Narrow Results

In this paper, we attempt to understand the propagation and stability feature of large-scale complex software from the perspective of complex networks. Specifically, we introduced the concept of "propagation scope" to investigate the problem of change propagation in complex software. Although many complex software networks exhibit clear "small-world" and "scale-free" features, we found that the propagation scope of complex software networks is much lower than that of small-world networks and scale-free networks. Furthermore, because the design of complex software always obeys the principles of software engineering, we introduced the concept of "edge instability" to quantify the structural difference among complex software networks, small-world networks and scale-free networks. We discovered that the edge instability distribution of complex software networks is different from that of small-world networks and scale-free networks. We also found a typical structure that contributes to the edge instability distribution of complex software networks. Finally, we uncovered the correlation between propagation scope and edge instability in complex networks by eliminating the edges with different instability ranges.

In recent years, community detection has gradually become a hot topic in the complex network data mining field. The research of community detection is helpful not only to understand network topology structure but also to explore network hiding function. In this paper, we improve FluidC which is a novel community detection algorithm based on fluid propagation, by ameliorating the quality of seed set based on positive feedback and determining the node update order. We first summarize the shortcomings of FluidC and analyze the reasons result in these drawbacks. Then, we took some effective measures to overcome them and proposed an efficient community detection algorithm, called FluidC+. Finally, experiments on the generated network and real-world network show that our method not only greatly improves the performance of the original algorithm FluidC but also is better than many state-of-the-art algorithms, especially in the performance on real-world network with ground truth.

In this work, I study the propagation of cosmic rays inside the magnetic field of the Earth, at distances d ≤ 500 Km from its surface; at these distances, the geomagnetic field deeply influences the diffusion motion of the particles. I compare the different effects of the interplanetary and of the geomagnetic fields, by also discussing their role inside the cosmic rays transport equation; finally, I present an analytical method to solve such an equation through a factorization technique.

The heliosphere is the region around the Sun that is filled by the solar wind and its embedded magnetic field. The interaction of the supersonic solar wind with the local interstellar medium leads to a transition from supersonic to subsonic speeds at the heliospheric termination shock. The latter is regarded to be the source of the anomalous component of cosmic rays. Within the heliosphere "local" energetic particle sources, like the Sun and interplanetary shock waves contribute to the cosmic ray flux, too. At energies below a few GeV the observed galactic and anomalous cosmic ray intensities are modulated by the heliospheric magnetic field. In my contribution, both the current knowledge and hypotheses about modulation and the transport of cosmic rays in the heliosphere are reviewed.

An overview is given on results from direct and indirect measurements of galactic cosmic rays. Their implications on the contemporary understanding of the origin of cosmic rays and the knee in their energy spectrum are discussed.

The origin of the knee in the energy spectrum of cosmic rays is one of the central questions of high-energy astrophysics. One possible explanation is the energy dependent leakage of nuclei from the Galaxy due to their propagation. The latter is investigated in a combined method using numerical calculations of trajectories and the diffusion approximation. The life time of cosmic rays in the Galaxy and the corresponding pathlength are presented. The resulting energy spectra as observed at Earth are discussed and compared to experimental data.

We phenomenologically developed a propagation model of high energy galactic cosmic rays. We derived the analytical solutions by adopting the semi-empirical diffusion equation, proposed by Berezinskii et al. (1990) and the diffusion tensor proposed by Ptuskin et al. (1993). This model takes into account both the symmetric diffusion and the antisymmetric diffusion due to the particle Hall drift. Our solutions are an extension of the model developed by Ptuskin et al. to a two-dimensional two-layer (galactic disk and halo) model, and they coincide completely with the solution derived by Berezinskii et al. in the absence of antisymmetric diffusion due to Hall drift. We showed that this relatively simple toy model can be used to explain the variation in the exponent of the cosmic ray energy spectrum, γ, around the knee E ≈10¹⁵eV.

The model used for analyzing the gain characteristics of Er-doped waveguide amplifier (EDWA) is based on the rate-propagation equations with intensity profiles of pump and signal light (IPPSL). This simulation indicates that the IPPSL have significant effect on the gain of signal light. The results show that a gain change 2.3 dB of signal light at 1534 nm is obtained for a 4 cm long channel waveguide amplifier with different intensity profiles pumped by 80 mW at 980 nm. Experiment also shows that a gain change about 2.31 dB at 1534 nm for the channel waveguide of 4 cm length is obtained for different IPPSL. Thus, the effect of IPPSL should be considered to enhance the pump efficiency in the design of EDWA.

Epileptic seizures have spatial features related to the propagation of seizure waves. As the main characteristic of absence seizures, 2–4Hz spike-wave discharges (SWDs) originate from the cortices and are maintained by the thalamus. In this study, we explore the onset and propagation effect of absence seizures based on a thalamocortical model. First, we develop a two-compartment model and consider the autapse of the thalamic reticular nucleus as a crucial parameter to investigate transition behaviors. Moreover, we present dynamical mechanisms through bifurcation analysis. Simulation results show that the absence seizures can be induced and advanced as the coupling strength increases. Second, we investigate excitatory and inhibitory coupling functions in a three-compartment model. Our research indicates that the excitatory coupling function can lead to SWDs when all the compartments are initially saturated. In the process of propagation, excitatory coupling also gives rise to SWDs in normal compartments, whereas inhibitory coupling plays a limited role. Finally, we reproduce the above results in a 10-compartment model and verify the robustness against the variation of the number of modules. This work may shed new light on the field of seizure propagation and provide potential dynamical mechanisms.

In this paper, we study propagation phenomena on the sphere using the bistable reaction–diffusion formulation. This study is motivated by the propagation of waves of calcium concentrations observed on the surface of oocytes, and the propagation of waves of kinase concentrations on the B-cell membrane in the immune system. To this end, we first study the existence and uniqueness of mild solutions for a parabolic initial-boundary value problem on the sphere with discontinuous bistable nonlinearities. Due to the discontinuous nature of reaction kinetics, the standard theories cannot be applied to the underlying equation to obtain the existence of solutions. To overcome this difficulty, we give uniform estimates on the Legendre coefficients of the composition function of the reaction kinetics function and the solution, and a priori estimates on the solution, and then, through the iteration scheme, we can deduce the existence and related properties of solutions. In particular, we prove that the constructed solutions are of $C^{2,1}$ class everywhere away from the discontinuity point of the reaction term. Next, we apply this existence result to study the propagation phenomenon on the sphere. Specifically, we use stationary solutions and their variants to construct a pair of time-dependent super/sub-solutions with different moving speeds. When applied to the case of sufficiently small diffusivity, this allows us to infer that if the initial concentration of the species is above the inhomogeneous steady state, then the species will exhibit the propagating behavior.

This paper is concerned with the use of the reassigned wavelet transform for mode identification in shallow water acoustic propagation. Mode identification is important for inverse procedures in underwater acoustics. An efficient way to recognize the modal structure of the acoustic field when a single hydrophone is available is to refer to the time frequency analysis of the recorded signal using wavelet transform. However, the standard wavelet transform in some cases may result in an obscure representation of the dispersion curves. Thus, a reassigned process is proposed which brings important improvements in the time frequency representation of the signal. This is achieved by moving the calculation point of the scalogram in the center of gravity of the energy concentration, associated with each one of the propagating modes. This argument is supported by two illustrative examples corresponding to propagation of low frequency tomographic signals, in shallow water.

Modeling of acoustic pulse propagation in nonideal fluids requires the inclusion of attenuation and its causal companion, dispersion. For the case of propagation in a linear, unbounded medium Szabo developed a convolutional propagation operator which, when introduced into the linear wave equation, accounts for attenuation and causal dispersion for any medium whose attenuation possesses a generalized Fourier transform. Utilizing a one dimensional Finite Difference Time Domain (FDTD) model Norton and Novarini showed that for an unbounded isotropic medium, the inclusion of this unique form of the convolutional propagation operator into the wave equation correctly carries the information of attenuation and dispersion into the time domain. This paper addresses the question whether or not the operator can be used as a basic building block for pulse propagation in a spatially dependent dispersive environment. The operator is therefore used to model 2-D pulse propagation in the presence of an interface separating two dispersive media. This represents the simplest description of a spatially dependent dispersive media. It was found that the transmitted and backscattered fields are in excellent agreement with theoretical expectations demonstrating the effectiveness of the local operator to model the field in spatially dependent dispersive media. [Work supported by ONR/NRL.]

In this paper we introduce a fuzzy propagation model to deal with the influence maximization (IM) problem. The IM problem for the most of existing propagation model is NP-hard. Here, we model social networks as fuzzy directed graphs to propose an application-oriented propagation process. To this aim, we investigate an interesting relationship between zero forcing set concept in graphs and IM problem in social networks. In spite of its attractive theory, its implementation is not efficient in the real world. Thus, we improve the fuzzy zero forcing set concept and suggest our fuzzy propagation model, simultaneously. Moreover, we present a polynomial time complexity algorithm to solve IM problems under the proposed propagation process. In particular, we consider a propagation parameter to control the size of the seed set and its coverage. Also, experimental results on some real world social networks show that the propagation model finds optimal and flexible seed set.

Based on the Collins formula in strongly nonlocal nonlinear media (SNNM), the analytical expression for Lorentz beam passing through SNNM has been derived. It is found that the propagation behavior of Lorentz beam is variable and closely related to the parameters of initial ellipticity $p$ and input power. The beam has its own critical power in $x$ and $y$ directions, respectively. If the Lorentz beam with critical power in a certain direction enters in SNNM, its beam width will remain constant in that direction during propagation, otherwise its beam width varies periodically, as either broad or compressed. Moreover, when $p=1$, the beam spot is always symmetrical in $x$ and $y$ directions; when $p\ne 1$, the beam spot is no longer symmetrical in $x$ and $y$ directions. Numerical simulations are carried out to illustrate these quintessential propagation properties.

The traveling wave is the most important phenomenon in cochlear macromechanics. The behaviors of the traveling wave that greatly alter the auditory discrimination, are tightly related with the mechanical properties of the basilar membrane (BM) and its surrounding lymph. As an addition to the blanks of related researches, this paper focuses on some of the key parameters that affect the cochlear response most: the BM stiffness, damping parameters and the fluid viscosity. The influence of these parameters on the traveling wave is discussed, based on our former developed 2D finite element hydrodynamic cochlear model. Moreover, the traveling wave velocity and its transmitting time are calculated based on the simulating results. Although generally a rapid fall of the velocity from the cochlear base to the characteristic frequency (CF) location is confirmed, our quantitative analysis also indicates the traveling wave velocity may be both location and frequency dependent.

Mathematical models that utilize network representations have proven to be valuable tools for investigating biological systems. Often dynamic models are not feasible due to their complex functional forms that rely on unknown rate parameters. Network propagation has been shown to accurately capture the sensitivity of nodes to changes in other nodes; without the need for dynamic systems and parameter estimation. Node sensitivity measures rely solely on network structure and encode a sensitivity matrix that serves as a good approximation to the Jacobian matrix. The use of a propagation-based sensitivity matrix as a Jacobian has important implications for network optimization. This work develops Integrated Graph Propagation and OptimizatioN (IGPON), which aims to identify optimal perturbation patterns that can drive networks to desired target states. IGPON embeds propagation into an objective function that aims to minimize the distance between a current observed state and a target state. Optimization is performed using Broyden’s method with the propagationbased sensitivity matrix as the Jacobian. IGPON is applied to simulated random networks, DREAM4 in silico networks, and over-represented pathways from STAT6 knockout data and YBX1 knockdown data. Results demonstrate that IGPON is an effective way to optimize directed and undirected networks that are robust to uncertainty in the network structure.

Our study starts from the interaction of a thin liquid layer and surface acoustic waves in an isotropic semi-infinite substrate, and we obtain the relationship between wave velocity and thickness of ideal fluid layer. This result is similar with earlier experimental and research results. We further extend substrate to an isotropic semi-infinite plate, at which both symmetric and anti-symmetric modes of a plate can be captured as thickness of liquid layer becomes extremely thin. This result is very close to plate vibrations without the liquid layer. Finally, we analyze the characteristics of surface acoustic waves propagating in an anisotropic semi-infinite solid and plates covered with an ideal liquid layer. It is observed from an ST-cut quartz crystal substrate that there are many displacement modes and corresponding velocities due to the interaction of waves in the plate and liquid layer.

The propagation behaviors of surface acoustic waves in an isotropic semi-infinite solid and infinite plate with initial stress field are investigated, and we obtain the phase velocity equations of Rayleigh waves in a semi-infinite solid and infinite plate. By comparing surface acoustic waves velocity in plate under initial stress with that without initial stress, it is clear that velocity of surface acoustic waves are evidently affected by initial stress. When the stress is in the same direction of the propagation of the surface acoustic waves, the change of the wave velocity of the surface acoustic waves has certain relation to the stress within small numerical value of stress.

In this work, I study the propagation of cosmic rays inside the magnetic field of the Earth, at distances d ≤ 500 Km from its surface; at these distances, the geomagnetic field deeply influences the diffusion motion of the particles. I compare the different effects of the interplanetary and of the geomagnetic fields, by also discussing their role inside the cosmic rays transport equation; finally, I present an analytical method to solve such an equation through a factorization technique.

Social media has become an indispensable part of modern life. Networks behind the social media act as channels that allow information to spread every day. However, there are few studies on how physical quantities are propagated through social networks, even though they are common in real life. This paper aims at studying this propagation phenomenon via constructing a mathematical model: , where P is the transition matrix that transforms the values of attribute iteratively, and we propose an algorithm to obtain this transition matrix under the influence of several factors. This model can trace the change of values of an attribute throughout the propagation mechanism. Given a defined network relationship among players, a token donation game is conducted as a physical experiment to collect data, which are analyzed to build the mathematical model. Computer experiments based on the model are conducted to study the diffusion and decay rates, which govern respectively the flow directions and magnitude decreases towards the steady state. Some numerical simulations are performed for studying the efficiency and accuracy of the proposed model.