Shilpa Khatri; Health Sciences Research Institute; University of California, Merced

Numerical methods for fluid-structure interactions and multiphase flow within marine phenomena 

To understand the fluid dynamics of marine phenomena, for example particles settling, droplets rising, pulsating coral, and sniffing crabs, fluid-structure and multiphase flow problems must be solved. Challenges exist in developing numerical methods and computational tools to solve these complex flow problems with boundary conditions at fluid-structure and fluid-fluid interfaces. I will present details of two different problems where these challenges are handled: (1) simulations of pulsating soft corals and (2) accurate evaluation of layer potentials near boundaries. The first problem of pulsating soft corals will be motivated by field and experimental work in the marine sciences. I will discuss these related data and provide comparisons with the simulations. For the second problem of accurate evaluation of layer potentials, I will show how classical numerical methods are problematic for evaluations close to boundaries and how newly developed numerical methods can be used to remove the error. Finally, I will briefly present some further work in this field. 

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Olaniyi Iyiola, Department of Mathematics and Physical Sciences, California University of Pennsylvania

Efficient Methods for Solving Diffusion-Reaction Systems of Fractional Order Type 

Nonlocality and spatial heterogeneity of many practical systems have made fractional differential equations very useful tools in Science and Engineering. However, solving these type of models is computationally demanding. In this talk, I will present an overview of fractional calculus and some of my recent results on solving fractional diffusion-reaction problems. In the first part, I will briefly discuss a novel method of determining the solution and the source function (inverse problem) for a two-parameter fractional diffusion equation. This problem models several physical processes such as the microwave heating and light propagation in photoelectric cells. The second part of my talk will focus on the numerical solution of nonlinear reaction-diffusion fractional models using exponential time differencing. Different approaches to spatial discretization of the reaction-diffusion fractional systems which are very important in reducing computational time will be discussed. Generally, the mechanisms of cell motility and/or the generation of chemical pre-patterns are modeled using ideas of biological pattern formation. Several models for pattern formation have been proposed to explain the regenerative properties of hydra which have been experimentally observed in various transplantations. Invoking the intrinsic properties of fractional calculus is therefore apparent in biological and biochemical systems due to these complexities. I will present some applications of fractional calculus in biological pattern formation. I will conclude the presentation with several open problems in this area and my new area of research in data science. 

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Eduardo Corona, Assistant Professor of Mathematics, New York Institute of Technology

Fast computational frameworks for particulate media simulation

Granular media and “wet” particle suspensions are two important models of soft matter. They are crucial to the study of soil mechanics, biological media self-assembly and smart material design. In this talk, we present general computational frameworks for the simulation of dense particulate soft matter in 3D featuring boundary integral formulations for long-range particle interactions, singular integral evaluation schemes and optimization-based collision resolution.

As algorithmic and learning frameworks continue to improve, addressing large data-set storage and management problems is imperative. Large-scale simulations can quickly generate a lot of data: particle positions, velocities and pairwise contact forces for one run can easily require GBs to TBs of memory. We present a streaming data compression scheme based on the tensor train decomposition that allows us to build a compressed version of the full data-set that can be quickly accessed and operated with in limited computing environments.

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Yunan Yang; Courant Instructor; Courant Institute of Mathematical Sciences, New York University

Optimal Transport for Inverse Problems and the Implicit Regularization

Optimal transport has been one interesting topic of mathematical analysis since Monge (1781). The problem's close connections with differential geometry and kinetic descriptions were discovered within the past century, and the seminal work of Kantorovich (1942) showed its power to solve real-world problems. Recently, we proposed the quadratic Wasserstein distance from optimal transport theory for inverse problems, tackling the classical least-squares method's longstanding difficulties such as nonconvexity and noise sensitivity. The work was soon adopted in the oil industry. As we advance, we discover that the advantage of changing the data misfit is more general in a broader class of data-fitting problems by examining the preconditioning and "implicit" regularization effects of different mathematical metrics as the objective function in optimization, as the likelihood function in Bayesian inference, and as the measure of residual in numerical solution to PDEs.

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The Postdoctoral Association of Colorado, �鶹ӰԺ has organized this series of monthly tutorials/workshops on topics that may be useful to postdocs, students, and faculties across different disciplines.

Everyone is invited to attend! If you'd like to offer to give one workshop, and/or have topic ideas, please fill out . We'll be adding new topics as people offer them!

Please note: These tutorials are given by postdocs, but are intended for all types of audience (students and faculties are welcome!).

In this tutorial, we will learn the fundamentals of programming in .

It is important that you have MATLAB installed on your machine and bring your laptop to the workshop. If you do not have a current MATLAB installation, please use the  of the University so that you can download it and activate it with your free license associated with the University.

We are going to explore different data types and structures (from the basic types, array and matrices, to the more advanced cells). We are going to learn how to display, print and publish our results in different formats. We are going to learn how to debug our code and how to do some data analysis and visualization. Materials useful for the MATLAB tutorial will be further available on this dedicated  for attendees to download.

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Engineers, like everyone, are influenced by media messages every day. Don’t miss this opportunity to interact with TED speaker, renowned media scholar and CU �鶹ӰԺ alumnus, Chris Bell, PhD and consider how media impacts your personal and professional life as an engineer working to address societal issues. Bell specializes in the study of popular culture, focusing on the ways in which race, class and gender intersect in different forms of children's media. He is a TED speaker, a diversity and inclusiveness consultant for Pixar Animation Studios, a 2017 David Letterman Award-winning media scholar, and the 2017 Denver Comic Con Popular Culture Educator of the Year. Recognized nationally for his expertise in the area of children's culture, he serves as the chair of the Southwest Popular/American Culture Association's Harry Potter Studies division. To learn more, check out his TED Talk about female superheroes! Bell will be giving a guest lecture on Thursday, October 24 from 5 p.m. to 7 p.m. in MATH 100. https://calendar.colorado.edu/event/christopher_bell_race_gender_and_inclusiveness_in_pop_culture

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The Postdoctoral Association of Colorado, �鶹ӰԺ has organized this series of monthly tutorials/workshops on topics that may be useful to postdocs, students, and faculties across different disciplines. Everyone is invited to attend! If you'd like to offer to give one workshop, and/or have topic ideas, please fill out this form. We'll be adding new topics as people offer them! Please note: These seminars are given by postdocs, but are intended for all types of audience (students are welcome!). Calendar of next tutorials: Friday, Oct. 4, 10:30 am - 12:00 pm: LaTeX Documents and Presentations, Valeria Barra, Department of Computer Science, CU �鶹ӰԺFriday Nov. 8, 10:00 am - 11:30 am: topic TBDFriday Dec. 6, 10:30 am - 12:00 pm: topic TBD In this LaTex tutorail we will learn some of the basics of LaTeX: typesetting different documents (such as, technical reports, books, and slide presentations), sectioning, cross-references, tables and different media (figures and videos), automatic generation of bibliographies and indexes, typing mathematical expressions; and, according to people's interest and time resources we can explore some more advanced topics, such as drawing graphic elements with the TikZ package. Attendees can download ahead a LaTeX compiler on their system... https://calendar.colorado.edu/event/postdoc_tutorial_latex_documents_and_presentations

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Brett Werner

Department of Mathematics, �鶹ӰԺ

On Machine Learning

Machine learning (ML) is the process of making computers learn without specifically programming them to do so. ML has a variety of applications including predicting revenue, detecting credit card fraud, and self-driving cars. We will begin by discussing the typical workflow in a ML modeling problem. A summary of several common ML modeling methods will be presented, including logistic regression and neural networks, and we will discuss the types of problems each type of model can solve.  Finally, we will discuss some of the projects that I have worked on and potential future projects.

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Osita Onyejekwe

Department of Mathematics, �鶹ӰԺ

Feature Detection in Observed Climate Factors

The detection of inflection points is an important task in science and engineering. This task is onerous with subjective results. Signals are often corrupted with noise and signal denoising is often required before feature extraction, such as change point detection can occur. The proposed techniques involve multi-scale kernel regression in conjunction with matched filtering. For each data point, the optimal denoising bandwidth is selected by maximizing the signal to noise ratio (SNR) via matched filtering. This is achieved by adaptively selecting the kernel bandwidth for each data point, based on the estimated standard error of the estimated signal at that spatial location. The bandwidth selection is addressed as a point-wise optimization problem. The SNR method can then be extended to the smoothed SNR method in that a quadratic function is fitted as a smoother on the bank of selected point-wise bandwidths in order to obtain an optimized bandwidth to denoise the entire noisy signal. The smoothed SNR method is then directly applied to climate data to determine change points in global temperature behaviors over the last century. It is shown that inflection point estimation can give an insight into abrupt changes in weather patterns. 

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Title: Flying snakes, attracting manifolds, and the trajectory divergence rate

Abstract: Inspired by the gliding behavior of the paradise tree snake, Chrysopelea paradisi, I will discuss a simplified model for passive aerodynamic flight which gives an intuitive and dynamically rich 2 degree-of-freedom system. Within this model, all trajectories collapse quickly onto an attracting codimension-1 manifold in velocity space: the terminal velocity manifold. This curve provides geometric insights into the possible dynamics of passively descending bodies such as gliding animals or falling leaves. As a tool to calculate and understand structures like the terminal velocity manifold, I introduce a scalar quantity, the trajectory divergence rate, which rapidly approximates attracting invariant manifolds based on an instantaneous vector field. This diagnostic may be applied to approximate a variety of structures including slow manifolds and hyperbolic Lagrangian coherent structures.

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