Yuki Sughiyama

Fluctuation Relations of Fitness and Information in Population Dynamics.

Phenotype switching with and without sensing environment is a common strategy of organisms to survive in a fluctuating environment. Understanding the evolutionary advantages of switching and sensing requires a quantitative evaluation of their fitness gain and its fluctuation together with the conditions for the switching and sensing strategies being adapted to a given environment. In this work, by using a pathwise formulation of the population dynamics, we show that the optimal switching strategy is characterized by a consistency condition for time-forward and backward path probabilities. The formulation also clarifies the underlying information-theoretic aspect of selection as a passive information compression. The loss of fitness by a suboptimal strategy is also shown to satisfy a fluctuation relation, which provides us with the information on how environmental fluctuation impacts the advantages of the optimal strategy. These results are naturally extended to the situation that organisms can use an environmental signal by actively sensing the environment. The fluctuation relations of the fitness gain by sensing are derived in which the multivariate mutual information among the phenotype, the environment, and the signal plays the role to quantify the relevant information in the signal for the fitness gain.

Stochastic and information-thermodynamic structures of population dynamics in a fluctuating environment

Adaptation in a fluctuating environment is a process of fueling environmental information to gain fitness. Living systems have gradually developed strategies for adaptation from random and passive diversification of the phenotype to more proactive decision making, in which environmental information is sensed and exploited more actively and effectively. Understanding the fundamental relation between fitness and information is therefore crucial to clarify the limits and universal properties of adaptation. In this work, we elucidate the underlying stochastic and information-thermodynamic structure in this process, by deriving causal fluctuation relations (FRs) of fitness and information. Combined with a duality between phenotypic and environmental dynamics, the FRs reveal the limit of fitness gain, the relation of time reversibility with the achievability of the limit, and the possibility and condition for gaining excess fitness due to environmental fluctuation. The loss of fitness due to causal constraints and the limited capacity of real organisms is shown to be the difference between time-forward and time-backward path probabilities of phenotypic and environmental dynamics. Furthermore, the FRs generalize the concept of the evolutionary stable state (ESS) for fluctuating environment by giving the probability that the optimal strategy on average can be invaded by a suboptimal one owing to rare environmental fluctuation. These results clarify the information-thermodynamic structures in adaptation and evolution.

Deterministic quantum annealing expectation-maximization algorithm

Maximum likelihood estimation (MLE) is one of the most important methods in machine learning, and the expectation-maximization (EM) algorithm is often used to obtain maximum likelihood estimates. However, EM heavily depends on initial configurations and fails to find the global optimum. On the other hand, in the field of physics, quantum annealing (QA) was proposed as a novel optimization approach. Motivated by QA, we propose a quantum annealing extension of EM, which we call the deterministic quantum annealing expectation-maximization (DQAEM) algorithm. We also discuss its advantage in terms of the path integral formulation. Furthermore, by employing numerical simulations, we illustrate how it works in MLE and show that DQAEM outperforms EM.

Relaxation of the EM algorithm via quantum annealing for Gaussian mixture models

We propose a modified expectation-maximization algorithm by introducing the concept of quantum annealing, which we call the deterministic quantum annealing expectation-maximization algorithm (DQAEM). The expectation-maximization algorithm (EM) is an established algorithm to compute maximum likelihood estimates and applied to many practical applications. However, it is known that EM heavily depends on initial values and its estimates are sometimes trapped by local optima. To solve such a problem, quantum annealing (QA) was proposed as a novel optimization approach motivated by quantum mechanics. By employing QA, we then formulate DQAEM and present a theorem that supports its stability. Finally, we demonstrate numerical simulations to confirm its efficiency.

Discreteness-induced transitions in multibody reaction systems.

A decrease in system size can induce qualitatively different behavior compared to the macroscopic behavior of the corresponding large-size system. The mechanisms of this transition, which is known as the small-size transition, can be attributed to either a relative increase in the noise intensity or to the discreteness of the state space due to the small system size. The former mechanism has been intensively investigated using several toy and realistic models. However, the latter has rarely been analyzed and is sometimes confused with the former, because a toy model that extracts the essence of the discreteness-induced transition mechanism is lacking. In this work, we propose a one- and three-body reaction system as a minimal model of the discreteness-induced transition and derive the conditions under which this transition occurs in more complex systems. This work enriches our understanding of the influence of small system size on system behavior.

Nonequilibrium work relation in a macroscopic system

We reconsider a well-known relationship between the fluctuation theorem and the second law of thermodynamics by evaluating a probability measure-valued process. In order to establish a bridge between microscopic and macroscopic behaviors, we consider the thermodynamic limit of a stochastic dynamical system following the fundamental procedure often used in statistical mechanics. The thermodynamic path characterizing a macroscopic dynamical behavior can be formulated as an infimum of the action functional for the probability measure-valued process. In our formulation, the second law of thermodynamics can be derived by symmetry of the action functional, which is generated from the fluctuation theorem. We find that our formulation not only confirms that the ordinary Jarzynski equality in the thermodynamic limit can be rederived, but also enables us to establish a nontrivial nonequilibrium work relation for metastable states.