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Many works confirm the anti-correlations between the default mode network (DMN) and the central-executive network (CEN) in the brain. However, the switching mechanism of the DMN itself is still lack of understanding from the viewpoint of neural network dynamics. Here we simulate the DMN with the Hindmarsh-Rose (HR) neuron model on the small-world network. We model the state of oscillator death and oscillatory firing as the inhibitory state and the activated state, respectively. We find that the DMN can regenerate from the inhibitory state when the input current of only one synapse is cut off at criticality.

Critical physical systems with large numbers of molecules can show universal and scaling behaviors. It is of interest to know whether human societies with large numbers of people can show the same behaviors. Here, we use network theory to analyze Chinese history in periods 209 BCE–23 CE and 515–618 CE) related to the Western Han–Xin Dynasty and the late Northern Wei–Sui Dynasty, respectively. Two persons are connected when they appear in the same historical event. We find that the historical networks from two periods separated about 500 years have interesting universal and scaling behaviors, and they are small-world networks; their average cluster coefficients as a function of degree are similar to the network of movie stars. In the historical networks, the persons with larger degrees prefer to connect with persons with a small degree; however, in the network of movie stars, the persons with larger degrees prefer to connect with persons with large degrees. We also find an interesting similar mechanism for the decline or collapse of historical Chinese dynasties. The collapses of the Xin dynasty (9–23 CE) and the Sui dynasty (581–618 CE) were initiated from their arrogant attitude toward neighboring states.

The objective of this article is to use a recent developed scheme to simulate reaction-diffusion-chemotaxis equations. The solution gradient required for an accurate discretization is computed directly as an additional variable rather than interpolated from solution values around neighboring computational nodes. To achieve this goal, a supplementary equation and its associated control volume are introduced to retain a compact and accurate discretization. Scheme essentials are exposed by the numerical analysis on two-dimensional chemotaxis problems to reveal its formal accuracy. Due to its highly comprehensible and practical features, this formulation can be easily extended to solve problems for other two-dimensional rectangular grid systems. One- and two-dimensional problems are solved to verify its simulation accuracy and to study the possible formation of bacteria bands. We further perform the linearization technique to the reaction term to increase the stability of the current scheme. From the numerical analysis and computational results, it is found that the present formulation is a useful tool to solve reaction-diffusion-chemotaxis equations.

Passenger flight delays, causing much disorder of air traffics, economic losses of airlines, and downgrading the travel quality of millions of people, are ubiquitous phenomena in airports all over the world. Investigation based on real data from the view point of statistical physics is rarely seen. In the present work, big data of such delay records over 20 years accumulated by Bureau of Transportation Statistics in the United States are downloaded and purified by us. We account the departure and arrival records of such flights between certain pair of airports as time series, and rectify them by defining dimensionless velocity of the flights. Furthermore, we find the varying cross-correlations among such time series with the approach of time delay stability, and describe the correlations with temporal networks for correlation states. Deterministic correspondences between the average degrees of temporal networks and delay ratios of passenger flights are verified in different sampling groups of flights with the longest records. The mean degrees of correlation networks usually emerge a peak prior to that of high delay ratios, which serves an indicator for the precaution to serious flight delays.

In this work, the interaction between spherical magnetic nanoparticles and amyloid fibrils as well as formation of self-assembled structures during drying process of such colloidal system were investigated. The final self assembled structures were observed experimentally by atomic force microscopy, scanning electron microscopy and polarizing microscopy. Our results show that the colloidal composites are self-assembled into flower-like patterns after the evaporation of liquid drop. These observations show that a large scale and well-organized multi-branched aggregates are formed during the process of drying. Moreover, observation by polarizing microscopy under crossed polarizers showed birefringence.

Noise has been recognized as an important factor in a range of physical and informational systems, including the elementary physics of life, such as cellular developments and functions. Here we use a stochastic differential equation to study the effects of noise on a typical system of antagonist actors, the Schlogl model. The phenomena of noise-induced bifurcation are observed. Detailed analysis demonstrates that the region revealing bistability can be modulated by the intensity of noise. This suggests that an external noise source can serve as an engineering tool for controlling antagonist inter-reacting systems in general, and in particular, for manipulating biochemical pathways.

We used the Hindmarsh–Rose (HR) model (Hindmarsh and Rose, 1984) to study the effect of time delay on the transition of firing behaviors and desynchronization in neural networks. As time delay is increased, neural networks exhibit diversity of firing behaviors, including regular spiking or bursting and firing patterns transitions (FPTs). Meanwhile, the desynchronization of firing and unstable bursting with decreasing amplitude in neural system, are also increasingly enhanced with the increase of time delay. Furthermore, we also studied the effect of coupling strength and network randomness on these phenomena. Our results imply that time delays can induce transition and desynchronization of firing behaviors in neural networks. These findings provide new insight into the role of time delay in the firing activities of neural networks, and can help to better understand the firing phenomena in complex systems of neural networks. A possible mechanism in brain that can cause the increase of time delay is discussed.

We investigate an integrate-and-fire model of an electronic relaxation oscillator, which can be described by the discontinuous and non-invertible composition of two mapping functions f 1 and f 2 , with f 1 being dissipative. Depending on a control parameter d , f 2 can be conservative (for d = d c = 1 ) or dissipative (for d > d c ). We find a kind of crisis, which is induced by the escape from a riddled-like attraction basin sea in the phase space. The averaged crisis transient lifetime ( 〈 τ 〉 ), the relative measure of the fat fractal forbidden network ( η ), and the measure of the escaping hole ( Δ ) show clear scaling behaviors: 〈 τ 〉 ∝ ( d − d c ) − γ , η ∝ ( d − d c ) σ , and Δ ∝ ( d − d c ) α . Extending an argument by Jiang et al. (2004), we derive γ = σ + α , which agrees well with numerical simulation data.

We have probed small molecule compound CID 9998128 as a potential multitarget drug for the Alzheimer’s disease (AD) using in silico and in vitro experiments. By all-atom simulation and molecular mechanics Poisson–Boltzmann surface area (MM-PBSA) method, we have demonstrated that this compound strongly binds to both amyloid β42 (Aβ42) fibrils and β-secretase, and the van der Waals interaction dominates over the electrostatic interaction in binding affinity. A detailed analysis at the atomic level revealed that indazole in CID 99998128 structure made a major contribution to instability of all studied complexes. In vitro experiments have shown that CID 9998128 inhibits the Aβ42 amyloid fibrillization and is capable to clear Aβ42 fibrils. Moreover, the compound dose-dependently decreases β-site amyloid precursor protein cleaving enzyme (BACE-1) activity with EC50 value in micromolar range. Thus, our study has revealed that CID 9998128 is a good candidate for AD treatment through preventing production of Aβ pe...

Local interneurons (LNs) in the Drosophila olfactory system exhibit neuronal diversity and variability, yet it is still unknown how these features impact information encoding capacity and reliability in a complex LN network. We employed two strategies to construct a diverse excitatory-inhibitory neural network beginning with a ring network structure and then introduced distinct types of inhibitory interneurons and circuit variability to the simulated network. The continuity of activity within the node ensemble (oscillation pattern) was used as a readout to describe the temporal dynamics of network activity. We found that inhibitory interneurons enhance the encoding capacity by protecting the network from extremely short activation periods when the network wiring complexity is very high. In addition, distinct types of interneurons have differential effects on encoding capacity and reliability. Circuit variability may enhance the encoding reliability, with or without compromising encoding capacity. Therefore, we have described how circuit variability of interneurons may interact with excitatory-inhibitory diversity to enhance the encoding capacity and distinguishability of neural networks. In this work, we evaluate the effects of different types and degrees of connection diversity on a ring model, which may simulate interneuron networks in the Drosophila olfactory system or other biological systems.

The second derivative techniques, which are used in spectroscopy to reveal poorly resolved bands, were adjusted for processing of calorimetric melting profiles of DNAs from higher organisms. The procedure strongly increased the sensitivity of the profiles to various distortions of the double helix and allowed clear resolution of the constituents arising from the melting of satellite DNA (minor narrow peaks) and the rest of genome (dominant wide peak). As an illustration of the advantages of the procedure, selective suppression of narrow satellite peaks was demonstrated as DNA was chemically modified by the antitumor drug cisplatin. As the cisplatin/nucleotide molar ratio increased from 0.001 to 0.05, the peaks decreased in height until they fully disappeared. The influence of cisplatin on the shape of the main peak, which corresponds to the rest of the genome, was much weaker. Transplatin, an ineffective analog of cisplatin, suppressed all constituents of the melting profile without selectivity.

We consider an evolution model, in which the mutation rates depend on the structure of population: the mutation rates from lower populated sequences to higher populated sequences are reduced. We have applied the Hamilton–Jacobi equation method to solve the model and calculate the mean fitness. We have found that the modulated mutation rates, directed to increase the mean fitness.

Selection in a time-periodic environment is modeled via the continuous-time two-player replicator dynamics, which for symmetric pay-offs reduces to the Fisher equation of mathematical genetics. For a sufficiently rapid and cyclic [fine-grained] environment, the time-averaged population frequencies are shown to obey a replicator dynamics with a non-linear fitness that is induced by environmental changes. The non-linear terms in the fitness emerge due to populations tracking their time-dependent environment. These terms can induce a stable polymorphism, though they do not spoil the polymorphism that exists already without them. In this sense polymorphic populations are more robust with respect to their time-dependent environments. The overall fitness of the problem is still given by its time-averaged value, but the emergence of polymorphism during genetic selection can be accompanied by decreasing mean fitness of the population. The impact of the uncovered polymorphism scenario on the models of diversity is examplified via the rock-paper-scissors dynamics, and also via the prisoner's dilemma in a time-periodic environment., 16 pages, 10 figures

There are three possible classifications of the dimer weights on the bonds of the checkerboard lattice and they are denoted as checkerboard $A$, $B$, and $C$ lattices [Phys. Rev. E 91, 062139 (2015)]. The dimer model on the checkerboard $B$ and $C$ lattices has much richer critical behavior compared to the dimer model on the checkerboard $A$ lattice. In this paper we study in full detail the dimer model on the checkerboard $B$ lattice. The dimer model on the checkerboard $B$ lattice has two types of critical behavior. In one limit this model is the anisotropic dimer model on rectangular lattice with algebraic decay of correlators and in another limit it is the anisotropic generalized Kasteleyn model with radically different critical behavior. We analyze the partition function of the dimer model on a $2M\ifmmode\times\else\texttimes\fi{}2N$ checkerboard $B$ lattice wrapped on a torus. We find very unusual behavior of the partition function zeros and the specific heat of the dimer model. Remarkably, the partition function zeros of finite-size systems can have very interesting structures, made of rings, concentric circles, radial line segments, or even arabesque structures. We find out that the number of the specific heat peaks and the number of circles of the partition function zeros increases with the system size. The lattice anisotropy of the model has strong effects on the behavior of the specific heat, dominating the relation between the correlation length exponent $\ensuremath{\nu}$ and the shift exponent $\ensuremath{\lambda}$, and $\ensuremath{\lambda}$ is generally unequal to $1/\ensuremath{\nu}$ ($\ensuremath{\lambda}\ensuremath{\ne}1/\ensuremath{\nu}$).

In some systems, the connecting probability (and thus the percolation process) between two sites depends on the geometric distance between them. To understand such process, we propose gravitationally correlated percolation models for link-adding networks on the two-dimensional lattice $G$ with two strategies $S_{\rm max}$ and $S_{\rm min}$, to add a link $l_{i,j}$ to connect site $i$ and site $j$ with mass $m_i$ and $m_j$, respectively; $m_i$ and $m_j$ are sizes of the clusters which contain site $i$ and site $j$, respectively. The probability to add the link $l_{i,j}$ is related to the generalized gravity $g_{ij} \equiv m_i m_j/r_{ij}^d$, where $r_{ij}$ is the geometric distance between $i$ and $j$, and $d$ is an adjustable decaying exponent. In the beginning of the simulation, all sites of $G$ are occupied and there is no link. In the simulation process, two inter-cluster links $l_{i,j}$ and $l_{k,n}$ are randomly chosen and the generalized gravities $g_{ij}$ and $g_{kn}$ are computed. In the strategy $S_{\rm max}$, the link with larger generalized gravity is added. In the strategy $S_{\rm min}$, the link with smaller generalized gravity is added, which include percolation on the Erd\H os-R\'enyi random graph and the Achlioptas process of explosive percolation as the limiting cases, $d \to \infty$ and $d \to 0$, respectively. Adjustable strategies facilitate or inhibit the network percolation in a generic view. We calculate percolation thresholds $T_c$ and critical exponents $\beta$ by numerical simulations. We also obtain various finite-size scaling functions for the node fractions in percolating clusters or arrival of saturation length with different intervening strategies., Comment: 26 pages, 8 figures, Chinese Journal of Physics, accepted for publication

Polymers are important macromolecules in many physical, chemical, biological and industrial problems. Studies on simple lattice polymer models are very helpful for understanding behaviors of polymers. We develop an efficient algorithm for computing exact partition functions of lattice polymer models, and we use this algorithm and personal computers to obtain exact partition functions of the interacting self-avoiding walks with N monomers on the simple cubic lattice up to N = 28 and on the square lattice up to N = 40 . Our algorithm can be extended to study other lattice polymer models, such as the HP model for protein folding and the charged HP model for protein aggregation. It also provides references for checking accuracy of numerical partition functions obtained by simulations.

Flight delays have negative impacts on passengers, carriers, and airports. To reduce these unpopular influence, we need to find the statistical law of the collective behavior of passenger flights. We use a mean-field approach to analyze big data listing the departure and arrival records of all American domestic passenger flights in 20 years. We treat passenger flights as particle gases and define their dimensionless velocity, quasi-thermodynamic quantities — pressure, volume, temperature, and mole number, respectively. By introducing phenomenological parameters a and b to set up van der Waals-like state equations, we erect a universal gaseous constant R for actually operated passenger flights, their counterparts on schedule, and ”delayor gases” defined as the difference between them. We find that the attractive coefficient of ”delayor gases” positively correlates with the average delay per flight on airports. Rescaling state equations for passenger flights across all 20 years, we find a universal function. This is a significant step toward understanding flight delays and dealing with temporal big data with the tools of statistical physics.

It is widely believed that the brains of human beings work at or near the state of self-organized criticality (SOC). In the present work, we investigate two-dimensional small-world neural networks (2D SWNN) with Bak–Sneppen (BS)-type neurons as their nodes. By taking threshold firing and refractory period as the key features of neurons in the simulations, a few power laws are obtained for suitable range of parameters. The SOC characterized by the power-law distribution of avalanche sizes as well as 1 ∕ f noise emerges in the present model. Moreover, a set of scaling relations are found to exhibit criticality. The exponent for the power spectrum of all return time is α = 0 . 71 , which is comparable with what were found in medical experiments.