbook.com
Zoom link for book club. Please contact Jennifer Ryan at jkryan@mines.edu for further information and the Zoom link and password.
Fall 2020
| September 18 | Zachary J. Grant Oak Ridge National Lab Analysis and Development of Strong Stability Preserving Time Stepping Schemes High order spatial discretizations with monotonicity properties are often desirable for the solution of hyperbolic partial differential equations. These methods can advantageously be coupled with high order strong stability preserving time scheme to accurately evolve solutions forward in time while preserving convex functionals that are satisfied from the design of the spatial discretization. The search for high order strong stability time- stepping methods with large allowable strong stability coefficient has been an active area of research over the last three decades. In this talk I will review the foundations of SSP time stepping schemes as in how to analyze a given scheme, and how to optimally build a method which allows the largest effective stable time step. We will then discuss some extensions of the SSP methods in recent years and some ongoing research problems in the field, and show some the need of the SSP property through simple yet demonstrative examples. |
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| September 25 | Book Club “Weapons of Math Destruction” Chapter 1-4 |
| October 2 | |
| October 16 | Minah Oh James Madison University Fourier Finite Element Methods and Multigrid for Axisymmetric H(div) Problems An axisymmetric problem is a problem defined on a three-dimensional (3D) axisymmetric domain, and it appears in numerous applications. An axisymmetric problem can be reduced to a sequence of two-dimensional (2D) problems by using cylindrical coordinates and a Fourier series decomposition. Fourier Finite Element Methods (Fourier-FEMs) can be used to approximate each Fourier-mode of the solution by using a suitable FEM. Such dimension reduction is an attractive feature considering computation time, but the resulting 2D problems are posed in weighted function spaces where the weight function is the radial component r. Furthermore, the grad, curl, and div operators appearing in these weighted problems are quite different from the standard ones, so the analysis of such weighted problems requires special attention. Multigrid is an effective iterative method that can be used to solve large matrix systems arising from FEMs. In this talk, I will present a multigrid algorithm that can be applied to weighted H(div) problems that arise after performing a dimension reduction to an axisymmetric H(div) problem. Theoretical results that show the uniform convergence of the multigrid V-cycle with respect to meshsize will be presented as well as numerical results. |
| October 30 | Book Club: “Weapons of Math Destruction” Chapters 5 - 7 |
| November 6 | Mokshay Madiman University of Delaware Concentration of information for log-concave distributions In 2011, S. Bobkov and the speaker showed that for a random vector X in R^n drawn from a log-concave density f=e^{-V}, the information content per coordinate, namely V(X)/n, is highly concentrated about its mean. The result demonstrated that high-dimensional log-concave measures are in a sense close to uniform distributions on the annulus between 2 nested convex sets (generalizing the well known fact that the standard Gaussian measure is concentrated on a thin spherical annulus). We present recent work that obtains an optimal concentration bound in this setting, using a much simplified proof. Applications that motivated the development of these results include high-dimensional convex geometry, random matrix theory, and shape-constrained density estimation. The talk is based on joint works with Sergey Bobkov (University of Minnesota), Matthieu Fradelizi (Université Paris Est), and Liyao Wang. |
| November 20 | Ayaboe Edoh Edwards AFRL Balancing Numerical Dispersion, Dissipation, and Aliasing for Time-Accurate Simulations The investigation of unsteady flow phenomena calls for the need to improve time-accurate simulation capabilities. Numerical errors responsible for affecting solution accuracy and robustness can be broadly categorized in terms of dispersion, dissipation, and aliasing. Their presence is a consequence of discretizing the continuous governing equations, and their impact may be felt at all scales (albeit to varying degrees). The task of constructing an effective numerical method may therefore be interpreted in terms of reducing the influence of these errors over as broad a range of scales as possible. Here, a concerted assembly of scheme components is chosen relative to a target aliasing limit. High-order and optimized finite difference stencils are employed in order to achieve accuracy; meanwhile, split representations for nonlinear transport terms are used in order to greatly improve robustness. Finally, tunable and scale-discriminant artificial-dissipation methods are incorporated for de-aliasing purposes and as a means of further enhancing both accuracy and stability. The proposed framework is motivated by the need to devise a numerical format capable of mitigating discretization effects in Large-Eddy Simulations. |
| December 4 | Book Club “Weapons of Math Destruction” Chapters 8-10 |
Spring 2020
| January 24 | Mevin Hooten Colorado State University Runnning on empty: Recharge dynamics from animal movement data |
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| February 14 | Mark Risser Lawrence Berkeley National Laboratory Bayesian inference for high-dimensional nonstationary Gaussian processes |
| February 21 | Donna Calhoun Boise State University A fully unsplit wave propagation algorithm for shallow water flows on GPUs |
| February 28 | Matthias Katzfuss Texas A&M Gaussian-Process Approximations for Big Data |
| March 20 | Nancy Rodriguez |
| April 3 | Dan Nordman |
| April 10 | Grady Wright |
| April 24 | Feng Bao |
Fall 2019
| August 23 | Chris Elvidge NOAA and Mines' Payne Institute of Public Policy VIIRS Data Gems From the Nights |
| September 13 | Cynthia Phillips Sandia National Laboratory Advanced Data Structures for National Cyber Security |
| September 20 | Will Kleiber University of Colorado - Boulder Mixed Graphical-Basis Models for Large Nonstationary and Multivariate Spatial Data Problems |
| October 4 | Igor Cialenco Illinois Institute of Technology Adaptive Robust Control Under Model Uncertainty |
| October 18 | Tathagata Bandyopadhyay Indian Institute of Management Ahmedabad Inference Problems in Binary Regression Model with Misclassified Responses Video |
| October 25 | Daniel Forger University of Michigan Math, Music and the Mind; Analysis of the performed Trio Sonatas of J.S. Bach |
| November 8 | Daniel Larremore University of Colorado - Boulder Complex Networks & Malaria: From Evolution to Epidemiology Video |
| November 22 | Marisa Eisenberg University of Michigan |
| December 3 | Russell Cummings United States Air Force Academy The DoD High Performance Computing Modernization Program’s Hypersonic Vehicle Simulation Institute: Objectives and Progress -A Mechanical Engineering Seminar- |
Spring 2019
| January 25 | Steve Sain Jupiter Intelligence Data Science @ Jupiter |
| February 1 | Xingping Sun Missouri State University Kernel Based Monte Carlo Approximation Methods |
| February 8 | Mandy Hering Baylor University Fault Detection and Attribution for a Complex Decentralized Wastewater Treatment Facility |
| February 22 | Bailey K. Fosdick Colorado State University Inference for Network Regressions with Exchangeable Errors |
| March 8 | Radu Cascaval University of Colorado - Colorado Springs The Mathematics of (Spatial) Mobility |
| March 15 | Amneet Bhalla San Diego State University A Robust and Efficient Wave-Structure Interaction Solver for High Density Ratio Multiphase Flows Video |
| March 22 | Robert Lund Clemson University Stationary Count Time Series |
| April 5 | Hua Wang Colorado School of Mines Learning Sparsity-Induced Models for Understanding Imaging Genetics Data Video |
| April 26 | Wen Zhou Colorado State University Estimation and Inference of Heteroskedasticity Models with Latent Semiparametric Factors for Multivariate Time Series Video |
| May 3 | Olivier Pinaud Colorado State University Time Reversal by Time-dependent Perturbations Video |
Fall 2018
| August 31 | Michael Wakin Colorado School of Mines Modal Analysis from Random and Compressed Samples Video |
| September 14 | Michael Scheuerer National Oceanic and Atmospheric Administration (NOAA) Generating Calibrated Ensembles of Physically Realistic, High-Resolution Precipitation Forecast Fields based on GEFS Model Output Video |
| September 28 | Kathryn Colborn CU Denver, Anschutz Medical Campus Spatio-Temporal Modelling of Malaria Incidence for Early Epidemic Detection in Mozambique Video |
| October 12 | Philippe Naveau Laboratoire des Sciences du Climat et de l'Environnement, IPSL-CNRS, France Analysis of Extreme Climate Events by Combining Multivariate Extreme Values Theory and Causality Theory Video |
| October 26 | Carrie Manore Los Alamos National Laboratory Modeling Disease Risk with Social and Environmental Drivers and Non-traditional Data Sources |
| November 2 | Jon Trevelyan Durham University, UK Enriched Simulations in Computational Mechanics Video |
| November 9 | Sarah Olson Worcester Polytechnic Institute Modeling Cell Motility: From Agent Based Models to Continuous Approximations Video |
| November 30 | Elwin van't Wout Pontificia Universidad Católica de Chile Efficient Numerical Simulations of Wave Propagation Phenomena Video |
| December 7 | Bruce Bugbee National Renewable Energy Laboratory (NREL) |
Spring 2018
| March 2 | Grant Brown University of Iowa Biostatistics Working with Approximate Bayesian Computation in Stochastic Compartmental Models Video |
| March 9 | Victoria Booth University of Michigan Mathematics Neuromodulation of Neural Network Dynamics Video |
| March 23 | Daniel Appelö University of Colorado Applied Math What’s New with the Wave Equation? Video |
| April 6 | Grad Student Showcase Video |
| April 20 | Jem Corcoran University of Colorado Applied Math A Birth-and-Death Process for the Discretization of Continuous Attributes in Bayesian Network Structure Recovery Video |
| May 4 | Ian Sloan University of New South Wales Mathematics Sparse Approximation and the Cosmic Microwave Background Video |
Fall 2017
| August 25 | Zachary Kilpatrick University of Colorado Boulder, Department of Applied Mathematics Evidence accumulation in changing environments: Neurons, organisms, and groups |
| September 8 | Lincoln Carr Colorado School of Mines, Department of Physics Many-Body Quantum Chaos of Ultracold Atoms in a Quantum Ratchet Video |
| September 22 | Joe Guinness North Carolina State University, Department of Statistics A General Framework for Vecchia Approximations of Gaussian Processes Video |
| October 13 | Eliot Fried Okinawa Institute of Science and Technology, Mathematics, Mechanics, and Materials Unit Shape Selection Induced by Competition Between Surface and Line Energy |
| October 20 | Arthur Sherman National Institutes of Health Diabetes Pathogenesis as a Threshold-Crossing Process Video |
| November 3 | Adrianna Gillman Rice University, Department of Computational and Applied Mathematics Fast Direct Solvers for Boundary Integral Equations Video |
| November 17 | Laura Miller University of North Carolina at Chapel Hill, Departments of Mathematics and Biology Using Computational Fluid Dynamics to Understand the Neuromechanics of Jellyfish Swimming Video |
| December 1 | AMS Graduate Student Showcase Video |
Spring 2017
| January 13 | Roger Ghanem University of Southern California, Department of Aerospace and Mechanical Engineering Uncertainty quantification at the interface of computing and everything else Special joint colloquium with Department of Mechanical Engineering Video |
| January 27 | Wolfgang Bangerth Colorado State University, Department of Mathematics Simulating complex flows in the Earth mantle Video |
| February 10 | Chris Mast Mercer, Actuary and Employee Benefits Consultant Actuarial problems in employer-sponsored healthcare Video |
| February 24 | Natasha Flyer National Center for Atmospheric Research, Computational Math Group Bengt Fornberg University of Colorado Boulder, Department of Applied Mathematics Radial basis functions: Freedom from meshes in scientific computing Video |
| March 10 | Michael Sprague National Renewable Energy Laboratory, Computational Science Center A computational model for a dilute biomass suspension undergoing mixing and settling Video |
| March 24 | Randall J. LeVeque University of Washington, Department of Applied Mathematics Generating random earthquakes for probabilistic hazard assessment Special joint colloquium with US Geological Survey Video |
| April 7 | Fred J. Hickernell Illinois Institute of Technology, Department of Applied Mathematics Think like an applied mathematician and a statistician Video |
| April 14 | Ian Sloan University of New South Wales, School of Mathematics How high is high dimensional? Video |
| April 21 | Mark Embree Virginia Tech, Department of Mathematics Using interpolatory approximations to learn from an instrumented building Video |
| April 28 | James A. Warren National Institute of Standards and Technology, Material Measurement Laboratory The Materials Genome Initiative: NIST, data, and open science Video Special joint colloquium with Department of Metallurgical and Materials Engineering |
| May 5 | Jessica F. Ellis Colorado State University, Department of Mathematics The features of college calculus programs: An overview of the MAA two calculus projects' main findings Video |
Fall 2016
| September 2 | Stephen Becker University of Colorado Boulder, Department of Applied Mathematics Subsampling large datasets via random mixing Video |
| September 16 | Art Owen Stanford University, Department of Statistics Permutation p-value approximation via generalized Stolarsky invariance Video |
| September 30 | Stefan Wild Argonne National Laboratory, Mathematics and Computer Science Division Beyond the black box in derivative-free and simulation-based optimization Video |
| October 14 | Erica Graham Bryn Mawr College, Department of Mathematics Modeling physiological and pathological mechanisms in ovulation Video |
| October 28 | Jim Koehler Google Boulder, Principal Statistician Statistical methods supporting Google's ad business |
| November 11 | Dennis Cook University of Minnesota, School of Statistics An Introduction to envelopes: Methods for improving efficiency in multivariate statistics Video |
| December 2 | Howard Elman University of Maryland, Department of Computer Science Efficient computational methods for parameterized partial differential equations Video |