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Stochastic differential equations (SDE) play an important role in a range of application areas, including biology, physics, chemistry, epidemiology, mechanics, microelectronics, economics, and finance [1]. However, most SDEs, especially nonlinear SDEs, do not have analytical solutions, so that one must resort to numerical approximation schemes in order to simulate trajectories of the solutions to the given equation. The simplest effective computational method for approximation of ordinary differential equations is the Euler’s method. The Euler–Maruyama method is the analogue of the Euler’s method for ordinary differential equations for numerical simulation of the SDEs [2]. Another numerical... 

Stochastic differential equations (SDE) play an important role in a range of application areas, including biology, physics, chemistry, epidemiology, mechanics, microelectronics, economics, and finance [1]. However, most SDEs, especially nonlinear SDEs, do not have analytical solutions, so that one must resort to numerical approximation schemes in order to simulate trajectories of the solutions to the given equation. The simplest effective computational method for approximation of ordinary differential equations is the Euler’s method. The Euler–Maruyama method is the analogue of the Euler’s method for ordinary differential equations for numerical simulation of the SDEs [2]. Another numerical... 

In this chapter we introduce jump-diffusion processes and provide a theoretical framework that justifies the nonparametric (data-based) extraction of the parameters and functions controlling the arrival of a jump and the distribution of the jump size from the estimated conditional Kramers–Moyal moments. The method and the results are applicable to both stationary and nonstationary time series in the presence of discontinuous jump components; see Chap. 17. © 2019, Springer Nature Switzerland AG  

In this chapter we introduce jump-diffusion processes and provide a theoretical framework that justifies the nonparametric (data-based) extraction of the parameters and functions controlling the arrival of a jump and the distribution of the jump size from the estimated conditional Kramers–Moyal moments. The method and the results are applicable to both stationary and nonstationary time series in the presence of discontinuous jump components; see Chap. 17. © 2019, Springer Nature Switzerland AG  

We study loop-erased random walk (LERW) on the percolation cluster, with occupation probability p≥pc, in two and three dimensions. We find that the fractal dimensions of LERWp are close to normal LERW in a Euclidean lattice, for all p>pc. However, our results reveal that LERW on critical incipient percolation clusters is fractal with df=1.217±0.002 for d=2 and 1.43±0.02 for d=3, independent of the coordination number of the lattice. These values are consistent with the known values for optimal path exponents in strongly disordered media. We investigate how the behavior of the LERWp crosses over from Euclidean to fractal geometry by gradually decreasing the value of the parameter p from 1 to... 

Traditional mathematical models of epidemic disease had for decades conventionally considered static structure for contacts. Recently, an upsurge of theoretical inquiry has strived towards rendering the models more realistic by incorporating the temporal aspects of networks of contacts, societal and online, that are of interest in the study of epidemics (and other similar diffusion processes). However, temporal dynamics have predominantly focused on link fluctuations and nodal activities, and less attention has been paid to the growth of the underlying network. Many real networks grow: Online networks are evidently in constant growth, and societal networks can grow due to migration flux and... 

We introduce the bivariate jump-diffusion process, consisting of two-dimensional diffusion and two-dimensional jumps, that can be coupled to one another. We present a data-driven, nonparametric estimation procedure of higher-order (up to 8) Kramers-Moyal coefficients that allows one to reconstruct relevant aspects of the underlying jump-diffusion processes and to recover the underlying parameters. The procedure is validated with numerically integrated data using synthetic bivariate time series from continuous and discontinuous processes. We further evaluate the possibility of estimating the parameters of the jump-diffusion model via data-driven analyses of the higher-order Kramers-Moyal... 

The diffusion phenomenon has a remarkable impact on Online Social Networks (OSNs). Gathering diffusion data over these large networks encounters many challenges which can be alleviated by adopting a suitable sampling approach. The contributions of this paper is twofold. First we study the sampling approaches over diffusion networks, and for the first time, classify these approaches into two categories, (1) Structure-based Sampling (SBS), and (2) Diffusion-based Sampling (DBS). The dependency of the former approach to topological features of the network, and unavailability of real diffusion paths in the latter, converts the problem of choosing an appropriate sampling approach to a trade-off.... 

Partially-observed data collected by sampling methods is often being studied to obtain the characteristics of information diffusion networks. However, these methods usually do not consider the behavior of diffusion process. In this paper, we propose a novel two-step (sampling/estimation) measurement framework by utilizing the diffusion process characteristics. To this end, we propose a link-tracing based sampling design which uses the infection times as local information without any knowledge about the latent structure of diffusion network. To correct the bias of sampled data, we introduce three estimators for different categories, link-based, node-based, and cascade-based. To the best of... 

The spread of information cascades over social networks forms the diffusion networks. The latent structure of diffusion networks makes the problem of extracting diffusion links difficult. As observing the sources of information is not usually possible, the only available prior knowledge is the infection times of individuals. We confront these challenges by proposing a new method called DNE to extract the diffusion networks by using the time-series data. We model the diffusion process on information networks as a Markov random walk process and develop an algorithm to discover the most probable diffusion links. We validate our model on both synthetic and real data and show the low dependency... 

Diffusion imaging with confinement tensor (DICT) is a new model that employs a tensorial representation of the geometry confining the movements of water molecules. The model differs substantially from the commonly employed diffusion tensor imaging (DTI) technique even at small diffusion weightings when the dependence of the signal on the timing parameters of the pulse sequence is concerned. In this work, we assess the accuracy of the two models on a data set acquired from an excised monkey brain. The publicly available data set features differing values for diffusion pulse duration and separation. Our results indicate that the normalized mean squared error is reduced in an overwhelming... 

The out-of-pack cementation method was applied to coat the Nickel-based super alloy IN738LC with Si-modified aluminide. Different mixtures of the pack containing pure Al, Si, alumina powders as an inert filler, and NH4Cl as a halide salt activator were used for co-deposition at 950 and 1,050°C. The results showed although the amount of subhalide vapour pressures of Al and Si were equal at 1,050°C, Al atoms diffused only after Si atoms had been deposited. Before heat treatment, the coating thickness formed by the pack containing 2.3 wt.% Al was 6 μm more than that containing 3.5 wt.% Al. After heat treatment, thickening coatings formed within the pack containing 2.3 wt.% Al was less than that... 

To get a deep understanding of a diffusion process and realizing the most efficient methods for investigating a real network, has always been of great interest and utility to us. In this work, we aim to study and compare our mobility in a network using a normal random walk and a long-range navigation strategy such as Lévy Walk. We study the Global Mean First Traverse Distance (GMFTD) and the entropy rate for this long-range navigation process and later, compare with a normal walk strategy. For this study, GMFTD is utilized instead of Global Mean First Passage Time (GMFPT). The reason for such a choice is the fact that for more accurate and precise results, we need to also take into account... 

A depleted naturally fractured gas condensate reservoir with extremely tight matrix permeability in the center of Iran is used for gas storage. Due to the tightness of the matrix, simulation of this process may present a unique challenge in terms of the importance of diffusion process in flow behavior of the injected gas in matrix blocks. This article presents a multimechanistic (Darcian-type flow and Fickian-type flow) mathematical model to investigate the importance of diffusion process as a function of important rock and fluid parameters. The authors' approach consists of the following steps: (a) development of a 1-D governing equations for a single matrix block consists of a gas... 

This work studies the electrochemical growth behavior of cobalt nanowires in highly ordered aluminum oxide membrane. Considering the electrodeposition of metallic nanowires, cation concentration profile in each nano pore was calculated. With assumption of linear diffusion zone on the growing surface of nanowires, a modified Cottrell equation was evaluated. To confirm the model, the Co nanowires were electrodeposited into porous anodic aluminum oxide (AAO) templates and the mechanism of deposition was studied. Comparing the results of model and the experiments has proved the accuracy of the model. Also, it was observed that the growth of the Co nanowires was controlled mainly by diffusion... 

A novel AC impedance study on three-dimensional hybrid structures of graphene sheets/MoS2 nanorose (GMS) toward ethanol vapor detection is presented in this work. These defective 3D hybrid porous structures are sensitive to the presence of different gases as a result of charge transfer with gas species, as well as a change in the effective capacitance of the system. The sensing behavior of the samples is investigated throughout time-dependent impedance measurement and electrochemical impedance spectroscopy (EIS). The sensor response is estimated at about 20% to 10 ppm ethanol vapor, with the response and recovery times about 3.2 s and 0.8 s, respectively. Sensing mechanism proposed to... 

Stochastic parameters of self-agglomerated metallic nanoparticles on a dielectric film surface were studied using atomic force microscopy (AFM) analysis. In this regard, the rough surfaces including the nanoparticles were analyzed and characterized using structure function, roughness exponent and power spectrum density of the AFM profiles and their gradients, for different metal concentrations and heat treatment temperatures. The diffusion parameters, such as activation energy, of the nanoparticles initially accumulated on the surface into a porous and aqueous silica thin film were obtained using the AFM spectral analysis of the profiles and their gradients. It was found that the tip...