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Yutaka Hori

Publications and source records attributed to Yutaka Hori.

At least 19 recordsLinked to original sources

Machine Learning of Temperature-dependent Chemical Kinetics Using Parallel Droplet Microreactors

Temperature is a fundamental regulator of chemical and biochemical kinetics, yet capturing nonlinear thermal effects directly from experimental data remains a major challenge due to limited throughput and model flexibility. Recent advances in machine learning have enabled flexible modeling beyond conventional physical laws, but most existing strategies remain confined to surrogate models of end-point yields rather than full kinetic dynamics. Consequently, an end-to-end framework that unifies systematic kinetic data acquisition with machine learning based modeling has been lacking. In this paper, we present a unified framework that integrates droplet microfluidics with machine learning for the systematic analysis of temperature-dependent reaction kinetics. The platform is specifically designed to enable stable immobilization and long-term time-lapse imaging of thousands of droplets under dynamic thermal gradients. This configuration yields massively parallel time-resolved datasets across diverse temperature conditions that capture transient kinetics and provides particularly suitable inputs for training machine-learning models of reaction dynamics. Leveraging these datasets, we train Neural ODE models, which embed neural networks within differential equations to flexibly represent nonlinear temperature dependencies beyond conventional formulations. We demonstrate accurate prediction of enzymatic kinetics across diverse thermal environments, highlighting the robustness and versatility of the approach. Our framework bridges high-throughput experimental data acquisition with data-driven modeling, establishing a versatile foundation for enhanced predictive ability and rational analysis and design of temperature-sensitive biochemical processes.

q-bio.QM

Exact Robust Instability Analysis for Networked Dynamical Systems with Biological Application

This paper investigates robust instability in nominally unstable uncertain networked dynamical systems, where all nominal agents share an identical single-input-single-output (SISO) linear time-invariant (LTI) system and each agent is subject to independent perturbations. This setting is motivated by the problem of sustaining periodic oscillations in nonlinear dynamics, for which exact analysis is generally intractable. We identify three classes of network structures including cyclic and certain rank-deficient networks for which the robust instability problem can be reduced to the analysis of a single representative SISO system. We derive sufficient conditions that exactly characterize the robust instability radius for these network classes. Finally, we demonstrate the practical utility of the proposed results by analyzing oscillatory behavior in a genetic regulatory network.

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Robust Instability Radius for Networked Dynamical Systems: Upper and Lower Bounds

This paper is concerned with robust instability of uncertain network systems. We consider the multi-agent system described as a network of single-input-single-output agents with identical nominal dynamics subject to heterogeneous perturbations. The network description is formalized as a feedback interconnection of a diagonal uncertainty, nominal identical agents, and a static interconnection matrix. Assuming that the nominal network is unstable, we seek the robust instability radius (RIR), defined as the smallest norm of the stable uncertainty that renders the network stable. Conditions for the network stability are developed, and upper and lower bounds on the RIR are derived. When the network connectivity matrix is rank one and all diagonal entries share the same sign or are zero, we give conditions under which the RIR is exactly characterized by a small gain argument.

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Observer-Based Stabilization for Linear Multi-Agent Dynamical Systems Using Generalized Frequency Variables

We address the conditions and design of controllers and observers for homogeneous networks of linear MIMO agents. We develop networked controllers and observers that ensure the stability of both the system state and the estimation error, leveraging the concept of generalized frequency variables. A separation principle for networks is then established, showing that the observer and controller can be designed independently and combined to achieve a stable output feedback. Our results are illustrated via a highly unstable, oscillatory network of locally actuated pendulums on carts. Finally, necessary conditions for controllability and observability -- derived from agent properties and network structure -- are established and discussed.

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Acceleration of Moment Bound Optimization for Stochastic Chemical Reactions Using Reaction-wise Sparsity of Moment Equations

Moment dynamics in stochastic chemical kinetics often involve an infinite chain of coupled equations, where lower-order moments depend on higher-order ones, making them analytically intractable. Moment bounding via semidefinite programming provides guaranteed upper and lower bounds on stationary moments. However, this formulation suffers from the rapidly growing size of semidefinite constraints due to the combinatorial growth of moments with the number of molecular species. In this paper, we propose a sparsity-exploiting matrix decomposition method for semidefinite constraints in stationary moment bounding problems to reduce the computational cost of the resulting semidefinite programs. Specifically, we characterize the sparsity structure of moment equations, where each reaction involves only a subset of variables determined by its reactants, and exploit this structure to decompose the semidefinite constraints into smaller ones. We demonstrate that the resulting formulation reduces the computational cost of the optimization problem while providing practically useful bounds.

math.OC

Bounding Transient Moments for a Class of Stochastic Reaction Networks Using Kolmogorov's Backward Equation

Stochastic chemical reaction networks (SRNs) in cellular systems are commonly modeled as continuous-time Markov chains (CTMCs) describing the dynamics of molecular copy numbers. The exact evaluation of transient copy number statistics is, however, often hindered by a non-closed hierarchy of moment equations. In this paper, we propose a method for computing theoretically guaranteed upper and lower bounds on transient moments based on the Kolmogorov's backward equation, which provides a dual representation of the CME, the governing equation for the probability distribution of the CTMC. This dual formulation avoids the moment closure problem by shifting the source of infinite dimensionality to the dependence on the initial state. We show that, this dual formulation, combined with the monotonicity of the CTMC generator, leads to a finite-dimensional linear time-invariant system that provides bounds on transient moments. The resulting system enables efficient evaluation of moment bounds across multiple initial conditions by simple inner-product operations without recomputing the bounding system. Further, for certain classes of SRNs, the bounding ODEs admit explicit construction from the reaction model, providing a systematic and constructive framework for computing provable bounds.

q-bio.QM

Parameter Invariance Analysis of Moment Equations Using Dulmage-Mendelsohn Decomposition

Living organisms maintain stable functioning amid environmental fluctuations through homeostasis, a property that preserves a system's behavior despite changes in environmental conditions. To elucidate homeostasis in stochastic biochemical reactions, theoretical tools for assessing population-level invariance under parameter perturbations are crucial. In this paper, we propose a systematic method for identifying the stationary moments that remain invariant under parameter perturbations by leveraging the structural properties of the stationary moment equations. A key step in this development is addressing the underdetermined nature of moment equations, which has traditionally made it difficult to characterize how stationary moments depend on system parameters. To overcome this, we utilize the Dulmage-Mendelsohn (DM) decomposition of the coefficient matrix to extract welldetermined subequations and reveal their hierarchical structure. Leveraging this structure, we identify stationary moments whose partial derivatives with respect to parameters are structurally zero, facilitating the exploration of fundamental constraints that govern homeostatic behavior in stochastic biochemical systems.

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Analysis of Signal Distortion in Molecular Communication Channels Using Frequency Response

Molecular communication (MC) is a concept in communication engineering, where diffusive molecules are used to transmit information between nano or micro-scale chemical reaction systems. Engineering MC to control the reaction systems in cells is expected for many applications such as targeted drug delivery and biocomputing. Toward control of the reaction systems as desired via MC, it is important to transmit signals without distortion by MC since the reaction systems are often triggered depending on the concentration of signaling molecules arriving at the cells. In this paper, we propose a method to analyze signal distortion caused by diffusion-based MC channels using frequency response of channels. The proposed method provides indices that quantitatively evaluate the magnitude of distortion and shows parameter conditions of MC channels that suppress signal distortion. Using the proposed method, we demonstrate the design procedure of specific MC channels that satisfy given specifications. Finally, the roles of MC channels in nature are discussed from the perspective of signal distortion.

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Stability analysis for large-scale multi-agent molecular communication systems

Molecular communication (MC) is recently featured as a novel communication tool to connect individual biological nanorobots. It is expected that a large number of nanorobots can form large multi-agent MC systems through MC to accomplish complex and large-scale tasks that cannot be achieved by a single nanorobot. However, most previous models for MC systems assume a unidirectional diffusion communication channel and cannot capture the feedback between each nanorobot, which is important for multi-agent MC systems. In this paper, we introduce a system theoretic model for large-scale multi-agent MC systems using transfer functions, and then propose a method to analyze the stability for multi-agent MC systems. The proposed method decomposes the multi-agent MC system into multiple single-input and single-output (SISO) systems, which facilitates the application of simple analysis technique for SISO systems to the large-scale multi-agent MC system. Finally, we demonstrate the proposed method by analyzing the stability of a specific large-scale multi-agent MC system and clarify a parameter region to synchronize the states of nanorobots, which is important to make cooperative behaviors at a population level.

eess.SY

Two-step reinforcement learning for model-free redesign of nonlinear optimal regulator

In many practical control applications, the performance level of a closed-loop system degrades over time due to the change of plant characteristics. Thus, there is a strong need for redesigning a controller without going through the system modeling process, which is often difficult for closed-loop systems. Reinforcement learning (RL) is one of the promising approaches that enable model-free redesign of optimal controllers for nonlinear dynamical systems based only on the measurement of the closed-loop system. However, the learning process of RL usually requires a considerable number of trial-and-error experiments using the poorly controlled system that may accumulate wear on the plant. To overcome this limitation, we propose a model-free two-step design approach that improves the transient learning performance of RL in an optimal regulator redesign problem for unknown nonlinear systems. Specifically, we first design a linear control law that attains some degree of control performance in a model-free manner, and then, train the nonlinear optimal control law with online RL by using the designed linear control law in parallel. We introduce an offline RL algorithm for the design of the linear control law and theoretically guarantee its convergence to the LQR controller under mild assumptions. Numerical simulations show that the proposed approach improves the transient learning performance and efficiency in hyperparameter tuning of RL.

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Exact Instability Margin Analysis and Minimum-Norm Strong Stabilization -- phase change rate maximization --

This paper is concerned with a new optimization problem named "phase change rate maximization" for single-input-single-output linear time-invariant systems. The problem relates to two control problems, namely robust instability analysis against stable perturbations and minimum-norm strong stabilization. We define an index of the instability margin called "robust instability radius (RIR)" as the smallest $H_\infty$-norm of a stable perturbation that stabilizes a given unstable system. This paper has two main contributions. It is first shown that the problem of finding the exact RIR via the small-gain condition can be transformed into the problem of maximizing the phase change rate at the peak frequency with a phase constraint. Then, we show that the maximum is attained by a constant or a first-order all-pass function and derive conditions, under which the RIR can be exactly characterized, in terms of the phase change rate. Two practical applications are provided to illustrate the utility of our results.

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A Control-theoretic Model for Bidirectional Molecular Communication Systems

Molecular communication (MC) enables cooperation of spatially dispersed molecular robots through the feedback control mediated by diffusing signal molecules. However, conventional analysis frameworks for the MC channels mostly consider the dynamics of unidirectional communication, lacking the effect of feedback interactions. In this paper, we propose a general control-theoretic modeling framework for bidirectional MC systems capable of capturing the dynamics of feedback control via MC in a systematic manner. The proposed framework considers not only the dynamics of molecular diffusion but also the boundary dynamics at the molecular robots that captures the lag due to the molecular transmission/reception process affecting the performance of the entire feedback system. Thus, methods in control theory can be applied to systematically analyze various dynamical properties of the feedback system. We perform a frequency response analysis based on the proposed framework to show a general design guideline for MC channels to transfer signal with desired control bandwidth. Finally, these results are demonstrated by showing the step-by-step design procedure of a specific MC channel satisfying a given specification.

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On Phase Change Rate Maximization with Practical Applications

We recapitulate the notion of phase change rate maximization and demonstrate the usefulness of its solution on analyzing the robust instability of a cyclic network of multi-agent systems subject to a homogenous multiplicative perturbation. Subsequently, we apply the phase change rate maximization result to two practical applications. The first is a magnetic levitation system, while the second is a repressilator with time-delay in synthetic biology.

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Stability analysis for circulant structured multi-agent molecular communication systems

In this paper, we introduce the system theoretic model for the multi-agent MC systems represented by multi-input and multi-output (MIMO) systems using the transfer functions, and then propose a method to analyze the stability for the special case of the circulant structured multi-agent MC systems. The proposed method decomposes the MIMO MC system into multiple single-input and single-output (SISO) systems, which facilitates to analyze of the stability of the large-scale multi-agent MC system. Finally, we demonstrate the proposed method to analyze the stability of a specific MC system.

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Interval Analysis of Worst-case Stationary Moments for Stochastic Chemical Reactions with Uncertain Parameters

The dynamics of cellular chemical reactions are variable due to stochastic noise from intrinsic and extrinsic sources. The intrinsic noise is the intracellular fluctuations of molecular copy numbers caused by the probabilistic encounter of molecules and is modeled by the chemical master equation. The extrinsic noise, on the other hand, represents the intercellular variation of the kinetic parameters due to the variation of global factors affecting gene expression. The objective of this paper is to propose a theoretical framework to analyze the combined effect of the intrinsic and the extrinsic noise modeled by the chemical master equation with uncertain parameters. More specifically, we formulate a semidefinite program to compute the intervals of the stationary solution of uncertain moment equations whose parameters are given only partially in the form of the statistics of their distributions. The semidefinite program is derived without approximating the governing equation in contrast with many existing approaches. Thus, we can obtain guaranteed intervals of the worst possible values of the moments for all parameter distributions satisfying the given statistics, which are prohibitively hard to estimate from sample-path simulations since sampling from all possible uncertain distributions is difficult. We demonstrate the proposed optimization approach using two examples of stochastic chemical reactions and show that the solution of the optimization problem gives informative upper and lower bounds of the statistics of the stationary copy number distributions.

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Frequency response of diffusion-based molecular communication channels in bounded environment

Recently, molecular communication (MC) has been studied as a micro-scale communication between cells or molecular robots. In previous works, the MC channels in unbounded environment was analyzed. However, many of the experimentally implemented MC channels are surrounded by walls, thus the boundary condition should be explicitly considered to analyze the dynamics of MC channels. In this paper, we propose a framework to analyze the frequency response of one-dimensional MC channels based on a diffusion equation with a boundary. In particular, we decompose the MC channel into the diffusion system and the boundary system, and show the relation between the cut-off frequency of the MC channel and the communication distance based on the transfer function. We then analyze the frequency response of a specific MC channel and reveal that the boundary can restrict the communication bandwidth of the MC channel.

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Instability Margin Analysis for Parametrized LTI Systems with Application to Repressilator

This paper is concerned with a robust instability analysis for the single-input-single-output unstable linear time-invariant (LTI) system under dynamic perturbations. The nominal system itself is possibly perturbed by the static gain of the uncertainty, which would be the case when a nonlinear uncertain system is linearized around an equilibrium point. We define the robust instability radius as the smallest $H_\infty$ norm of the stable linear perturbation that stabilizes the nominal system. There are two main theoretical results: one is on a partial characterization of unperturbed nominal systems for which the robust instability radius can be calculated exactly, and the other is a numerically tractable procedure for calculating the exact robust instability radius for nominal systems parametrized by a perturbation parameter. The results are applied to the repressilator in synthetic biology, where hyperbolic instability of a unique equilibrium guarantees the persistence of oscillation phenomena in the global sense, and the effectiveness of our linear robust instability analysis is confirmed by numerical simulations.

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Robust Instability Radius for Multi-agent Dynamical Systems with Cyclic Structure

This paper is concerned with robust instability analysis for linear multi-agent dynamical systems with cyclic structure. This relates to interesting and important periodic oscillation phenomena in biology and neuronal science, since the nonlinear phenomena often occur when the linearized model around an equilibrium point is unstable. We first make a problem setting on the analysis and define the notion of robust instability radius (RIR) as a quantitative measure for maximum allowable stable dynamic perturbation in terms of the H-infinity norm. After showing lower bounds of the RIR, we derive the exact RIR, which is analytic and scalable, for first order time-lag agents. Finally, we make a remark on the potential applicability to some classes of higher order systems.

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