Evolutionary origin of power-laws in Biochemical Reaction Network; embedding abundance distribution into topology

The evolutionary origin of universal statistics in biochemical reaction network is studied, to explain the power-law distribution of reaction links and the power-law distributions of chemical abundances. Using cell models with catalytic reaction network, we find evidence that the power-law distribution in abundances of chemicals emerges by the selection of cells with higher growth speeds. Through the further evolution, this inhomogeneity in chemical abundances is shown to be embedded in the distribution of links, leading to the power-law distribution. These findings provide novel insights into the nature of network evolution in living cells.Comment: 11 pages, 3 figure

Desynchronization in diluted neural networks

The dynamical behaviour of a weakly diluted fully-inhibitory network of pulse-coupled spiking neurons is investigated. Upon increasing the coupling strength, a transition from regular to stochastic-like regime is observed. In the weak-coupling phase, a periodic dynamics is rapidly approached, with all neurons firing with the same rate and mutually phase-locked. The strong-coupling phase is characterized by an irregular pattern, even though the maximum Lyapunov exponent is negative. The paradox is solved by drawing an analogy with the phenomenon of ``stable chaos'', i.e. by observing that the stochastic-like behaviour is "limited" to a an exponentially long (with the system size) transient. Remarkably, the transient dynamics turns out to be stationary.Comment: 11 pages, 13 figures, submitted to Phys. Rev.

Interaction of Phonons and Dirac Fermions on the Surface of Bi2Se3: A Strong Kohn Anomaly

We report the first measurements of phonon dispersion curves on the (001) surface of the strong three-dimensional topological insulator Bi2Se3. The surface phonon measurements were carried out with the aid of coherent helium beam surface scattering techniques. The results reveal a prominent signature of the exotic metallic Dirac fermion quasi-particles, including a strong Kohn anomaly. The signature is manifest in a low energy isotropic convex dispersive surface phonon branch with a frequency maximum of 1.8 THz, and having a V-shaped minimum at approximately 2kF that defines the Kohn anomaly. Theoretical analysis attributes this dispersive profile to the renormalization of the surface phonon excitations by the surface Dirac fermions. The contribution of the Dirac fermions to this renormalization is derived in terms of a Coulomb-type perturbation model

Fabrication of Spherical CaO-SrO-ZnO-SiO2 Particles by Sol-Gel Processing

This study was concerned with the fabrication of ceramic CaO-SrO-ZnO-SiO2 spherical particles, which are novel candidates for the glass phase in glass polyalkenoate cements (GPCs). GPCs made from these glasses have potential as bone cements because, unlike conventional GPCs, they do not contain aluminum ions, which inhibit the calcification of hydroxyapatite in the body. The glass phase of GPCs require a controllable glass morphology and particle size distribution. Sol-gel processing can potentially be used to fabricate homogenous ceramic particles with controlled morphology. However, a thorough study on preparation conditions of spherical CaO-SrO-ZnO-SiO2 particles by sol-gel processing has, to date, not been reported. In this study, gels were prepared by hydrolysis and polycondensation of tetraethoxysilane (TEOS) in an aqueous solution containing polyethylene glycol and nitrates of calcium, strontium and zinc. It was possible to control the morphology and size of the gels by varying the H2O/TEOS molar ratio and the metal ion content in the starting compositions. An aliquot of 3-5 μm homogenous spherical particles were obtained at a H2O/TEOS molar ratio of 42.6 when the starting composition molar ratios were Sr(NO 3):Ca(NO3)2:Zn(NO3) 2:Si(OC2H5)4 = x:0.12:(0.40 - x):0.48 (0 ≤ x ≤ 0.8). Starting composition limitations are caused by the low solubility of strontium ions in the minimal amount of water used and the acceleration of hydrolysis as well as polycondensation at higher water content. © 2009 Springer Science+Business Media, LLC

Crossover between Levy and Gaussian regimes in first passage processes

We propose a new approach to the problem of the first passage time. Our method is applicable not only to the Wiener process but also to the non--Gaussian L$\acute{\rm e}$vy flights or to more complicated stochastic processes whose distributions are stable. To show the usefulness of the method, we particularly focus on the first passage time problems in the truncated L$\acute{\rm e}$vy flights (the so-called KoBoL processes), in which the arbitrarily large tail of the L$\acute{\rm e}$vy distribution is cut off. We find that the asymptotic scaling law of the first passage time $t$ distribution changes from $t^{-(\alpha +1)/\alpha}$-law (non-Gaussian L$\acute{\rm e}$vy regime) to $t^{-3/2}$-law (Gaussian regime) at the crossover point. This result means that an ultra-slow convergence from the non-Gaussian L$\acute{\rm e}$vy regime to the Gaussian regime is observed not only in the distribution of the real time step for the truncated L$\acute{\rm e}$vy flight but also in the first passage time distribution of the flight. The nature of the crossover in the scaling laws and the scaling relation on the crossover point with respect to the effective cut-off length of the L$\acute{\rm e}$vy distribution are discussed.Comment: 18pages, 7figures, using revtex4, to appear in Phys.Rev.

Spin and charge gaps in the one-dimensional Kondo-lattice model with Coulomb interaction between conduction electrons

The density-matrix renormalization-group method is applied to the one-dimensional Kondo-lattice model with the Coulomb interaction between the conduction electrons. The spin and charge gaps are calculated as a function of the exchange constant $J$ and the Coulomb interaction $U_c$. It is shown that both the spin and charge gaps increase with increasing $J$ and $U_c$. The spin gap vanishes in the limit of $J \rightarrow 0$ for any $U_c$ with an exponential form, $\Delta_s\propto \exp{[-1/\alpha (U_c) J \rho]}$. The exponent, $\alpha (U_c)$, is determined as a function of $U_c$. The charge gap is generally much larger than the spin gap. In the limit of $J \rightarrow 0$, the charge gap vanishes as $\Delta_c=\frac{1}{2}J$ for $U_c=0$ but for a finite $U_c$ it tends to a finite value, which is the charge gap of the Hubbard model.Comment: RevTeX, 4 pages, 3 Postscript figure

Characteristics of Glass Ionomer Cements Composed of Glass Powders in CaO-SrO-ZnO-SiO2 System Prepared by Two Different Synthetic Routes

Glass ionomer cements (GICs) are composed of an acid degradable glass, polyacrylic acid and water. Sol-gel processing to prepare the glass phase has certain advantages, such as the ability to employ lower synthesis temperatures than melt quenching and glasses that are reported to have higher purity. A previous study reported the effects of glass synthesis route on GIC fabrication. However, in that study, the sol-gel derived glass exhibited a reduced concentration of cations. This study investigates increasing the cation content of a sol-gel derived glass, 12CaO·4SrO·36ZnO·48SiO2 (molar ratio) by heating before aging to reduce dissolution of cations. This glass was prepared by both sol-gel and melt-quenched routes. GICs were subsequently prepared using both glasses. The resultant cement based on the sol-gel derived glass had a shorter working time than the cement based on the melt-quenched one. Contrary to this, setting time was considerably longer for the cement based on the sol-gel derived glass than for the cement based on the melt-quenched one. The cements based on the sol-gel derived glass were stronger in both compression and biaxial flexure than the cements prepared from the melt-quenched glass. The differences in setting and mechanical properties were associated with both cation content in the glass phase and the different surface area of the resultant cements. © 2013 Springer Science+Business Media New York

Friedel oscillations in the one-dimensional Kondo-lattice model

The paramagnetic metallic phase of the one-dimensional Kondo lattice model is studied by the density-matrix renormalization- group method. We observe charge and spin Friedel oscillations. They reflect the long range charge-charge and spin-spin correlation functions. The observed oscillations are consistent with a Tomonaga-Luttinger liquid. From the period of the oscillations it is concluded that the Fermi surface is large, including both the conduction electrons and the localized spins, $k_F=\pi (1+n_c)/2$, where $n_c$ is the density of conduction electrons.Comment: RevTeX, 4 pages, 4 Postscript figures, to be published in Physical review

Multipole correlations of t2gt_{\rm 2g}-orbital Hubbard model with spin-orbit coupling

We investigate the ground-state properties of a one-dimensional $t_{\rm 2g}$-orbital Hubbard model including an atomic spin-orbit coupling by using numerical methods, such as Lanczos diagonalization and density-matrix renormalization group. As the spin-orbit coupling increases, we find a ground-state transition from a paramegnetic state to a ferromagnetic state. In the ferromagnetic state, since the spin-orbit coupling mixes spin and orbital states with complex number coefficients, an antiferro-orbital state with complex orbitals appears. According to the appearance of the complex orbital state, we observe an enhancement of $\Gamma_{4u}$ octupole correlations.Comment: 3 pages, 3 figures, To appear in J. Phys. Soc. Jpn. Suppl., Proceedings of ICHE2010 (September 17-20, 2010, Hachioji, Japan

Dynamical response of the Hodgkin-Huxley model in the high-input regime

The response of the Hodgkin-Huxley neuronal model subjected to stochastic uncorrelated spike trains originating from a large number of inhibitory and excitatory post-synaptic potentials is analyzed in detail. The model is examined in its three fundamental dynamical regimes: silence, bistability and repetitive firing. Its response is characterized in terms of statistical indicators (interspike-interval distributions and their first moments) as well as of dynamical indicators (autocorrelation functions and conditional entropies). In the silent regime, the coexistence of two different coherence resonances is revealed: one occurs at quite low noise and is related to the stimulation of subthreshold oscillations around the rest state; the second one (at intermediate noise variance) is associated with the regularization of the sequence of spikes emitted by the neuron. Bistability in the low noise limit can be interpreted in terms of jumping processes across barriers activated by stochastic fluctuations. In the repetitive firing regime a maximization of incoherence is observed at finite noise variance. Finally, the mechanisms responsible for spike triggering in the various regimes are clearly identified.Comment: 14 pages, 24 figures in eps, submitted to Physical Review