Dimensional Reduction in Evolving Spin-Glass Model: Correlation of Phenotypic Responses to Environmental and Mutational Changes.

The evolution of high-dimensional phenotypes is investigated using a statistical physics model consisting of interacting spins, in which phenotypes, genotypes, and environments are represented by spin configurations, interaction matrices, and external fields, respectively. We found that phenotypic changes upon diverse environmental change and genetic variation are highly correlated across all spins, consistent with recent experimental observations of biological systems. The dimension reduction in phenotypic changes is shown to be a result of the evolution of the robustness to thermal noise, achieved at the replica symmetric phase.

Active pooling design in group testing based on Bayesian posterior prediction.

For identifying infected patients in a population, group testing is an effective method to reduce the number of tests and correct test errors. In group testing, tests are performed on pools of specimens collected from patients, where the number of pools is lower than that of patients. The performance of group testing considerably depends on the design of pools and algorithms that are used for inferring the infected patients from the test outcomes. In this paper, an adaptive design method of pools based on the predictive distribution is proposed in the framework of Bayesian inference. The proposed method, executed using a belief propagation algorithm, results in more accurate identification of the infected patients compared with the group testing performed on random pools determined in advance.

Partial annealing of a coupled mean-field spin-glass model with an embedded pattern.

A partially annealed mean-field spin-glass model with a locally embedded pattern is studied. The model consists of two dynamical variables, spins and interactions, that are in contact with thermal baths at temperatures T(S) and T(J), respectively. Unlike the quenched system, characteristic correlations among the interactions are induced by the partial annealing. The model exhibits three phases: paramagnetic, ferromagnetic and spin-glass. In the ferromagnetic phase, the embedded pattern is stably realized. The phase diagram depends significantly on the ratio of the two temperatures, n=T(S)/T(J). In particular, a reentrant transition from the embedded ferromagnetic to the spin-glass phase with T(S) decreasing is found only below a certain value of n. This indicates that above the critical value n(c) the embedded pattern is supported by a local field from a nonembedded region. Some equilibrium properties of the interactions in the partial annealing are also discussed in terms of frustration.

Funnel landscape and mutational robustness as a result of evolution under thermal noise.

Using a statistical-mechanical model of spins, the evolution of phenotype dynamics is studied. Configurations of spins and their interaction J represent the phenotype and genotype, respectively. The fitness for selection of J is given by the equilibrium spin configurations determined by a Hamiltonian with J under thermal noise. The genotype J evolves through mutational changes under selection pressure to raise its fitness value. From Monte Carlo simulations we find that the frustration around the target spins disappears for J evolved under temperature beyond a certain threshold. The evolved Js give the funnel-like dynamics, which is robust to noise and also to mutation.

Statistical-mechanical study of evolution of robustness in noisy environments.

In biological systems, expression dynamics that can provide fitted phenotype patterns with respect to a specific function have evolved through mutations. This has been observed in the evolution of proteins for realizing folding dynamics through which a target structure is shaped. We study this evolutionary process by introducing a statistical-mechanical model of interacting spins, where a configuration of spins and their interactions J represent a phenotype and genotype, respectively. The phenotype dynamics are given by a stochastic process with temperature TS under a Hamiltonian with J. The evolution of J is also stochastic with temperature TJ and follows mutations introduced into J and selection based on a fitness defined for a configuration of a given set of target spins. Below a certain temperature TS(c2), the interactions J that achieve the target pattern evolve, whereas another phase transition is observed at TS(c1)