Steady state thermodynamics in population dynamics

We report that population dynamics in fluctuating environment accompanies mathematically equivalent structure to steady state thermodynamics. By employing the structure, population growth in fluctuating environment is decomposed into housekeeping and excess parts. The housekeeping part represents the integral of stationary growth rate for each condition during a history of the environmental change. The excess part accounts for the excess growth generated when environment is switched. Focusing on the excess growth, we obtain Clausius inequality, which gives the upper bound of the excess growth. The equality is shown to be achieved in quasistatic environmental changes. We also clarify that this bound can be evaluated by "lineage fitness" that is an experimentally observable quantity.Comment: 5 pages, 2 figure

The explicit form of the rate function for semi-Markov processes and its contractions

We derive the explicit form of the rate function for semi-Markov processes. Here, the "random time change trick" plays an essential role. Also, by exploiting the contraction principle of the large deviation theory to the explicit form, we show that the fluctuation theorem (Gallavotti-Cohen Symmetry) holds for semi-Markov cases. Furthermore, we elucidate that our rate function is an extension of the Level 2.5 rate function for Markov processes to semi-Markov cases.Comment: 22 pages, 3 figure

Individual Sensing can Gain more Fitness than its Information

Mutual information and its causal variant, directed information, have been widely used to quantitatively characterize the performance of biological sensing and information transduction. However, once coupled with selection in response to decision-making, the sensing signal could have more or less evolutionary value than its mutual or directed information. In this work, we show that an individually sensed signal always has a better fitness value, on average, than its mutual or directed information. The fitness gain, which satisfies fluctuation relations (FRs), is attributed to the selection of organisms in a population that obtain a better sensing signal by chance. A new quantity, similar to the coarse-grained entropy production in information thermodynamics, is introduced to quantify the total fitness gain from individual sensing, which also satisfies FRs. Using this quantity, the optimizing fitness gain from individual sensing is shown to be related to fidelity allocations for individual environmental histories. Our results are supplemented by numerical verifications of FRs, and a discussion on how this problem is linked to information encoding and decoding.Comment: 5figure

Fluctuation Relations of Fitness and Information in Population Dynamics

Phenotype-switching with and without sensing environment is a ubiquitous strategy of organisms to survive in fluctuating environment. Fitness of a population of organisms with phenotype-switching may be constrained and restricted by hidden relations as the entropy production in a thermal system with and without sensing and feedback is well-characterized via fluctuation relations (FRs) . In this work, we derive such FRs of fitness together with an underlying information-theoretic structure in selection. By using path-integral formulation of a multi-phenotype population dynamics, we clarify that the optimal switching strategy is characterized as a consistency condition for time-forward and backward path probabilities. Within the formulation, the selection is regarded as passive information compression, and the loss of fitness from the optimal strategy is shown to satisfy various FRs that constrain the average and fluctuation of the loss. These results are naturally extended to the situation that organisms can use an environmental signal by actively sensing the environment. FRs of 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 fitness gain.Comment: Submitted to PRL on 25/Jul/2014; resubmitted to PRL for revision on 10/Apr/201

Stochastic and Information-thermodynamic Structures of Population Dynamics in 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 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.Comment: 5figure

Latent Mixture Modeling for Clustered Data

This article proposes a mixture modeling approach to estimating cluster-wise conditional distributions in clustered (grouped) data. We adapt the mixture-of-experts model to the latent distributions, and propose a model in which each cluster-wise density is represented as a mixture of latent experts with cluster-wise mixing proportions distributed as Dirichlet distribution. The model parameters are estimated by maximizing the marginal likelihood function using a newly developed Monte Carlo Expectation-Maximization algorithm. We also extend the model such that the distribution of cluster-wise mixing proportions depends on some cluster-level covariates. The finite sample performance of the proposed model is compared with some existing mixture modeling approaches as well as linear mixed model through the simulation studies. The proposed model is also illustrated with the posted land price data in Japan.Comment: 17 page

Vortex Tiling in a Spin-2 Spinor Bose-Einstein Condensate

We point out that the internal spin symmetry of the order parameter manifests itself at the core of a fractional vortex in real space without spin-orbit coupling. Such symmetry breaking arises from a topological constraint and the commensurability between spin symmetries of the order parameters inside and outside the core. Our prediction can be applied to probe the cyclic order parameter in a rotating spin-2 $^{87}$Rb condensate as a non-circular vortex core in a biaxial nematic state.Comment: 4 pages, 4 figure

Breaking of Vainshtein screening in scalar-tensor theories beyond Horndeski

The Horndeski theory of gravity is known as the most general scalar-tensor theory with second-order field equations. Recently, it was demonstrated by Gleyzes et al. that the Horndeski theory can further be generalized in such a way that although field equations are of third order, the number of propagating degrees of freedom remains the same. We study small-scale gravity in the generalized Horndeski theory, focusing in particular on an impact of the new derivative interaction beyond Horndeski on the Vainshtein screening mechanism. In the absence of the quintic galileon term and its generalization, we show that the new interaction does not change the qualitative behavior of gravity outside and near the source: the two metric potentials coincide, $\Phi = \Psi \;(\sim r^{-1})$, while the gravitational coupling is given by the cosmological one and hence is time-dependent in general. We find, however, that the gravitational field inside the source shows a novel behavior due to the interaction beyond Horndeski: the gravitational attraction is not determined solely from the enclosed mass and two potentials do not coincide, indicating breaking of the screening mechanism.Comment: 14 pages, 1 figure; v2: additional material added, published versio

Topological Influence between Monopoles and Vortices: a Possible Resolution of the Monopole Problem

Grand unified theories of fundamental forces predict that magnetic monopoles are inevitable in the Universe because the second homotopy group of the order parameter manifold is $\mathbb{Z}$. We point out that monopoles can annihilate in pairs due to an influence of Alice strings. As a consequence, a monopole charge is charactarized by $\mathbb{Z}_2$ rather than $\mathbb{Z}$ if the Universe can accommodate Alice strings, which is the case of certain grand unified theories.Comment: 4 pages, 3 figure

Generalized Berry phase for a bosonic Bogoliubov system with exceptional points

We discuss the topology of Bogoliubov excitation bands from a Bose-Einstein condensate in an optical lattice. Since the Bogoliubov equation for a bosonic system is non-Hermitian, complex eigenvalues often appear and induce dynamical instability. As a function of momentum, the onset of appearance and disappearance of complex eigenvalues is an exceptional point (EP), which is a point where the Hamiltonian is not diagonalizable and hence the Berry connection and curvature are ill-defined, preventing defining topological invariants. In this paper, we propose a systematic procedure to remove EPs from the Brillouin zone by introducing an imaginary part of the momentum. We then define the Berry phase for a one-dimensional bosonic Bogoliubov system. Extending the argument for Hermitian systems, the Berry phase for an inversion-symmetric system is shown to be $Z_2$. As concrete examples, we numerically investigate two toy models and confirm the bulk-edge correspondence even in the presence of complex eigenvalues. The $Z_2$ invariant associated with particle-hole symmetry and the winding number for a time-reversal-symmetric system are also discussed.Comment: 22 pages, 9 figure