This page contains a list of seminars that I am organizing within the Department of Computer Science and Department of Applied Mathematics
at CU Boulder. For a list of seminars that I gave, please see my CV.

This series of talks aims at encouraging networking among postdocs and promoting the exchange of ideas for potential collaborations.
We have started this series of relatively informal seminars where the postdocs from the two Departments, and occasionally from other local universities,
can showcase their research and foster relationships and collaborations between the two Departments and other universities. Moreover,
we have decided to consider a different format in this series of talks, by also providing tutorials/workshops on topics that may be useful to
postdocs, students, and faculties across different disciplines.

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

The Fall 2019 Workshop/Tutorial series is organized in collaboration with PAC Boulder.

**Fall 2019 Workshops/Tutorials:**

**Fri. December 6, 2019:**

**Time:**10:30 am - 12 pm

**Location:**DLC 1B70

**Workshop instructor: Valeria Barra**, Department of Computer Science, CU Boulder

**Title:**

*MATLAB*(link to event)

In this tutorial we will learn the fundamentals of programming in MATLAB. 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 Software Downloads and Licensing website of the University so that you can download it and activate it with your free licence associated to 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. Material useful for the LaTeX tutorial will be further available on this dedicated GitHub repository for attendees to download.

**Wed. November 6, 2019:**

**Time:**10:30 am - 12 pm

**Location:**DLC 1B70

**Workshop instructor: Gary Nave**, BioFrontiers Institute, CU Boulder

**Title:**

*Intermediate Python*(link to event)

This workshop will provide an introduction to using Python for scientific research, including manipulating arrays with NumPy, loading and saving data with SciPy and Pandas, and plotting results with Matplotlib. The workshop is intended for those with some basic familiarity with Python syntax who are interested in learning more and applying it to their research. However, beginners are still welcome! If you have specific questions you'd like to see addressed, send Gary an email at Gary.Nave@colorado.edu.

**Fri. October 4, 2019:**

**Time:**10:30 am - 12 pm

**Location:**DLC 1B70

**Workshop instructor: Valeria Barra**, Department of Computer Science, CU Boulder

**Title:**

*Introduction to LaTeX documents and presentations*(link to event)

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 (MikTeX for Windows and Linux and MacTeX for Mac) and a LaTeX editor of their choice, or use the free online editor that we are going to use for the demo. Material useful for the LaTeX tutorial will be further available on this dedicated GitHub repository for attendees to download.

**Fri. September 6, 2019:**

**Time:**10:30 am - 12 pm

**Location:**DLC 1B70

**Workshop instructor: Gary Nave**, BioFrontiers Institute, CU Boulder

**Title:**

*Introduction to LaTeX documents and presentations*

For those who hope to attend the Intro to Python workshop, please go ahead and install Python on your laptop. It is recommended to download Anaconda, which is a distribution including basic Python and all the extra stuff you'll need. If you run into issues with the download, Gary Nave be glad to help you out before/after the workshop and we'll plan to work together in groups. Material used for this workshop can be found in this dedicated GitHub repository.

**APPM + CS Postdoc Seminar:**

**Fri. May 3, 2019:**

**Time:**11 am

**Location:**ECOT 831

**Speaker: Gary Nave**, BioFrontiers Institute, CU Boulder

**Title:**

*Workshop on Python*(link to event)

**Tutorial description:**The second workshop will be on Python. Gary Nave from the BioFrontiers Institute of CU Boulder will give a brief overview on the basics of using Python, particularly in regards to scientific computing, and will provide hands-on exercises. He will talk about basic syntax, structure, and package management to provide a starting point for anyone hoping to use Python in their research or studies. Feel free to bring your questions or email (Gary.Nave@colorado.edu) about specific questions you have in advance. The material used in this tutorial can be found in this GitHub Repo.

**Fri. Apr. 19, 2019:**

**Time:**11 am

**Location:**ECOT 831

**Speaker: Sophie Giffard**, Department of Computer Science, CU Boulder

**Title:**

*Workshop on Dimensionality Reduction*(link to event)

**Tutorial description:**Sophie Giffard from the Computer Science Department will give a brief overview on dimensionality reduction techniques that are useful to compress, explain, pre-process and interpret any data. A hands-on exercise with Python and scikit-learn will be the second part of the tutorial. The workshop material can be found in this GitHub Repo. Attendees are encouraged to download or clone the repository before coming, and install python3 with numpy, scikitlearn and pandas libraries on their machine.

**Fri. Apr. 5, 2019:**

**Time:**11 am

**Location:**ECOT 831

**Speaker: Gary Nave**BioFrontiers Institute, CU Boulder

**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.

**Fri. Mar. 15, 2019:**

**Time:**11 am

**Location:**ECOT 831

**Speaker: Sophie Giffard**, Department of Computer Science, CU Boulder

**Title:**

*Deep learning for hurricane forecasting*

**Abstract:**The forecast of hurricane trajectories is crucial for the protection of people and property, but machine learning techniques have been scarce for this so far. I will present a method that we developed recently, a fusion of neural networks, that is able to combine past trajectory data and reanalysis atmospheric images (wind and pressure 3D fields). Our network is trained to estimate the longitude and latitude displacement of hurricanes and depressions from a large database from both hemispheres (more than 3000 storms since 1979, sampled at a 6 hour frequency). Finally, I will give an overview of the hackathon that I organized on a very close topic at the Climate Informatics Workshop in September.

**Fri. Feb. 15, 2019:**

**Time:**10:30 am

**Location:**ECCR 257 (Newton's Lab)

**Speaker: Valeria Barra**, Department of Computer Science, CU Boulder

**Title:**

*Efficient representation of high-order finite element operators*

**Abstract:**We present an extensible low-level library that provides a versatile algebraic interface and optimized implementations suitable for high-order operators: libCEED. This library aims to overcome the challenges in high-order methods that use global sparse matrices as operator representations. In fact, one of the challenges with high-order methods is that a global sparse matrix is no longer a good representation of a high-order operator, both with respect to the FLOPs needed for its evaluation, as well as the memory transfer needed for simple matrix-vector multiplies. Thus, high-order methods require a new "format" that represents a linear (or more generally non-linear) operator, not associated with a sparse matrix. The goal of libCEED is to propose such a format, as well as supporting implementations and data structures, that enable efficient operator evaluation and composition, on a variety of computational device types (CPUs, GPUs, etc.) and enables portable performance through nearly optimal memory transfers and FLOPs for operator evaluation. We investigate operator composition and design of coupled solvers in the context of atmospheric modeling, providing examples of the usage of libCEED with PETSc. We will show examples of solutions of the advection equation and the full compressible Navier-Stokes equations, to investigate the dynamics of density currents in the stratified atmosphere.

For the remainder of the talk, I am going to show some of my past research in the field of Computational Fluid Dynamics, regarding numerical simulations of the dynamics of free-boundary/interfacial flows of thin viscoelastic liquid films and membranes of Maxwell and Jeffreys type.

**Fri. Feb. 1, 2019:**

**Time:**11 am

**Location:**ECOT 831

**Speaker: Tahra Lucene Eissa**, Department of Applied Mathematics, CU Boulder

**Title:**

*Interactions between hierarchical decision-making processes in dynamic environments*

**Abstract:**In a constantly changing world, accurate decisions require flexible evidence accumulation where old information is discounted at a rate adapted to the frequency of environmental changes. However, sometimes humans and other animals must simultaneously infer the state of the environment and its volatility (hazard rate). To probe how these estimates impact one another when performed hierarchically, we develop and analyze a model of an ideal observer who makes noisy measurements of a two-state environment with an initially unknown hazard rate that is either high (changes happen often) or low (changes are rare). Using log-likelihood ratios of the state and hazard rate to represent the observer’s beliefs about the environment, we track how the observer’s estimates evolve over time. We find that the accuracy of the hazard rate estimate builds up slowly, with information at change points (CPs) providing evidence for a high hazard rate and the time between CPs suggesting the hazard rate is low. In contrast, state estimation accuracy drops immediately after CPs when the observer has yet to track the change and recovers at a rate dependent on the observer’s estimated hazard rate. Quantifying this recovery rate, we find that there is a tradeoff between recovery speed and overall state accuracy and that the speed of post-CP recovery changes with trial duration as the observer becomes more confident about their hazard rate estimate. We then compare our model that includes hazard rate inference to results from a normative model with a known hazard rate to assess how hierarchical inference processes impact state belief. We analyze the normative model using a set of nonlinear partial differential equations (PDEs), leading to faster and more accurate estimates than sampling methods. Comparing our model to this gold standard for state inference, we find that our model’s state inference improves over trial duration to match normative models as the hazard rate is learned. Thus, our setup can be used to identify situations that utilize hierarchical inference strategies and improve dynamic decision-making task design.

**Fri. Jan. 18, 2019:**

**Time:**11 am

**Location:**ECOT 831

**Speaker: Olena Burkovska**, Florida State University, Visiting Scholar at the Department of Applied Mathematics, CU Boulder

**Title:**

*Approximation of parametrized kernels arising in nonlocal and fractional Laplace models*

**Abstract:**We consider parametrized linear and obstacle problems driven by a spatially nonlocal integral operator. These problems have a broad impact on current developments in different fields such as, e.g., peridynamics, contact mechanics, and finance. We focus on integral kernels with nonlocal interactions limited to a ball of radius greater than 0 or (truncated) fractional Laplace kernels, which are also parametrized by the fractional power s ∈ (0,1). Compared to the fractional problems with infinite horizon of interaction, these type of problems are of independent interest, since they form a connection between purely nonlocal and classical local PDE problems. Our goal is to provide an efficient and reliable approximation of the solution for different values of the kernel parameters. To reduce the high computational cost associated with multi-query solution evaluations, we employ the reduced basis method (RBM) as a parametric model order reduction approach. A major difficulty in the construction of the method arises in the non-affinity of the integral kernel w.r.t. the parameters, which can not be directly treated by empirical interpolation due to the singularity and a lack of continuity of the kernel. This substantially affects the efficiency of the RBM. As a remedy, we propose suitable approximations of the kernel, based on the parametric regularity of the bilinear form and the improved spatial regularity of the solution. The results we provide are of independent interest for other approximation techniques and applications such as, e.g., optimization or parameter identification. Finally, we certify the RBM by providing reliable a posteriori error estimators and support the theoretical findings by numerical experiments.

**Fri. Dec. 14, 2018:**

**Time:**1 pm

**Location:**ECOT 831

**Speaker: Jeffrey Hokanson**, Department of Computer Science, CU Boulder

**Title:**

*H2-optimal Model Order Reduction Using Projected Nonlinear Least Squares*

**Abstract:**In many applications throughout science and engineering, model reduction plays an important role replacing expensive large-scale linear dynamical systems by inexpensive reduced order models that capture key features of the original, full order model. One approach to model reduction is to find reduced order models that are locally optimal approximations in the H2 norm, an approach taken by the Iterative Rational Krylov Algorithm (IRKA) and several others. Here we introduce a new approach for H2-optimal model reduction using the projected nonlinear least squares framework. At each iteration, we project the H2 optimization problem onto a finite-dimensional subspace yielding a weighted least rational approximation problem. Subsequent iterations append this subspace such that the least squares rational approximant asymptotically satisfies the first order necessary conditions of the original, H2 optimization problem. This enables us to build reduced order models with similar error in the H2 norm as competing methods but using far fewer evaluations of the expensive, full order model. Moreover our new algorithm only requires access to the transfer function of the full order model, unlike IRKA which requires a state-space representation or TF-IRKA which requires both the transfer function and its derivative. This application of projected nonlinear least squares to the H2-optimal model reduction problem suggests extensions of this approach related model reduction problems.

**Fri. Nov. 30, 2018:**

**Time:**1 pm

**Location:**ECOT 831

**Speaker: Tahra Lucene Eissa**, Department of Applied Mathematics, CU Boulder

**Title:**

*Spatiotemporal Dynamics of Neocortical Seizure Activity*

**Abstract:**Seizures are defined as sudden, abnormal electrical disturbances in the brain. Patients diagnosed with epilepsy have chronic, recurrent seizures and often require clinical intervention to prevent these episodes. Unfortunately, a large portion of epilepsy patients do not respond to current treatment options, in part due to a lack of understanding on how seizures develop in the brain. This talk will discuss some of the complex dynamics associated with seizure activity and how these dynamics can educate epilepsy treatment. Using a combination of human electrical recordings, biological experiments and computational modeling, we studied the dynamics of seizures at various spatial scales, ranging from a single neuron up to large neuronal networks (centimeter scale). At each scale, we analyzed the interactions between the seizure-producing neurons and the surrounding tissue to determine how the interactions can define a seizure's trajectory and the activity observed clinically. The findings were then used to identify representative electrical markers that could be applied to clinical treatment.

**Fri. Nov. 16, 2018:**

**Time:**1 pm

**Location:**ECOT 831

**Speaker: Giacomo Capodaglio**, Florida State University, Visiting Scholar at the Department of Applied Mathematics, CU Boulder

**Title:**

*Approximation of probability density functions for SPDEs using truncated series expansions*

**Abstract:**The probability density function (PDF) of a random variable associated with the solution of a stochastic partial differential equation (SPDE) is approximated using a truncated series expansion. The SPDE is solved using two stochastic finite element (SFEM) methods, Monte Carlo sampling and the stochastic Galerkin method with global polynomials. The random variable is a functional of the solution of the SPDE, such as the average over the physical domain. The truncated series are obtained considering a finite number of terms in the Gram-Charlier (GC) or Edgeworth (ED) series expansions. These expansions approximate the PDF of a random variable in terms of another PDF, and involve coefficients that are functions of the known cumulants of the random variable. While the GC and ED series have been employed in a variety of fields such as chemistry, astrophysics and finance, their use in the framework of SPDEs has not yet been explored. This is a joint work with Max Gunzburger and Henry P. Wynn.