Modelling temporal networks of human face-to-face contacts with public activity and individual reachability

Modelling temporal networks of human face-to-face contacts is vital both for understanding the spread of airborne pathogens and word-of-mouth spreading of information. Although many efforts have been devoted to model these temporal networks, there are still two important social features, public activity and individual reachability, have been ignored in these models. Here we present a simple model that captures these two features and other typical properties of empirical face-to-face contact networks. The model describes agents which are characterized by an attractiveness to slow down the motion of nearby people, have event-triggered active probability and perform an activity-dependent biased random walk in a square box with periodic boundary. The model quantitatively reproduces two empirical temporal networks of human face-to-face contacts which are testified by their network properties and the epidemic spread dynamics on them.     

Modeling the effects of social impact on epidemic spreading in complex networks

We investigate by mean-field analysis and extensive simulations the effects of social impact on epidemic spreading in various typical networks with two types of nodes: active nodes and passive nodes, of which the behavior patterns are modeled according to the social impact theory. In this study, nodes are not only the media to spread the virus, but also disseminate their opinions on the virus—whether there is a need for certain self-protection measures to be taken to reduce the risk of being infected. Our results indicate that the interaction between epidemic spreading and opinion dynamics can have significant influences on the spreading of infectious diseases and related applications, such as the implementation of prevention and control measures against the infectious diseases.     

Statistical theory versus shell model in a large pf configuration space

Spectral distribution method and exact shell-model predictions for the strength sums of different transition operators are compared in detail for the J=0, T−T_z=0 states of ⁴⁶V and ⁵⁰Sc using the full pf shell. Good agreement of both models is observed in the high level density region of the energy spectrum, where chaotic motion is dominant, and larger discrepancies are observed in the ground state region, where nuclear motion is more regular. The agreement in the chaotic region becomes especially good in the 5986 dimensional space of ⁵⁰Sc, illustrating the quality of the statistical theory in large configuration spaces.     

移动环境下网络病毒传播模型及其稳定性研究

考虑网络节点的随机移动, 基于平均场理论 提出一个移动环境下网络病毒传播的数学模型, 利用微分动力学系统理论研究了病毒传播行为. 研究表明, 当病毒基本再生数R₀ ≤ 1时, 网络中病毒逐渐消除, 系统的无病毒平衡点全局渐进稳定; 当R₀ > 1时, 网络中病毒持续存在, 系统的地方病平衡点全局渐进稳定.通过仿真验证了所得结论的正确性.     

Epidemic propagation on adaptive coevolutionary networks with preferential local-world reconnecting strategy

In the propagation of an epidemic in a population, individuals adaptively adjust their behavior to avoid the risk of an epidemic. Differently from existing studies where new links are established randomly, a local link is established preferentially in this paper. We propose a new preferentially reconnecting edge strategy depending on spatial distance (PR- SD). For the PR-SD strategy, the new link is established at random with probability p and in a shortest distance with the probability 1 p. We establish the epidemic model on an adaptive network using Cellular Automata, and demonstrate the effectiveness of the proposed model by numerical simulations. The results show that the smaller the value of parameter p, the more difficult the epidemic spread is. The PR-SD strategy breaks long-range links and establishes as many short-range links as possible, which causes the network efficiency to decrease quickly and the propagation of the epidemic is restrained effectively.     

Comparison of immunization strategies in geographical networks

The epidemic spread and immunizations in geographically embedded scale-free (SF) and Watts-Strogatz (WS) networks are numerically investigated. We make a realistic assumption that it takes time which we call the detection time, for a vertex to be identified as infected, and implement two different immunization strategies: one is based on connection neighbors (CN) of the infected vertex with the exact information of the network structure utilized and the other is based on spatial neighbors (SN) with only geographical distances taken into account. We find that the decrease of the detection time is crucial for a successful immunization in general. Simulation results show that for both SF networks and WS networks, the SN strategy always performs better than the CN strategy, especially for more heterogeneous SF networks at long detection time. The observation is verified by checking the number of the infected nodes being immunized. We found that in geographical space, the distance preferences in the network construction process and the geographically decaying infection rate are key factors that make the SN immunization strategy outperforms the CN strategy. It indicates that even in the absence of the full knowledge of network connectivity we can still stop the epidemic spread efficiently only by using geographical information as in the SN strategy, which may have potential applications for preventing the real epidemic spread.     

Coevolutionary motion and swarming in a niche space model of ecological species interactions

Organisms are involved in coevolutionary relationships with their competitors, predators, preys and parasites. In this context, we present a simple model for the co-evolution of species in a common niche space, where the fitness of each species is defined via the network of interactions with all other species. In our model, the sign and type of the pairwise interactions (being either beneficial, harmful or neutral) is given by a pre-determined community matrix, while the interaction strength depends on the niche-overlap, i.e. the pairwise distances between species in niche space. The evolutionary process drives the species toward the places with the higher local fitness along the fitness gradient. This gives rise to a dynamic fitness landscape, since the evolutionary motion of a single species can change the landscape of the others (known as the Red Queen Principle). In the simplest case of only two-species we observe either a convergence/divergence equilibrium or a coevolutionary arms race. For a larger number of species our analysis concentrates on an antisymmetric interaction matrix, where we observe a large range of dynamic behaviour, from oscillations, quasiperiodic to chaotic dynamics. In dependence of the value of a first integral of motion we observe either quasiperiodic motion around a central region in niche space or unbounded movement, characterised by chaotic scattering of species pairs. Finally, in a linear food-chain we observe complex swarming behaviour in which the swarm moves as a whole only if the chain consists of an even number of species. Our results could be an important contribution to evolutionary niche theory.     

On the structure of the Galilean and translationally invariant operator algebra describing intrinsic properties of finite nuclear systems

The structure of the Galilean and translationally invariant operator algebra for finite systems of fermions is investigated. After performing the decomposition of the Fock space into Hilbert spaces for the center-of-mass motion and the intrinsic motion, “intrinsic” field operators are defined and their commutation relations established. These relations deviate in a certain particle number-dependent way from the usual fermion relations. It is shown that the operators corresponding to the intrinsic (e.g. nuclear) observables can be represented in the familiar way, the usual field operators being replaced by the intrinsic ones. In this theory the normal shell model calculations appear as the approximation performed by treating matrix elements of nuclear observables as if the intrinsic field operators were satisfying the exact Fermi commutation relations.     

The geodesic approximation for the Yang-Mills-Higgs equations

In this paper we consider the dynamics of the monopole solutions of Yang-Mills-Higgs theory on Minkowski space. The monopoles are solutions of the Yang-Mills-Higgs equations on three dimensional Euclidean space. It is of interest to understand how they evolve in time when considered as solutions of the Yang-Mills-Higgs equations on Minkowski space-i.e. the time dependent equations. It was suggested by Manton that in certain situations the monopole dynamics could be understood in terms of geodesics with respect to a certain, metric on the space of guage equivalence classes of monopoles-the moduli space. The metric is defined by taking theL ² inner product of tangent vectors to this space. In this paper we will prove that Manton's approximation is indeed valid in the right circumstances, which correspond to the slow motion of monopoles. The metric on the moduli space of monopoles was analysed in a book by Atiyah and Hitchin, so together with the results of this paper a detailed and rigorous understanding of the low energy dynamics of monopoles in Yang-Mills-Higgs theory is obtained. The strategy of the proof is to develop asymptotic expansions using appropriate gauge conditions, and then to use energy estimates to prove their validity. For the case of monopoles to be considered here there is a technical obstacle to be overcome-when the equations are linearised about the monopole the continuous spectrum extends all the way to the origin. This is overcome by using a norm introduced by Taubes in a discussion of index, theory for the Yang-Mills-Higgs functional.Supported by grant DMS-9214067 from the National Science Foundation.     

Projection operator techniques and Hilbert space averaging in the quantum theory of nonequilibrium systems

The development of efficient strategies for the treatment of the dynamics of relevant observables in complex quantum systems plays a decisive role in the theory of quantum relaxation and transport behavior. Here we discuss the most important tools that are based on the projection operator techniques of nonequilibrium statistical mechanics. For both the Nakajima-Zwanzig and the time-convolutionless projection operator technique we derive the equations of motion for a set of relevant observables and develop explicit expressions in second and fourth order of the corresponding perturbation expansions. We also discuss the Hilbert space average method which is based on the idea of a best guess of conditional quantum expectations determined by an average over a suitable region in the underlying Hilbert space, and relate this method to the projection operator technique.     

Quantifying the transmission potential of pandemic influenza

This article reviews quantitative methods to estimate the basic reproduction number of pandemic influenza, a key threshold quantity to help determine the intensity of interventions required to control the disease. Although it is difficult to assess the transmission potential of a probable future pandemic, historical epidemiologic data is readily available from previous pandemics, and as a reference quantity for future pandemic planning, mathematical and statistical analyses of historical data are crucial. In particular, because many historical records tend to document only the temporal distribution of cases or deaths (i.e. epidemic curve), our review focuses on methods to maximize the utility of time-evolution data and to clarify the detailed mechanisms of the spread of influenza.

First, we highlight structured epidemic models and their parameter estimation method which can quantify the detailed disease dynamics including those we cannot observe directly. Duration-structured epidemic systems are subsequently presented, offering firm understanding of the definition of the basic and effective reproduction numbers. When the initial growth phase of an epidemic is investigated, the distribution of the generation time is key statistical information to appropriately estimate the transmission potential using the intrinsic growth rate. Applications of stochastic processes are also highlighted to estimate the transmission potential using similar data. Critically important characteristics of influenza data are subsequently summarized, followed by our conclusions to suggest potential future methodological improvements.     

Tomographic Description of a Quantum Wave Packet in an Accelerated Frame

The tomography of a single quantum particle (i.e., a quantum wave packet) in an accelerated frame is studied. We write the Schrödinger equation in a moving reference frame in which acceleration is uniform in space and an arbitrary function of time. Then, we reduce such a problem to the study of spatiotemporal evolution of the wave packet in an inertial frame in the presence of a homogeneous force field but with an arbitrary time dependence. We demonstrate the existence of a Gaussian wave packet solution, for which the position and momentum uncertainties are unaffected by the uniform force field. This implies that, similar to in the case of a force-free motion, the uncertainty product is unaffected by acceleration. In addition, according to the Ehrenfest theorem, the wave packet centroid moves according to classic Newton’s law of a particle experiencing the effects of uniform acceleration. Furthermore, as in free motion, the wave packet exhibits a diffraction spread in the configuration space but not in momentum space. Then, using Radon transform, we determine the quantum tomogram of the Gaussian state evolution in the accelerated frame. Finally, we characterize the wave packet evolution in the accelerated frame in terms of optical and simplectic tomogram evolution in the related tomographic space.     

A theory of the successive production of moving striations in the plasma of inert gases

On the basis of results already published of experiments carried out by the method of excitation of transient processes with small perturbation, a theory is elaborated on the successive production of moving striations (waves of stratification) in an inert gas. The stratification of the plasma is interpreted as the successive production of regions with an alternately positive and negative space charge, i. e. as the producti n of a characteristic macroscopic periodic polarization of the plasma. The basic assumption of the theory is the relative independence of the chain of processes in each dark or light region of the striations, so that interaction between the regions occurs as a result of the electric field of the space charge in the neighbouring region.Equations are derived expressing the chronological order of the processes leading to the production of a space charge in each individual region and the interaction of the regions. The solution of the equations leads to functions, some of which are in agreement with experimental data while others cannot be verified on the basis of the experimental material at present at our disposal and require the carrying out of new experiments.The main results contained in this paper were reported on at the Conference on the Physics of Plasma in Leipzig on October 8th, 1956.     

基于数字射线成像的运动降质图像的恢复

当利用X射线数字成像技术对在流水线上运动的工件进行检测时,图像采集系统与工件在曝光时间内发生相对运动,造成了采集到的图像运动模糊降质。通过对运动降质产生机理的理论分析,建立了图像降质的离散退化模型。提出了利用运动模糊降质点扩展函数频域特性加上投影均值最大法来测量模糊运动方向的方法。旋转运动模糊图像的幅度谱图像,利用整列投影值最小法提取运动模糊降质点扩展函数长度。利用维纳滤波法对模糊降质图像进行了恢复,取得了较好的效果。     

Effects of population mixing on the spread of SIR epidemics

We study dynamics of spread of epidemics of SIR type in a realistic spatially-explicit geographical region, Southern and Central Ontario, using census data obtained from Statistics Canada, and examine the role of population mixing in epidemic processes. Our model incorporates the random nature of disease transmission, the discreteness and heterogeneity of distribution of host population.We find that introduction of a long-range interaction destroys spatial correlations very easily if neighbourhood sizes are homogeneous. For inhomogeneous neighbourhoods, very strong long-range coupling is required to achieve a similar effect. Our work applies to the spread of influenza during a single season.     

Influenza epidemic spread simulation for Poland — a large scale, individual based model study

In this work a construction of an agent based model for studying the effects of influenza epidemic in large scale (38 million individuals) stochastic simulations, together with the resulting various scenarios of disease spread in Poland are reported. Simple transportation rules were employed to mimic individuals’ travels in dynamic route-changing schemes, allowing for the infection spread during a journey. Parameter space was checked for stable behaviour, especially towards the effective infection transmission rate variability. Although the model reported here is based on quite simple assumptions, it allowed to observe two different types of epidemic scenarios: characteristic for urban and rural areas. This differentiates it from the results obtained in the analogous studies for the UK or US, where settlement and daily commuting patterns are both substantially different and more diverse. The resulting epidemic scenarios from these ABM simulations were compared with simple, differential equations based, SIR models — both types of the results displaying strong similarities. The pDYN software platform developed here is currently used in the next stage of the project employed to study various epidemic mitigation strategies.