### Stability of entrainment of a continuum of coupled oscillators

Jordan Snyder, Anatoly Zlotnik, Aric Hagberg, "Stability of entrainment of a continuum of coupled oscillators." Chaos: An Interdisciplinary Journal of Nonlinear Science, 2017. link

Department of Applied Mathematics, University of Washington

email: jsnyd@uw.edu

Updated 15 May 2020

Phase transitions and critical phenomena on networks

Collective phenomena and self-organization

Dynamical systems

Data-driven modeling

PhD. in Applied Mathematics

**June 2019**

UC Davis, Davis, CA

Advisor: Raissa D’SouzaM.S. in Applied Mathematics

**March 2016**

UC Davis, Davis, CA

Advisor: Raissa D’SouzaB.S. in Physics and Mathematics

**May 2013**

Cum Laude

Rensselaer Polytechnic Institute, Troy, NY

Advisor: Joel Giedt

Graduate Student Researcher

**Fall 2015 - Spring 2019**

UC Davis, Complexity Sciences Center and Department of Mathematics

Advisor: Raissa D’SouzaWorking in the Complexity Sciences Center with major advisor Raissa D’Souza on analytic and numerical techniques to discover general principles underlying the relationship between network structures and the dynamics on those networks.

Research Intern

**Summer 2018**

Center for Nonlinear Studies at Los Alamos National Lab

Mentor: Anatoly ZlotnikDeveloped numerical techniques for discovering lower-dimensional equations of motion that accurately reproduce the dynamics of phase oscillators coupled by a modular network, and supported these results with rigorous approximation bounds.

Research Intern

**Summer 2017**

Center for Nonlinear Studies at Los Alamos National Lab

Mentor: Anatoly ZlotnikStudied the potential optimality of hierarchical communication and control structures for efficient control of network dynamical systems, with the goal of applying insights to the electric power grid and systems of thermostatically-controlled loads (such as A/C and heating).

Research Intern

**Summer 2016**

Center for Nonlinear Studies at Los Alamos National Lab

Mentor: Aric HagbergAnalyzed a mathematical model of interacting oscillatory units subject to common forcing. Found analytical and numerical results elucidating the effect on synchronization of an externally-imposed common frequency.

Associate Instructor

**Summers 2014, 2015**

UC Davis, Department of Mathematics

Davis, CA

Teaching Mentor: E. G. Puckett

MAT 22B: Differential Equations

Prepared and delivered lectures, quizzes and exams. Course materials can be found hereTeaching Assistant

**Fall 2013 - Present**

UC Davis, Department of Mathematics

Davis, CA

Led discussion sections, held office hours, and graded course material for:MAT-17A, Calculus for Biological Sciences

MAT-21B, Calculus

MAT-21D, Vector Analysis

MAT-67, Abstract Linear Algebra

MAT-119A, Ordinary Differential Equations

### Stability of entrainment of a continuum of coupled oscillators

Jordan Snyder, Anatoly Zlotnik, Aric Hagberg, "Stability of entrainment of a continuum of coupled oscillators." Chaos: An Interdisciplinary Journal of Nonlinear Science, 2017. link

### A Pulse-gated, Neural Implementation of the Backpropagation Algorithm

Andrew Sornborger, Louis Tao, Jordan Snyder, Anatoly Zlotnik, "A Pulse-gated, Neural Implementation of the Backpropagation Algorithm." Proceedings of the 7th Annual Neuro-inspired Computational Elements Workshop on - NICE '19, 2019. link

### Collective Behavior in Dynamics on Networks

Jordan Snyder, "Collective Behavior in Dynamics on Networks." University of California, Davis, 2019. link

### Thresholding normally distributed data creates complex networks

George Cantwell, Yanchen Liu, Benjamin Maier, Alice Schwarze, Carlos Serv{\'{a}}n, Jordan Snyder, Guillaume St-Onge, "Thresholding normally distributed data creates complex networks." arXiv, 2019. link

### Degree-targeted cascades in modular, degree-heterogeneous networks

Jordan Snyder, Weiran Cai, Raissa D'Souza, "Degree-targeted cascades in modular, degree-heterogeneous networks." arXiv, 2020. link

### Thresholding normally distributed data creates complex networks

George Cantwell, Yanchen Liu, Benjamin Maier, Alice Schwarze, Carlos Serv{\'{a}}n, Jordan Snyder, Guillaume St-Onge, "Thresholding normally distributed data creates complex networks." Physical Review E, 2020. link

### Data-driven selection of coarse-grained models of coupled oscillators

Jordan Snyder, Anatoly Zlotnik, Andrey Lokhov, "Data-driven selection of coarse-grained models of coupled oscillators." Physical Review Research, 2020. link

### Mutualistic networks emerging from adaptive niche-based interactions

Weiran Cai, Jordan Snyder, Alan Hastings, Raissa D'Souza, "Mutualistic networks emerging from adaptive niche-based interactions." Nature Communications, 2020. link

**J. Snyder**, A. Lokhov, and A. Zlotnik,*Coarse-Graining for Coupled Oscillators: A case study in discovering low-dimensional dynamics*Center for Nonlinear Studies, Los Alamos, NM, September 2018

APS Far West Section annual meeting, Fullerton, CA, October 2018

Student-run Math / Applied Math Seminar, UC Davis, Davis, CA, November 2018

SIAM Conference on Applications of Dynamical Systems (DS19), Snowbird, UT, May 2019

CSU Northridge Applied Math Seminar, Northridge, CA, October 2019,

*Invited*

**J. Snyder**, W. Cai, and R. M. D’Souza,*Critical Slowing Down in Mutualistic Population Dynamics*, Complexnets Group Meeting, Davis, CA, March 2018**J. Snyder**, A. Zlotnik and A. Hagberg,*Modeling collective behavior in hierarchically-organized systems*, Center for Nonlinear Studies, Los Alamos, NM, August 2017**J. Snyder**, A. Zlotnik and A. Hagberg,*Entrainment of Coupled Phase Oscillators*MURI Grant Review Meeting, California Institute of Technology, Pasadena, CA, December 2016

Student-run Math / Applied Math Seminar, UC Davis, Davis, CA, October 2016

SIAM Student Chapter, UC Merced, Merced, CA, October 2016

Center for Nonlinear Studies, Los Alamos, NM, August 2016

**J. Snyder**,*Computing Geometric Integrated Information*, Student-run Math / Applied Math Seminar, UC Davis, Davis, CA, June 2016

*Data-Driven Model Selection for Coarse-Graining Coupled Oscillators*, Dynamics Days 2019, Evanston, IL,*January 2019**Entrainment of Coupled Oscillators*, CRITICS Workshop, Kulhuse, Denmark,*September 2016**Stability of Entrainment in Coupled Oscillators*Dynamics Days 2017, Silver Spring, MD,

*January 2017*2017 SIAM Conference on Dynamical Systems, Snowbird, UT,

*May 2017*International Physics of Living Systems (iPoLS) 2017 Annual Meeting, Paris, France,

*June 2017*

*Critical Slowing Down Inidicators in a Mutualistic Network*, Third Central Valley Regional SIAM Student Chapter Conference, Merced, CA,*April 2018*

Summer School: Data Science for Dynamical Systems

**July 2019**

Lorenz Center, Leiden, NetherlandsSanta Fe Institute Applied Complexity Studio

**July 2018**

Complexity, Quantitative Social Science & National Security

Santa Fe Institute, Santa Fe, NMParticipated in brainstorming sessions with members of the complexity science and national security communities, generating research ideas of potential interest to national security stakeholders.

Santa Fe Institute Complex Systems Summer School

**Summer 2018**

Santa Fe Institute and Institute for American Indian Arts, Santa Fe, NMAttended lectures and research talks on nonlinear dynamics, network theory, information theory, sociology, ecology, animal behavior, computation theory, power engineering, evolution, and many other topics. Participated in intensive group project work on 1) random graph theory and 2) criticality in neuronal dynamics.

Santa Fe Institute Working Group

**September 2017**

Information Networks and the Evolution of Social Organizations

Santa Fe Institute, Santa Fe, NMParticipated in brainstorming sessions among scholars of archeology, anthropology, economics, sociology, physics, and network science to develop a research agenda focused on illuminating possible mechanisms underlying the emergence of hierarchical social structures in early human societies.

Physics of Living Systems International Meeting

**June 2017**

Institute Pierre-Gilles de Gennes for microfluidics, Paris, FranceAttended lectures and participated in conversations on physics-informed modeling approaches to understand mechanisms in biological systems, at scales from single cells to populations of organisms.

1

^{st}CRITICS Workshop and Summer School

**August-September 2016**

Critical Transitions in Complex Systems: Mathematical theory and applications

Kulhuse, DenmarkAttended lectures and research presentations on cutting-edge techniques in mathematical modeling of systems that exhibit critical transitions, with particular focus on the global climate. Participated in group project work on modeling (both analytically and numerically) a system of interacting particles subject to noise.

*Coarse-Graining for Coupled Oscillators*, research project at Los Alamos National Lab,*Summer 2018*- Extracted effective equations of motion for coarse-grained degrees of freedom describing synchronization of phase oscillators on a modular network. Used numerical and analytical results to deduce transitions between high- and low-dimensional dynamical behavior. Work in progress with Anatoly Zlotnik and Andrey Lokhov.

*A Dynamic Niche Model for the Spontaneous Emergence of Mutualistic Network Structures*, research project at UC Davis,*Fall 2017 - present*- Developed a theoretical model of the evolution of a mutualistic ecosystem, incorporating a feedback between the species abundances and the structure of the species-species interaction network. Reproduced network properties that are seen in the real world, and that were previously not explained by any single model. Work to be submitted with Weiran Cai and Raissa D’Souza.

*Early Warning Signals in Mutualistic Population Dynamics*, research project at UC Davis,*Fall 2017 - present*- Investigated statistical signatures of correlated extinction events in a stylized model of population dynamics on empirical mutualistic networks. Connected modularity and nestedness of interaction networks with the course of ecosystem-wide extinction. Work in progress with Raissa D’Souza and Weiran Cai.

*Entrainment of Coupled Oscillators*, research project at Los Alamos National Lab,*Summer 2016-2017*Developed a model of coupled phase oscillators subject to common forcing, and derived analytic results capturing the trade-offs between coupling and forcing. Corroborated analysis with numerical simulation, including numerical continuation using AUTO software. Work done in collaboration with staff scientists Anatoly Zlotnik and Aric Hagberg.

Published in

*Chaos*, aip.scitation.org/doi/full/10.1063/1.4994567

*Mean-field limits for interacting diffusions*, group project at CRITICS Summer School, Kulhuse, Denmark,*September 2016*- Studied a system of attractively coupled particles in a bistable potential using a nonlinear Fokker-Planck equation, with support from numerical simulation. Work done in collaboration with fellow students at the CRITICS summer school.

*Computing Geometric Integrated Information*, class project for Numerical Optimization (MAT-258A),*Fall 2015*- Implemented an optimization algorithm to compute an information measure which quantifies the extent of causal interactions between components of a stochastic process, and applied this algorithm to primate social network data.

*Pathwise Information Theory in Two Dimensions*, class project for Natural Computation (PHY-256B),*Spring 2014*- Studied information-theoretic signatures of spatial pattern formation by sampling two-dimensional synthetic data along self-avoiding paths.

Reading in Classical and Quantum Statistical Mechanics with Prof. Bruno Nachtergaele,

*Summer 2014 - Winter 2015*- Studied representation of quantum spin system partition functions by random loops.

Stochastic Population Dynamics,

*PBG 298, Spring 2016, Spring 2017*Rigorous results for discrete-time population models under demographic and environmental stochasticity. Random Perron-Frobenius theorem.

Probability generating functions, asymptotics for Markov chains with and without absorbing states

Network Theory,

*ECS 253, Spring 2016*- Basic formalism of networks, including generating functions for analysis of random graphs, simple dynamics on networks, and network analysis of real-world datasets.

Stochastic Dynamics,

*MAT 236A, Fall 2014*- Brownian motion, Itô calculus, Fokker-Planck equations, martingales. Applications to finance.

Probability Theory,

*MAT 235A-B, Fall 2014 - Winter 2015*- Measure-theoretic foundations, convergence of probability measures, conditional probability

Natural Computation and Self-Organization,

*PHY 256A-B, Winter - Spring 2014*- Information theory, inference of causal architecture for discrete stochastic processes

Applied Math,

*MAT 207A,B,C, academic year 2013-2014*- Three-quarter sequence covering dynamical systems, bifurcation theory, calculus of variations, Fourier series, basics of PDE, and asymptotic methods

Mx16 Conference on Multilayer Networks Co-Organizer,

*Spring 2016*International student-run conference featuring Alex Arenas, Lada Adamic, Matt Brashears, Francesco Sorrentino, and Mikko Kivelä

Galois Group (Math grad student association)

Vice President,

*academic year 2015-2016*President,

*academic years 2016-2018*

Davis Math Conference Co-Organizer,

*Fall 2015*

UC Davis Graduate Studies Travel Award,

*Spring 2019*UC Davis Math Department Travel Award,

*January 2017, January 2019*Graduate Assistance in Areas of National Need (GAANN) Fellowship,

*academic year 2014-2015*Rensselaer Dean’s List,

*Fall 2009 - Spring 2013*

Programming

Python (packages: NumPy, SciPy, NetworkX, CMPy)

AUTO-07p software for continuation and bifurcation problems in ordinary differential equations

MATLAB

Julia