Ilex kudingcha C.J. Tseng Mitigates Phenotypic Characteristics of Human Autism Spectrum Disorders in a Drosophila Melanogaster Rugose Mutant.

Autism spectrum disorders (ASD) have heterogeneous etiologies involving dysfunction of central nervous systems, for which no effective pan-specific treatments are available. Ilex kudingcha (IK) C.J. Tseng is a nootropic botanical used in Asia for neuroprotection and improvement of cognition. This study establishes that a chemically characterized extract from IK (IKE) mitigates behavioral traits in the Drosophila melanogaster rugose mutant, whose traits resemble human ASD, and examines possible mechanisms. IKE treatment significantly ameliorated deficits in social interaction, short-term memory, and locomotor activity in Drosophila rugose, and significantly increased synaptic bouton number of size more than 2 µm2 in the neuromuscular junctions (NMJs) of Drosophila rugose. To clarify mechanism(s) of IKE action, methylphenidate (MPH), a dopamine transporter inhibitor, was included as a reference drug in the behavioral assays: MPH significantly improved social interaction and short-term memory deficit in Drosophila rugose; administration of the dopamine D1 receptor antagonist SCH23390 and dopamine D2 receptor antagonist sulpiride reversed the ameliorative effects of both MPH and IKE on the social interaction deficits of Drosophila rugose. To extend analysis of IKE treatment to the vertebrate central nervous system, ASD-associated gene expression in mouse hippocampus was studied by RNA-seq: IKE treatment altered the expression of genes coding phosphoinositide 3-kinases/protein kinase B (PI3K-Akt), proteins in glutamatergic, dopaminergic, serotonergic, and GABAergic synapses, cAMP response element-binding protein (CREB), and RNA transporter proteins. These results provide a foundation for further analysis of IKE as a candidate for treatment of some forms of ASD.

Field theory of bicritical and tetracritical points. IV. Critical dynamics including reversible terms.

This article concludes a series of papers [Folk, Holovatch, and Moser, Phys. Rev. E 78, 041124 (2008); 78, 041125 (2008); 79, 031109 (2009)] where the tools of the field theoretical renormalization group were employed to explain and quantitatively describe different types of static and dynamic behavior in the vicinity of multicritical points. Here we give the complete two-loop calculation and analysis of the dynamic renormalization-group flow equations at the multicritical point in anisotropic antiferromagnets in an external magnetic field. We find that the time scales of the order parameters characterizing the parallel and perpendicular ordering with respect to the external field scale in the same way. This holds independent whether the Heisenberg fixed point or the biconical fixed point in statics is the stable one. The nonasymptotic analysis of the dynamic flow equations shows that due to cancellation effects the critical behavior is described, in distances from the critical point accessible to experiments, by the critical behavior qualitatively found in one-loop order. Although one may conclude from the effective dynamic exponents (taking almost their one-loop values) that weak scaling for the order parameter components is valid, the flow of the time-scale ratios is quite different, and they do not reach their asymptotic values.

Entropic equation of state and scaling functions near the critical point in uncorrelated scale-free networks.

We analyze the entropic equation of state for a many-particle interacting system in a scale-free network. The analysis is performed in terms of scaling functions, which are of fundamental interest in the theory of critical phenomena and have previously been theoretically and experimentally explored in the context of various magnetic, fluid, and superconducting systems in two and three dimensions. Here, we obtain general scaling functions for the entropy, the constant-field heat capacity, and the isothermal magnetocaloric coefficient near the critical point in uncorrelated scale-free networks, where the node-degree distribution exponent λ appears to be a global variable and plays a crucial role, similar to the dimensionality d for systems on lattices. This extends the principle of universality to systems on scale-free networks and allows quantification of the impact of fluctuations in the network structure on critical behavior.

Critical phenomena on scale-free networks: logarithmic corrections and scaling functions.

In this paper, we address the logarithmic corrections to the leading power laws that govern thermodynamic quantities as a second-order phase transition point is approached. For phase transitions of spin systems on d-dimensional lattices, such corrections appear at some marginal values of the order parameter or space dimension. We present scaling relations for these exponents. We also consider a spin system on a scale-free network which exhibits logarithmic corrections due to the specific network properties. To this end, we analyze the phase behavior of a model with coupled order parameters on a scale-free network and extract leading and logarithmic correction-to-scaling exponents that determine its field and temperature behavior. Although both nontrivial sets of exponents emerge from the network structure rather than from the spin fluctuations they fulfill the respective thermodynamic scaling relations. For the scale-free networks the logarithmic corrections appear at marginal values of the node degree distribution exponent. In addition we calculate scaling functions, which also exhibit nontrivial dependence on intrinsic network properties.

Dynamic scaling functions and amplitude ratios of stochastic models with energy conservation above Tc.

Dynamical scaling functions above Tc for the characteristic frequencies and the dynamical correlation functions of the order parameter and the conserved density of model C are calculated in one loop order. By a proper exponentiation procedure these results can be extended in order to consider the changes in these functions using the fixed point values and exponents in two loop order. The dynamical amplitude ratio R of the characteristic frequencies is generalized to the critical region. Surprisingly the decay of the shape functions at large scaled frequency does not behave as expected from applying scaling arguments. The exponent upsilon of the decay does not change when going from the critical to the hydrodynamic region although the shape functions change. The value of upsilon for the order parameter is in agreement with its value in the critical region, whereas for the conserved density it is equal to 2, the value in the hydrodynamic region.

Concentration and mass dependence of transport coefficients and correlation functions in binary mixtures with high mass asymmetry.

Correlation functions and transport coefficients of self-diffusion and shear viscosity of a binary Lennard-Jones mixture with components differing only in their particle mass are studied up to high values of the mass ratio mu, including the limiting case mu = infinity, for different mole fractions x. Within a large range of x and mu the product of the diffusion coefficient of the heavy species D(2) and the total shear viscosity of the mixture eta(m) is found to remain constant, obeying a generalized Stokes-Einstein relation. At high liquid density, large mass ratios lead to a pronounced cage effect that is observable in the mean square displacement, the velocity autocorrelation function, and the van Hove correlation function.

Coupled order-parameter system on a scale-free network.

The system of two scalar order parameters on a complex scale-free network is analyzed in the spirit of Landau theory. To add a microscopic background to the phenomenological approach, we also study a particular spin Hamiltonian that leads to coupled scalar order behavior using the mean-field approximation. Our results show that the system is characterized by either of two types of ordering: either one of the two order parameters is zero or both are nonzero but have the same value. While the critical exponents do not differ from those of a model with a single order parameter on a scale-free network, there are notable differences for the amplitude ratios and the susceptibilities. Another peculiarity of the model is that the transverse susceptibility is divergent at all T

Field theory of bicritical and tetracritical points. III. Relaxational dynamics including conservation of magnetization (model C).

We calculate the relaxational dynamical critical behavior of systems of O(n_{ parallel}) plus sign in circleO(n_{ perpendicular}) symmetry including conservation of magnetization by renormalization group theory within the minimal subtraction scheme in two-loop order. Within the stability region of the Heisenberg fixed point and the biconical fixed point, strong dynamical scaling holds, with the asymptotic dynamical critical exponent z=2varphinu-1 , where varphi is the crossover exponent and nu the exponent of the correlation length. The critical dynamics at n_{ parallel}=1 and n_{ perpendicular}=2 is governed by a small dynamical transient exponent leading to nonuniversal nonasymptotic dynamical behavior. This may be seen, e.g., in the temperature dependence of the magnetic transport coefficients.

Liquid-vapor interfaces in XY -spin fluids: an inhomogeneous anisotropic integral-equation approach.

An integral-equation approach is developed to study interfacial properties of anisotropic fluids with planar spins in the presence of an external magnetic field. The approach is based on the coupled set of the Lovett-Mou-Buff-Wertheim integro-differential equation for the inhomogeneous anisotropic one-particle density and the Ornstein-Zernike equation for the orientationally dependent two-particle correlation functions. Using the proposed inhomogeneous angle-harmonics expansion formalism we show that these integral equations can be reduced to a much simpler form similar to that inherent for a system of isotropic fluids. The interfacial orientationally dependent direct correlation function can be consistently constructed by means of a nonlinear interpolation via its values obtained in the coexisting anisotropic bulk phases. A soft mean spherical approximation is employed for the closure relation. This has allowed us to solve the complicated integral equations in the situation when both spatial inhomogeneity and orientational anisotropy are present simultaneously. The approach introduced is applied to an XY fluid model with ferromagnetic spin interactions. As a result, the density-orientation and magnetization profiles at the liquid-vapor interfaces are calculated in a wide range of temperatures up to subcritical regions. The influence of the external field on the microscopic structure of the interfaces and the surface tension is also analyzed in detail.

Field theory of bicritical and tetracritical points. I. Statics.

We calculate the static critical behavior of systems of O(n_||)(plus sign in circle)O(n_perpendicular) symmetry by the renormalization group method within the minimal subtraction scheme in two-loop order. Summation methods lead to fixed points describing multicritical behavior. Their stability border lines in the space of the order parameter components n_|| and n_perpendicular and spatial dimension d are calculated. The essential features obtained already in two-loop order for the interesting case of an antiferromagnet in a magnetic field ( n_|| =1, n_perpendicular =2 ) are the stability of the biconical fixed point and the neighborhood of the stability border lines to the other fixed points, leading to very small transient exponents. We are also able to calculate the flow of static couplings, which allows us to consider the attraction region. Depending on the nonuniversal background parameters, the existence of different multicritical behavior (bicritical or tetracritical) is possible, including a triple point.

Field theory of bicritical and tetracritical points. II. Relaxational dynamics.

We calculate the relaxational dynamical critical behavior of systems of O(n_||)(plus sign in circle)O(n_perpendicular) symmetry by renormalization group method within the minimal subtraction scheme in two-loop order. The three different bicritical static universality classes previously found for such systems correspond to three different dynamical universality classes within the static borderlines. The Heisenberg and the biconical fixed point lead to strong dynamic scaling whereas in the region of stability of the decoupled fixed point weak dynamic scaling holds. Due to the neighborhood of the stability border between the strong and the weak scaling dynamic fixed point to the dynamical stable fixed point a very small dynamic transient exponent of omega(Beta)_(v) =0.0044 is present in the dynamics for the physically important case n_|| =1 and n_perpendicular =2 in d=3 .

Possibility of Fisher renormalization of the critical exponents in an Ising fluid.

Using Monte Carlo simulation techniques, we study the ferromagnetic order-disorder phase transition in Ising spin fluids with hard-core Yukawa interaction truncated at various cutoff radii r{c}. We focus our interest on the dependence of critical quantities such as the Binder cumulant and various exponent ratios on the value of r{c}, and on the question whether the Fisher-renormalized exponents expected for such systems can be observed in the simulations. It turns out that the corrections to scaling decaying with a rather small exponent prevent reaching the asymptotic region with the computational power available. Thus, we observe only effective exponents, with different (nonuniversal) values depending on the cutoff radius. The same behavior is also found for the critical Binder cumulant. Nevertheless, an exact investigation of the effective susceptibility exponent gamma{eff} as a function of temperature seems to point towards a Fisher-renormalized value. For two selected cutoff radii, the critical temperature is determined more accurately using, in addition to the cumulant crossing technique, the scanning technique and the shifting technique, taking into account corrections to scaling. Simulations of Ising fluids with constant cutoff radius and varying Yukawa-tail screening lengths lambda also show a nonuniversal dependence of U{c} on lambda. Finally, we have performed simulations of the Ising lattice model with increasing number of couplings which show the expected asymptotic behavior, independent of the range of interactions.

Liquid-vapor and liquid-liquid interfaces in Ising fluids: an integral equation approach.

The microscopic structure and thermodynamic properties of liquid-vapor and liquid-liquid interfaces in Ising fluids are studied using an integral equation approach. The calculations are performed in the absence and presence of an external magnetic field by solving the corresponding set of Lovett-Mou-Buff-Wertheim integrodifferential equations for the one-particle density distribution functions. The two-particle inhomogeneous direct correlation functions are consistently constructed by nonlinear interpolation between the bulk ones. The bulk correlation functions of the coexisting phases are obtained from the Ornstein-Zernike equations with a modified soft mean spherical approximation for the closure relation. As a result, the density and magnetization profiles at liquid-vapor and liquid-liquid interfaces as well as the surface tension and adsorption coefficients are evaluated in a wide temperature range including subcritical regions. The influence of an external magnetic field on the liquid-vapor interfaces is also considered.

Two-loop field theory and nonasymptotic properties of the dynamical model for the lambda transition in 3He-4He mixtures.

Model F' introduced by Siggia and Nelson [Phys. Rev. B 15, 1427 (1977)] describes the critical dynamics of 3He-4He mixtures near the superfluid transition. Using the minimal subtraction scheme this model is renormalized within dynamical field theory. The dynamic zeta functions needed for the nonasymptotic flow properties are presented in two-loop order. The fixed points are discussed and the stable fixed points are identified. The transition to limiting models contained in model F' is shown analytically by performing the corresponding limits and numerically by calculating the nonlinear flow. These results are the basis for further experimental comparison of the transport coefficents in 3He-4He mixtures at higher concentrations including the tricritical point.

Integral equation study of an ideal Ising mixture.

We construct an integral equation scheme for magnetic binary mixtures of an ideal soft-core Ising fluid and a soft-sphere fluid by mapping the system onto an equivalent nonmagnetic ternary mixture. We apply the multicomponent Ornstein-Zernike equation together with a closure relation based on the soft mean spherical approximation and a field constraint for the Ising fluid component. Phase coexistence curves are calculated both by directly evaluating the chemical potentials via the bridge function, and by using a Maxwell-like construction which is derived in the text. Our results are compared to Monte Carlo data obtained earlier, and we find that the second method yields a much better agreement with the simulations.

XY-spin fluids in an external magnetic field: an integral equation approach.

We develop an integral equation approach to study anisotropic fluids with planar spins in the presence of an external field. As a result, the integral equation calculations for these systems appear to be no more difficult than those for ordinary isotropic liquids. The method presented is applied to the investigation of phase coexistence properties of ferromagnetic XY-spin fluids in a magnetic field. The soft mean spherical approximation is used for the closure relation connecting the orientationally dependent two-particle direct and total correlation functions. The Lovett-Mou-Buff-Wertheim and Born-Green-Yvon equations are employed to describe the one-particle orientational distribution. The phase diagrams are obtained in the whole range of varying the external field for a wide class of XY-spin fluid models with various ratios of the strengths of magnetic to nonmagnetic Yukawa-like interactions. The influence of changing the screening radii of the interaction potentials is also considered. Different types of the phase diagram topology are identified. They are characterized by the existence of critical, tricritical, critical end, and triple points related to transitions between gas, liquid, and para- and ferromagnetic states, accompanied by different external field dependencies of critical temperatures and densities corresponding to the gas-liquid and liquid-liquid transitions. As is demonstrated, the integral equation approach leads to accurate predictions of the complicated phase diagram behavior which coincide well with those evaluated by the cumbersome Gibbs ensemble simulation and multiple-histogram reweighting techniques.

Critical dynamics of diluted relaxational models coupled to a conserved density.

We consider the influence of quenched disorder on the relaxational critical dynamics of a system characterized by a nonconserved order parameter coupled to the diffusive dynamics of a conserved scalar density (model C). Disorder leads to model A critical dynamics in the asymptotics; however, it is the effective critical behavior that is often observed in experiments and in computer simulations, and this is described by the full set of dynamical equations of diluted model C. Indeed, different scenarios of effective critical behavior are predicted.

Phase behavior of Ising mixtures.

We present phase diagrams that were calculated both in mean-field theory and via Monte Carlo (MC) simulations for binary mixtures of a ferromagnetic Ising fluid and a nonmagnetic fluid (Ising mixtures) in the absence of an external field. We look at both the simple ideal Ising mixture, consisting of an ideal Ising fluid and a hard-sphere fluid, as well as at the general case with one component being a nonideal Ising fluid and the other a van der Waals fluid. It is shown that the mean-field phase diagram of the ideal Ising mixture in the limit of infinite pressure is identical to that of the Blume-Capel model for 3He-4He mixtures. The MC phase diagrams were obtained using the Gibbs ensemble, the cumulant intersection technique, and the multi-histogram re-weighting method, adapted to the semi-grand ensemble. The results are qualitatively compared with mean-field theory, and both types of tri-critical lines occurring there are verified in the computer simulations.

Critical dynamics of stochastic models with two conserved densities (model C' ).

We calculate the field-theoretic functions of the generalized dynamical model C(*') , where two conserved secondary densities are coupled to a nonconserved complex order parameter (OP), in two-loop order. A transformation to "orthogonalized" densities can be performed where only one secondary density with nontrivial static coupling to the OP exists while the second one remains Gaussian. The secondary densities remain dynamically coupled by the nondiagonal diffusion coefficent. General relations for the field-theoretic functions allow us to relate the asymptotic critical properties of model C(*') to the simpler model C(*) with only one conserved density coupled to the OP. The nonasymptotic properties, however, differ as can be seen from the flow of the dynamic parameters, which is presented for the case of a real OP with componets n=1,2,3 .

XY spin fluid in an external magnetic field.

A method of integral equations is developed to study anisotropic fluids with planar spins in an external field. As a result, the calculations for these systems appear to be no more difficult than those for ordinary homogeneous liquids. The approach proposed is applied to the ferromagnetic XY spin fluid in a magnetic field using a soft mean spherical closure and the Born-Green-Yvon equation. This provides an accurate reproduction of the complicated phase diagram behavior obtained by cumbersome Gibbs ensemble simulation and multiple histogram reweighting techniques.