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Julian Lee

Publications and source records attributed to Julian Lee.

At least 19 recordsLinked to original sources
arXiv2024

Identifying Influential and Vulnerable Nodes in Interaction Networks through Estimation of Transfer Entropy Between Univariate and Multivariate Time Series

Transfer entropy (TE) is a powerful tool for measuring causal relationships within interaction networks. Traditionally, TE and its conditional variants are applied pairwise between dynamic variables to infer these causal relationships. However, identifying the most influential or vulnerable node in a system requires measuring the causal influence of each component on the entire system and vice versa. In this paper, I propose using outgoing and incoming transfer entropy-where outgoing TE quantifies the influence of a node on the rest of the system, and incoming TE measures the influence of the rest of the system on the node. The node with the highest outgoing TE is identified as the most influential, or "hub", while the node with the highest incoming TE is the most vulnerable, or "anti-hub". Since these measures involve transfer entropy between univariate and multivariate time series, naive estimation methods can result in significant errors, particularly when the number of variables is comparable to or exceeds the number of samples. To address this, I introduce a novel estimation scheme that computes outgoing and incoming TE only between significantly interacting partners. The feasibility of this approach is demonstrated by using synthetic data, and by applying it to real data of oral microbiota. The method successfully identifies the bacterial species known to be key players in the bacterial community, demonstrating the power of the new method.

cond-mat.stat-mech↗
arXiv2024

Deep Learning Models for Flapping Fin Unmanned Underwater Vehicle Control System Gait Optimization

The last few decades have led to the rise of research focused on propulsion and control systems for bio-inspired unmanned underwater vehicles (UUVs), which provide more maneuverable alternatives to traditional UUVs in underwater missions. Recent work has explored the use of time-series neural network surrogate models to predict thrust and power from vehicle design and fin kinematics. We develop a search-based inverse model that leverages kinematics-to-thrust and kinematics-to-power neural network models for control system design. Our inverse model finds a set of fin kinematics with the multi-objective goal of reaching a target thrust under power constraints while creating a smooth kinematics transition between flapping cycles. We demonstrate how a control system integrating this inverse model can make online, cycle-to-cycle adjustments to prioritize different system objectives, with improvements in increasing thrust generation or reducing power consumption of any given movement upwards of 0.5 N and 3.0 W in a range of 2.2 N and 9.0 W. As propulsive efficiency is of utmost importance for flapping-fin UUVs in order to extend their range and endurance for essential operations but lacks prior research, we develop a non-dimensional figure of merit (FOM), derived from measures of propulsive efficiency, that is able to evaluate different fin designs and kinematics, and allow for comparison with other bio-inspired platforms. We use the developed FOM to analyze optimal gaits and compare the performance between different fin materials, providing a better understanding of how fin materials affect thrust generation and propulsive efficiency and allowing us to inform control systems and weight for efficiency on the developed inverse gait-selector model.

cs.RO↗
arXiv2024

Data-Driven Approaches for Thrust Prediction in Underwater Flapping Fin Propulsion Systems

Flapping-fin underwater vehicle propulsion systems provide an alternative to propeller-driven systems in situations that require involve a constrained environment or require high maneuverability. Testing new configurations through experiments or high-fidelity simulations is an expensive process, slowing development of new systems. This is especially true when introducing new fin geometries. In this work, we propose machine learning approaches for thrust prediction given the system's fin geometries and kinematics. We introduce data-efficient fin shape parameterization strategies that enable our network to predict thrust profiles for unseen fin geometries given limited fin shapes in input data. In addition to faster development of systems, generalizable surrogate models offer fast, accurate predictions that could be used on an unmanned underwater vehicle control system.

cs.RO↗
arXiv2023

Computational Approaches for Modeling Power Consumption on an Underwater Flapping Fin Propulsion System

The last few decades have led to the rise of research focused on propulsion and control systems for bio-inspired unmanned underwater vehicles (UUVs), which provide more maneuverable alternatives to traditional UUVs in underwater missions. Propulsive efficiency is of utmost importance for flapping-fin UUVs in order to extend their range and endurance for essential operations. To optimize for different gait performance metrics, we develop a non-dimensional figure of merit (FOM), derived from measures of propulsive efficiency, that is able to evaluate different fin designs and kinematics, and allow for comparison with other bio-inspired platforms. We create and train computational models using experimental data, and use these models to predict thrust and power under different fin operating states, providing efficiency profiles. We then use the developed FOM to analyze optimal gaits and compare the performance between different fin materials. These comparisons provide a better understanding of how fin materials affect our thrust generation and propulsive efficiency, allowing us to inform control systems and weight for efficiency on an inverse gait-selector model.

cs.RO↗
arXiv2022

Few-body hydrodynamic interactions probed by optical trap pulling experiment

We study the hydrodynamic coupling of neighboring micro-beads placed in a dual optical trap setup allowing us to precisely control the degree of coupling and directly measure time-dependent trajectories of the entrained beads. Average experimental trajectories of a probe bead entrained by the motion of a neighboring scan bead are compared with theoretical computation, illustrating the role of viscous coupling and setting timescales for probe bead relaxation. The findings provide direct experimental corroborations of hydrodynamic coupling at larger, micron spatial scales and millisecond timescales, of relevance to hydrodynamic-assisted colloidal assembly as well as improving the resolution of optical tweezers. We repeat the experiments for three bead setups.

physics.flu-dyn↗
arXiv2022

Data-Driven Machine Learning Models for a Multi-Objective Flapping Fin Unmanned Underwater Vehicle Control System

Flapping-fin unmanned underwater vehicle (UUV) propulsion systems provide high maneuverability for naval tasks such as surveillance and terrain exploration. Recent work has explored the use of time-series neural network surrogate models to predict thrust from vehicle design and fin kinematics. We develop a search-based inverse model that leverages a kinematics-to-thrust neural network model for control system design. Our inverse model finds a set of fin kinematics with the multi-objective goal of reaching a target thrust and creating a smooth kinematic transition between flapping cycles. We demonstrate how a control system integrating this inverse model can make online, cycle-to-cycle adjustments to prioritize different system objectives.

cs.RO↗
arXiv2022

The origin of the Poisson distribution in stochastic dynamics of gene expression

The Poisson distribution is the probability distribution of the number of independent events in a given period of time. Although the Poisson distribution appears ubiquitously in various stochastic dynamics of gene expression, both as time-dependent distributions and the stationary distributions, underlying independent events that give rise to such distributions have not been clear, especially in the presence of the degradation of gene products, which is not a Poisson process. I show that, in fact, the variable that follows the Poisson distribution is the number of independent events where biomolecules are created, which are destined to survive until the end of a given time duration. This new viewpoint allows us to derive time-dependent Poisson distributions as solutions of master equations for general class of protein production and degradation dynamics, including models with time-dependent rates and a non-Markovian model with delayed degradation. I then derive analytic forms of general time-dependent probability distributions by combining the Poisson distribution with the binomial or the multinomial distributions.

cond-mat.stat-mech↗
arXiv2019

Enhanced Transport of Two Spheres in Viscous Fluid

We obtain a numerical solution for the synchronous motion of two spheres moving in viscous fluid. We find that for a given amount of work performed, the final distance travelled by each sphere is increased by the presence of the other sphere. The result suggests that the transport efficiency of molecular motor cargo in vivo may be improved due to an effective hydrodynamic interaction with neighboring cargos moving along the same direction.

cond-mat.soft↗
arXiv2018

Quantitative Analysis of a Transient Dynamics of a Gene Regulatory Network

In a stochastic process, noise often modifies the picture offered by the mean field dynamics. In particular, when there is an absorbing state, the noise erases a stable fixed point of the mean field equation from the stationary distribution, and turns it into a transient peak. We make a quantitative analysis of this effect for a simple genetic regulatory network with positive feedback, where the proteins become extinct in the presence of stochastic noise, contrary to the prediction of the deterministic rate equation that the protein number converges to a non-zero value. We show that the transient peak appears near the stable fixed point of the rate equation, and the extinction time diverges exponentially as the stochastic noise approaches zero. We also show how the baseline production from the inactive gene ameliorates the effect of the stochastic noise, and interpret the opposite effects of the noise and the baseline production in terms of the position shift of the unstable fixed point. The order of magnitude estimates using biological parameters suggest that for a real gene regulatory network, the stochastic noise is sufficiently small so that not only is the extinction time much larger than biologically relevant time-scales, but also the effect of the baseline production dominates over that of the stochastic noise, leading to the protection from the catastrophic rare event of protein extinction.

cond-mat.stat-mech↗
arXiv2018

The derivation of Markov processes that violate detailed balance

Time-reversal symmetry of microscopic laws dictates that the equilibrium distribution of a stochastic process must obey the detailed balance. On the other hand, cyclic Markov processes that do not admit equilibrium distributions with detailed balance, are often used to model open systems driven out of equilibrium by external agents. I show that for a Markov model without detailed balance, an extended Markov model that explicitly includes the degrees of freedom for the driving agent can be constructed, such that the original cyclic Markov model for the driven system can be recovered as an approximation at early times, by summing over the degrees of freedom for the driving agent. In the process, the widely accepted formula for the entropy production in a cyclic Markov model is explicitly expressed as a time derivative of an entropy component in the extended model. I also find an analytic formula for the entropy component that is hidden in the cyclic Markov model.

cond-mat.stat-mech↗
arXiv2016

Transfer matrix algorithm for computing the exact partition function of a square lattice polymer

I develop a transfer matrix algorithm for computing the exact partition function of a square lattice polymer with nearest-neighbor interaction, by extending a previous algorithm for computing the total number of self-avoiding walks. The computation time scales as ~1.6^N with the chain length N, in contrast to the explicit enumeration where the scaling is ~ 2.7^N. The exact partition function can be obtained faster with the transfer matrix method than with the explicit enumeration, for N>25. The new results for up to N=42 are presented.

cond-mat.stat-mech↗
arXiv2015

Microcanonical analysis of a nonequilibrium phase transition

Microcanonical analysis is a powerful method for studying phase transitions of finite-size systems. This method has been used so far only for studying phase transitions of equilibrium systems, which can be described by microcanonical entropy. I show that it is possible to perform microcanonical analysis of a nonequilibrium phase transition, by generalizing the concept of microcanonical entropy. One-dimensional asymmetric diffusion process is studied as an example where such a generalized entropy can be explicitly found, and the microcanonical method is used to analyze a nonequilibrium phase transition of a finite-size system.

cond-mat.stat-mech↗
arXiv2014

Analytic stability analysis of three-component self-regulatory genetic circuit

A self-regulatory genetic circuit, where a protein acts as a positive regulator of its own production, is known to be a simplest form of biological network with a positive feedback loop. Although at least three components, DNA, RNA, and the protein, are required to form such a circuit, the stability analysis of fixed points of the self-regulatory circuit has been performed only after reducing the system into to a two-component system consisting of RNA and protein only, assuming a fast equilibration of the DNA component. Here, the stability of fixed points of the three-component positive feedback loop is analyzed by obtaining eigenvalues of full three dimensional Hessian matrix. In addition to rigorously identifying the stable fixed points and the saddle points, detailed information can be obtained, such as the number of positive eigenvalues near a saddle point. In particular, complex eigenvalues is shown to exist for sufficiently slow binding and unbinding of the auto-regulatory transcription factor to DNA, leading to oscillatory convergence to the steady states, a novel feature unseen in the two-dimensional analysis.

physics.bio-ph↗
arXiv2014

Low temperature behavior of finite-size one-dimensional Ising model and the partition function zeros

In contrast to the infinite chain, the low-temperature expansion of a one-dimensional free-field Ising model has a strong dependence on boundary conditions. I derive explicit formula for the leading term of the expansion both under open and periodic boundary conditions, and show they are related to different distributions of partition function zeros on the complex temperature plane. In particular, when the periodic boundary condition is imposed, the leading coefficient of the expansion grows with size, due to the zeros approaching the origin.

cond-mat.stat-mech↗
arXiv2014

Phase diagram of the Wako-Saito-Munoz-Eaton beta-hairpin Model obtained with partition function zeros

I study the partition function zeros of the Wako-Saito-Munoz-Eaton (WSME) beta hairpin model in the complex temperature plane. For various values of the entropy cost of disordering a bond, the zeros show clear locus corresponding to the folding transition. By extrapolating the locus to the real axis, transition temperature can be determined for various values of the entropy cost, leading to the phase diagram of the WSME beta hairpin model.

cond-mat.stat-mech↗
arXiv2013

Nonadditive Entropies Yield Probability Distributions with Biases not Warranted by the Data

Different quantities that go by the name of entropy are used in variational principles to infer probability distributions from limited data. Shore and Johnson showed that maximizing the Boltzmann- Gibbs form of the entropy ensures that probability distributions inferred satisfy the multiplication rule of probability for independent events in the absence of data coupling such events. Other types of entropies that violate the Shore and Johnson axioms, including nonadditive entropies such as the Tsallis entropy, violate this basic consistency requirement. Here we use the axiomatic framework of Shore and Johnson to show how such nonadditive entropy functions generate biases in probability distributions that are not warranted by the underlying data.

cond-mat.stat-mech↗
arXiv2013

Exact Partition Function Zeros of the Wako-Saito-Muñoz-Eaton Protein Model

I compute exact partition function zeros of the Wako-Saito-Muñoz-Eaton model for various secondary structural elements and for two proteins, 1BBL and 1I6C, using both analytic and numerical methods. Two-state and barrierless downhill folding transitions can be distinguished by a gap in the distribution of zeros at the positive real axis.

cond-mat.stat-mech↗