Jared McBride

Jared McBride

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

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A list of all the posts and pages found on the site. For you robots out there is an XML version available for digesting as well.

Pages

Spectral Estimation using Reversible Jump Markov Chain Monte Carlo

Published in in preparation, 2022

The present work serves as a stepping stone to the task of rational spectral approximation given signal observations. Rational approximations can be preferred over the common Laurent polynomial approximation since they often can achieve great accuracy with much fewer parameters. The task of Rational approximation is essentially that of ARMA fitting. And the hope of this work is to provide guidance for solving that problem by first considering AR fitting by reversible jump Markov chain Monte Carlo over the space of poles and error variance, which things determine the centered AR process. In a sense this is a proof of concept or trial run to understand the problem well enough to better determine whether the full ARMA problem is worthwhile.

Posts

Numerical Spectral Factorization by Kalman Recursion

less than 1 minute read

Published:

Here is note on spectral factorization using the Kalman recursions. It is mainly a restatement on the same material by Kailath. However there are a number of details that are made more transparent.

Question for Dr. Lin

less than 1 minute read

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I am perhaps trying to be too technical. By I am curious, even if this doesn’t belong in the note that I am writing about spectral factorization. In the context of a state-space model,

Meeting with Dr. Lin

1 minute read

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Had a brief meeting and reiterated points from last time.

Meeting with Dr. Lin

less than 1 minute read

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Today we meet came up with the following tasks for me to do:

CKMS+

less than 1 minute read

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Dec 31, 2021

Kalman Filtering Explained

less than 1 minute read

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Here I explore the Kalman filter. I am seeking an intuitive, conceptually if not geometric understanding of the Kalman gain matrix.

Update

less than 1 minute read

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Here are the papers I referenced:

Blog Post number 4

less than 1 minute read

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This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.

Blog Post number 3

less than 1 minute read

Published:

This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.

Blog Post number 2

less than 1 minute read

Published:

This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.

Blog Post number 1

less than 1 minute read

Published:

This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.

portfolio

publications

Steady State Configurations of Cells Connected by Cadherin Sites

Published in BYU THESES AND DISSERTATIONS, 2016

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. Then a method for analyzing the general cell system is presented. This method involves 0-row-sum, symmetric matrices. A few results are presented as well as conjectures made that we feel will greatly simplify such analyses. The thesis concludes with the proposal of a framework for analyzing a dynamic cell system in which stochastic processes govern the attachment and detachment of c-sites.

Recommended citation: McBride, Jared Adam, "Steady State Configurations of Cells Connected by Cadherin Sites" (2016). Theses and Dissertations. 6023. https://scholarsarchive.byu.edu/etd/6023 https://scholarsarchive.byu.edu/etd/6023

talks

Steady State Configurations of Cells Connected by Cadherin Sites

Published:

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

Published:

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.

Data-driven Model Reduction by Wiener Projection

Published:

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.

Spectral Factorization and Spectral Estimation by Kalman Filtering

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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.

Numerical Wiener Filtering using CKMS

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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.

Fitting autoregressive models by reversible jump Markov chain Monte Carlo

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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.

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

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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.

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

Published:

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.

Spectral Estimation and Iterated Whitening

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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.

Spectral Estimation and Iterated Whitening

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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.

teaching

MATH 129: Calculus II

Undergraduate course, University of Arizona, Math Department, 2021

Welcome to second semester calculus! In this course we will explore integration techniques and applications and then study sequences and series with the goal of reaching Taylor series approximation and a brief introduction to differential equations.

Math 196V: Vector Calculus Supplemental Instruction Seminar

Undergraduate course, University of Arizona, Math Department, 2021

Welcome to vector calculus! This course is designed as a complement to Math 223. Students enrolled in the course will participate in a weekly problem session pertaining to material covered in Math 223. Concurrent registration in Math 223 is required.

Conversational Calculus

Popular instruction, almost outreach, University of Arizona, Math Department, 2022

Here are a series of materials I am developing to teach calculus very briefly to adult (non math major) learners.

MATH 115: College Algebra

Undergraduate course, Southern Virginia University, 2023

This brief lesson is about how you will use college algebra in your everyday life.

MATH 221: Statistics

Undergraduate course, Southern Virginia University, 2024

This mainly houses the data for the ANOVA Lesson.