Semiflexible polymer solutions. I. Phase behavior and single-chain statistics

We study the thermodynamics and single-chain statistics of wormlike polymer solutions with Maier–Saupe-type interactions using self-consistent-field (SCF) theory. The SCF equations are derived using a systematic field-theoretical approach which yields the SCF equations as the lowest order approximation, but permits fluctuation corrections to be incorporated. We solve the SCF equations using the spheroidal functions, which provides a nonperturbative description of the thermodynamics and single-chain statistics in the nematic state for arbitrary degrees of nematic order. Several types of phase diagrams are predicted, with an emphasis on the limit of metastability (spinodal) associated with each phase. The shape and location of these spinodals suggest interesting scenarios for the phase transition kinetics. A large but finite persistence length is shown to significantly decrease the isotropic–nematic transition temperature relative to that for rigid rods. In the nematic state, the mean-square end-to-end distance in the parallel and perpendicular directions are governed by two separate correlation lengths. An exact relationship between these correlation lengths and the eigenvalues of the spheroidal functions is provided, which reproduces the analytical expressions predicted from earlier studies in the limit of large nematic strength. The dominant contribution to the single-chain thermodynamics is shown to arise from small amplitude undulations in the directions perpendicular to the nematic direction; the presence of hairpins, though crucial for determining the dimensions of the polymer, has insignificant consequences on the single-chain thermodynamics

End-to-end distance vector distribution with fixed end orientations for the wormlike chain model

We find exact expressions for the end-to-end distance vector distribution function with fixed end orientations for the wormlike chain model. This function in Fourier-Laplace space adopts the form of infinite continued fractions, which emerges upon exploiting the hierarchical structure of the moment-based expansion. Our results are used to calculate the root-mean-square end displacement in a given direction for a chain with both end orientations fixed. We find that the crossover from rigid to flexible chains is marked by the root-mean-square end displacement slowly losing its angular dependence as the coupling between chain conformation and end orientation wanes. However, the coupling remains strong even for relatively flexible chains, suggesting that the end orientation strongly influences chain conformation for chains that are several persistence lengths long. We then show the behavior of the distribution function by a density plot of the probability as a function of the end-to-end distance vector for a wormlike chain in two dimensions with one end pointed in a fixed direction and the other end free (in its orientation). As we progress from high to low rigidity, the distribution function shifts from being peaked at a location near the full contour length of the chain in the forward direction, corresponding to a straight configuration, to being peaked near zero end separation, as in the Gaussian limit. The function exhibits double peaks in the crossover between these limiting behaviors

Semiflexible Polymer Confined to a Spherical Surface

We develop a formalism for describing the kinematics of a wormlike chain confined to the surface of a sphere that simultaneously satisfies the spherical confinement and the inextensibility of the chain contour. We use this formalism to study the statistical behavior of the wormlike chain on a spherical surface. In particular, we provide an exact, closed-form expression for the mean square end-to-end distance that is valid for any value of chain length L, persistence length lp, and sphere radius R. We predict two qualitatively different behaviors for a long polymer depending on the ratio R/lp. For R/lp>4, the mean square end-to-end distance increases monotonically with the chain length, whereas for R/lp<4, a damped oscillatory behavior is predicted

Dynamically generated cyclic dominance in spatial prisoner's dilemma games

We have studied the impact of time-dependent learning capacities of players in the framework of spatial prisoner's dilemma game. In our model, this capacity of players may decrease or increase in time after strategy adoption according to a step-like function. We investigated both possibilities separately and observed significantly different mechanisms that form the stationary pattern of the system. The time decreasing learning activity helps cooperator domains to recover the possible intrude of defectors hence supports cooperation. In the other case the temporary restrained learning activity generates a cyclic dominance between defector and cooperator strategies, which helps to maintain the diversity of strategies via propagating waves. The results are robust and remain valid by changing payoff values, interaction graphs or functions characterizing time-dependence of learning activity. Our observations suggest that dynamically generated mechanisms may offer alternative ways to keep cooperators alive even at very larger temptation to defect.Comment: 7 pages, 6 figures, accepted for publication in Physical Review

Many-body Green's function theory of ferromagnetic Heisenberg systems with single-ion anisotropies in more than one direction

The behaviour of ferromagnetic systems with single-ion anisotropies in more than one direction is investigated with many-body Green's function theory generalizing earlier work with uniaxial anisotropies only. It turns out to be of advantage to construct Green's functions in terms of the spin operators S^x, S^y and S^z, instead of the commonly used S^+,S^- and S^z operators. The exchange energy terms are decoupled by RPA and the single-ion anisotropy terms by a generalization of the Anderson-Callen decoupling. We stress that in the derivation of the formalism none of the three spatial axes is special, so that one is always able to select a reference direction along which a magnetization component is not zero. Analytical expressions are obtained for all three components of the magnetization and the expectation values , and for any spin quantum number S. The formalism considers both in-plane and out-of-plane anisotropies. Numerical calculations illustrate the behaviour of the magnetization for 3-dimensional and 2-dimensional systems for various parameters. In the 2-dimensional case, the magnetic dipole-dipole coupling is included, and a comparison is made between in-plane and out-of-plane anisotropies.Comment: 16 pages, 8 figures, missing figures adde

Composite Correlation Quantization for Efficient Multimodal Retrieval

Efficient similarity retrieval from large-scale multimodal database is pervasive in modern search engines and social networks. To support queries across content modalities, the system should enable cross-modal correlation and computation-efficient indexing. While hashing methods have shown great potential in achieving this goal, current attempts generally fail to learn isomorphic hash codes in a seamless scheme, that is, they embed multiple modalities in a continuous isomorphic space and separately threshold embeddings into binary codes, which incurs substantial loss of retrieval accuracy. In this paper, we approach seamless multimodal hashing by proposing a novel Composite Correlation Quantization (CCQ) model. Specifically, CCQ jointly finds correlation-maximal mappings that transform different modalities into isomorphic latent space, and learns composite quantizers that convert the isomorphic latent features into compact binary codes. An optimization framework is devised to preserve both intra-modal similarity and inter-modal correlation through minimizing both reconstruction and quantization errors, which can be trained from both paired and partially paired data in linear time. A comprehensive set of experiments clearly show the superior effectiveness and efficiency of CCQ against the state of the art hashing methods for both unimodal and cross-modal retrieval

Aspiring to the fittest and promotion of cooperation in the prisoner's dilemma game

Strategy changes are an essential part of evolutionary games. Here we introduce a simple rule that, depending on the value of a single parameter $w$, influences the selection of players that are considered as potential sources of the new strategy. For positive $w$ players with high payoffs will be considered more likely, while for negative $w$ the opposite holds. Setting $w$ equal to zero returns the frequently adopted random selection of the opponent. We find that increasing the probability of adopting the strategy from the fittest player within reach, i.e. setting $w$ positive, promotes the evolution of cooperation. The robustness of this observation is tested against different levels of uncertainty in the strategy adoption process and for different interaction network. Since the evolution to widespread defection is tightly associated with cooperators having a lower fitness than defectors, the fact that positive values of $w$ facilitate cooperation is quite surprising. We show that the results can be explained by means of a negative feedback effect that increases the vulnerability of defectors although initially increasing their survivability. Moreover, we demonstrate that the introduction of $w$ effectively alters the interaction network and thus also the impact of uncertainty by strategy adoptions on the evolution of cooperation.Comment: 7 two-column pages, 5 figures; accepted for publication in Physical Review

Genetic and clinical assessment of 2009 pandemic influenza in southern China

Introduction: South China has a proven role in the global epidemiology of previous influenza outbreaks due to its dual seasonal pattern. We present the virologic, genetic and clinical characterization of pandemic H1N1 influenza infection (pH1N1) in Shantou and Nanchang, cities in southern China, during the second wave of the 2009-2010 pandemic. Methodology: Nasopharyngeal swabs were collected from 165 individuals with influenza-like illness (ILI) who presented to the hospitals in Shantou and Nanchang. Laboratory diagnosis and characterization was performed by real-time PCR, virus isolation in embryonated chicken eggs, and sequencing. Results: pH1N1 activity was sustained in three different temporal patterns throughout the study period. The overall positivity rate of pH1N1 was 50% with major distribution among young adults between the ages of 13 and 30 years. High fever, cough, expectoration, chest pain, myalgia, nasal discharge and efficient viral replication were observed as major clinical markers whereas a substantial number of afebrile cases (17%) was also observed. Rate of hospitalization and disease severity (39%) and recovery (100%) were also high within the region. Furthermore, severe complications were likely to develop in young adults upon pH1N1 infection. Genetic characterization of the HA and NA genes of pH1N1 strains exhibited homogenous spread of pH1N1 strains with 99% identity with prototypic strains; however, minor unique mutations were also observed in the HA gene. Conclusion: The study illustrates the detailed characteristics of 2009 influenza pandemic in southern parts of China that might help to strategize preparedness for future pandemics and subsequent influenza seasons.</br