Article
Mathematics, Applied
Yuya Tanaka
Summary: This paper focuses on the two-species chemotaxis-competition model with degenerate diffusion and proves the blow-up of weak solutions in finite time under certain conditions. Before proving this result, the paper also presents a finite-time blow-up under the same conditions for a modified version of the model with nondegenerate diffusion terms.
ACTA APPLICANDAE MATHEMATICAE
(2023)
Article
Mathematics
Chenyu Dong, Juntang Ding
Summary: This paper discusses the blow-up problem of positive solutions for degenerate parabolic equations, provides conditions leading to blow-up, and obtains upper bounds for blow-up time and rate for positive blow-up solutions. The research is mainly conducted through maximum principles and first-order differential inequality techniques.
Article
Mathematics, Applied
Sachiko Ishida, Tomomi Yokota
Summary: This paper discusses the stabilization of the initial-boundary value problem for a degenerate parabolic equation with no-flux boundary condition.
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
Santanu Saha Ray
Summary: In this paper, the similarity method is employed to solve a fractional Keller-Segel model with a nonlocal fractional Laplace operator, and the results are verified through comparison of the fractional centred difference method and the weighted shifted Gruwald-Letnikov difference method, demonstrating the accuracy and efficiency of the proposed numerical schemes.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
Wenjing Song, Wenhuo Su
Summary: In this paper, a blow-up criterion is established for the classical solutions of the compressible Navier-Stokes equations with degenerate viscosities, as well as the shallow water equations. Furthermore, it is proven that the maximum norm of the gradient of velocity plays a crucial role in controlling the possible breakdown of regular solutions for the compressible Navier-Stokes equations with degenerate viscosities.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Tong Tang, Xu Wei, Zhi Ling
Summary: In this paper, the blow-up phenomena of classical solutions to the compressible Navier-Stokes-Korteweg system with degenerate viscosity in arbitrary dimensions are studied. The upper and lower decay rates of the internal energy are obtained based on previous work. Furthermore, the results of blow-up phenomena do not require specific initial data conditions.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics
Razvan Gabriel Iagar, Ariel Sanchez
Summary: This study conducts a thorough examination of blow up profiles associated with a second order reaction-diffusion equation with non-homogeneous reaction, exploring the impact of different exponents and coefficients on the blow up behavior, with a particular focus on the influence of the non-homogeneous term on the qualitative aspects of finite time blow up.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
Salah Boulaaras, Abdelbaki Choucha, Praveen Agarwal, Mohamed Abdalla, Sahar Ahmed Idris
Summary: In this study, we analyze the blow-up phenomenon of solutions in a quasilinear system of viscoelastic equations with degenerate damping and general source terms, extending the recent results of Boulaaras et al.
ADVANCES IN DIFFERENCE EQUATIONS
(2021)
Article
Mathematics
Charles Elbar, Jakub Skrzeczkowski
Summary: There has been a recent interest in rigorously deriving the Cahn-Hilliard equation from the nonlocal equation, particularly with regards to degenerate mobilities. In this study, a new method is presented to show the convergence of the nonlocal to the local degenerate Cahn-Hilliard equation, using nonlocal Poincare and compactness inequalities. This research is motivated by models for the biomechanics of living tissues.(c)2023 Elsevier Inc. All rights reserved.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics
Li Chen, Veniamin Gvozdik, Yue Li
Summary: The aim of this paper is to provide the analysis result of the partial differential equations derived from the rigorous derivation of the degenerate parabolic-elliptic Keller-Segel system from a moderately interacting stochastic particle system. The solution theory of the degenerate parabolic-elliptic Keller-Segel problem and its non-local version is established, and the existence and well-posedness of the solution are derived through the introduction of a parabolic regularized system and perturbation method.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
Yuzhu Han
Summary: This paper investigates the blow-up property of solutions to an initial boundary value problem for a reaction diffusion equation with special diffusion processes. By combining Hardy inequality, 'moving' potential well methods, and some differential inequalities, it is proven that the solutions to this problem blow up in finite time under certain conditions on the initial data. Moreover, the upper and lower bounds for the blow-up time are also derived when blow-up occurs.
APPLICABLE ANALYSIS
(2022)
Article
Computer Science, Interdisciplinary Applications
Hui Guo, Xueting Liang, Yang Yang
Summary: In this paper, numerical algorithms are investigated to capture the blow-up time for a class of convection-diffusion equations with blow-up solutions. The positivity-preserving technique is used to enforce stability and the L1-stability and L2-norm of numerical approximations are utilized to detect the blow-up phenomenon. Two methods for defining the numerical blow-up time are proposed and their convergence to the exact time is proven.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Applied
Jose Carrillo Antonio, Ke Lin
Summary: In this paper, we consider a degenerate chemotaxis model with two-species and two-stimuli. We find two critical curves intersecting at one point which separate the global existence and blow up of weak solutions to the problem. By constructing initial data and analyzing the properties of solutions, we obtain some conclusions about the existence of solutions. In addition, we investigate the crossing point between the critical lines and provide a refined criteria to distinguish the dichotomy between global existence and blow up.
ADVANCES IN NONLINEAR ANALYSIS
(2022)
Article
Mathematics, Applied
Juntang Ding
Summary: This paper studies the blow-up solutions of weakly coupled degenerate parabolic systems with nonlinear boundary conditions by combining maximum principles and first-order differential inequality technique. The sufficient conditions for blow-up of nonnegative solutions and upper bounds on blow-up time and rate are provided for the problem.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2021)
Article
Mathematics, Applied
Soon-Yeong Chung, Jaeho Hwang
Summary: In this paper, blow-up solutions to nonlinear parabolic equations under mixed boundary conditions are studied. New conditions are introduced to obtain blow-up solutions, which depend on the domain and boundary conditions, as demonstrated through examples.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Chemistry, Physical
Kristopher K. Barr, Naihao Chiang, Andrea L. Bertozzi, Jerome Gilles, Stanley J. Osher, Paul S. Weiss
Summary: Scanning probe techniques have been enhanced by improving data acquisition and image processing algorithms, enabling more detailed analysis of surfaces and interfaces, including image segmentation by domains, detection of dipole direction, and hydrogen-bonding interactions. The computational algorithms used in these techniques are continually evolving, with the incorporation of machine learning to the next level of iteration. However, real-time adjustments during data recording are still a challenge for significantly enhancing microscopy and spectroscopic imaging methods.
JOURNAL OF PHYSICAL CHEMISTRY C
(2022)
Article
Chemistry, Multidisciplinary
Joseph de Rutte, Robert Dimatteo, Maani M. Archang, Mark van Zee, Doyeon Koo, Sohyung Lee, Allison C. Sharrow, Patrick J. Krohl, Michael Mellody, Sheldon Zhu, James Eichenbaum, Monika Kizerwetter, Shreya Udani, Kyung Ha, Richard C. Willson, Andrea L. Bertozzi, Jamie B. Spangler, Robert Damoiseaux, Dino Di Carlo
Summary: Techniques to analyze and sort single cells based on functional outputs have the potential to transform cellular biology and accelerate the development of cell and antibody therapies. This study describes a method to fabricate chemically functionalized microcontainers, called nanovials, for sorting single cells based on their secreted products. The nanovials can be easily used with commonly accessible laboratory infrastructure and allow high-throughput screening of cells.
Article
Engineering, Multidisciplinary
Kyung Ha, Joseph de Rutte, Dino Di Carlo, Andrea L. Bertozzi
Summary: This paper introduces a new method to create templated droplets using amphiphilic microparticles and presents a mathematical model to explain the key properties of droplet formation.
JOURNAL OF ENGINEERING MATHEMATICS
(2022)
Article
Computer Science, Artificial Intelligence
Bao Wang, Tan Nguyen, Tao Sun, Andrea L. Bertozzi, Richard G. Baraniuk, Stanley J. Osher
Summary: This paper proposes a new DNN training scheme called scheduled restart SGD (SRSGD), which replaces the constant momentum in SGD with increasing momentum and stabilizes the iterations by resetting the momentum to zero according to a schedule. Experimental results demonstrate that SRSGD significantly improves the convergence and generalization of DNNs across various models and benchmarks.
SIAM JOURNAL ON IMAGING SCIENCES
(2022)
Article
Oncology
Hangjie Ji, Kyle Lafata, Yvonne Mowery, David Brizel, Andrea L. Bertozzi, Fang-Fang Yin, Chunhao Wang
Summary: A biologically guided deep learning method was developed to predict post-radiation (18)FDG-PET image outcome based on pre-radiation images and radiotherapy dose information. The method incorporates a novel biological model and a 7-layer CNN to generate predicted images with breakdown biological components. The results showed good agreement with ground-truth and can be used for adaptive radiotherapy decision-making.
FRONTIERS IN ONCOLOGY
(2022)
Article
Mathematics, Applied
Marcelo Bongarti, Luke Diego Galvan, Lawford Hatcher, Michael R. Lindstrom, Christian Parkinson, Chuntian Wang, Andrea L. Bertozzi
Summary: In this paper, two ways of understanding and quantifying the effect of non-compliance to non-pharmaceutical intervention measures on the spread of infectious diseases are proposed using modified versions of the SIAR model. The first modification assumes a known proportion of the population does not comply with government mandates, while the second modification treats non-compliant behavior as a social contagion. The paper also explores different scenarios and provides local and asymptotic analyses for both models.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Yifan Hua, Kevin Miller, Andrea L. Bertozzi, Chen Qian, Bao Wang
Summary: This paper proposes near-optimal overlay networks based on d-regular expander graphs for accelerating decentralized federated learning and improving its generalization. By integrating spectral graph theory and the theoretical convergence and generalization bounds for DFL, the proposed overlay networks provide theoretical guarantees for accelerated convergence, improved generalization, and enhanced robustness to client failures in DFL. Additionally, an efficient algorithm is presented to convert a given graph into a practical overlay network and maintain the network topology after potential client failures. Numerical experiments demonstrate the advantages of DFL with the proposed networks on various benchmark tasks involving hundreds of clients.
SIAM JOURNAL ON APPLIED MATHEMATICS
(2022)
Article
Engineering, Multidisciplinary
Dominic Yang, Yurun Ge, Thien Nguyen, Denali Molitor, Jacob D. Moorman, Andrea L. Bertozzi
Summary: Symmetry is important in subgraph matching and affects both the graph description and the search process. This work quantifies the effects of symmetry and proposes using it to improve subgraph isomorphism algorithms' efficiency. The authors define structural equivalence and establish conditions for safely generating more solutions. They demonstrate how to modify search routines to utilize symmetries and efficiently describe the solution space. The methods are tested on a benchmark set and extended to multiplex graphs with results from transportation systems, social media, adversarial attacks, and knowledge graphs.
IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING
(2023)
Article
Criminology & Penology
Jiaoying Ren, Karina Santoso, David Hyde, Andrea L. Bertozzi, P. Jeffrey Brantingham
Summary: This paper examines the impact of COVID-19 on the activities of front-line workers in the City of Los Angeles Mayor's Office of Gang Reduction and Youth Development (GRYD), and finds that proactive peacemaking and violence interruption activities either remained stable or increased with the onset of the lockdown. However, the causal connection between these activities and gang-related crime needs further evaluation.
JOURNAL OF AGGRESSION CONFLICT AND PEACE RESEARCH
(2023)
Proceedings Paper
Computer Science, Artificial Intelligence
Jason Brown, Riley O'Neill, Jeff Calder, Andrea L. Bertozzi
Summary: By using data augmentations specific to SAR imagery, this paper develops a contrastive SimCLR framework for feature extraction from MSTAR images. The results show that our contrastive embedding performs better than the autoencoder embedding in automatic target recognition on the MSTAR dataset.
ALGORITHMS FOR SYNTHETIC APERTURE RADAR IMAGERY XXX
(2023)
Proceedings Paper
Computer Science, Artificial Intelligence
Joshua Enwright, Harris Hardiman-Mostow, Jeff Calder, Andrea Bertozzi
Summary: This article introduces two new methods for classifying SAR data. The first method involves using Convolutional Neural Network (CNN) for feature extraction and combining with graph-based semi-supervised learning techniques to improve classification performance in small labeled datasets. The second method involves using Pseudo Label Propagation Neural Networks (PsLaPN Networks) to enhance training signal and address overconfidence and poor model calibration in neural networks. In experiments, both methods outperform the previous state-of-the-art on the OpenSARShip dataset.
ALGORITHMS FOR SYNTHETIC APERTURE RADAR IMAGERY XXX
(2023)
Proceedings Paper
Acoustics
Harlin Lee, Andrea L. Bertozzi, Jelena Kovacevic, Yuejie Chi
Summary: This study investigates multi-task learning and proposes a fusion framework for federated multi-task linear regression. The proposed method combines local estimates and achieves improved performance in terms of mean squared error. Experimental results show the effectiveness of the method on real-world data.
2022 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP)
(2022)
Proceedings Paper
Computer Science, Interdisciplinary Applications
Kevin Miller, Jack Mauro, Jason Setiadi, Xoaquin Baca, Zhan Shi, Jeff Calder, Andrea L. Bertozzi
Summary: The article presents a novel method for classifying Synthetic Aperture Radar (SAR) data using a combination of graph-based learning and neural network methods. The method uses a Convolutional Neural Network Variational Autoencoder (CNNVAE) to embed SAR data into a feature space, and then constructs a similarity graph for classification. The method reduces overfitting and improves generalization performance, and can be easily combined with human-in-the-loop active learning.
ALGORITHMS FOR SYNTHETIC APERTURE RADAR IMAGERY XXIX
(2022)
Article
Automation & Control Systems
Karthik Elamvazhuthi, Bahman Gharesifard, Andrea L. Bertozzi, Stanley Osher
Summary: The controllability problem of the continuity equation corresponding to neural ordinary differential equations is explored, showing strong controllability properties. Specifically, given solutions of the continuity equation define trajectories on sets of probability measures. The study establishes the approximate controllability of the continuity equation of the neural ODE on sets of compactly supported probability measures.
IEEE CONTROL SYSTEMS LETTERS
(2022)
Article
Mathematics, Interdisciplinary Applications
Xia Li, Chuntian Wang, Hao Li, Andrea L. Bertozzi
Summary: Deterministic compartmental models can provide the mean behavior of stochastic agent-based models, but they may significantly deviate from the mean in finite size populations due to chance variations. In this article, a martingale formulation is derived for the stochastic Susceptible-Infected-Recovered (SIR) model, consisting of a deterministic part coinciding with the classical SIR model and an upper bound for the stochastic part. Theoretical explanation of finite size effects is provided through analysis of the stochastic component depending on varying population size, supported by quantitative and direct numerical simulations.
NETWORKS AND HETEROGENEOUS MEDIA
(2022)
Article
Mathematics, Applied
Melanie Kobras, Valerio Lucarini, Maarten H. P. Ambaum
Summary: In this study, a minimal dynamical system derived from the classical Phillips two-level model is introduced to investigate the interaction between eddies and mean flow. The study finds that the horizontal shape of the eddies can lead to three distinct dynamical regimes, and these regimes undergo transitions depending on the intensity of external baroclinic forcing. Additionally, the study provides insights into the continuous or discontinuous transitions of atmospheric properties between different regimes.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Shu-hong Xue, Yun-yun Yang, Biao Feng, Hai-long Yu, Li Wang
Summary: This research focuses on the robustness of multiplex networks and proposes a new index to measure their stability under malicious attacks. The effectiveness of this method is verified in real multiplex networks.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Julien Nespoulous, Guillaume Perrin, Christine Funfschilling, Christian Soize
Summary: This paper focuses on optimizing driver commands to limit energy consumption of trains under punctuality and security constraints. A four-step approach is proposed, involving simplified modeling, parameter identification, reformulation of the optimization problem, and using evolutionary algorithms. The challenge lies in integrating uncertainties into the optimization problem.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Alain Bourdier, Jean-Claude Diels, Hassen Ghalila, Olivier Delage
Summary: In this article, the influence of a turbulent atmosphere on the growth of modulational instability, which is the cause of multiple filamentation, is studied. It is found that considering the stochastic behavior of the refractive index leads to a decrease in the growth rate of this instability. Good qualitative agreement between analytical and numerical results is obtained.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Ling An, Liming Ling, Xiaoen Zhang
Summary: In this paper, an integrable fractional derivative nonlinear Schrodinger equation is proposed and a reconstruction formula of the solution is obtained by constructing an appropriate Riemann-Hilbert problem. The explicit fractional N-soliton solution and the rigorous verification of the fractional one-soliton solution are presented.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Marzia Bisi, Nadia Loy
Summary: This paper proposes and investigates general kinetic models with transition probabilities that can describe the simultaneous change of multiple microscopic states of the interacting agents. The mathematical properties of the kinetic model are proved, and the quasi-invariant asymptotic regime is studied and compared with other models. Numerical tests are performed to demonstrate the time evolution of distribution functions and macroscopic fields.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Carlos A. Pires, David Docquier, Stephane Vannitsem
Summary: This study presents a general theory for computing information transfers in nonlinear stochastic systems driven by deterministic forcings and additive and/or multiplicative noises. It extends the Liang-Kleeman framework of causality inference to nonlinear cases based on information transfer across system variables. The study introduces an effective method called the 'Causal Sensitivity Method' (CSM) for computing the rates of Shannon entropy transfer between selected causal and consequential variables. The CSM method is robust, cheaper, and less data-demanding than traditional methods, and it opens new perspectives on real-world applications.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Feiting Fan, Minzhi Wei
Summary: This paper focuses on the existence of periodic and solitary waves for a quintic Benjamin-Bona-Mahony (BBM) equation with distributed delay and diffused perturbation. By transforming the corresponding traveling wave equation into a three-dimensional dynamical system and applying geometric singular perturbation theory, the existence of periodic and solitary waves are established. The uniqueness of periodic waves and the monotonicity of wave speed are also analyzed.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Wangbo Luo, Yanxiang Zhao
Summary: We propose a generalized Ohta-Kawasaki model to study the nonlocal effect on pattern formation in binary systems with long-range interactions. In the 1D case, the model displays similar bubble patterns as the standard model, but Fourier analysis reveals that the optimal number of bubbles for the generalized model may have an upper bound.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Corentin Correia, Ana Cristina Moreira Freitas, Jorge Milhazes Freitas
Summary: The emergence of clustering of rare events is due to periodicity, where fast returns to target sets lead to a bulk of high observations. In this research, we explore the potential of a new mechanism to create clustering of rare events by linking observable functions to a finite number of points belonging to the same orbit. We show that with the right choice of system and observable, any given cluster size distribution can be obtained.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Enyu Fan, Changpin Li
Summary: This paper numerically studies the Allen-Cahn equations with different kinds of time fractional derivatives and investigates the influences of time derivatives on the solutions of the considered models.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Yuhang Zhu, Yinghao Zhao, Chaolin Song, Zeyu Wang
Summary: In this study, a novel approach called Time-Variant Reliability Updating (TVRU) is proposed, which integrates Kriging-based time-dependent reliability with parallel learning. This method enhances risk assessment in complex systems, showcasing exceptional efficiency and accuracy.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Chiara Cecilia Maiocchi, Valerio Lucarini, Andrey Gritsun, Yuzuru Sato
Summary: The predictability of weather and climate is influenced by the state-dependent nature of atmospheric systems. The presence of special atmospheric states, such as blockings, is associated with anomalous instability. Chaotic systems, like the attractor of the Lorenz '96 model, exhibit heterogeneity in their dynamical properties, including the number of unstable dimensions. The variability of unstable dimensions is linked to the presence of finite-time Lyapunov exponents that fluctuate around zero. These findings have implications for understanding the structural stability and behavior modeling of high-dimensional chaotic systems.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Christian Klein, Goksu Oruc
Summary: A numerical study on the fractional Camassa-Holm equations is conducted to construct smooth solitary waves and investigate their stability. The long-time behavior of solutions for general localized initial data from the Schwartz class of rapidly decreasing functions is also studied. Additionally, the appearance of dispersive shock waves is explored.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Vasily E. Tarasov
Summary: This paper extends the standard action principle and the first Noether theorem to consider the general form of nonlocality in time and describes dissipative and non-Lagrangian nonlinear systems. The general fractional calculus is used to handle a wide class of nonlocalities in time compared to the usual fractional calculus. The nonlocality is described by a pair of operator kernels belonging to the Luchko set. The non-holonomic variation equations of the Sedov type are used to describe the motion equations of a wide class of dissipative and non-Lagrangian systems. Additionally, the equations of motion are considered not only with general fractional derivatives but also with general fractional integrals. An application example is presented.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
