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Investigation of passenger flight delays with statistical physics has been less focused by previous researchers. We consider the flights as special particles, and take quasi-thermodynamic variables to describe their van der Waals - like gaseous equations. Improved from our former model, we download data of 6 more years (2015–2020) with 20 original ones (1995–2014), and redefine pressure as two average number of departure/arrival flights per airport in a given day. Therefore, we enact an empirical gaseous constant R , and get a new kind of “delayor gases” as the daily average delays per flight at all airports. The approach could be applied to passenger flights of any other countries and different complex systems.

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.

The scale-free features widely concerned by previous weighted network models seemed to not be the best choice to describe the link weight distributions of passenger air transportation networks. In this paper, by introducing an exponent α to the weight evolution rule of the earliest weighted model, and considering the spatial constraints of two-dimensional distances on linking probability, we have conducted rigorous analyses leading to the exponentially truncated power-law distribution for weights: P ( w ) = A ⋅ w − α ⋅ e − B w 1 − α , where A and B are parameters, α < 1. The theoretical expression is consistent with the empirical results of the American domestic passenger flight records from 1995 to 2020. The model would be applicable to different air transportation systems and to problems in other fields.

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.

Departure delays are a major cause of economic loss and inefficiency in the growing industry of passenger flights. A departure delay of a current flight is inevitably affected by the late arrival of the flight immediately preceding it with the same aircraft. We seek to understand the mechanisms of such propagated delays, and to obtain universal metrics by which to evaluate an airline’s operational effectiveness in delay alleviation. Here we use big data collected by the American Bureau of Transportation Statistics to design models of flight delays. Offering two dynamic models of delay propagation, we divided all carriers into two groups exhibiting a shifted power law or an exponentially truncated shifted power law delay distribution, revealing two universal delay propagation classes. Three model parameters, extracted directly from dual data mining, help characterize each airline’s operational efficiency in delay mitigation. Therefore, our modeling framework provides the crucially lacking evaluation indicators for airlines, potentially contributing to the mitigation of future departure delays.

This paper explores the internal mechanism of flight departure delay for the Delta Air Lines (IATA-Code: DL) from the viewpoint of statistical law. We roughly divide all of delay factors into two sorts: propagation factor (PF), and nonpropagation factors (NPF). From the statistical results, we find that the distribution of the flight departure delay caused by only NPF exhibits obvious power law (PL) feature, which can be explained by queuing model, while the original distribution of flight departure delay follows the shift power law (SPL). The mechanism of SPL distribution of flight departure delay is considered as the results of the aircraft queue for take-off due to the airports congestion and the propagation delay caused by late-arriving aircraft. Based on the above mechanism, we develop a specific measure for formulating flight planning from the perspective of mathematical statistics, which is easy to implement and reduces flight delays without increasing operational costs. We analyze the punctuality performance for 10 of the busiest and the highest delay ratio airports from 155 airports where DL took off and landed in the second half of 2017. Then, the scheduled turnaround time for all flights and the average scheduled turnaround time for all aircraft operated by DL has been counted. At last, the effectiveness and practicability of our method is verified by the flights operation data of the first half of 2018.

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

Air traffic controllers play critical roles in the safety, efficiency, and capacity of air traffic management. However, there is inadequate knowledge of the dynamics of the controllers' activities, especially from a quantitative perspective. This paper presents a novel network approach to uncover hidden patterns of the controllers' behavior based on the voice communication data. We convert the time series of the controllers' communication activities, which contain flights' information, into a time-varying network and a static network, referred to as temporal network and time-aggregated network, respectively. These networks reflect the interaction between the controllers and the flights on a sector level, and allow us to leverage network techniques to yield new and insightful findings regarding regular patterns and unique characteristics of the controllers' communication activities. The proposed methodology is applied to three real-world datasets, and the resulting networks are closely examined and compared in terms of degree distribution, community structure, and motifs. This network approach introduces a "spatial" element to the conventional analysis of the controllers' communication events, by identifying connectivity and proximity among flights. It constitutes a major step towards the quantitative description of the controller-flight dynamics, which is not widely seen in the literature. Language: en

Recent human dynamics research has unmasked astonishing statistical characteristics such as scaling behaviors in human daily activities. However, less is known about the general mechanism that governs the task-specific activities. In particular, whether scaling law exists in human activities under high pressure remains an open question. In air traffic management system, safety is the most important factor to be concerned by air traffic controllers who always work under high pressure, which provides a unique platform to study human activity. Here we extend fluctuation scaling method to study air traffic controller’s communication activity by investigating two empirical communication datasets. Taken the number of controlled flights as the size-like parameter, we show that the relationships between the average communication activity and its standard deviation in both datasets can be well described by Taylor’s power law, with scaling exponent α ≈ 0.77 ± 0.01 for the real operational data and α ≈ 0.54 ± 0.01 for the real-time training data. The difference between the exponents suggests that human dynamics under pressure is more likely dominated by the exogenous force. Our findings may lead to further understanding of human behavior.

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.

The distribution of the geometric distances of connected neurons is a practical factor underlying neural networks in the brain. It can affect the brain’s dynamic properties at the ground level. Karbowski derived a power-law decay distribution that has not yet been verified by experiment. In this work, we check its validity using simulations with a phenomenological model. Based on the in vitro two-dimensional development of neural networks in culture vessels by Ito, we match the synapse number saturation time to obtain suitable parameters for the development process, then determine the distribution of distances between connected neurons under such conditions. Our simulations obtain a clear exponential distribution instead of a power-law one, which indicates that Karbowski’s conclusion is invalid, at least for the case of in vitro neural network development in two-dimensional culture vessels.

We introduce a model to study the effects of coupling-frequency correlations on synchronization in complete graphs. When the linear correlation is adopted, we find a symmetric network where frequencies of the oscillators are distributed in a bipolar way, having values either −1 or +1. In the network, the oscillators either all drift or all phase-locked. The behavior can separate qualitatively two other types of correlations, where slow and fast oscillators can remain unsynchronized respectively. It is obvious that the weighting exponent plays an important role. Besides, the numerical simulation results indicate that the linear correlation has the best performance in synchronization ability among three types of correlations in view of the average node cost.

Large flocks of wild beings can have coordinated motion with neither leading center nor global information. The Vicsek model and its new versions explained such collective behavior of self-propelled agents with the mechanism of un-weighted influence of neighbors and global visual field (GVF), which may not always fit the reality. In the present work, we take both exponential ( λ ) neighbor weight (ENW) and restricted visual field (RVF) into account, and investigate the combinatory effect of them. Based on this mechanism, in most cases of our simulation, stationary direction consensus V a exhibits a maximum or decreases with V F , and a minimum convergence time T m i n appears in RVF, which demonstrates that GVF is not necessary for coordinated motion, while RVF matched ENW would be reasonable. Moreover, we simulated various recipes for optimizing V a and T in unfavorable cases, and found critical points separating inverse λ -dependent variations of T . The present work may be useful in improving the efficiency of direction consensus of large flocks of artificial individuals besides the understanding of biological collective motion in nature.

In this paper, we investigate percolation in a sort of networks inspired by the observation of a Collatz graph (CG) which is the network version of the famous 3 x + 1 problem in mathematics. The CG consists of positive integers that are connected based on the iteration relations. Actually, we never mean to solve the 3 x + 1 problem exactly but we observe it from the viewpoint of statistical physics. We focus on the so-called reduced Collatz graph (RCG) that is a subgraph with all odd numbers since even numbers can be iterated into odd ones through 3 x + 1 rules. Considering boundary conditions, we obtain a special degree distribution of RCG for finite size set of odd integers, and treat the infinite case as its limit. With the percolation criterion through the approach of a generating function, we determine the critical condition for the network ensemble of RCG. Furthermore, we generalize the graph model with RCG-type degree distributions beyond the 3 x + 1 problem, get the generic criterion of percolation and phase diagram for an ensemble of positive-integer networks with RCG as its extreme case.

Scale-free topology and high clustering coexist in some real networks, and keep invariant for growing sizes of the systems. Previous models could hardly give out size-independent clustering with selforganized mechanism when succeeded in producing power-law degree distributions. Always ignored, some empirical statistic results display flat-head power-law behaviors. We modify our recent coevolutionary model to explain such phenomena with the inert property of nodes to retain small portion of unfavorable links in self-organized rewiring process. Flat-head power-law and size-independent clustering are induced as the new characteristics by this modification. In addition, a new scaling relation is found as the result of interplay between node state growth and adaptive variation of connections.

In some co-evolutionary networks, the nodes always flip their states between two opposite ones, changing the types of the links to others correspondingly. Meanwhile, the link-rewiring and state-flipping processes feed back each other, and only the links between the nodes in the opposite states are productive in generating flow for the network. We propose an inverse voter model to depict the basic features of them. New phase transitions from full efficiency to deficiency state are found by both the analysis and simulations starting from the random graphs and small-world networks. We suggest a new way to measure the efficiency of networks.

In this paper, we model the worm spreading in the ad hoc communication network on a two-dimensional triangular lattice. The medium access control mechanism used to reduce interference among transmitting nodes causes a side-effect on worm spreading. It increases threshold of epidemics and reduces the prevalence of infected nodes in the network.

In this paper, we model the mobile ad hoc communication network on a two-dimensional square lattice. Both structure and function of it depend on transmission range and site-occupancy of nodes. Critical occupancies σc for different transmission ranges r to maintain global connection are found. Universal scaling function behaves as η:_ f(Rβσ), where |R = (r − r0)/r0, and the scaling exponent β = −0.61, which distinguishes itself from percolation in previous lattice or network models. When the occupancy σ is near the threshold σc, individual nodes self-organize into a dynamic small world network relative to geometric distance. The network has a cut-off degree below which clustering coefficient keeps constant, which distinguish itself from other systems and has its potential application in technical designs.

In this paper, we propose a generalized deactivation model to characterize weighted networks. By introducing the special aging mechanism, the model can produce power-law distributions of degree, strength, and weight, as confirmed in many real networks. We also characterize the clustering and correlation properties of this class of networks. A scaling behavior of clustering coefficient C ∼ 1 / M is observed, where M refers to the number of active nodes. The generated network simultaneously exhibits hierarchical organization and disassortative degree correlation. All of these structural properties are confirmed by present empirical evidence.

We investigate the localization behavior of electrons in a random lattice which is constructed from a quasi-one-dimensional chain with large coordinate number $Z$ and rewired bonds, resembling the small-world network proposed recently but with site-energy disorder and quantum links instead of classical ones. The random rewiring of bonds in the chain with large $Z$ enhances both the topological disorder and the effective dimensionality. From the competition between disorder and dimensionality enhancement a transition from localization to delocalization is found by using the level statistics method combined with the finite-size scaling analysis. The critical value of the rewiring rate for this transition is determined numerically. We obtain a universal critical integrated distribution of level spacing $s$ in the form $I_{p_{c}}(s)\propto \exp (-A_{c}s^{\alpha})$, with $A_{c}\simeq 1.50$ and $\alpha \simeq 1.0$. This reveals the possible existence of metal-insulator transition in materials with chains as the backbones., Comment: 12 pages, 4 figures

In the coevolving voter model, each voter has one of two diametrically opposite opinions, and a voter encountering a neighbor with the opposite opinion may either adopt it or rewire the connection to another randomly chosen voter sharing the same opinion. As we smoothly change the relative frequency of rewiring compared to that of adoption, there occurs a phase transition between an active phase and a frozen phase. By performing extensive Monte Carlo calculations, we show that the phase transition is characterized by critical exponents {\beta}=0.54(1) and {\nu} =1.5(1), which differ from the existing mean-field-type prediction. We furthermore extend the model by introducing a contrarian type that tries to have neighbors with the opposite opinion, and show that the critical behavior still belongs to the same universality class irrespective of such contrarians' fraction., Comment: 11 pages, 5 figures

To explore the infiltration pathogenesis of CD4(+);T cells following the spinal nerve ligation.Healthy adult male SD rats were randomly divided into the spinal nerve ligation group (Tx), sham operation group (S), control group (C). the 50mechanical paw withdrawal threshold ( 50MWT ) was determined by up-down method; CD4(+);T cells infiltration was assessed by FACS; the mRNA levels of CCL2, CCL5 and CXCL10 were quantitated by RT-qPCR; serum cytokines were tested by ELISA kits.After 3 days since operation, 50MWT of Tx group was significantly reduced (P0.01) comparing with S group, C group; on day 14, 50MWT was up to the minimum value; whereas S group and C group were no difference (P0.05). After 7 days since operation, CD4(+);T cells infiltration into lumbar segments of the spinal cord in the Tx group increased significantly (P0.01), and the CCL2, CCL5mRNA expression increased (P0.05); on day 14, the CD4(+);T cells infiltration in Tx group was higher than S group, C group; but there was no statistical significance. On day 7 and 14 days, serum levels of cytokines were no difference in the three groups.Following spinal nerve ligation, high expression of chemokine promoted peripheral CD4(+);T cells to infiltrate into spinal cord; and the infiltrated CD4(+);T cells maintained the neuropathic pain.

Mapping the streets and street-crossings of the Nanjing city plan onto nodes and edges of a dual graph, we implement the traffic model of vehicles moving towards specified destinations with navigation and queuing. The navigation rules with local search within the next-nearst-neighborhood are applied both with and without dynamical feedback. The traffic is autonomously driven with a parameter which controls traffic density and maximum queue lengths are limited by the actual lengths of streets. The analysis of the simulated traffic load time series indicates three regimes, depending on the traffic density: free flow, regime with temporal congestions, and congested traffic. We determine the probability distributions of the waiting times in queues and travel times of vehicles, as well as the distributions of the local loads on nodes and edges. With the spectral analysis of the weighted matrix of traffic load on the edges of the dual graph, and mapping back to the real space, we identify geographically distinct regions which have different congestion patterns.

In this paper, critical global connectivity of mobile ad hoc networks (MANETs) is investigated. We model the two-dimensional plane on which nodes move randomly with a triangular lattice. Demanding the best communication of the network, we account the global connectivity eta as a function of occupancy sigma of sites in the lattice by mobile nodes. Critical phenomena of the connectivity for different transmission ranges r are revealed by numerical simulations, and these results fit well to the analysis based on the assumption of homogeneous mixing. Scaling behavior of the connectivity is found as eta approximately f(R;{beta}sigma) , where R=(r-r_{0})r_{0} , r_{0} is the length unit of the triangular lattice, and beta is the scaling index in the universal function f(x) . The model serves as a sort of geometric distance-dependent site percolation on dynamic complex networks. Moreover, near each critical sigma_{c}(r) corresponding to certain transmission range r , there exists a cutoff degree k_{c} below which the clustering coefficient of such self-organized networks keeps a constant while the averaged nearest-neighbor degree exhibits a unique linear variation with the degree k , which may be useful to the designation of real MANETs.

Competitive exclusion, a key principle of ecology, can be generalized to understand many other complex systems. Individuals under surviving pressure tend to be different from others, and correlations among them change correspondingly to the updating of their states. We show with numerical simulation that these aptitudes can contribute to group formation or speciation in social fields. Moreover, they can lead to power-law topological correlations of complex networks. By coupling updating states of nodes with variation of connections in a network, structural properties with power-laws and functions like multifractality, spontaneous ranking and evolutionary branching of node states can emerge out simultaneously from the present self-organized model of coevolutionary process., 5 figures and 5 pages

A co-evolutionary neuronal network model based on previous ones is proposed, and both functional and structural properties are numerically calculated. Recent experiments have revealed power-law behavior in electrocorticogram (ECoG) spectrum related with synaptic plasticity and reorganization. In the present neuronal network model, the network starts its evolution from the initial configuration of random network which is the least biased and without special structure, and the interaction rules among neurons are modified from both models by Bornholdt's and Arcangelis' groups to simulate the process of synaptic development and maturation. The system exhibits dynamic small-world structure which is the result of evolution instead of the assumption beforehand. Meanwhile, the power spectrum of electrical signals reproduces the power-law behavior with the exponent 2.0 just as what is experimentally measured in ECoG spectrum. Moreover, the power spectrum of the average degree per neuron over time also exhibits power-law behavior, with the exponent 2.0 again over more than 5 orders of magnitude. Different from previous results, our network exhibits assortative degree-degree correlation which is expected to be checked by experiments.

We propose a model of network growth that generalizes the deactivation model previously suggested for complex networks. Several topological features of this generalized model, such as the degree distribution and clustering coefficient, have been investigated analytically and by simulations. A scaling behavior of clustering coefficient $C \sim 1/M$ is theoretically obtained, where $M$ refers to the number of active nodes in the network. We discuss the relationship between the recently observed numerical behavior of clustering coefficient in the coauthor and paper citation networks and our theoretical result. It shows that both of them are induced by deactivation mechanism. By introducing a perturbation, the generated network undergoes a transition from large- to small-world, meanwhile the scaling behavior of $C$ is conserved. It indicates that $C \sim 1/M$ is a universal scaling behavior induced by deactivation mechanism., 8 pages, 9 figures. To be published in Physical Review E

In this paper, by extending the concept of Kuramoto oscillator to the left-invariant flow on general Lie group, we investigate the generalized phase synchronization on networks. The analyses and simulations of some typical dynamical systems on Watts-Strogatz networks are given, including the $n$-dimensional torus, the identity component of 3-dimensional general linear group, the special unitary group, and the special orthogonal group. In all cases, the greater disorder of networks will predict better synchronizability, and the small-world effect ensures the global synchronization for sufficiently large coupling strength. The collective synchronized behaviors of many dynamical systems, such as the integrable systems, the two-state quantum systems and the top systems, can be described by the present phase synchronization frame. In addition, it is intuitive that the low-dimensional systems are more easily to synchronize, however, to our surprise, we found that the high-dimensional systems display obviously synchronized behaviors in regular networks, while these phenomena can not be observed in low-dimensional systems., Comment: 5 pages, and 3 figures

Motivated by a recently introduced network growth mechanism that rely on the ranking of node prestige measures [S. Fortunato \emph{et al}., Phys. Rev. Lett. \textbf{96}, 218701 (2006)], a rank-based model for weighted network evolution is studied. The evolution rule of the network is based on the ranking of node strength, which couples the topological growth and the weight dynamics. Both analytical solutions and numerical simulations show that the generated networks possess scale-free distributions of degree, strength, and weight in the whole region of the growth dynamics parameter ($\alpha>0$). We also characterize the clustering and correlation properties of this class of networks. It is showed that at $\alpha=1$ a structural phase transition occurs, and for $\alpha>1$ the generated network simultaneously exhibits hierarchical organization and disassortative degree correlation, which is consistent with a wide range of biological networks., Comment: 4 pages, 5 figures

A dynamical model of small-world network, with directed links which describe various correlations in social and natural phenomena, is presented. Random responses of every site to the imput message are introduced to simulate real systems. The interplay of these ingredients results in collective dynamical evolution of a spin-like variable S(t) of the whole network. In the present model, global average spreading length \langel L >_s and average spreading time _s are found to scale as p^-\alpha ln N with different exponents. Meanwhile, S behaves in a duple scaling form for N>>N^*: S ~ f(p^-\beta q^\gamma t'_sc), where p and q are rewiring and external parameters, \alpha, \beta, \gamma and f(t'_sc) are scaling exponents and universal functions, respectively. Possible applications of the model are discussed., Comment: 4 pages, 6 Figures

We prove that the hierarchical fractal model recently proposed for describing the stretched polymers [A. N. Samukhin et al, Phys. Rev. Lett.{\bf 78}, 326(1997)] is equivalent to a one-dimensional chain with hierarchical aperiodic structure. By use of the transfer matrix technique we calculate the electronic transmission and the dc conductance. We find that there exist sharp-edged transmission subbands and gaps, but the transmission subbands are rich in substructures which show self-similarity. The temperature dependence of conductance $g (T)$ is sensitive to the variation of the Fermi level and to the structure parameters $m$ and $n$ of the original fractal structure. The relationship of the obtained results to the experimental data and other theoretical works is discussed., Comment: 5 pages, 7 figures

We investigate the worm spreading process in mobile ad hoc networks with a susceptible-infected-recovered model on a two-dimensional plane. A medium access control mechanism operates within it, inhibiting transmission and relaying a message by using other nodes inside the node's transmitting circle during speaking. We measure the rewiring probability p with the transmitting range r and the average relative velocity of the moving nodes, and map the problem into a directed dynamic small-world network. A new scaling relation for the recovered portion of the nodes reveals the effect caused by geometric distance, which has been ignored by previous models.