ResearchCurrent ProjectsSnaking Bifurcation on Rings Summer 2020 - Now Starting from Summer 2020, I have been doing a research project instructed by Professor Björn Sandstede that studies the stationary patterns and bifurcation diagrams in bistable dynamical systems on graphs with small coupling strength. We initially explored numerically on random graphs, and then started focusing on the analysis of localized patterns on ring graphs with symmetric coupling. Specifically, we proved that the sparse coupling case (nearest-neighbor/next-nearest-neighbor coupling) has bifurcation diagram that exhibits a “snaking” pattern where the number of folds increases with the number of nodes, while the all-to-all coupling case always leads to a closed curve with six nodes that begins and ends at two symmetry-breaking bifurcations from the homogeneous solution branch. Localized Patterns on Graphs, minisymposium talk at SIAM Conference on Applications of Dynamical Systems (DS23) See Github page
Inferring Interaction Structure in Opinion Dynamics Collaborative research project starting from the American Mathematical Society’s Mathematics Research Communities program on Complex Social Systems, Summer 2023 - Now Population opinions follow dynamics that can be modeled as stochastic agent-based systems on the network of individual interactions where opinions can be treated as random variables. We observe evolutions in opinions due to individual interactions, but the underlying microscopic mechanisms are often unknown. In this study, we develop likelihood-based methods, including the derivative-free and EM algorithms, to infer interaction structure from different function families given opinion time-series data. Talk: Inferring Interaction Kernels for Stochastic Agent-Based Opinion Dynamics at JMM 2024
Learning Temporal Exponential Random Graph Models (TERGMs) from Dynamics of Many-Body Interactions Research with Dr. Andrey Lokhov at Los Alamos National Laboratory, Fall 2023 - Now Many problems in fields such as social and biological sciences involve analyzing populations of entities that are interconnected by relations. Understanding these underlying networks can provide rich information that reveals properties such as what kinds of motifs are the fundamental building blocks and how they change over time, in which way do the microscopic interactions affect each other and contribute to new ties, and how individuals organize themselves into groups. When studying network models, it is important to include stochastic properties since the observed networks are samples from some population distribution and the observed network attributes may be only partial. It is also important to allow temporal evolution of network topology in the studied models since real systems often change over time. To handle these problems, TERGMs, a family of generalized statistical model that supports inference and network evolution, have been proposed and studied as a helpful modeling framework. Our work is to develop an efficient learning algorithm for TERGMs with generalized interaction relations which requires low sampling complexity. The inspiration is from previous work on learning Ising models with efficient sampling method of dynamics data. We extend the algorithm from learning pairwise interactions in Ising models to a more general model with many-body interactions (i.e. higher-order correlations) and construct a framework of learning the corresponding TERGMs using data obtained from dynamical processes. Previous ProjectsCommunity Robustness under Edge Addition Research with Dr. Pablo Moriano at Oak Ridge National Laboratory, Summer 2022 - Now Many complex systems such as critical infrastructures, biological networks and social groups, exhibits network structures, and among network properties, communities (or clusters) typically represent essential functional or behavioral units in the networks. These real networks change dynamically and their underlying community structure therefore also evolves over time. Our study focuses on understanding how the community robustness is affected by edge-addition perturbation to the networks. We propose different edge-addition strategies and analyze the effect in synthetic and empirical temporal networks based on computational experiments using community detection algorithms and community similarity metrics. We find that the robustness of communities depends strongly on the choice of detection method. Community Robustness in Temporal Networks under Edge Addition, poster presentation at Dynamics Days US 2023 See Github page
Class Project: Mesh Texture: Learning Continuous Texture Representation for Conditional and Unconditional Texture Synthesis of 3D Meshes CSCI 2470: Deep Learning, Brown University, Fall 2020 I did a project in a group of four focusing on designing an architecture that can learn detailed textures across a latent space of images and shapes, thus capable of probabilistically generating realistic, novel textures for previously unseen meshes. Inspired by recent work, TextureFields and SIREN, we explored varying methods of shape-representations, alternative loss metrics, and high-frequency learning techniques. We demonstrated that applying Fourier feature transformations through a positional encoding is an effective means for learning more detailed textures. See our write-up
Undergraduate Research ProjectsHonors Project in Mathematics: Topological and Algebraic Properties of Braids and Annular Braids Dickinson College, Carlisle, PA, September 2018-May 2019 I did an honors project advised by Professor David Richeson on using various algebraic descriptions of the annular braid group to analyze maypole dancing during my senior year at Dickinson College. I studied the background knowledge in knots and links, the Artin braid group and the annular braids and explored how we can examine and understand maypole dances using the theories. In my thesis, I gave three presentations to describe the annular braid group and used the annular braid group as a medium to abstract the braids in maypole dances and therefore apply an algebraic analysis. Also, I discussed some essential properties embedded in the maypole braids, which are related to the invariants of annular braids - the crossing number and the step number.
Physics Senior Research: Experimental Realization of Symmetry Breaking in Coupled Logistic Maps Dickinson College, Carlisle, PA, September 2018-May 2019 During my senior year at Dickinson College, I did a physics project on the coupled logistic maps with my lab partner Houssem Mhiri advised by Professor Lars English. Using the mathematical model of the logistic maps as the theoretical foundation, we modified L’Her’s electronic design, a physical representation of coupled discrete-time logistic maps published in 2016, by implementing it using an Arduino and adding power supplies to control the initial conditions. We further reduced the number of outlets and produced the desired input signals and voltages using a single multifunction DAQ device with LabView. Then, we examined that symmetry-broken solutions manifest in this circuit for appropriately chosen initial conditions, and investigated experimentally the basins of attraction of these solutions, as well as their dependence on the coupling strength. Moreover, we delved into the chaotic regime and constructed experimental bifurcation diagrams. One intriguing phenomenon captured here involves the transition from synchronized chaos to decoherent chaos as the coupling is increased. Finally, we experimentally implemented uni-directional coupling and explored the dynamics of a driven logistic map. Using an Arduino in a Coupled Logistic Map Circuit to Explore Basins of Attraction for Symmetry-broken States, poster presentation at the American Physical Society March Meeting 2019 |