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As a universal concept in nonlinear science, synchronization has been broadly interested and extensively studied over the past decades. Whereas numerical and theoretical studies have unveiled abundant synchronization phenomena in coupled oscillators, few of them have been replicated in experiments, due to the sensitivity the synchronization dynamics to the noise perturbations and parameter mismatches. In the work by Jing Zhang, et al., the authors designed a new experimental [Detail] ...
Agent-based modeling and controlled human experiments serve as two fundamental research methods in the field of econophysics. Agent-based modeling has been in development for over 20 years, but how to design virtual agents with high levels of human-like “intelligence” remains a challenge. On the other hand, experimental econophysics is an emerging field; however, there is a lack of experience and paradigms related to the field. Here, we review some of the most recent research results obtained through the use of these two methods concerning financial problems such as chaos, leverage, and business cycles. We also review the principles behind assessments of agents’ intelligence levels, and some relevant designs for human experiments. The main theme of this review is to show that by combining theory, agent-based modeling, and controlled human experiments, one can garner more reliable and credible results on account of a better verification of theory; accordingly, this way, a wider range of economic and financial problems and phenomena can be studied.
Mutually interacting components form complex systems and these components usually have longrange cross-correlated outputs. Using wavelet leaders, we propose a method for characterizing the joint multifractal nature of these long-range cross correlations; we call this method joint multifractal analysis based on wavelet leaders (MF-X-WL). We test the validity of the MF-X-WL method by performing extensive numerical experiments on dual binomial measures with multifractal cross correlations and bivariate fractional Brownian motions (bFBMs) with monofractal cross correlations. Both experiments indicate that MF-X-WL is capable of detecting cross correlations in synthetic data with acceptable estimating errors. We also apply the MF-X-WL method to pairs of series from financial markets (returns and volatilities) and online worlds (online numbers of different genders and different societies) and determine intriguing joint multifractal behavior.
Agent-based modeling is a powerful simulation technique to understand the collective behavior and microscopic interaction in complex financial systems. Recently, the concept for determining the key parameters of agent-based models from empirical data instead of setting them artificially was suggested. We first review several agent-based models and the new approaches to determine the key model parameters from historical market data. Based on the agents’ behaviors with heterogeneous personal preferences and interactions, these models are successful in explaining the microscopic origination of the temporal and spatial correlations of financial markets. We then present a novel paradigm combining big-data analysis with agent-based modeling. Specifically, from internet query and stock market data, we extract the information driving forces and develop an agent-based model to simulate the dynamic behaviors of complex financial systems.
We ascertain the modularity-like objective function whose optimization is equivalent to the maximum likelihood in annotated networks. We demonstrate that the modularity-like objective function is a linear combination of modularity and conditional entropy. In contrast with statistical inference methods, in our method, the influence of the metadata is adjustable; when its influence is strong enough, the metadata can be recovered. Conversely, when it is weak, the detection may correspond to another partition. Between the two, there is a transition. This paper provides a concept for expanding the scope of modularity methods.
Morphological transformations of amphiphilic AB diblock copolymers in mixtures of a common solvent (S1) and a selective solvent (S2) for the B block are studied using the simulated annealing method. We focus on the morphological transformation depending on the fraction of the selective solvent CS2, the concentration of the polymer Cp, and the polymer–solvent interactions εij (i = A, B; j = S1, S2). Morphology diagrams are constructed as functions of Cp, CS2, and/or εAS2. The copolymer morphological sequence from dissolved→sphere→rod→ring/cage→vesicle is obtained upon increasing CS2 at a fixed Cp. This morphology sequence is consistent with previous experimental observations. It is found that the selectivity of the selective solvent affects the self-assembled microstructure significantly. In particular, when the interaction εBS2 is negative, aggregates of stacked lamellae dominate the diagram. The mechanisms of aggregate transformation and the formation of stacked lamellar aggregates are discussed by analyzing variations of the average contact numbers of the A or B monomers with monomers and with molecules of the two types of solvent, as well as the mean square end-to-end distances of chains. It is found that the basic morphological sequence of spheres to rods to vesicles and the stacked lamellar aggregates result from competition between the interfacial energy and the chain conformational entropy. Analysis of the vesicle structure reveals that the vesicle size increases with increasing Cp or with decreasing CS2, but remains almost unchanged with variations in εAS2.
We study the scaling and universal behavior of temperature-driven first-order phase transitions in scalar models. These transitions are found to exhibit rich phenomena, though they are controlled by a single complex-conjugate pair of imaginary fixed points of φ3 theory. Scaling theories and renormalization group theories are developed to account for the phenomena, and three universality classes with their own hysteresis exponents are found: a field-like thermal class, a partly thermal class, and a purely thermal class, designated, respectively, as Thermal Classes I, II, and III. The first two classes arise from the opposite limits of the scaling forms proposed and may cross over to each other depending on the temperature sweep rate. They are both described by a massless model and a purely massive model, both of which are equivalent and are derived from φ3 theory via symmetry. Thermal Class III characterizes the cooling transitions in the absence of applied external fields and is described by purely thermal models, which include cases in which the order parameters possess different symmetries and thus exhibit different universality classes. For the purely thermal models whose free energies contain odd-symmetry terms, Thermal Class III emerges only at the mean-field level and is identical to Thermal Class II. Fluctuations change the model into the other two models. Using the extant three- and twoloop results for the static and dynamic exponents for the Yang–Lee edge singularity, respectively, which falls into the same universality class as φ3 theory, we estimate the thermal hysteresis exponents of the various classes to the same precision. Comparisons with numerical results and experiments are briefly discussed.
Revealing how a biological network is organized to realize its function is one of the main topics in systems biology. The functional backbone network, defined as the primary structure of the biological network, is of great importance in maintaining the main function of the biological network. We propose a new algorithm, the tinker algorithm, to determine this core structure and apply it in the cell-cycle system. With this algorithm, the backbone network of the cell-cycle network can be determined accurately and efficiently in various models such as the Boolean model, stochastic model, and ordinary differential equation model. Results show that our algorithm is more efficient than that used in the previous research. We hope this method can be put into practical use in relevant future studies.
Coupled metronomes serve as a paradigmatic model for exploring the collective behaviors of complex dynamical systems, as well as a classical setup for classroom demonstrations of synchronization phenomena. Whereas previous studies of metronome synchronization have been concentrating on symmetric coupling schemes, here we consider the asymmetric case by adopting the scheme of layered metronomes. Specifically, we place two metronomes on each layer, and couple two layers by placing one on top of the other. By varying the initial conditions of the metronomes and adjusting the friction between the two layers, a variety of synchronous patterns are observed in experiment, including the splay synchronization (SS) state, the generalized splay synchronization (GSS) state, the anti-phase synchronization (APS) state, the in-phase delay synchronization (IPDS) state, and the in-phase synchronization (IPS) state. In particular, the IPDS state, in which the metronomes on each layer are synchronized in phase but are of a constant phase delay to metronomes on the other layer, is observed for the first time. In addition, a new technique based on audio signals is proposed for pattern detection, which is more convenient and easier to apply than the existing acquisition techniques. Furthermore, a theoretical model is developed to explain the experimental observations, and is employed to explore the dynamical properties of the patterns, including the basin distributions and the pattern transitions. Our study sheds new lights on the collective behaviors of coupled metronomes, and the developed setup can be used in the classroom for demonstration purposes.
On the basis of the transport features and experimental phenomena observed in studies of molecular motors, we propose a double-temperature ratchet model of coupled motors to reveal the dynamical mechanism of cooperative transport of motors with two heads, where the interactions and asynchrony between two motor heads are taken into account. We investigate the collective unidirectional transport of coupled system and find that the direction of motion can be reversed under certain conditions. Reverse motion can be achieved by modulating the coupling strength, coupling free length, and asymmetric coefficient of the periodic potential, which is understood in terms of the effective potential theory. The dependence of the directed current on various parameters is studied systematically. Directed ransport of coupled Brownian motors can be manipulated and optimized by adjusting the pulsation period or the phase shift of the pulsation temperature.
The transport of a walker in rocking feedback-controlled ratchets is investigated. The walker consists of two coupled “feet” that allow the interchange of the order of particles while the walker moves. In the underdamped case, the deterministic dynamics of the walker in a tilted asymmetric ratchet with an external periodic force is considered. It is found that delayed feedback ratchets with a switching-on and-off dependence of the states of the system can lead to absolute negative mobility. In such a novel phenomenon, the particles move against the bias. Moreover, the walker can acquire a series of resonant steps for different values of the current. It is interesting to find that the resonant currents of the walker are induced by the phase locked motion that corresponds to the synchronization of the motion with the change in the frequency of the external driving. These resonant steps can be well predicted in terms of time-space symmetry analysis, which is in good agreement with dynamics simulations. The transport performances can be optimized and controlled by suitably adjusting the parameters of the delayed-feedback ratchets.
The process by which a kinesin motor couples its ATPase activity with concerted mechanical handover-hand steps is a foremost topic of molecular motor physics. Two major routes toward elucidating kinesin mechanisms are the motility performance characterization of velocity and run length, and single-molecular state detection experiments. However, these two sets of experimental approaches are largely uncoupled to date. Here, we introduce an integrative motility state analysis based on a theorized kinetic graph theory for kinesin, which, on one hand, is validated by a wealth of accumulated motility data, and, on the other hand, allows for rigorous quantification of state occurrences and chemomechanical cycling probabilities. An interesting linear scaling for kinesin motility performance across species is discussed as well. An integrative kinetic graph theory analysis provides a powerful tool to bridge motility and state characterization experiments, so as to forge a unified effort for the elucidation of the working mechanisms of molecular motors.
The collective behaviors of populations of coupled oscillators have attracted significant attention in recent years. In this paper, an order parameter approach is proposed to study the low-dimensional dynamical mechanism of collective synchronizations, by adopting the star-topology of coupled oscillators as a prototype system. The order parameter equation of star-linked phase oscillators can be obtained in terms of the Watanabe–Strogatz transformation, Ott–Antonsen ansatz, and the ensemble order parameter approach. Different solutions of the order parameter equation correspond to the diverse collective states, and different bifurcations reveal various transitions among these collective states. The properties of various transitions in the star-network model are revealed by using tools of nonlinear dynamics such as time reversibility analysis and linear stability analysis.
An innovative theoretical framework for stochastic dynamics based on the decomposition of a stochastic differential equation (SDE) into a dissipative component, a detailed-balance-breaking component, and a dual-role potential landscape has been developed, which has fruitful applications in physics, engineering, chemistry, and biology. It introduces the A-type stochastic interpretation of the SDE beyond the traditional Ito or Stratonovich interpretation or even the α-type interpretation for multidimensional systems. The potential landscape serves as a Hamiltonian-like function in nonequilibrium processes without detailed balance, which extends this important concept from equilibrium statistical physics to the nonequilibrium region. A question on the uniqueness of the SDE decomposition was recently raised. Our review of both the mathematical and physical aspects shows that uniqueness is guaranteed. The demonstration leads to a better understanding of the robustness of the novel framework. In addition, we discuss related issues including the limitations of an approach to obtaining the potential function from a steady-state distribution.