Diversity, Stability, Recursivity, and Rule Generation in Biological System: Intra-inter Dynamics Approach

Basic problems for the construction of a scenario for the Life are discussed. To study the problems in terms of dynamical systems theory, a scheme of intra-inter dynamics is presented. It consists of internal dynamics of a unit, interaction among the units, and the dynamics to change the dynamics itself, for example by replication (and death) of units according to their internal states. Applying the dynamics to cell differentiation, isologous diversification theory is proposed. According to it, orbital instability leads to diversified cell behaviors first. At the next stage, several cell types are formed, first triggered by clustering of oscillations, and then as attracting states of internal dynamics stabilized by the cell-to-cell interaction. At the third stage, the differentiation is determined as a recursive state by cell division. At the last stage, hierarchical differentiation proceeds, with the emergence of stochastic rule for the differentiation to sub-groups, where regulation of the probability for the differentiation provides the diversity and stability of cell society. Relevance of the theory to cell biology is discussed.Comment: 19 pages, Int.J. Mod. Phes. B (in press

Differentiation and Replication of Spots in a Reaction Diffusion System with Many Chemicals

The replication and differentiation of spots in reaction diffusion equations are studied by extending the Gray-Scott model with self-replicating spots to include many degrees of freedom needed to model systems with many chemicals. By examining many possible reaction networks, the behavior of this model is categorized into three types: replication of homogeneous fixed spots, replication of oscillatory spots, and differentiation from `m ultipotent spots'. These multipotent spots either replicate or differentiate into other types of spots with different fixed-point dynamics, and as a result, an inhomogeneous pattern of spots is formed. This differentiation process of spots is analyzed in terms of the loss of chemical diversity and decrease of the local Kolmogorov-Sinai entropy. The relevance of the results to developmental cell biology and stem cells is also discussed.Comment: 8 pages, 12 figures, Submitted to EP

Self-organized and driven phase synchronization in coupled maps

We study the phase synchronization and cluster formation in coupled maps on different networks. We identify two different mechanisms of cluster formation; (a) {\it Self-organized} phase synchronization which leads to clusters with dominant intra-cluster couplings and (b) {\it driven} phase synchronization which leads to clusters with dominant inter-cluster couplings. In the novel driven synchronization the nodes of one cluster are driven by those of the others. We also discuss the dynamical origin of these two mechanisms for small networks with two and three nodes.Comment: 4 pages including 2 figure

Leptogenesis in a Hybrid Texture Neutrino Mass Model

We investigate the CP asymmetry for a hybrid texture of the neutrino mass matrix predicted by $Q_8$ family symmetry in the context of the type-I seesaw mechanism and examine its consequences for leptogenesis. We, also, calculate the resulting Baryon Asymmetry of the Universe (BAU) for this texture.Comment: Accepted for publication in Mod. Phys. Lett.

Short Gamma-Ray Bursts with Extended Emission Observed with Swift/BAT and Fermi/GBM

Some short GRBs are followed by longer extended emission, lasting anywhere from ~10 to ~100 s. These short GRBs with extended emission (EE) can possess observational characteristics of both short and long GRBs (as represented by GRB 060614), and the traditional classification based on the observed duration places some of them in the long GRB class. While GRBs with EE pose a challenge to the compact binary merger scenario, they may therefore provide an important link between short and long duration events. To identify the population of GRBs with EE regardless of their initial classifications, we performed a systematic search of short GRBs with EE using all available data (up to February 2013) of both Swift/BAT and Fermi/GBM. The search identified 16 BAT and 14 GBM detected GRBs with EE, several of which are common events observed with both detectors. We investigated their spectral and temporal properties for both the spikes and the EE, and examined correlations among these parameters. Here we present the results of the systematic search as well as the properties of the identified events. Finally, their properties are also compared with short GRBs with EE observed with BATSE, identified through our previous search effort. We found several strong correlations among parameters, especially when all of the samples were combined. Based on our results, a possible progenitor scenario of two-component jet is discussed.Comment: Published in MNRAS; matched to the published versio

Recursiveness, Switching, and Fluctuations in a Replicating Catalytic Network

A protocell model consisting of mutually catalyzing molecules is studied in order to investigate how chemical compositions are transferred recursively through cell divisions under replication errors. Depending on the path rate, the numbers of molecules and species, three phases are found: fast switching state without recursive production, recursive production, and itinerancy between the above two states. The number distributions of the molecules in the recursive states are shown to be log-normal except for those species that form a core hypercycle, and are explained with the help of a heuristic argument.Comment: 4 pages (with 7 figures (6 color)), submitted to PR

Identifying dynamical systems with bifurcations from noisy partial observation

Dynamical systems are used to model a variety of phenomena in which the bifurcation structure is a fundamental characteristic. Here we propose a statistical machine-learning approach to derive lowdimensional models that automatically integrate information in noisy time-series data from partial observations. The method is tested using artificial data generated from two cell-cycle control system models that exhibit different bifurcations, and the learned systems are shown to robustly inherit the bifurcation structure.Comment: 16 pages, 6 figure

Amplitude death in coupled chaotic oscillators

Amplitude death can occur in chaotic dynamical systems with time-delay coupling, similar to the case of coupled limit cycles. The coupling leads to stabilization of fixed points of the subsystems. This phenomenon is quite general, and occurs for identical as well as nonidentical coupled chaotic systems. Using the Lorenz and R\"ossler chaotic oscillators to construct representative systems, various possible transitions from chaotic dynamics to fixed points are discussed.Comment: To be published in PR

Spectral Properties and Synchronization in Coupled Map Lattices

Spectral properties of Coupled Map Lattices are described. Conditions for the stability of spatially homogeneous chaotic solutions are derived using linear stability analysis. Global stability analysis results are also presented. The analytical results are supplemented with numerical examples. The quadratic map is used for the site dynamics with different coupling schemes such as global coupling, nearest neighbor coupling, intermediate range coupling, random coupling, small world coupling and scale free coupling.Comment: 10 pages with 15 figures (Postscript), REVTEX format. To appear in PR

Two-photon decay of the neutral pion in lattice QCD

We perform non-perturbative calculation of the \pi^0 to {\gamma}{\gamma} transition form factor and the associated decay width using lattice QCD. The amplitude for two-photon final state, which is not an eigenstate of QCD, is extracted through an Euclidean time integral of the relevant three-point function. We utilize the all-to-all quark propagator technique to carry out this integral as well as to include the disconnected quark diagram contributions. The overlap fermion formulation is employed on the lattice to ensure exact chiral symmetry on the lattice. After examining various sources of systematic effects except for possible discretization effect, we obtain \Gamma=7.83(31)(49) eV for the pion decay width, where the first error is statistical and the second is our estimate of the systematic error.Comment: 5 pages, 4 figures. Changes made addressing to referee's comments, version accepted by PR