Disease dynamics in a dynamic social network

We develop a framework for simulating a realistic, evolving social network (a city) into which a disease is introduced. We compare our results to prevaccine era measles data for England and Wales, and find that they capture the quantitative and qualitative features of epidemics in populations spanning two orders of magnitude. Our results provide unique insight into how and why the social topology of the contact network influences the propagation of the disease through the population. We argue that network simulation is suitable for concurrently probing contact network dynamics and disease dynamics in ways that prior modeling approaches cannot and it can be extended to the study of less well-documented diseases.     

Langevin dynamics simulations of phase separation in a one-component system

Langevin dynamics computer simulations have been performed for a two-dimensional Lennard-Jones fluid quenched into the coexistence region of its liquid-vapor phase diagram. For late stages of the phase-separation process, the average radius of the liquid clusters is found to grow proportional to (time)^1/4. This growth law is analyzed theoretically and compared to recent molecular dynamics and Monte Carlo results. Details of the different simulation methods are critically discussed.     

Reconstruction of Superoperators from Incomplete Measurements

We present strategies how to reconstruct (estimate) properties of a quantum channel described by the map E based on incomplete measurements. In a particular case of a qubit channel a complete reconstruction of the map E can be performed via complete tomography of four output states E[ρ_j] that originate from a set of four linearly independent “test” states ρ_j (j = 1,2,3,4) at the input of the channel. We study the situation when less than four linearly independent states are transmitted via the channel and measured at the output. We present strategies how to reconstruct the channel when just one, two or three states are transmitted via the channel. In particular, we show that if just one state is transmitted via the channel then the best reconstruction can be achieved when this state is a total mixture described by the density operator ρ = I/2. To improve the reconstruction procedure one has to send via the channel more states. The best strategy is to complement the total mixture with pure states that are mutually orthogonal in the sense of the Bloch-sphere representation. We show that unitary transformations (channels) can be uniquely reconstructed (determined) based on the information of how three properly chosen input states are transformed under the action of the channel.We have originally dedicated this paper to Asher Peres on the occasion of his 70th birthday. Unfortunately, since the submission of the paper for publication Asher Peres passed away so we dedicate this paper to his memory.     

Non-Markovian random unitary qubit dynamics

We compare two approaches to non-Markovian quantum evolution: one based on the concept of divisible maps and the other one based on distinguishability of quantum states. The former concept is fully characterized in terms of local generator whereas it is in general not true for the latter one. A simple example of random unitary dynamics of a qubit shows the intricate difference between those approaches. Moreover, in this case both approaches are fully characterized in terms of local decoherence rates.     

Enhanced wavefront reconstruction by random phase modulation with a phase diffuser

A phase retrieval technique for enhanced wavefront reconstruction using random phase modulation and a phase diffuser is proposed. The speckle field generated is sampled at multiple axially displaced planes and the speckle patterns are used in an iterative algorithm based on the optical wave propagation in free space. The presentation of this technique is carried out using two setups. In the first setup, a diffuser plate is placed at the image plane of a metallic test object. The benefit of randomizing the phase of the object wave is the enhanced intensity recording due to high dynamic range of the diffusely scattered beam. The use of demagnification optics will also allow the investigations of relatively large objects. In the second setup, a transparent object is illuminated using a wavefront with random phase and constant amplitude by positioning the phase diffuser close to the object. The benefit of phase-only modulation is the increased resolution of the phase structures of the transparent test objects.     

First-principles study of the high pressure phase transition and lattice dynamics of cerium

We present a first-principles study of the phase transition and lattice dynamics of Ce within the framework of the density functional theory using the GGA+U method. Our calculated results denote that under pressure the transition path is α-Ce (fcc)→α″-Ce (monoclinic, with two atoms per unit cell)→bct-Ce (body centered tetragonal), and the transition pressures are located at 5.36 and 14.37 GPa, respectively. The equation of state in a wide range of pressure is consistent with the experimental data. During the γ-α phase transition, the magnetic moment disappears gradually, which is mainly due to the strong interaction between the 4f and 5d electrons. By calculating the free energies from phonon dispersions including electronic contribution, the obtained γ-α transition temperature at zero pressure is 148 K. From the Blackman diagram of dimensionless elastic constant ratios, we can find that both γ- and α-Ce show negative Cauchy pressure—C₄₄>C₁₂.     

随机中毒对神经元网络时空动力学行为的影响

神经元细胞膜上的离子通道能够被一些有毒的化学物质阻断. 离子通道阻断会降低离子通道的电导率和激活通道数, 影响神经元的放电活动, 进而影响神经网络时空模式的动力学行为. 本文采用具有周期边界的近邻耦合Hodgkin-Huxley神经元网络, 数值研究了钠离子和钾离子通道随机中毒时神经网络时空模式的演化过程. 发现钠离子和钾离子通道随机中毒可以导致螺旋波破裂. 通过分析网络的放电概率, 发现钠离子通道随机中毒降低了神经网络的兴奋性, 且其对中毒的敏感程度与噪声强度有关; 钾离子通道随机中毒增强了神经网络的兴奋性. 与均匀的通道中毒相比, 随机通道中毒的神经网络具有更丰富的动力学行为. 最后, 采用无流边界条件对神经网络进行数值仿真, 得到了类似的结果. 该研究更真实地反映神经系统中毒时整体兴奋性的变化, 从另一个方面揭示离子通道中毒对网络时空行为的影响, 有利于更进一步理解离子通道在网络整体行为中的作用. 关键词： 神经网络 离子通道 随机中毒 时空动力学     

Reconstruction of shared nonlinear dynamics in a network

We study a general physical network consisting of a collection of response systems with complex nonlinear dynamics, influenced by a common driver. The goal is to reconstruct dynamics, regular or chaotic, that are common to all of the response systems, working from simultaneous time series measured at the responses systems only. A fundamental theorem is stated concerning the reconstruction of the common driver. An algorithm is developed, based on the theorem, to carry out the reconstruction, and is demonstrated with several examples.     

Lattice dynamics and phase transition of NiTi alloy

We have performed detailed first-principles calculations to investigate the structural and lattice dynamical properties of NiTi alloy. The calculated static structures consist well with the experimental data and other theoretical results. With quasi harmonic approximation, the phase boundary between B19′ and BCO phases can be described as a five order polynomial $T=100?89.28P+296.75P^2?717.94P^3+734.62P^4?274.25P^5$. The change of vibrational entropy is $0.07k_B$/atom at the transition temperature 100 K under zero pressure.     

Influence of a network structure on the network effect in the communication service market

In this study, we analyze the network effect in a model of a personal communication market, by using a multi-agent based simulation approach. We introduce into the simulation model complex network structures as the interaction patterns of agents. With complex network models, we investigate the dynamics of a market in which two providers are competing. We also examine the structure of networks that affect the complex behavior of the market. By a series of simulations, we show that the structural properties of complex networks, such as the clustering coefficient and degree correlation, have a major influence on the dynamics of the market. We find that the network effect is increased if the interaction pattern of agents is characterized by a high clustering coefficient, or a positive degree correlation. We also discuss a suitable model of the interaction pattern for reproducing market dynamics in the real world, by performing simulations using real data of a social network.     

Phase ordering dynamics in a gravitational field

We study the dynamics of phase ordering in the presence of an external gravitational field, namely a field that varies linearly with distance in one direction. Starting from microscopic considerations, we motivate reasonable phenomenological models for cases with nonconserved and conserved order parameter. We present detailed numerical results from our model for the case with conserved order parameter.     

The dynamics of a mobile phone network

The empirical study of network dynamics has been limited by the lack of longitudinal data. Here we introduce a quantitative indicator of link persistence to explore the correlations between the structure of a mobile phone network and the persistence of its links. We show that persistent links tend to be reciprocal and are more common for people with low degree and high clustering. We study the redundancy of the associations between persistence, degree, clustering and reciprocity and show that reciprocity is the strongest predictor of tie persistence. The method presented can be easily adapted to characterize the dynamics of other networks and can be used to identify the links that are most likely to survive in the future.     

Molecular phase space transport in water: Non-stationary random walk model

Molecular transport in phase space is crucial for chemical reactions because it defines how pre-reactive molecular configurations are found during the time evolution of the system. Using Molecular Dynamics (MD) simulated atomistic trajectories we test the assumption of the normal diffusion in the phase space for bulk water at ambient conditions by checking the equivalence of the transport to the random walk model. Contrary to common expectations we have found that some statistical features of the transport in the phase space differ from those of the normal diffusion models. This implies a non-random character of the path search process by the reacting complexes in water solutions. Our further numerical experiments show that a significant long period of non-stationarity in the transition probabilities of the segments of molecular trajectories can account for the observed non-uniform filling of the phase space. Surprisingly, the characteristic periods in the model non-stationarity constitute hundreds of nanoseconds, that is much longer time scales compared to typical lifetime of known liquid water molecular structures (several picoseconds).     

On the motif distribution in random block-hierarchical networks

The distribution of motifs in random hierarchical topological networks defined by nonsymmetric random block-hierarchical adjacency matrices, is constructed for the first time. According to the classification of U. Alon et al. of network superfamilies (Milo et al., 2004 [11]) by their motifs distributions, our artificial directed random hierarchical networks fall into the superfamily of natural networks to which the neuron networks belong. This is the first example of a class of “handmade” topological networks with the motifs distribution as in a special class of natural networks of essential biological importance.     

Geometric phase of a qubit driven by a phase noise laser under non-Markovian dynamics

Robustness of the geometric phase (GP) with respect to the environmental effects is a basic condition for an effective quantum computation. Here, we study quantitatively the GP of a two-level atom system driven by a phase noise laser under non-Markovian dynamics in terms of different parameters involved in the whole system. We find that with the change of the damping coupling, the GP is very sensitive to its properties exhibiting long collapse and revival phenomena, which play a significant role in enhancing the stabilization and control of the system dynamics. Moreover, we show that the GP can be considered as a tool for testing and characterizing the nature of the qubit–environment coupling. Due to the significance of how a system is quantum correlated with its environment in the construction of a scalable quantum computer, the entanglement dynamics between the qubit with its environment under external classical noise is evaluated and investigated during the time evolution.     

The friction coefficient of a Lennard-Jones fluid from the random force autocorrelation function determined as a memory function by molecular dynamics calculations

A recent molecular dynamics (MD) study showed that the friction coefficient of a simple fluid is obtainable by the integral over the autocorrelation function (ACF) of the total force of a Brownian-type particle. The results indicated that mass ratios 50M/m200 of the massive and the light particle suffice to yield accurate friction coefficients. Complementarily, we calculate the random force ACF of the light particle, which is the memory function force of the ACF of the velocity apart from a constant factor, for all the states of the Lennard-Jones system investigated previously. A detailed comparison is presented of the memory function, the total force ACF of the fluid particle, and the total force ACF of the massive particle. The MD results confirm quantitatively our theoretical predictions: (i) on a time scale corresponding to the dynamics of the massive particle the total force ACF of that particle approximates well the memory function, while there are slight differences between them on a short time scale, (ii) the total force ACF of the liquid particle deviates significantly from the memory function already after extremely short time and is thus completely useless for the determination of the friction coefficient, (iii) using the total force ACF of a heavy particle for the determination of the friction constant with mass ratios ofM/m=50 up to 200, the pseudo plateau value of the time integral is often not very noticeable, as the memory function is only approximated and the total force ACF of the massive particle has a negative part at medium times. In those cases the integration has to be extended to include the negative part.     

基于相移技术的显微数字全息重构细胞相位

介绍了用显微镜物镜、压电陶瓷和CCD建立的一套测量细胞相位的显微数字全息光路,基于相移技术,给出了重构相位的理论分析,并用洋葱磷片叶细胞作为测试样品,完成了测量细胞相位的实验.结果表明：该系统可以完成细胞相位重构,系统分辨率不低于1 μm.