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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]

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]

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.

We investigate diffusion processes on fractal networks at different length scales. This is achieved by the application of a box covering procedure. We find that a clearly scaling law emerges on a great variety of fractal networks. Specifically, a number of metrics for quantifying diffusion processes, such as Kemeny's constant, the expected search time and its variation, follow a power-law with the number of boxes for covering. Furthermore, we identify a power-law relation between energy and the number of boxes. Remarkably, we show that the expected time for hunting a moving target similarly presents a power law behavior on a given fractal network. Our work reveals that scaling law is a common characteristic of fractal networks beyond their structural organization. • We investigate diffusion processes on fractal networks via a box covering procedure. • We find a clearly scaling law emerges on a great variety of fractal networks. • We identify a power-law relation between energy and the number of boxes. • Our work reveals that scaling law is a common feature of fractal networks. [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., Competing Interests: Conflict of interest The authors declare that they have no conflict of interest.