Article
Computer Science, Artificial Intelligence
Dalia Yousri, Mohamed Abd Elaziz, Laith Abualigah, Diego Oliva, Mohammed A. A. Al-qaness, Ahmed A. Ewees
Summary: This study proposes an alternative method for classifying COVID-19 X-ray images by extracting informative features and using a new feature selection method, leveraging an enhanced cuckoo search optimization algorithm and four different heavy-tailed distributions. Experimental results show that the method can provide accurate results for both UCI and COVID-19 datasets.
APPLIED SOFT COMPUTING
(2021)
Article
Computer Science, Interdisciplinary Applications
Victor F. F. Araman, Peter W. W. Glynn
Summary: This paper explores the limit process of the arrival counting process in a scheduled arrival model. It is found that when the delay of the arrivals has a super-heavy tail or a Cauchy-like tail, the limit processes are Brownian motion and fractional Brownian motion respectively.
Article
Mathematics, Applied
Edgardo Alvarez, Stiven Diaz, Carlos Lizama
Summary: In this paper, we introduce the concept of Levy alpha-stable distribution within the discrete setting and prove a subordination principle that relates solution operators for the abstract Cauchy problem of first order in discrete-time and the abstract Cauchy problem of fractional order 0 < alpha < 1 in discrete-time. As an application, we provide an explicit solution for the abstract Cauchy problem in discrete-time involving the Hilfer fractional difference operator and show that, in some cases, this solution converges to zero. Our findings offer new insights, propose original concepts, and extend and improve recent results in related literature.
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
(2022)
Article
Mathematics
Reem Abdullah Aljethi, Adem Kilicman
Summary: This paper proposes a generalized fractional Fokker-Planck equation based on a stable Levy stochastic process. By using the Levy process instead of the Brownian motion, this fractional equation provides a better description of heavy tails and skewness. The analytical solution is used to solve the fractional equation and is expressed using the H-function to demonstrate the indicator entropy production rate. Market data is modeled using a stable distribution to show the relationships between tails and the new fractional Fokker-Planck model, and an R code is developed for drawing figures from real data.
Article
Engineering, Mechanical
Shouwu Duan, Wanqing Song, Enrico Zio, Carlo Cattani, Ming Li
Summary: This paper proposes a multi-modal FLSM degradation model for predicting the product technical life or remaining useful life of equipment. By identifying multi-modes, switching points, and modal categories, and utilizing Markov state transition matrix and Monte Carlo Simulation, the effectiveness of the prediction model is validated.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2021)
Article
Engineering, Industrial
Yunfei Shao, Wujun Si, Yong Chen
Summary: Spatial modeling and monitoring are crucial for characterizing and controlling the quality of material/product surfaces. This article proposes a novel spatial model to capture long-range dependence (LRD) on material surfaces, and develops an LRD-integrated quality control framework. Simulation studies and a real case study validate the effectiveness of the proposed approach, showing significant improvement in anomaly detection compared to existing models.
JOURNAL OF QUALITY TECHNOLOGY
(2023)
Article
Automation & Control Systems
He Liu, Wanqing Song, Enrico Zio
Summary: This article describes a RUL prediction method based on fractional order Levy stable motion (fLsm), which solves the issue of unclear LRD in integer-order models. By revealing the LRD characteristics of fLsm through stability index and integral kernel function, a degradation prediction model is established and verified through Monte Carlo simulation.
Article
Mathematics
Xin Chen, Panki Kim, Jian Wang
Summary: This paper considers symmetric stable processes on horn-shaped regions, establishing two-sided Dirichlet heat kernel estimates using probabilistic methods. The results show that the reference function corresponding to each region has a significant impact on the estimates, and the Varopoulos-type estimates do not hold in general even when the associated Dirichlet semigroup is intrinsically ultracontractive.
MATHEMATISCHE ANNALEN
(2022)
Article
Statistics & Probability
Francis Comets, Joseba Dalmau, Santiago Saglietti
Summary: This study considers an alternative version of the ballistic deposition model with blocks of random heights and heavy-tailed distribution, and shows a phase transition as the adhesion probability p varies from 1 to 0.
ANNALS OF PROBABILITY
(2023)
Article
Mathematics
Saulius Paukstys, Jonas Siaulys, Remigijus Leipus
Summary: This paper examines the relationship between the distribution function and the truncated moment function of a random variable, as well as the transferability of this relationship to heavy-tailed distribution classes. The results show that the truncated moment function preserves the closure properties of heavy-tailed distribution classes, and conversely, it can transform the distribution function into the corresponding heavy-tailed distribution class.
Article
Mathematics, Applied
Xianming Liu
Summary: The study investigates the convergence behavior of solutions to stochastic differential equations (SDEs) as alpha approaches 2, focusing on SDEs with Lipschitz and Holder drifts, driven by alpha-stable Levy processes. Results show weak convergence in Skorokhod space and strong convergence via subordinated Brownian motion. Additionally, continuity of solutions at alpha* is discussed for alpha-stable Levy process-driven SDEs.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Automation & Control Systems
Hongpo Fu, Yongmei Cheng
Summary: In this paper, a new switching Gaussian-heavy-tailed (SGHT) distribution is proposed to model the non-stationary heavy-tailed measurement noise in the integrated inertial navigation system and global navigation satellite system (INS/GNSS). By utilizing two auxiliary parameters satisfying categorical and Bernoulli distributions, the SGHT distribution is constructed as a hierarchical Gaussian representation. A novel SGHT distribution based robust Gaussian approximate filter is derived using variational Bayesian inference. Meanwhile, an improved fixed-point iteration method is designed to reduce the computational complexity of the filtering process. The simulation results on integrated navigation for an aircraft demonstrate the effectiveness and superiority of the proposed filter compared to existing robust filters.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2022)
Article
Mathematics
Vassili N. Kolokoltsov
Summary: Levy walks are important modeling tools for various real-life processes. They are described by material fractional derivatives, which are known to represent their natural scaling limits. In this study, we derive the limiting equations for Levy walks with position-dependent times and velocities, where Fourier transforms cannot be effectively applied. We find three different limits, corresponding to different boundary conditions for the related Feller semigroups and processes, leading to three different multi-dimensional versions of Caputo-Dzherbashian derivatives. We also analyze other extensions and generalizations.
Article
Mathematics
Marco Cococcioni, Francesco Fiorini, Michele Pagano
Summary: One-sided heavy tailed distributions are important in engineering applications, but the LogNormal distribution is often discarded due to its finite variance. This work introduces a LogNormal distribution with a finite mean and a converging variance using Non-Standard Analysis. It allows for numerical and experimental verification of the expected mean and variance, which is more cumbersome in the traditional framework.
Article
Statistics & Probability
Lu-Jing Huang, Mateusz B. Majka, Jian Wang
Summary: This paper presents a rigorous theoretical framework for approximating heavy-tailed distributions using ergodic SDEs driven by symmetric alpha-stable processes.
Article
Environmental Sciences
Emanuela Bianchi Janetti, Monica Riva, Alberto Guadagnini
Summary: This study presents a comprehensive framework for the protection of natural springs and probabilistic risk assessment in uncertain groundwater system characterizations. The research focuses on a regional-scale hydrogeological setting in Northern Italy, with high-quality springs forming a unique system of critical importance. By considering uncertainties in model parameters and conceptual models, the study quantifies the risk of system failure due to various groundwater extraction strategies and identifies the most vulnerable springs.
SCIENCE OF THE TOTAL ENVIRONMENT
(2021)
Article
Water Resources
Guillem Sole-Mari, Monica Riva, Daniel Fernandez-Garcia, Xavier Sanchez-Vila, Alberto Guadagnini
Summary: The study reveals that the Sub-Gaussian model captures distinctive scale-dependent features of hydrogeological and soil science variables and is able to capture key aspects of this pattern. Computational analyses show that plume spreading is smaller in Sub-Gaussian fields compared to Gaussian fields, but it induces enhanced plume stretching. Local dispersion may mask the influence of Sub-Gaussianity on major transport metrics.
ADVANCES IN WATER RESOURCES
(2021)
Article
Environmental Sciences
Dustin Knabe, Alberto Guadagnini, Monica Riva, Irina Engelhardt
Summary: Managed aquifer recharge through bank filtration is important for sustainable drinking water production, but the water quality related to transport of pathogens into groundwater systems is concerning. A reactive transport model developed for a site in Germany revealed sensitivity of bacteria transport models to inactivation coefficients, straining coefficients, and bacteria size. The model calibration highlighted the key role of permeability in colmation layers and seasonal variability in groundwater conditions on bacteria transport.
WATER RESOURCES RESEARCH
(2021)
Article
Energy & Fuels
Ehsan Ranaee, Hamzeh Ghorbani, Sajjad Keshavarzian, Pejman Ghazaeipour Abarghoei, Monica Riva, Fabio Inzoli, Alberto Guadagnini
Summary: This study focuses on developing a methodological approach to assess the workflow and performance of a crude-oil desalting/demulsification system, using Global Sensitivity Analysis, machine learning, and rigorous model discrimination criteria. By analyzing a large dataset, the study quantifies the impact of system variables on industrial plant performance and formulates candidate models to represent system behavior.
Article
Water Resources
Fadji Zaouna Maina, Alberto Guadagnini, Monica Riva
Summary: The study evaluates the importance of uncertainty related to parameters characterizing groundwater flow on head and gravity changes during pumping tests in homogeneous and heterogeneous porous media. By conducting a Global Sensitivity Analysis and Monte Carlo simulations, the study quantifies the influence of uncertain parameters on the probability distribution of head and gravity changes, with a focus on the variance and correlation scale of spatially heterogeneous properties.
ADVANCES IN WATER RESOURCES
(2021)
Article
Engineering, Chemical
Martina Siena, Gianlorenzo Bussetti, Chiara Recalcati, Monica Riva, Lamberto Duo, Alberto Guadagnini
Summary: This study documents the evolution of surface topography of a calcite crystal during dissolution process using in situ real-time imaging obtained via atomic force microscopy (AFM). The analysis reveals that the statistical features of dissolution rates are influenced by the spreading rate of multilayer pits and parameters of GSG distribution.
TRANSPORT IN POROUS MEDIA
(2021)
Article
Engineering, Environmental
Laura Ceresa, Alberto Guadagnini, Giovanni M. Porta, Monica Riva
Summary: This study presents a mathematical framework for a biodegradation model that explains the reversibility of Diclofenac in groundwater, overcoming the issue of oversimplification in existing models.
Article
Thermodynamics
Felipe P. J. de Barros, Alberto Guadagnini, Monica Riva
Summary: The goal of this work is to investigate the transport behavior of an inert solute in non-Gaussian random fields. The analysis focuses on the transport dynamics through porous media with spatially heterogeneous non-Gaussian log-conductivity fields. The results indicate that the effects of non-Gaussianity on solute concentration statistics are more pronounced near the solute source zone and at early times.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2022)
Article
Engineering, Civil
Massimiliano Schiavo, Monica Riva, Laura Guadagnini, Erwin Zehe, Alberto Guadagnini
Summary: We use an energetic and probabilistic perspective to characterize key features of subsurface flow paths, primarily driven by gravity. By employing stochastic simulations and the concept of optimal channel networks, we identify and describe Preferential Groundwater Networks (PGNs), which are consistent with piezometric data. This study provides important insights for understanding groundwater flow.
JOURNAL OF HYDROLOGY
(2022)
Article
Engineering, Chemical
Leonardo Sandoval, Monica Riva, Ivo Colombo, Alberto Guadagnini
Summary: The study utilizes global sensitivity analysis methods to evaluate the behavior of recent models on gas migration, quantifies the impact of uncertain parameters and probability distribution types on methane flow assessment, and derives the structure of an effective diffusion coefficient to quantify the contribution of each flow mechanism to overall gas flow.
TRANSPORT IN POROUS MEDIA
(2022)
Article
Engineering, Chemical
Ehsan Ranaee, Fabio Inzoli, Monica Riva, Alberto Guadagnini
Summary: Our study aims to develop a stochastic characterization framework for coreflooding simulation models under two- and three-phase flow conditions with preferential flow associated with a system of fractures. We consider various modeling strategies based on single- and dual-continuum formulations and use a global sensitivity-driven stochastic parameter calibration. Monte Carlo simulations are conducted to evaluate the sensitivity of the models and obtain probability distributions of key model parameters through stochastic inverse modeling. The results show that the dual-continuum formulation performs the best in representing the system behavior, with petrophysical attributes and relative permeability having a stronger effect on model outputs than capillary pressure parameters.
TRANSPORT IN POROUS MEDIA
(2022)
Article
Engineering, Civil
Martina Siena, Chiara Recalcati, Alberto Guadagnini, Monica Riva
Summary: We propose theoretical formulations for characterizing the spatial distributions of variables in hydrogeological and/or geochemical scenarios associated with randomly heterogeneous geomaterials. Our approach integrates the assessment of the probability distribution of a target variable and its spatial increments between locations separated by any given distance. The spatial distribution is interpreted using a bimodal Gaussian mixture model, with each mode related to different processes and/or geomaterials within the observation domain.
JOURNAL OF HYDROLOGY
(2023)
Article
Environmental Sciences
Laura Ceresa, Alberto Guadagnini, Paula Rodriguez-Escales, Monica Riva, Xavier Sanchez-Vila, Giovanni M. M. Porta
Summary: We propose a methodology to quantify the impact of model structure and parametric uncertainty on biotransformation processes of Emerging Contaminants in subsurface water resources. The study aims to address the uncertainty and complexity of modeling bio-mediated reactions of recalcitrant compounds in soil and aquifers. We apply a suite of quantitative tools to diagnose uncertainty sources, estimate parameters, and select models, with the objective of balancing complexity and reliability.
WATER RESOURCES RESEARCH
(2023)
Article
Environmental Sciences
Emanuela Bianchi Janetti, Alberto Guadagnini, Monica Riva
Summary: We propose a reliable and efficient methodological framework for interpreting laboratory-scale partitioning tracer test data under uncertainty. The framework is based on a Time domain random walk (TDRW) particle tracking methodology, which is extended to include transport of partitioning tracers considering retardation and trapping mechanisms. The maximum likelihood (ML) approach is used to estimate model parameters, including residual immobile phase saturation and the partition coefficient. Experimental observations of the partition coefficient are included in the objective function with a regularization term. The results show that the TDRW-based approach effectively captures the observed breakthrough curves of partitioning tracers and provides satisfactory estimates of residual immobile phase saturation.
WATER RESOURCES RESEARCH
(2023)
Article
Environmental Sciences
Aronne Dell'Oca, Alberto Guadagnini, Monica Riva
Summary: We study the quantification of the probability of failure (PF) for infiltration structures in urban settings. Various uncertainties, such as mathematical models and design variables, are considered in our approach. We use a multi-model global sensitivity analysis framework to investigate the importance of model parameters and model selection on PF. Our results suggest that the choice of model has a significant impact on the importance associated with each uncertain parameter.
JOURNAL OF ENVIRONMENTAL MANAGEMENT
(2023)