Article
Mathematics, Applied
Gabriel G. da Rocha, Ervin K. Lenzi
Summary: In this study, we investigate a diffusion process by simultaneously considering stochastic resetting and linear reaction kinetics. We initially discuss the formalism for a single species and then extend it to multiple species. By analyzing a general probability density function for the random walk, we obtain diverse behaviors for the waiting time and jumping probability distributions. These distributions' behaviors have implications for the diffusion-like equations derived from this approach and can be connected to different fractional operators with singular or nonsingular kernels. We also demonstrate that diffusion-like equations can exhibit a wide range of behaviors associated with various processes, particularly anomalous diffusion.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Mechanics
Tian Zhou, Pece Trajanovski, Pengbo Xu, Weihua Deng, Trifce Sandev, Ljupco Kocarev
Summary: We investigate a one-dimensional Brownian search with trapping. The particle's diffusion equation is described by a memory kernel in the general waiting time probability density function. We determine the general form of the first arrival time density, search reliability, and efficiency, and examine various special cases of the memory kernel. We also analyze the Levy search with trapping for single and multiple targets, as well as combined Levy-Brownian search strategies for a single target. These findings are general and have implications for studying optimal search strategies and the spread of contamination in animal foraging or environmental settings.
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2022)
Article
Statistics & Probability
Wagner Barreto-Souza, Ngai Hang Chan
Summary: This paper introduces a Nearly Unstable INteger-valued AutoRegressive Conditional Heteroscedastic (NU-INARCH) process and proves its asymptotic convergence property and the asymptotic distribution of the conditional least squares estimator. Monte Carlo simulations are used to verify the performance of the proposed method and a unit root test is proposed.
SCANDINAVIAN JOURNAL OF STATISTICS
(2023)
Article
Physics, Multidisciplinary
Chris D. Greenman
Summary: Reaction diffusion systems can be modeled using the machinery of quantum stochastic processes, which generalize Brownian motion and Poisson processes. This approach provides efficient analyses and alternative tools for investigating these systems, exemplified with spatial birth-death processes. The usual methods for such systems are master equations or Doi-Peliti path integration techniques.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2023)
Article
Physics, Multidisciplinary
Grigory Sarnitsky, Stefan Heinz
Summary: The dynamics of complex systems can be successfully modeled as stochastic diffusion processes, even when the real dynamics are not strictly diffusive. Current nonparametric estimation methods may lead to inconsistent results with the probability distribution of the system. We propose a novel estimation technique that provides drift and diffusion consistent with the observed probability density functions for turbulent flow and molecular motion in gas.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2022)
Article
Environmental Sciences
Dayang Li, Lucy Marshall, Zhongmin Liang, Ashish Sharma, Yan Zhou
Summary: The study shows that by combining a residual error model based on deep learning with process-based hydrological models, better estimates of uncertainty in catchment modeling can be achieved. In the comparison of two catchments in China, the Bayesian LSTM method provides superior uncertainty estimates compared to the Bayesian linear regression model.
WATER RESOURCES RESEARCH
(2021)
Article
Computer Science, Hardware & Architecture
Salman Jahani, Shiyu Zhou, Dharmaraj Veeramani, Jeff Schmidt
Summary: This study introduces a nonparametric prognostic framework for individualized event prediction based on event streams. The framework utilizes a multivariate Gaussian convolution process to predict intensity functions, enabling information sharing from historical data to current units and allowing for analysis of flexible event patterns.
IEEE TRANSACTIONS ON RELIABILITY
(2021)
Article
Engineering, Environmental
Ahmed Nafidi, Abdenbi El Azri, Ramon Gutierrez Sanchez
Summary: This paper explores the use of a stochastic non-homogeneous diffusion process to model the evolution of CO2 in Morocco. A new process and statistical methodology are established, with a simulated annealing method used to solve the nonlinear equation and validate the methodology through simulation examples before applying it to real data.
STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT
(2022)
Article
Computer Science, Artificial Intelligence
Kolade M. Owolabi, Berat Karaagac, Dumitru Baleanu
Summary: This paper explores the suitability of space fractional-order reaction-diffusion scenarios to model emergent pattern formation in predator-prey models. By considering the local dynamics of the systems, guidelines for parameter choice during numerical simulation are obtained. The biological wave scenarios are verified through presenting numerical results in two dimensions to mimic spatiotemporal dynamics such as spots, stripes and spiral patterns.
Article
Mathematics, Applied
Bartosz J. Bartmanski, Ruth E. Baker
Summary: The study explores the impact of various discretisations and methods for derivation of the diffusive jump rates on the outputs of stochastic simulations of reaction-diffusion models. It shows that while minor differences are observed for simple systems, significant variations can occur in model predictions for complex systems like Turing's diffusion-driven instability model of pattern formation. Care must be taken when using the reaction-diffusion master equation framework to make predictions for stochastic reaction-diffusion systems.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Physics, Multidisciplinary
Eman A. AL-hada, Xiangong Tang, Weihua Deng
Summary: Stochastic processes play a significant role in various fields such as ecology, biology, chemistry, and computer science. Anomalies in diffusion, known as anomalous diffusion (AnDi), are important in transport dynamics. However, identifying AnDi can be challenging, and machine learning algorithms like convolutional neural networks can help tackle this issue.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Mathematics, Applied
Yu Liu, Guanggan Chen, Shuyong Li
Summary: In this paper, the nonlinear orbital stability of the traveling wave solution for deterministic and stochastic delayed reaction-diffusion equation is established. The exponential stability of the traveling wave solution for the deterministic equation is obtained by employing a deterministic phase shift and establishing a delayed-integral inequality. It is verified that the traveling wave solution of the deterministic equation retains the nonlinear orbital stability when the noise intensity is sufficiently small and the initial value sufficiently closes the traveling wave by applying a stochastic phase shift and time transformation.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Multidisciplinary Sciences
R. S. MacKay
Summary: This paper presents methods to infer dominant modes of dynamical systems in real time, which can be real or complex, with specific characteristics such as damping rate and frequency. This work is motivated by the problem of oscillation detection in power flow in AC electrical networks, with suggestions for other potential applications provided.
ROYAL SOCIETY OPEN SCIENCE
(2021)
Article
Engineering, Chemical
Chance Parrish, Nelson Bell, Marvin E. Larsen, Kristianto Tjiptowidjojo, P. Randall Schunk
Summary: The coating and drying of inks and slurries are crucial steps in manufacturing various products. Drying processes, in particular, have significant impacts on product cost and quality due to their energy-intensive nature. This study develops a computational model and conducts benchtop drying experiments to address challenges in dryer modeling and predict process limits for drying polymer-laden coatings. The findings highlight the variability in Flory-Huggins parameter and the need for caution in choosing predictive approaches, as well as the importance of additional experiments to fully characterize and optimize drying processes.
Article
Mechanics
Alain Mazzolo, Cecile Monthus
Summary: This study focuses on imposing various conditioning constraints on a diffusion process with a space-dependent killing rate for a finite or infinite time horizon. The conditioned processes are constructed through optimization of dynamical large deviations under the desired conditioning constraints. Illustrative examples are provided to generate stochastic trajectories that satisfy different types of conditioning constraints.
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2022)
Article
Physics, Multidisciplinary
Kaan Ocal, Ramon Grima, Guido Sanguinetti
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2020)
Article
Genetics & Heredity
Giulio Caravagna, Timon Heide, Marc J. Williams, Luis Zapata, Daniel Nichol, Ketevan Chkhaidze, William Cross, George D. Cresswell, Benjamin Werner, Ahmet Acar, Louis Chesler, Chris P. Barnes, Guido Sanguinetti, Trevor A. Graham, Andrea Sottoriva
Article
Genetics & Heredity
Kashyap Chhatbar, Justyna Cholewa-Waclaw, Ruth Shah, Adrian Bird, Guido Sanguinetti
Article
Biochemical Research Methods
Giulio Caravagna, Guido Sanguinetti, Trevor A. Graham, Andrea Sottoriva
BMC BIOINFORMATICS
(2020)
Review
Biochemistry & Molecular Biology
Viplove Arora, Guido Sanguinetti
Summary: RNA-protein interactions play a crucial role in gene expression regulation. The development of scalable experimental techniques has revolutionized the field and generated large-scale datasets for machine learning. This note discusses the challenges of applying machine learning in computational RNA biology, with a focus on predicting RNA-protein interactions from next-generation sequencing data.
STATISTICAL APPLICATIONS IN GENETICS AND MOLECULAR BIOLOGY
(2022)
Article
Biochemical Research Methods
Christos Maniatis, Catalina Vallejos, Guido Sanguinetti
Summary: Single-cell multi-omics assays provide unprecedented opportunities to explore epigenetic regulation at the cellular level. However, high levels of technical noise and data sparsity often result in a lack of statistical power in correlative analyses. SCRaPL is a novel computational tool that addresses this issue by carefully modeling noise in the experimental systems.
PLOS COMPUTATIONAL BIOLOGY
(2022)
Article
Chemistry, Physical
Kaan oecal, Guido Sanguinetti, Ramon Grima
Summary: Model reduction is a crucial tool for quantitative biologists due to the complexity of mathematical models in biology. In this paper, we demonstrate that common approaches to model reduction for Chemical Master Equation can be viewed as minimizing the Kullback-Leibler divergence between the full model and its reduction. This enables us to transform the task of model reduction into a variational problem that can be solved using numerical optimization methods, and we also derive general expressions for propensities of a reduced system.
JOURNAL OF CHEMICAL PHYSICS
(2023)
Proceedings Paper
Computer Science, Artificial Intelligence
Ginevra Carbone, Luca Bortolussi, Guido Sanguinetti
Summary: This article explores the stability of saliency-based explanations of Neural Network predictions under adversarial attacks. Empirical evidence shows that interpretations provided by Bayesian Neural Networks are more stable under adversarial perturbations and attacks. The article also provides a theoretical explanation based on the geometry of the data manifold.
2022 INTERNATIONAL JOINT CONFERENCE ON NEURAL NETWORKS (IJCNN)
(2022)
Article
Multidisciplinary Sciences
Kaan oecal, Michael U. Gutmann, Guido Sanguinetti, Ramon Grima
Summary: Estimating uncertainty in model predictions is a central task in quantitative biology. We propose a flexible procedure for uncertainty quantification in a wide class of reaction networks describing stochastic gene expression including those with feedback. The method is based on creating a tractable coarse-graining of the model that is learned from simulations, a synthetic model, to approximate the likelihood function. Synthetic models can substantially outperform state-of-the-art approaches, providing an accurate and computationally viable solution to uncertainty quantification in stochastic models of gene expression.
JOURNAL OF THE ROYAL SOCIETY INTERFACE
(2022)
Article
Biochemistry & Molecular Biology
Yuanhua Huang, Guido Sanguinetti
Summary: This review discusses model-based approaches in single-cell RNA sequencing analysis within the framework of Bayesian statistics, highlighting the advantages and remaining challenges in this expanding research area.
CURRENT OPINION IN SYSTEMS BIOLOGY
(2021)
Proceedings Paper
Computer Science, Artificial Intelligence
Ginevra Carbone, Guido Sanguinetti, Luca Bortolussi
Summary: In this study, two training techniques, namely RP-Ensemble and RP-Regularizer, are proposed to enhance the robustness of Neural Networks against adversarial attacks. Both methods leverage random projections to exploit dimensionality reduction and geometric properties of adversarial perturbations, aiming to improve the network's resistance to input manipulations.
2021 INTERNATIONAL JOINT CONFERENCE ON NEURAL NETWORKS (IJCNN)
(2021)
Article
Biotechnology & Applied Microbiology
Yuanhua Huang, Guido Sanguinetti
Summary: RNA splicing plays a crucial role in driving heterogeneity in single cells through alternative transcript expression and transcriptional kinetics. BRIE2, a scalable computational method, effectively identifies differential disease-associated alternative splicing events and improves RNA velocity analysis, enabling exploration of the association between splicing phenotypes and biological changes.
Article
Biotechnology & Applied Microbiology
Paolo Marangio, Ka Ying Toby Law, Guido Sanguinetti, Sander Granneman
Summary: The diffBUM-HMM model accurately detects RNA flexibility and conformational changes from high-throughput RNA structure-probing data, accounting for noise and variability. It demonstrates higher sensitivity than existing methods and is robust against false positives, showing its value in quantitatively detecting RNA structural changes and RNA-binding protein binding sites.
Article
Biotechnology & Applied Microbiology
Chantriolnt-Andreas Kapourani, Ricard Argelaguet, Guido Sanguinetti, Catalina A. Vallejos
Summary: High-throughput single-cell measurements of DNA methylomes reveal the role of methylation heterogeneity in gene regulation. The hierarchical Bayesian model scMET addresses technical limitations, quantifies biological heterogeneity, identifies highly variable epigenetic features, and facilitates the characterization of epigenetically distinct cell populations.
Article
Biotechnology & Applied Microbiology
Chantriolnt-Andreas Kapourani, Guido Sanguinetti