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In this paper we consider the filtering of partially observed multidimensional diffusion processes that are observed regularly at discrete times. This is a challenging problem which requires the use of advanced numerical schemes based upon time-discretization of the diffusion process and then the application of particle filters. Perhaps the state-of-the-art method for moderate-dimensional problems is the multilevel particle filter of Jasra et al. (SIAM J. Numer. Anal. 55 (2017), 3068–3096). This is a method that combines multilevel Monte Carlo and particle filters. The approach in that article is based intrinsically upon an Euler discretization method. We develop a new particle filter based upon the antithetic truncated Milstein scheme of Giles and Szpruch (Ann. Appl. Prob. 24 (2014), 1585–1620). We show empirically for a class of diffusion problems that, for $\epsilon>0$ given, the cost to produce a mean squared error (MSE) of $\mathcal{O}(\epsilon^2)$ in the estimation of the filter is $\mathcal{O}(\epsilon^{-2}\log(\epsilon)^2)$. In the case of multidimensional diffusions with non-constant diffusion coefficient, the method of Jasra et al. (2017) requires a cost of $\mathcal{O}(\epsilon^{-2.5})$ to achieve the same MSE. [ABSTRACT FROM AUTHOR]

Widely used volatility forecasting methods are usually based on low‐frequency time series models. Although some of them employ high‐frequency observations, these intraday data are often summarized into low‐frequency point statistics, for example, daily realized measures, before being incorporated into a forecasting model. This paper contributes to the volatility forecasting literature by instead predicting the next‐period intraday volatility curve via a functional time series forecasting approach. Asymptotic theory related to the estimation of latent volatility curves via functional principal analysis is formally established, laying a solid theoretical foundation of the proposed forecasting method. In contrast with nonfunctional methods, the proposed functional approach fully exploits the rich intraday information and hence leads to more accurate volatility forecasts. This is confirmed by extensive comparisons between the proposed method and those widely used nonfunctional methods in both Monte Carlo simulations and an empirical study on a number of stocks and equity indices from the Chinese market. [ABSTRACT FROM AUTHOR]

The article discusses Vili Lehdonvirta's book "Cloud Empires," which explores the role of digital platforms in shaping economic and social structures. Lehdonvirta argues that digital firms act as private providers of institutional foundations, resembling states in their governance functions. The book highlights the power dynamics between platforms and users, advocating for democratizing platforms to address inequalities. It also critiques antitrust regulations, suggesting alternative policies to empower platform users. The article praises the book's innovative approach to understanding platform power and its potential implications for future research and policy-making. [Extracted from the article]

We study numerical methods for simulating diffusions that exploit the orthogonal invariance of the Gaussian law, building on the work of Cruzeiro, Malliavin and Thalmeier. [ABSTRACT FROM AUTHOR]

Phosphorus in brass can have both a positive effect, such as improving mechanical properties, increasing corrosion resistance and machinability, and a negative effect, such as adversely affecting weldability and causing cracking. The study of the role of phosphorus in the processes of brass structure formation is of practical relevance, since it helps optimise the properties of the material, reduce the risk of defects, improve treatment processes and control properties and quality. The work covers the study of the role of phosphorus in brass, the need to control its content during production by limiting the share of secondary use. The study revealed the possibility of a positive effect of modifying copper alloys with phosphorus in order to improve performance properties, as well as the prospects of using phosphorus as a safe replacement for lead in brass. The authors assessed the content and distribution of phosphorus impurity at a concentration of 0.005 % in a brass sample of the CuZn32Mn3Al2FeNi grade, studied the nature of its interaction with other components of the alloy and the changes occurring at different temperatures of heat treatment. It has been found that phosphorus actively participates in diffusion processes and forms phosphides in both defective and defect-free blanks. When heated to the hot deformation temperature range, phosphorus redistribution occurs, phosphide locally dissolves, and metastable inclusions form. Due to differences in the concentration of elements in areas adjacent to the phosphide, the brass structure changes leading to the formation of areas different from the matrix β-phase. Manganese phosphide in brass can improve its mechanical properties and cutting ability, but an excess of this compound can lead to problems with strength, crack resistance, and moulding.

In this article we consider the estimation of static parameters for a partially observed diffusion process with discrete-time observations over a fixed time interval. In particular, we assume that one must time-discretize the partially observed diffusion process and work with the model with bias and consider maximizing the resulting log-likelihood. Using a novel double randomization scheme, based upon Markovian stochastic approximation we develop a new method to, in principle, unbiasedly estimate the static parameters, that is, to obtain the maximum likelihood estimator with no time discretization bias. Under appropriate mathematical assumptions we prove that our estimator is unbiased and investigate the method in several numerical examples, showing that it can empirically outperform the unbiased method in [J. Heng, J. Houssineau, and A. Jasra, J. Mach. Learn. Res., 25 (2024)]. [ABSTRACT FROM AUTHOR]

In this study, a nonlinear degenerate parabolic equation is used to describe a nonlinear-Laplacian equation process that arises in many areas of science and engineering in mechanics, quantum physics, and chemical design. This work has the objective of proving the existence of the local weak solution of a nonlinear p(x)- Laplacian equation by the compactness theorem. The uniformly local characteristics of the solutions for the gradients by estimating the regularization problem and using the Moser iterative techniques. Moreover, some properties of the local solutions depend on uniformly bounded situations and the Lp(x)-norm to the gradient is considered. [ABSTRACT FROM AUTHOR]

We establish a general framework using a diffusion approximation to simulate forward-in-time state counts or frequencies for cladogenetic state-dependent speciation-extinction (ClaSSE) models. We apply the framework to various two- and three-region geographic-state speciation-extinction (GeoSSE) models. We show that the species range state dynamics simulated under tree-based and diffusion-based processes are comparable. We derive a method to infer rate parameters that are compatible with given observed stationary state frequencies and obtain an analytical result to compute stationary state frequencies for a given set of rate parameters. We also describe a procedure to find the time to reach the stationary frequencies of a ClaSSE model using our diffusion-based approach, which we demonstrate using a worked example for a two-region GeoSSE model. Finally, we discuss how the diffusion framework can be applied to formalize relationships between evolutionary patterns and processes under state-dependent diversification scenarios. [ABSTRACT FROM AUTHOR]

We assume that the one-dimensional difiusion X satisffes a stochastic differential equation of the form: dXt = õ(Xt)dt + ö(Xt)=Wt, X0 = x0, t ≥ 0. Let (Xiùn; 0 ≥ i ≥ n) be discrete observations along a fixed time interval [0; T]. We prove that random vectors whose j-th component is p1 ....converge stably in law to a mixed normal random vector with a covariance matrix which depends on the path (Xt; 0 ≥ t ≥ T), when n ! 1. We use this result to prove stable convergence in law for ...)). [ABSTRACT FROM AUTHOR]

Interaction networks are a widely used tool to understand the dynamics of plant–pollinator ecological communities. However, while most mutualistic networks have been defined at the species level, ecological processes such as pollination take place at different scales, including the individual or patch levels. Yet, current approaches studying fine‐grain sub‐specific plant–pollinator networks only account for interactions among nodes belonging to a single plant species due to the conceptual and mathematical limitations of modeling simultaneously several plant species each composed of several nodes. Here, we introduce a multilayer diffusion network framework that allows modeling simple diffusion processes between nodes pertaining to the same or different layers (i.e. species). It is designed to depict from the network structure the potential conspecific and heterospecific pollen flows among plant individuals or patches. This potential pollen flow is modeled as a transport‐like system, in which pollen grain movements are represented as random‐walkers that diffuse on an ensemble of bipartite layers of conspecific plants and their shared pollinators. We exemplify this physical conceptualization using a dataset of nine fine‐grain sub‐specific plant–pollinator networks from a Mediterranean grassland of annual plants, where plant nodes represent groups of conspecifics within patches of 1 m2. The diffusion networks show pollinators effectively connecting sets of patches of the same and different plant species, forming a modular structure. Interestingly, different properties of the network structure, such as the conspecific pollen arrival probability and the number of conspecific subgraphs in which plants are embedded, are critical for the seed production of different plant species. We provide a simple but robust set of metrics to calculate potential pollen flow and scale down network ecology to functioning properties at the individual or patch level, where most ecological processes take place, hence moving forward the description and interpretation of species‐rich communities across scales. [ABSTRACT FROM AUTHOR]

In recent years, significant efforts have been made to understand oral drug absorption mechanisms and to develop new research models. These studies have been conducted using both in vitro and in vivo models and play a crucial role in determining the rate and extent of drug absorption in the intestines. Specifically, the permeability value (Peff value) is a common measure used to assess drug intestinal passage. Today, there is an increasing need for reliable gastrointestinal absorption models that can be used in preclinical studies to develop new drugs and appropriate dosages. However, collaboration and integration across different disciplines are important for further advancements in this field. Strengthening connections between pharmaceutical, biopharmaceutical, biochemical, and physiological research areas can contribute to a better understanding of drug absorption mechanisms and biopharmaceutical progress. Particularly, the use of animal models that mimic human intestinal drug permeability and the role of human cell culture models in investigating drug absorption in the intestine are highlighted as significant steps in this regard. Such research enables a more detailed examination of intestinal drug diffusion processes, which are crucial for the biopharmaceutical advancement of pharmaceutical compounds. Understanding factors such as the interactions between drug molecules and membrane transport molecules that affect the intestinal Peff value can further advance the assessment and improvement of drug absorption processes. [ABSTRACT FROM AUTHOR]

In this paper, we consider the filtering of partially observed multi-dimensional diffusion processes that are observed regularly at discrete times. We assume that, for numerical reasons, one has to time-discretize the diffusion process, which typically leads to filtering that is subject to discretization bias. The approach in [A. Jasra, K. J. H. Law and F. Yu, Unbiased filtering of a class of partially observed diffusions, Adv. Appl. Probab.54 (2022), 3, 661–687] establishes that, when only having access to the time discretized diffusion, it is possible to remove the discretization bias with an estimator of finite variance. We improve on this method by introducing a modified estimator based on the recent work [A. Jasra, M. Maama and H. Ombao, Antithetic multilevel particle filters, preprint (2023), https://arxiv.org/abs/2301.12371]. We show that this new estimator is unbiased and has finite variance. Moreover, we conjecture and verify in numerical simulations that substantial gains are obtained. That is, for a given mean square error (MSE) and a particular class of multi-dimensional diffusion, the cost to achieve the said MSE falls. [ABSTRACT FROM AUTHOR]

This article analyses the development of FinTech companies in relation to traditional banks in four countries: Denmark, Estonia, the Netherlands and Sweden. Based on approaches drawn from the sociology of markets and field theory, we analyse and theorize about empirical data from secondary sources, official documents and 38 interviews with key actors. Whereas digital technologies have been commonly depicted as a source of disruption for established business models, suggesting that the rise of FinTech leads to competitive upheaval in the financial sector, more recent studies argue that such interpretations are exaggerated. Here, we propose the emergence of a 'coopetitive' market ecosystem that combines co-operative and competitive connections between incumbents and challengers who often share the same infrastructure. FinTech firms are shown to function as catalysts in the transformation towards this ecosystem shaped by coopetitive interdependence between the actors. [ABSTRACT FROM AUTHOR]

The restructuring of the national economy, the processes of transformation taking place in it, actualize the problems of controlled vector development of complex hierarchical systems in the economy. The purpose of this study is to analyze the theoretical and methodological aspects of the development of complex hierarchical systems (CIS) in the economy in the context of unpredictability and stochasticity of the external and internal environment, as well as the uneven development of socioeconomic processes that require controlled vector development. It is the controllability of the vector development of the CIS that makes it possible to ensure the security of the processes of non-linear development of the CIS. The object of the research is the processes of non-linear development of the CIS in the conditions of unpredictability, stochasticity of the external environment and uneven development of socioeconomic processes caused by globalization transformations of the world economy. The study used general and special methods to achieve the goal and solve the tasks. The general methods include the abstract and logical method, which was used to explain the theoretical foundations of the security of the development of complex hierarchical systems, and the methods of theoretical generalization, system and behavioral-economic analysis, which helped to formulate the qualitative goals and objectives of the CIS, identify the problems of managing controlled dynamic processes, conduct a critical analysis of development concepts and find out the genesis of approaches. Special research methods include system-structural analysis, which was used for the formation, selection and implementation of hypotheses, construction of forecasts, and the system approach and methods of analysis and synthesis, which helped to identify and aggregate the qualitative characteristics of the concept of management of secured development of CIS. As a result of the application of these methods, a synergistic approach to the management of CIS processes was achieved and the problems related to stochasticity and uncertainty of the external and internal environment, uneven development of socioeconomic processes and other factors affecting the security of the development of the intellectual economy are addressed. The influence of endogenous and exogenous factors on the development of CIS is substantiated. A methodology based on process-functional management has been proposed to analyze the level of development of the CIS, which can help to increase the efficiency of the use of production resources. The conception of modeling mechanisms for the development of information security systems (ISS) based on the transformation of management processes and investment processes has been developed.

Behind the nice unification provided by the notion of the level 2.5 in the field of large deviations for time-averages over a long Markov trajectory, there are nevertheless very important qualitative differences between the meaning of the level 2.5 for diffusion processes on one hand, and the meaning of the level 2.5 for Markov chains either in discrete-time or in continuous-time on the other hand. In order to analyze these differences in detail, it is thus useful to consider two types of random walks converging towards a given diffusion process in dimension d involving arbitrary space-dependent forces and diffusion coefficients, namely (i) continuous-time random walks on the regular lattice of spacing b ; (ii) discrete-time random walks in continuous space with a small time-step τ. One can then analyze how the large deviations at level 2.5 for these two types of random walks behave in the limits b → 0 and τ → 0 respectively, in order to describe how the fluctuations of some empirical observables of the random walks are suppressed in the limit of diffusion processes. One can then also study the limits b → 0 and τ → 0 for any trajectory observable of the random walks that can be decomposed on its empirical density and its empirical flows in order to see how it is projected on the appropriate trajectory observable of the diffusion process involving its empirical density and its empirical current. [ABSTRACT FROM AUTHOR]

The restructuring of the national economy, the processes of transformation taking place in it, actualize the problems of controlled vector development of complex hierarchical systems in the economy. The purpose of this study is to analyze the theoretical and methodological aspects of the development of complex hierarchical systems (CIS) in the economy in the context of unpredictability and stochasticity of the external and internal environment, as well as the uneven development of socioeconomic processes that require controlled vector development. It is the controllability of the vector development of the CIS that makes it possible to ensure the security of the processes of non-linear development of the CIS. The object of the research is the processes of non-linear development of the CIS in the conditions of unpredictability, stochasticity of the external environment and uneven development of socioeconomic processes caused by globalization transformations of the world economy. The study used general and special methods to achieve the goal and solve the tasks. The general methods include the abstract and logical method, which was used to explain the theoretical foundations of the security of the development of complex hierarchical systems, and the methods of theoretical generalization, system and behavioral-economic analysis, which helped to formulate the qualitative goals and objectives of the CIS, identify the problems of managing controlled dynamic processes, conduct a critical analysis of development concepts and find out the genesis of approaches. Special research methods include system-structural analysis, which was used for the formation, selection and implementation of hypotheses, construction of forecasts, and the system approach and methods of analysis and synthesis, which helped to identify and aggregate the qualitative characteristics of the concept of management of secured development of CIS. As a result of the application of these methods, a synergistic approach to the management of CIS processes was achieved and the problems related to stochasticity and uncertainty of the external and internal environment, uneven development of socioeconomic processes and other factors affecting the security of the development of the intellectual economy are addressed. The influence of endogenous and exogenous factors on the development of CIS is substantiated. A methodology based on process-functional management has been proposed to analyze the level of development of the CIS, which can help to increase the efficiency of the use of production resources. The conception of modeling mechanisms for the development of information security systems (ISS) based on the transformation of management processes and investment processes has been developed. [ABSTRACT FROM AUTHOR]

Atomic diffusion is at the basis of chemical ordering transformations in nanoalloys. Understanding the diffusion mechanisms at the atomic level is therefore a key issue in the study of the thermodynamic behavior of these systems and, in particular, of their evolution from out-of-equilibrium chemical ordering types often obtained in the experiments. Here, the diffusion is studied in the case of a single-atom impurity of Ag or Au moving within otherwise pure magic-size icosahedral clusters of Cu or Co by means of two different computational techniques, i.e., molecular dynamics and metadynamics. Our simulations reveal unexpected diffusion pathways, in which the displacement of the impurity is coupled with the creation of vacancies in the central part of the cluster. We show that the observed mechanism is quite different from the vacancy-mediated diffusion processes identified so far, and we demonstrate that it can be related to the presence of non-homogeneous compressive stress in the inner part of the icosahedral structure. [ABSTRACT FROM AUTHOR]

A novel approach to simulate simple protein–ligand systems at large time and length scales is to couple Markov state models (MSMs) of molecular kinetics with particle-based reaction-diffusion (RD) simulations, MSM/RD. Currently, MSM/RD lacks a mathematical framework to derive coupling schemes, is limited to isotropic ligands in a single conformational state, and lacks multiparticle extensions. In this work, we address these needs by developing a general MSM/RD framework by coarse-graining molecular dynamics into hybrid switching diffusion processes. Given enough data to parameterize the model, it is capable of modeling protein–protein interactions over large time and length scales, and it can be extended to handle multiple molecules. We derive the MSM/RD framework, and we implement and verify it for two protein–protein benchmark systems and one multiparticle implementation to model the formation of pentameric ring molecules. To enable reproducibility, we have published our code in the MSM/RD software package. [ABSTRACT FROM AUTHOR]

We present new conditions on the drift of the Morrey type with mixed norms allowing us to obtain Aleksandrov type estimates of potentials of time inhomogeneous diffusion processes in spaces with mixed norms and, for instance, in L d 0 + 1 with d 0 < d . [ABSTRACT FROM AUTHOR]

We propose a discrete-time discrete-space Markov chain approximation with a Brownian bridge correction for computing curvilinear boundary crossing probabilities of a general diffusion process on a finite time interval. For broad classes of curvilinear boundaries and diffusion processes, we prove the convergence of the constructed approximations in the form of products of the respective substochastic matrices to the boundary crossing probabilities for the process as the time grid used to construct the Markov chains is getting finer. Numerical results indicate that the convergence rate for the proposed approximation with the Brownian bridge correction is $O(n^{-2})$ in the case of $C^2$ boundaries and a uniform time grid with n steps. [ABSTRACT FROM AUTHOR]

This manuscript explores the interaction between methylene blue dye and gelatin within a membrane using spectroscopy and image analysis. Emphasis is placed on methylene blue's unique properties, specifically its ability to oscillate between two distinct resonance states, each with unique light absorption characteristics. Image analysis serves as a tool for examining dye diffusion and absorption. The results indicate a correlation between dye concentrations and membrane thickness. Thinner layers exhibit a consistent dye concentration, implying an even distribution of the dye during the diffusion process. However, thicker layers display varying concentrations at different edges, suggesting the establishment of a diffusion gradient. Moreover, the authors observe an increased concentration of gelatin at the peripheries rather than at the center, possibly due to the swelling of the dried sample and a potential water concentration gradient. The manuscript concludes by suggesting image analysis as a practical alternative to spectral analysis, particularly for detecting whether methylene blue has been adsorbed onto the macromolecular network. These findings significantly enhance the understanding of the complex interactions between methylene blue and gelatin in a membrane and lay a solid foundation for future research in this field. [ABSTRACT FROM AUTHOR]

Matching a five-axis toolpath and a vector field (VF) of preferred directions (VFPD) is increasingly popular in the five-axis machining industry. However, surfaces represented by industrial formats often produce irregular non-homogeneous VFPD. The current methods are often unable to match such complicated VFs. We propose a new technique based on an enhanced vector flow (EVF), similar to the gradient flow by Xu and Prince (1998. "Generalized Gradient Vector Flow External Forces for Active Contours." Signal Processing 71 (2): 131–139) for image processing. The EVF keeps the high-rank vectors unchanged while extending them to unimportant regions, using a diffusion process based on a system of parabolic equations. The resulting enhanced vector field of statistically significant directions (EVFSD) is close to the original VFPD but is characterised by better continuity and regularity. Our second contribution is the clustering of the EVFSD using a prescribed library of templates by means of complex moments. The library includes three basic patterns: 'parallel'-zigzag, 'circular'-contour, and 'star'-radial patterns. The toolpaths are generated by an extension of transfinite interpolation (TFI). Virtual and real machining shows the advantages of EVFSD with reference to the standard iso-parametric paths and several state-of-the-art VF-based methods. The experiments have been performed on a five-axis machining centre, Haas VF-2TR. A video, illustrating the proposed procedure is at . [ABSTRACT FROM AUTHOR]

By applying the locally optimal rotation method to deal with the lowest eigenvalue of a Hessian matrix, we have efficiently incorporated the hyperdynamics method into the ab initio scheme. In the present method, we only need to calculate the first derivative of the potential and several more force calls in each molecular dynamics (MD) step, which makes hyperdynamics simulation applicable in ab initio MD simulations. With this implementation, we are able to simulate defect diffusion in silicon with boost factors up to 105. We utilized both direct MD and the hyperdynamics method to investigate diffusion of lithium atoms and silicon vacancies in silicon. We identified the complex diffusion process. The obtained diffusion coefficients of Li atoms and Si vacancies are in good agreement with the direct MD results. [ABSTRACT FROM AUTHOR]

We investigate the anomalous dynamics in smectic phases of short host rods where, counter-intuitively, long guest rod-shaped particles diffuse faster than the short host ones due to their precise size mismatch. In addition to the previously reported mean-square displacement, we analyze the time evolution of the self-Van Hove functions G(r, t), as this probability density function uncovers intrinsic heterogeneous dynamics. Through this analysis, we show that the dynamics of the host particles parallel to the director becomes non-Gaussian and therefore heterogeneous after the nematic-to-smectic-A phase transition, even though it exhibits a nearly diffusive behavior according to its mean-squared displacement. In contrast, the non-commensurate guest particles display Gaussian dynamics of the parallel motion, up to the transition to the smectic-B phase. Thus, we show that the self-Van Hove function is a very sensitive probe to account for the instantaneous and heterogeneous dynamics of our system and should be more widely considered as a quantitative and complementary approach of the classical mean-squared displacement characterization in diffusion processes. [ABSTRACT FROM AUTHOR]

Solid-state electrolyte materials with superior lithium ionic conductivities are vital to the next-generation Li-ion batteries. Molecular dynamics could provide atomic scale information to understand the diffusion process of Li-ion in these superionic conductor materials. Here, we implement the deep potential generator to set up an efficient protocol to automatically generate interatomic potentials for Li10GeP2S12-type solid-state electrolyte materials (Li10GeP2S12, Li10SiP2S12, and Li10SnP2S12). The reliability and accuracy of the fast interatomic potentials are validated. With the potentials, we extend the simulation of the diffusion process to a wide temperature range (300 K–1000 K) and systems with large size (∼1000 atoms). Important technical aspects such as the statistical error and size effect are carefully investigated, and benchmark tests including the effect of density functional, thermal expansion, and configurational disorder are performed. The computed data that consider these factors agree well with the experimental results, and we find that the three structures show different behaviors with respect to configurational disorder. Our work paves the way for further research on computation screening of solid-state electrolyte materials. [ABSTRACT FROM AUTHOR]

We investigate the dependence of the diffusion coefficient of a large solute particle on the solvation structure around a solute. The diffusion coefficient of a hard-sphere system is calculated by using a perturbation theory of large-particle diffusion with radial distribution functions around the solute. To obtain the radial distribution function, some integral equation theories are examined, such as the Percus–Yevick (PY), hypernetted-chain (HNC), and modified HNC theories using a bridge function proposed by Kinoshita (MHNC) closures. In one-component solvent systems, the diffusion coefficient depends on the first-minimum value of the radial distribution function. The results of the MHNC closure are in good agreement with those of calculation using the radial distribution functions of Monte Carlo simulations since the MHNC closure very closely reproduces the radial distribution function of Monte Carlo simulations. In binary-solvent mixtures, the diffusion coefficient is affected by the larger solvent density distribution in the short-range part, particularly the height and sharpness of the first peak and the depth of the first minimum. Since the HNC closure gives the first peak that is higher and sharper than that of the MHNC closure, the calculated diffusion coefficient is smaller than the MHNC closure result. In contrast, the results of the PY closure are qualitatively and quantitatively different from those of the MHNC and HNC closures. [ABSTRACT FROM AUTHOR]

A qualitative study for a second-order boundary value problem with local or nonlocal diffusion and a cubic nonlinear reaction term, endowed with in-homogeneous Cauchy–Neumann (Robin) boundary conditions, is addressed in the present paper. Provided that the initial data meet appropriate regularity conditions, the existence of solutions to the nonlocal problem is given at the beginning in a function space suitably chosen. Next, under certain assumptions on the known data, we prove the well posedness (the existence, a priori estimates, regularity, uniqueness) of the classical solution to the local problem. At the end, we present a particularization of the local and nonlocal problems, with applications for image processing (reconstruction, segmentation, etc.). Some conclusions are given, as well as new directions to extend the results and methods presented in this paper.

In this paper we offer a comprehensive review of Sociophysics, focusing on relevant models as well as selected applications in social trading, behavioral finance and business. We discuss three key aspects of social diffusion dynamics, namely Opinion Dynamics (OD), Group Decision-Making (GDM) and Knowledge Dynamics (KD). In the OD case, we highlight special classes of social agents, such as informed agents, contrarians and extremists. As regards GDM, we present state-of-the-art models on various kinds of decision-making processes. In the KD case, we discuss processes of knowledge diffusion and creation via the presence of self-innovating agents. The primary question we wish to address is: to what extent does Sociophysics correspond to social reality? For that purpose, for each social diffusion model category, we present notable Sociophysics applications for real-world socioeconomic phenomena and, additionally, we provide a much-needed critique of the existing Sociophysics literature, so as to raise awareness of certain issues that currently undermine the effective application of Sociophysics, mainly in terms of modelling assumptions and mathematical formulation, on the investigation of key social processes.

Modulating the soft magnetic properties of amorphous magnetic thin films is important for constructing energy-efficient and high performance thin film inductors. Here, a metal (Pt) and an oxide (Al2O3) are selected as the covering layer to investigate the effect of the interfacial microstructure on the magnetic properties of CoZrTa thin films. The results show that the magnetic dead layer thickness (tDL) and coercivity (Hc) decrease and saturation magnetization (Ms) increases with the annealing temperature for the CoZrTa/Al2O3 sample. However, tDL, Hc, and Ms of the CoZrTa/Pt sample show an opposite variation tendency with the annealing temperature. Interfacial structural results indicate that different magnetisms can be ascribed to different interfacial oxygen migration and interfacial diffusion processes. The effective interfacial oxygen migration in CoZrTa/Al2O3 reconstructs oxygen atom distribution at the interface and provides an effective way to enhance the magnetic properties of CoZrTa, whereas the intensified interfacial diffusion between CoZrTa and Pt after annealing in the CoZrTa/Pt sample caused the deterioration of the magnetism. This study will be helpful in advancing the development of magnetic thin film inductor devices. [ABSTRACT FROM AUTHOR]

A film/substrate system is a common structural form. In its fabrication and/or operation process, diffusion is a basic and key procedure. However, there still exist unclear points in the diffusion process, i.e., the effects of stress, creep, and interface properties. To clarify these unclear points, in this paper, a coupled diffusion model including stress, creep, and interface property is established. The obtained results indicate that compressive stress retards the diffusion of guest atoms. Meanwhile, creep reduces the retardation of diffusion through releasing the induced compressive stress, and then the concentration of the guest atoms can reach the prescribed value, which overcomes the much lower concentration predicted by the previous models without creep. In addition, interfacial diffusivity affects diffusion and the maximum stress in the film. [ABSTRACT FROM AUTHOR]

Among the many different types of molecules that form clathrate hydrates, H2 is unique as it can easily diffuse into and out of clathrate cages, a process that involves the physical–chemical interactions between guest (H2) and host (water) molecules, and is unlike any other molecular system. The dynamic and nano-scale process of H2 diffusion into binary structure II hydrates, where the large cages are occupied by larger molecules, was studied using molecular dynamics simulation. As the H2 molecules diffused from one cage to another, two types of diffusion processes were observed: (i) when moving between a pair of large cages, the H2 molecules pass through the central part of the hexagonal rings; (ii) however, when the H2 molecules move from a large cage to a small one, it requires one of the pentagonal rings to partially break, as this allows the H2 molecule to pass through the widened space. While the diffusion of H2 molecules between large cages was found to occur more frequently, the presence of SF6 molecules in the large cages was found to inhibit diffusion. Therefore, in order to attain higher H2 storage capacities in binary hydrates, it is suggested that there is an optimal number of large cages that should be occupied by SF6 molecules. [ABSTRACT FROM AUTHOR]

This paper provides insights into the degradation of InGaN-based LEDs by presenting a comprehensive analysis carried out on devices having two quantum wells (QWs) with different emission wavelengths (495 nm and 405 nm). Two different configurations are considered: one with the 495 nm QW closer to the p-side and one with the 495 nm QW closer to the n-side. The original results collected within this work indicate that (i) during stress, the devices show an increase in defect-related leakage both in reverse and low-forward voltage ranges: current increases with the square-root of stress time, indicating the presence of a diffusion process; (ii) stress induces a decrease in the luminescence signal emitted by both quantum wells: the drop in luminescence is stronger when measurements are carried out at low current levels, indicating that degradation is due to the generation of Shockley–Read–Hall recombination centers; (iii) remarkably, the degradation rate is linearly dependent on the luminescence signal emitted before stress by the well, indicating that carrier density impacts on degradation; and (iv) the optical degradation rate has a linear dependence on the stress current density. The results strongly suggest the existence of a recombination-driven degradation process: the possible role of Shockley–Read–Hall and Auger recombination is discussed. The properties of the defects involved in the degradation process are described through steady-state photocapacitance measurements. [ABSTRACT FROM AUTHOR]

Kinetic Monte Carlo (kMC) simulations are frequently used to study (electro-)chemical processes within science and engineering. kMC methods provide insight into the interplay of stochastic processes and can link atomistic material properties with macroscopic characteristics. Significant problems concerning the computational demand arise if processes with large time disparities are competing. Acceleration algorithms are required to make slow processes accessible. Especially, the accelerated superbasin kMC (AS-kMC) scheme has been frequently applied within chemical reaction networks. For larger systems, the computational overhead of the AS-kMC is significant as the computation of the superbasins is done during runtime and comes with the need for large databases. Here, we propose a novel acceleration scheme for diffusion and transport processes within kMC simulations. Critical superbasins are detected during the system initialization. Scaling factors for the critical rates within the superbasins, as well as a lower bound for the number of sightings, are derived. Our algorithm exceeds the AS-kMC in the required simulation time, which we demonstrate with a 1D-chain example. In addition, we apply the acceleration scheme to study the time-of-flight (TOF) of charge carriers within organic semiconductors. In this material class, time disparities arise due to a significant spread of transition rates. The acceleration scheme allows a significant acceleration up to a factor of 65 while keeping the error of the TOF values negligible. The computational overhead is negligible, as all superbasins only need to be computed once. [ABSTRACT FROM AUTHOR]

The chemo-mechanical coupling effect has been widely investigated due to its important impact on many areas, such as Li-ion batteries, biomechanical engineering, hydrogen embrittlement, etc. Meanwhile, the chemo-mechanical coupling effect on the high temperature oxidation process is drawing increasing attention. During oxidation, stress can be induced in the oxide film and will in turn influence the diffusion process and oxidation kinetics. Understanding the coupling effect between stress and oxidation helps to illuminate the mechanism of material degradation and failure. In this work, a concise physical model is developed for oxidation kinetics at elevated temperatures considering the diffusion-stress coupling effect, where both the inward and outward diffusion are considered. The model prediction shows an excellent agreement with the experimental observation. Based on this physical model, we also proposed a parameter to characterize the effects of cation/anion diffusion as well as a phase diagram to describe the universal diffusion–oxidation growth process. [ABSTRACT FROM AUTHOR]

The influence of Co micro-alloying (1 at. %) on the shear band diffusion and the relaxation processes in a model PdNiP bulk metallic glass is investigated. The shear bands are induced by one-pass cold-rolling. In addition to a fast shear band diffusion branch (D sb ≃ 10 − 16 m 2 / s at 473 K), with the diffusivity being similar to that observed for the cold-rolled standard Pd 40 Ni 40 P 20 composition, an ultrafast diffusion branch (D sb ≃ 10 − 14 m 2 / s at the same temperature) is found to exist in the micro-alloyed glass. Combined with previously reported observations of faster relaxation of both the Boson peak height and the fictive temperature, the results indicate that Co micro-alloying affects the excess free volume distribution and thus changes the potential energy landscape of the glass, introducing a higher number of local atomic arrangements prone to the formation of shear transformation zones under plastic deformation. [ABSTRACT FROM AUTHOR]

Atomic layer deposition (ALD) is a powerful tool for achieving atomic level control in the deposition of thin films. However, several physical and chemical phenomena can occur which cause deviation from "ideal" film growth during ALD. Understanding the underlying mechanisms that cause these deviations is important to achieving even better control over the growth of the deposited material. Herein, we review several precursor chemisorption mechanisms and the effect of chemisorption on ALD growth. We then follow with a discussion on diffusion and its impact on film growth during ALD. Together, these two fundamental processes of chemisorption and diffusion underlie the majority of mechanisms which contribute to material growth during a given ALD process, and the recognition of their role allows for more rational design of ALD parameters. [ABSTRACT FROM AUTHOR]

The propagation of fake news in online social networks nowadays is becoming a critical issue. Consequently, many mathematical models have been proposed to mimic the related time evolution. In this work, we first consider a deterministic model that describes rumor propagation and can be viewed as an extended logistic model. In particular, we analyze the main features of the growth curve, such as the limit behavior, the inflection point, and the threshold-crossing-time, through fixed boundaries. Then, in order to study the stochastic counterparts of the model, we consider two different stochastic processes: a time non-homogeneous linear pure birth process and a lognormal diffusion process. The conditions under which the means of the processes are identical to the deterministic curve are discussed. The first-passage-time problem is also investigated both for the birth process and the lognormal diffusion process. Finally, in order to study the variability of the stochastic processes introduced so far, we perform a comparison between their variances. [ABSTRACT FROM AUTHOR]

We employ a generalization of Einstein's random walk paradigm for diffusion to derive a class of multidimensional degenerate nonlinear parabolic equations in nondivergence form. Specifically, in these equations, the diffusion coefficient can depend on both the dependent variable and its gradient, and it vanishes when either one of the latter does. It is known that solutions of such degenerate equations can exhibit finite speed of propagation (so‐called localization property of solutions). We give a proof of this property using a De Giorgi–Ladyzhenskaya iteration procedure for nondivergence form equations. A mapping theorem is then established to a divergence‐form version of the governing equation for the case of one spatial dimension. Numerical results via a finite‐difference scheme are used to illustrate the main mathematical results for this special case. For completeness, we also provide an explicit construction of the one‐dimensional self‐similar solution with finite speed of propagation function, in the sense of Kompaneets–Zel'dovich–Barenblatt. We thus show how the finite speed of propagation quantitatively depends on the model's parameters. [ABSTRACT FROM AUTHOR]

This article presents the results of comparative analysis of diffusion and chemical processes running upon contact interaction with processed material of a regular cutting tool and of a tool with the surface layer of the working part modified by the impact of gas discharge. [ABSTRACT FROM AUTHOR]

The complex network has attracted increasing attention and shown effectiveness in modeling multifarious systems. Focusing on selecting members with good spreading ability, the influence maximization problem is of great significance in network-based information diffusion tasks. Plenty of attention has been paid to simulating the diffusion process and choosing influential seeds. However, errors and attacks typically threaten the normal function of networked systems, and few studies have considered the influence maximization problem under structural failures. Therefore, a quantitative measure with a changeable parameter is first developed in this paper to tackle the unpredictable destruction percentage on networks. Further, limitations on the existing methods are shown experimentally. To address these limitations, the evolutionary multitasking paradigm is employed, and several problem-specific operators are developed. On top of these developments, a multi-factorial evolutionary algorithm is devised to find seeds with robust influence ability, termed MFEARIM, where the genetic information for both myopia and holistic areas is considered to improve the search ability. Additionally, an asynchronous strategy is designed to efficiently tackle tasks with distinct costs, and the convergence of the search process can thus be accelerated. Experiments on several synthetic and real-world networks validate the competitive performance of MFEARIM over the existing methods. [ABSTRACT FROM AUTHOR]

In this article, we compare two ways of modelling measures of fetal growth. The goal is to impute the missing information for certain ultrasound measurements that are observed at different times and with different numbers of observations. To analyze the effect that other variables have, such as environmental exposure to certain substances or diet, on fetal growth based on these data, we need to handle the information measured at the same instant of time for all the individuals under study, preferably in three time windows of pregnancy (first trimester, week 12; second trimester, week 20; third trimester, week 34). For this, data at these chosen times, in case they are not available, must be imputed from the available information using an appropriate statistical model. One option is to use a linear model, specifically a generalized least squares model that is fitted to the features shown in the data. The other option is to use diffusion processes, estimating their parameters based on the available information. In both options, missing data can be estimated with the unconditional fitted model, conditional on the previous available measurement, or conditional to the closest measurement. [ABSTRACT FROM AUTHOR]

It is known that swelling of Nafion polymer membrane in water is accompanied by unwinding of polymer fibers into the bulk of the surrounding liquid. This effect is controlled by the deuterium content in water. In this paper, we report the results of studying the adsorption dynamics of methylene blue (MB) dye on the Nafion surface for MS solutions based on natural water (deuterium content 157 ppm, unwinding effect occurs) and based on deuterium-depleted water (DDW; deuterium content 3 ppm, unwinding effect is absent). In addition, we investigated the water desorption dynamics upon drying a Nafion polymer membrane after soaking in an MB solution based on natural water and DDW. It turned out that the MB adsorption rate in MB solutions based on natural water is lower than in the DDW-based MB solutions. Finally, the water desorption upon drying was found to be accompanied by a change in the Nafion absorption spectrum. Specifically, upon water desorption, the low-frequency band of the doublet in the range from 600 to 800 nm in the absorption spectrum of Nafion with MB particles on its surface undergoes transformation with a shift to the short-wavelength region. This transition occurred earlier for Nafion soaked in a DDW-based MB solution. The found effects are related to the retardation of diffusion processes in the layer of polymer fibers unwound near the membrane surface. Thus, changing the deuterium content in the aqueous solution in which the polymer membrane is swollen by very small steps (from 3 to 157 ppm), one can control the dynamics of adsorption and desorption processes. [ABSTRACT FROM AUTHOR]