Jared McBride

Jared McBride

I am a PhD candatite in the University of Arizona Aplied Math GIDP

Talks and presentations

Spectral Estimation and Iterated Whitening

May 23, 2023

Talk, Southern Virginia University, Special Colloquium, Buena Vista, Virginia

Abstract

Most of my talk will be about my dissertation work at a fairly high level, the target audience being around the level of a senior undergraduate math major. Though to do it any justice, I will need to get a bit technical for what I hope is not too long. I plan on mentioning applications and ways undergrads can get involved with this sort of research. Then in the last 10 or so minutes I discuss the research I hope to pursue after graduation and emphasize undergraduate research opportunities within that research as well. I also provide a brief summary of my teaching background, mention classes I would like to teach, and say a few words about my vision for a math program at SVU.

Spectral Estimation and Iterated Whitening

January 22, 2023

Talk, Southern Utah University, Math Department, Seminar, Cedar City, Utah

Abstract

The power spectrum of a stationary stochastic process characterizes the amount of “energy” in different frequencies, and power spectra are a fundamental tool in data analysis, signal processing, and linear prediction and control. Standard methods for estimating power spectra from data can be highly inaccurate when the dynamic range of the spectrum is large. In this talk, I present a novel method for accurately estimating the power spectra of signals from data. The method, based on an iterated “whitening” procedure, is designed to work well for spectra with high dynamic range. I compare the iterated whitening method with two standard methods, and illustrate its use on a prototypical model of spatiotemporal chaos.

A comparison of spectral estimation methods for the analysis of chaotic and stochastic dynamical systems

September 27, 2022

Poster, The Fields Institute, Third Symposium on Machine Learning and Dynamical Systems, Poster Session, Toronto, Canada

Abstract

Estimating power spectra is frequently a first step in the analysis of stationary time series generated by chaotic and/or stochastic dynamical systems. Accurate estimates are needed for, e.g., data driven modeling and model reduction. Common challenges include the presence of multiple timescales and slow decay of correlations, and when the range of the power spectrum is large. Here, we present a comparison of some spectral estimation methods in current use. We also propose and test a general variance reduction technique, based on the method of control variates, which can be combined with any estimator. We compare these tools on spectral estimation and some related tasks, including spectral factorization and whitening. We apply the techniques to the Kuramoto-Sivashinsky equation, a prototypical model of spatiotemporal chaos.

A comparison of spectral estimation methods for the analysis of chaotic and stochastic dynamical systems

September 21, 2022

Talk, University of Arizona, Math Department, Brown Bag Seminar, Tucson, Arizona

Abstract

Estimating power spectra is frequently a first step in the analysis of stationary time series generated by chaotic and/or stochastic dynamical systems. Accurate estimates are needed for, e.g., data driven modeling and model reduction. Common challenges include the presence of multiple timescales and slow decay of correlations, and when the range of the power spectrum is large. In this talk, I review the definition of the power spectrum of a stationary stochastic process as well as some estimation techniques. Spectral factorization and modeling and whitening filters are also briefly discussed, with examples. I then describe how the variance reduction method of control variates can be applied to power spectrum estimation. A comparison of these tools on spectral estimation and some related tasks, including spectral factorization and whitening is presented. Time permitting, I apply the techniques to the Kuramoto-Sivashinsky equation, a prototypical model of spatiotemporal chaos.

Fitting autoregressive models by reversible jump Markov chain Monte Carlo

May 10, 2022

Talk, University of Arizona, Math Department, Monte Carlo Methods Course Student Presentation, Tucson, Arizona

Abstract

In this report I apply a reversible jump Markov chain Monte Carlo technique to the problem of estimating an autoregressive (AR) model to data. In doing this I focus on the proposed poles of the AR model. A review of relevant background material is included. And a full specification of the implementation is provided. At this time the attempt has been unsuccessful and only partial results are reported.

Numerical Wiener Filtering using CKMS

October 27, 2021

Talk, University of Arizona, Math Department, Data & Dynamics Group, Tucson, Arizona

Abstract

Wiener filtering has a rich theoretical foundation, which includes a technique for solving Wiener-Hopf equations. In this talk I discuss a numerical implementation of the Wiener-Hopf technique for discrete Wiener-Hopf equations that arise is computing Wiener filters.

Spectral Factorization and Spectral Estimation by Kalman Filtering

October 15, 2021

Talk, University of Arizona, Math Department, Brown Bag Seminar, Tucson, Arizona

Abstract

In this talk I review some signal processing theory including common techniques of spectral estimation. Some shortcomings of these common techniques are exposed under curtain conditions. I then demonstrate how the Kalman filter may be employed in spectral factoring (which is not new) and then show how this can be extended to spectral estimation (which to the best of my knowledge is new). I end by reporting that the aforementioned shortcomings of certain spectral estimation technique are not shared by this new technique. Examples are frequently used to demonstrate concepts and one of the example timeseries is a solution to the Kuromoto-Sivashinsky equation.

Data-driven Model Reduction by Wiener Projection

March 06, 2020

Talk, University of Arizona, Math Department, Brown Bag Seminar, Tucson, Arizona

Abstract

Many models used in industry are large and require a run (often repeated runs) of a full, computationally expensive model to produce results of tolerable accuracy. These systems may have limited data available, in that the number of variables that are observable is small, or the frequency of observation is low. Here we discuss a technique of model reduction informed by data from, as well as the dynamical equations of, the full model. The technique makes use of results from signal processing as well as statistical mechanics. The method for producing the reduced model uses the so-called Wiener projection.

Steady State Configurations of Cells Connected by Cadherin Sites

March 20, 2019

Talk, University of Arizona, Math Department, Graduate Student Colloquium, Tucson, Arizona

Abstract

Many cells employ cadherin complexes (c-sites) on the cell membrane to attach to neighboring cells, as well as integrin complexes (i-sites) to attach to a substrate in order to accomplish cell migration. This paper analyzes a model for the motion of a group of cells connected by c-sites. We begin with two cells connected by a single c-site and analyze the resultant motion of the system. We find that the system is irrotational. We present a result for reducing the number of c-sites in a system with c-sites between pairs of cells. This greatly simplifies the general system and provides an exact solution for the motion of a system of two cells and several c-sites.

Steady State Configurations of Cells Connected by Cadherin Sites

June 19, 2016

Talk, Brigham Young University, Math Department, Thesis Defense, Utah, Provo

Abstract

Many cells employ cadherin complexes (c-sites) on the cell membrane to attach to neighboring cells, as well as integrin complexes (i-sites) to attach to a substrate in order to accomplish cell migration. This paper analyzes a model for the motion of a group of cells connected by c-sites. We begin with two cells connected by a single c-site and analyze the resultant motion of the system. We find that the system is irrotational. We present a result for reducing the number of c-sites in a system with c-sites between pairs of cells. This greatly simplifies the general system, and provides an exact solution for the motion of a system of two cells and several c-sites.