Approximate master equations for the spatial public goods game.

The spatial public goods game has been used to examine factors that promote cooperation. Owing to the complexity of the dynamics of this game, previous studies on this model neglected analytical approaches and relied entirely on numerical calculations using the Monte Carlo (MC) simulations. In this paper, we present the approximate master equations (AMEs) for this model. We report that the results obtained by the AMEs are mostly qualitatively consistent with those obtained by the MC simulations. Furthermore, we show that it is possible to obtain phase boundaries analytically in certain parameter regions. In the region where the noise in strategy decisions is very large, the phase boundary can be obtained analytically by considering perturbations from the steady state of the voter model. In the noiseless region, discontinuous phase transitions occur because of the characteristics of the function that represents strategy updating. Our approach is useful for clarifying the details of the mechanisms that promote cooperation and can be easily applied to other group interaction models.

Improving thermal and mechanical properties of biomass-based polymers using structurally ordered polyesters from ricinoleic acid and 4-hydroxycinnamic acids.

Biomass-based copolymers with alternating ricinoleic acid and 4-hydroxycinnamic acid derivatives (p-coumaric acid, ferulic acid, and sinapinic acid) exhibit a repeating structure based on soft and hard segments, derived from ricinoleic and 4-hydroxycinnamic acids, respectively. To achieve this alternating sequence, copolymers were synthesised by the self-condensation of hetero-dimeric monomers derived by the pre-coupling of methyl ricinolate and 4-hydroxycinnamic acid. The glass transition temperature (T g) was observed to increase as the number of methoxy groups on the main chain increased; the T g values of poly(coumaric acid-alt-ricinoleic acid), poly(ferulic acid-alt-ricinoleic acid), and poly(sinapinic acid-alt-ricinoleic acid) are -15 °C, -4 °C, and 24 °C respectively, 58 °C, 69 °C, and 97 °C higher than that of poly(ricinoleic acid). The polymers were processed into highly flexible, visually transparent films. Among them, poly(sinapinic acid-alt-ricinoleic acid) bearing two methoxy groups on each cinnamoyl unit, is mechanically the strongest polymer, with an elastic modulus of 126.5 MPa and a tensile strength at break of 15.47 MPa.

Efficiency of prompt quarantine measures on a susceptible-infected-removed model in networks.

This study focuses on investigating the manner in which a prompt quarantine measure suppresses epidemics in networks. A simple and ideal quarantine measure is considered in which an individual is detected with a probability immediately after it becomes infected and the detected one and its neighbors are promptly isolated. The efficiency of this quarantine in suppressing a susceptible-infected-removed (SIR) model is tested in random graphs and uncorrelated scale-free networks. Monte Carlo simulations are used to show that the prompt quarantine measure outperforms random and acquaintance preventive vaccination schemes in terms of reducing the number of infected individuals. The epidemic threshold for the SIR model is analytically derived under the quarantine measure, and the theoretical findings indicate that prompt executions of quarantines are highly effective in containing epidemics. Even if infected individuals are detected with a very low probability, the SIR model under a prompt quarantine measure has finite epidemic thresholds in fat-tailed scale-free networks in which an infected individual can always cause an outbreak of a finite relative size without any measure. The numerical simulations also demonstrate that the present quarantine measure is effective in suppressing epidemics in real networks.

Outbreaks in susceptible-infected-removed epidemics with multiple seeds.

We study a susceptible-infected-removed (SIR) model with multiple seeds on a regular random graph. Many researchers have studied the epidemic threshold of epidemic models above which a global outbreak can occur, starting from an infinitesimal fraction of seeds. However, there have been few studies of epidemic models with finite fractions of seeds. The aim of this paper is to clarify what happens in phase transitions in such cases. The SIR model in networks exhibits two percolation transitions. We derive the percolation transition points for the SIR model with multiple seeds to show that as the infection rate increases epidemic clusters generated from each seed percolate before a single seed can induce a global outbreak.

Hierarchical scale-free network is fragile against random failure.

We investigate site percolation in a hierarchical scale-free network known as the Dorogovtsev-Goltsev-Mendes network. We use the generating function method to show that the percolation threshold is 1, i.e., the system is not in the percolating phase when the occupation probability is less than 1. The present result is contrasted to bond percolation in the same network of which the percolation threshold is zero. We also show that the percolation threshold of intentional attacks is 1. Our results suggest that this hierarchical scale-free network is very fragile against both random failure and intentional attacks. Such a structural defect is common in many hierarchical network models.

Criticality governed by the stable renormalization fixed point of the Ising model in the hierarchical small-world network.

We study the Ising model in a hierarchical small-world network by renormalization group analysis and find a phase transition between an ordered phase and a critical phase, which is driven by the coupling strength of the shortcut edges. Unlike ordinary phase transitions, which are related to unstable renormalization fixed points (FPs), the singularity in the ordered phase of the present model is governed by the FP that coincides with the stable FP of the ordered phase. The weak stability of the FP yields peculiar criticalities, including logarithmic behavior. On the other hand, the critical phase is related to a nontrivial FP, which depends on the coupling strength and is continuously connected to the ordered FP at the transition point. We show that this continuity indicates the existence of a finite correlation-length-like quantity inside the critical phase, which diverges upon approaching the transition point.

Generalized scaling theory for critical phenomena including essential singularities and infinite dimensionality.

We propose a generic scaling theory for critical phenomena that includes power-law and essential singularities in finite and infinite dimensional systems. In addition, we clarify its validity by analyzing the Potts model in a simple hierarchical network, where a saddle-node bifurcation of the renormalization-group fixed point governs the essential singularity.

Phase transition without global ordering in a hierarchical scale-free network.

We study the site-bond percolation on a hierarchical scale-free network, namely, the decorated (2,2)-flower, by using the renormalization group technique. The phase diagram essentially depends on the fraction of occupied sites. Surprisingly, when each site is unoccupied even with a small probability, the system permits neither the percolating phase nor the nonpercolating phase, but rather only critical phases. Although the order parameter always remains zero, a transition still exists between the critical phases that is characterized by the value of the fractal exponent, which measures the degree of criticality; the system changes from one critical state to another with the jump of the fractal exponent at the transition point. The phase boundary depends on the fraction of occupied sites. When the fraction of unoccupied sites exceeds a certain value, the transition line between the critical phases disappears, and a unique critical phase remains.

Direct carboxylation of arenes and halobenzenes with CO2 by the combined use of AlBr3 and R3SiCl.

The Lewis acid-mediated direct carboxylation of aromatic compounds with CO2 is efficiently promoted by the addition of silyl chlorides bearing three alkyl and/or aryl substituents in total on the silicon atom. Thus, toluene, xylenes, mesitylene, and some other alkylbenzenes are treated with a 1:1 mixture of AlBr3 and Ph3SiCl in neat substrates under CO2 pressure (3.0 MPa) at room temperature, to give the corresponding carboxylic acids in 60-97% yields, based on AlBr3. Polycyclic arenes, including naphthalene, phenanthrene, and biphenyl, are regioselectively carboxylated in 91-98% yields with the aid of 1 molar equiv of AlBr3 and Ph3SiCl in an appropriate solvent, chosen from benzene, chlorobenzene, and fluorobenzene. These solvents, as well as bromobenzene, resist carboxylation; however, they are also carboxylated in moderate yields when treated with a 1:5 mixture of AlBr3 and (i)PrSiCl at elevated temperatures. The FT-IR spectrum of a mixture prepared by exposing a suspension of AlBr3 and Ph3SiCl in cyclohexane to CO2 exhibits an absorption band around 1650 cm(-1), assigned to the C═O stretching vibration of a species consisting of CO2, AlBr3, and Ph3SiCl, which suggests that the silyl chlorides activate CO2 in cooperation with AlBr3. (1)H NMR analysis of unworked-up reaction mixtures reveals that the products merge as aluminum carboxylates. The mass balance concerning silicon indicates that the silyl chlorides are recycled during the reaction sequence. On the basis of these observations, a feasible mechanism is proposed for the present carboxylation.

Critical phase of bond percolation on growing networks.

The critical phase of bond percolation on the random growing tree is examined. It is shown that the root cluster grows with the system size N as N ψ and the mean number of clusters with size s per node follows a power function n s ∝ s(-τ) in the whole range of open bond probability p . The exponent τ and the fractal exponent ψ are also derived as a function of p and the degree exponent γ and are found to satisfy the scaling relation τ=1+ψ(-1). Numerical results with several network sizes are quite well fitted by a finite-size scaling for a wide range of p and γ, which gives a clear evidence for the existence of a critical phase.

Generating-function approach for bond percolation in hierarchical networks.

We study bond percolations on hierarchical scale-free networks with the open bond probability of the shortcuts p and that of the ordinary bonds p. The system has a critical phase in which the percolating probability P takes an intermediate value 0 < P < 1. Using generating function approach, we calculate the fractal exponent ψ of the root clusters to show that ψ varies continuously with p in the critical phase. We confirm numerically that the distribution n(s) of cluster size s in the critical phase obeys a power law n(s) ∝ s(-τ), where τ satisfies the scaling relation τ=1+ψ(-1). In addition the critical exponent ß(p) of the order parameter varies as p, from ß ≃ 0.164694 at p=0 to infinity at p=p(c)=5/32.

Ferromagnetic Ising spin systems on the growing random tree.

We analyze the ferromagnetic Ising model on a scale-free tree; the growing random tree model with the linear attachment kernel A(k) = k + alpha . We derive an estimate of the divergent temperature T(s) below which the zero-field susceptibility of the system diverges. Our result shows that T(s) is related to alpha as tanh(J/T(s)) = alpha/[2(alpha+1)] , where J is the ferromagnetic interaction. An analysis of exactly solvable limit for the model and numerical calculation supports the validity of this estimate.

Simple and effective 3D recognition of domoic acid using a molecularly imprinted polymer.

We have developed a simple and effective molecular imprinting technique to target compounds with flexible structure. Domoic acid (DA), an amnesic shellfish poison, was used as the target compound while many acidic compounds (mono-, di-, and tricarboxylic acids) were used as template molecules for molecularly imprinted polymers (MIPs). Evaluation of selective recognition abilities using liquid chromatography revealed that the highest selective recognition ability for DA was found when pentane-1,3,5-tricarboxylic acid (1,3,5-PeTA) was used as the template. Computer modeling studies of the DA structure suggested that the observed selective recognition depended on the structural changes in DA at the recognition site of the MIPs as well as spatial distance between the COOH groups in DA and 1,3,5-PeTA. Using the 1,3,5-PeTA-MIP, we could easily purify DA from blue mussel extracts by solid-phase extraction.

Selective separation of hydroxy polychlorinated biphenyls (HO-PCBs) by the structural recognition on the molecularly imprinted polymers: direct separation of the thyroid hormone active analogues from mixtures.

We developed novel separation media for hydroxy polychlorinated biphenyls (HO-PCBs) using the molecular imprinting techniques. The results of evaluation for the molecularly imprinted polymers (MIPs) by the liquid chromatography (LC) suggested that MIPs had selective separation ability for certain HO-PCB analogues. The results of the LC evaluations and molecular modeling indicated that the molecular volumes and pK(a) values of template molecules were related with the retention factor of HO-PCBs. Additionally, according to the detail evaluation toward the selective separation behaviors of MIPs, these HO-PCB analogues have low pK(a) values dependent on their chemical structures. In other words, the prepared MIPs had selective recognition ability against the analogues, which have an OH group on a phenyl carbon and two chlorine atoms on the both neighboring carbons of the carbon attached with the OH group. Moreover, these analogues may have a potential for thyroid hormone activities so that we attempted to separate these analogues directly from mixtures of HO-PCBs using a prepared MIP.

Ising model on the scale-free network with a Cayley-tree-like structure.

We derive an exact expression for the magnetization and the zero-field susceptibility of the Ising model on a random graph with degree distribution P(k) proportional, k-gamma and with a boundary consisting of leaves, that is, vertices whose degree is 1. The system has no magnetization at any finite temperature, and the susceptibility diverges below a certain temperature Ts depending on the exponent gamma. In particular, Ts reaches infinity for gamma

Chromatographic separation for domoic acid using a fragment imprinted polymer.

We prepared molecularly imprinted polymers for an amnesic shellfish poison, domoic acid. To prepare the polymer, we tested several commercial aromatic dicarboxylic compounds such as isomers of phthalic acid for templates of molecularly imprinted polymers. The highest selective recognition ability of the polymer for domoic acid in the tested compounds was found when o-phthalic acid was used as the template. The ability was due to the acidity of the carboxylic acids in the domoic acid and the similarity of the shape around the carboxylic acids of domoic acid and the templates. The effective chromatographic separation of domoic acid in the extract from blue mussels was achieved with a LC column packed with the fragment imprinted polymer using o-phthalic acid as the template. This polymer can be utilized for a clean up procedure of domoic acid in toxic shellfish.