Article
Mathematics
Sergio Albeverio, Carlo Marinelli, Elisa Mastrogiacomo
Summary: This article studies the dependence of mild solutions to linear stochastic evolution equations in Hilbert space driven by Wiener noise on the parameter epsilon. The limit and asymptotic expansions in powers of epsilon of these solutions, as well as functionals thereof, as epsilon -> 0, are investigated with good control on the remainder. These results of convergence and series expansion are then applied to a parabolic perturbation of the Musiela SPDE in mathematical finance modeling the dynamics of forward rates.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Automation & Control Systems
Hao Zhang, Zhenyu Li, Xilin Liu, Chunpeng Wang, Xingyuan Wang
Summary: This paper proposes a novel watermarking algorithm based on quaternion wavelet transform (QWT) and quaternion singular value decomposition (QSVD) for copyright protection. The algorithm converts color images from RGB space to YCbCr space and applies QWT transform to the luminance component Y. The watermark bits are embedded in singular vectors or singular values after decomposing the image into non-overlapping blocks using QSVD. Additionally, a 2D Chebyshev-Logistic map is used to encrypt the watermarks and scramble the embedding positions. Experimental results demonstrate that the proposed algorithm has good robustness against common attacks and achieves good invisibility.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Peter Gangl, Kevin Sturm
Summary: The paper investigates the asymptotic behavior of the quasilinear curl-curl equation of 3D magnetostatics with a singular perturbation of the differential operator, and proves the existence of the topological derivative using a Lagrangian approach. A systematic and concise method for deriving topological derivatives for quasi-linear elliptic problems is introduced, and an efficient way for numerical evaluation of the topological derivative in the design domain is discussed. This allows for the optimization of electrical machine design using the topological derivative.
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS
(2021)
Article
Computer Science, Artificial Intelligence
Qingtang Su, Xueting Zhang, Huanying Wang
Summary: A blind color image watermarking algorithm combining spatial domain and singular value decomposition (SVD) is designed in this paper to enhance the invisibility and geometric correction, thereby improving the robustness of the watermark.
INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS
(2022)
Article
Mathematics, Applied
Chong Cui, Hongxing Wang, Yimin Wei
Summary: This paper presents explicit expressions for the Moore-Penrose inverse of a perturbation matrix under the rank condition in the real field. An estimation for the error between the Moore-Penrose inverse and dual Moore-Penrose generalized inverse (DMPGI) is obtained, along with an upper bound for the error. Special conditions are also discussed in relation to the aforementioned results.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2023)
Article
Automation & Control Systems
Youness Braidiz, Andrey Polyakov, Denis Efimov, Wilfrid Perruquetti
Summary: This article considers the problem of finite-time and fixed-time stability analysis for a class of nonlinear systems. By utilizing the method of homogeneous extensions, the article presents important results and generalizes them to a more general class of systems.
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
(2022)
Article
Mathematics, Applied
Won-Kwang Park
Summary: This contribution presents a non-iterative technique based on topological derivative for solving an inverse conductivity problem. A mathematical structure of topological derivative is established, and a new imaging function with appropriate boundary conditions is proposed.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Biochemical Research Methods
Weiguang Mao, Javad Rahimikollu, Ryan Hausler, Maria Chikina
Summary: The study introduces a reconstruction method called DataRemix based on singular value decomposition, which can effectively prioritize biological signals over noise, and can be efficiently optimized for computationally expensive tasks such as eQTL analysis.
Article
Mathematics, Applied
Liliana Borcea, Beatrice Riviere, Yingpei Wang
Summary: This study introduces a nonoverlapping domain decomposition method for steady flow in high contrast heterogeneous media, with coefficients that have very large amplitude variations on a small spatial scale. Through analysis and numerical simulations, it shows how to use an asymptotic approximation of the Dirichlet to Neumann map to obtain a preconditioner for an efficient domain decomposition algorithm.
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
(2021)
Article
Acoustics
Amirali Sadeqi, Shapour Moradi
Summary: The paper introduces a time-domain filtering technique based on singular value decomposition for eliminating excitation/noise in operational modal analysis. The technique selects and explores components from the decomposed vibrational response, removes those associated with steady-state response and noise, and uses the transient response for identifying modal parameters. The effectiveness of the technique is demonstrated through numerical and experimental case studies, showing its capability to eliminate noise and excitation harmonics and reconstruct vibration signals.
JOURNAL OF SOUND AND VIBRATION
(2021)
Article
Ecology
Michael L. Collyer, Dean C. Adams
Summary: Phylogenetically aligned component analysis (PACA) is a new ordination approach that aligns phenotypic data with phylogenetic signal, allowing visualization of trends in phylogenetic signal in multivariate data spaces. By maximizing variation in directions that describe phylogenetic signal, PACA can distinguish between weak and strong phylogenetic signals, providing a more precise description of the phylogenetic signal in studies focused on phylogenetic signal. Comparing PACA and Phy-PCA results can help determine the relative importance of phylogenetic and other signals in the data.
METHODS IN ECOLOGY AND EVOLUTION
(2021)
Article
Automation & Control Systems
Weijia Yao, Bohuan Lin, Brian D. O. Anderson, Ming Cao
Summary: A path-following control algorithm ensures convergence of system trajectories to a given desired path. Control algorithms using a guiding vector field can guarantee almost global convergence, except for some trajectories that converge to the vector field's singular set. In this article, the guiding vector field is generalized to smooth Riemannian manifolds, and theoretical results are provided from a topological viewpoint regarding the existence of singular points and nonpath-converging trajectories.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2023)
Article
Physics, Fluids & Plasmas
Karl B. Hoffmann, Ivo F. Sbalzarini
Summary: Topological defects, important in various applications, can be identified in discrete domains through a robustness measure, achieving optimal trade-off between localization precision and robustness. This method enables uncertainty quantification for topological defects in noisy discretized nematic fields and polar fields.
Article
Mathematics, Applied
Matheus C. Bortolan, Leonardo Pires
Summary: This paper introduces the concept of spectral decomposition for global attractors of gradient semigroups, allowing for the definition of saddles for non-differentiable semigroups. Using this concept, necessary and sufficient conditions are given for the topological equivalence between two global attractors A1 and A2 of gradient semigroups T1 and T2, respectively, both having a spectral decomposition. An application is shown where Lipschitz perturbations of the Chafee-Infante equation produce gradient semigroups with global attractors with spectral decomposition, and that are topologically equivalent to the unperturbed attractor.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2023)
Article
Mathematics, Applied
Konstantin Pileckas, Alicija Raciene
Summary: The study investigates the initial boundary value problem for the non-stationary Navier-Stokes equations in a 2D bounded domain with a power cusp singular point O on the boundary. It considers the case of the boundary value with a nonzero flow rate, leading to a source/sink at O and the solution having an infinite energy integral. The paper constructs a formal asymptotic expansion of the solution near the singular point and proves the justification of the asymptotic expansion and the existence of a solution.
ADVANCES IN NONLINEAR ANALYSIS
(2021)
Article
Engineering, Multidisciplinary
Raquel Mattoso, Antonio A. Novotny
Summary: This work focuses on pointwise antennas design in hyperthermia treatment to selectively heat a specified target using optimal current densities. The methodology involves solving the steady-state heat equation and Helmholtz problem, minimizing an objective functional, and using sensitivities to devise antenna design algorithms. Numerical experiments demonstrate the capability of the proposed methodology to selectively heat the target up to the desired temperature.
APPLIED MATHEMATICAL MODELLING
(2021)
Article
Computer Science, Interdisciplinary Applications
Dirlei Ruscheinsky, Fernando Carvalho, Carla Anflor, Andre Antonio Novotny
Summary: This study conducted sensitivity analysis using the topological derivative method and devised a topology design algorithm based on a level-set representation method, resulting in simple analytical expressions. These findings provide useful insights for practical applications such as heat exchange topology design and membrane eigenvalue maximization.
ENGINEERING COMPUTATIONS
(2021)
Article
Engineering, Multidisciplinary
P. Menoret, M. Hrizi, A. A. Novotny
Summary: This work focuses on an inverse source problem related to the Poisson equation, aiming to reconstruct the unknown support location and size of a mass distribution using the Kohn-Vogelius formulation and topological derivative method. The resulting reconstruction procedure is non-iterative and robust with respect to noisy data. Numerical results from different examples of the Kohn-Vogelius type functional demonstrate the method's effectiveness and compare the robustness of each functional in solving the inverse source problem.
INVERSE PROBLEMS IN SCIENCE AND ENGINEERING
(2021)
Article
Computer Science, Interdisciplinary Applications
F. S. Carvalho, D. Ruscheinsky, S. M. Giusti, C. T. M. Anflor, A. A. Novotny
Summary: This work introduces the topological derivatives of L(2) and energy norms associated with the solution to Kirchhoff and Reissner-Mindlin plate bending models. Closed forms of the sensitivities are presented based on existing theoretical results. An analytical formula is used with a level-set domain representation method to devise a simple topology design algorithm for plates under elastic support and free vibration condition. Several finite element-based numerical experiments demonstrate its applications for compliance minimization and eigenvalue maximization of Kirchhoff and Reissner-Mindlin plate structures under bending effects.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2021)
Article
Computer Science, Interdisciplinary Applications
A. A. Novotny, C. G. Lopes, R. B. Santos
Summary: This paper proposes a regularization formulation to address the difficulties of topology optimization of structures subject to self-weight loading, introduces a 0-1 topology design algorithm using the topological derivative method, and validates the effectiveness of the approach through numerical experiments.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2021)
Article
Engineering, Industrial
Andre Jacomel Torii, Antonio Andre Novotny
Summary: This work presents priori error estimates for local reliability-based sensitivity analysis using the Score Function Method and Weak Approach with Monte Carlo Simulation. The results are crucial for practical parameter selection in local sensitivity analysis, and can also be utilized for future development of a posteriori error estimates and adaptive schemes. The theoretical results, initially obtained for the one dimensional case, are also applicable in multidimensional contexts, as evidenced by numerical experiments.
RELIABILITY ENGINEERING & SYSTEM SAFETY
(2021)
Editorial Material
Computer Science, Interdisciplinary Applications
Antonio Andre Novotny, Sebastian Miguel Giusti, Samuel Amstutz
ENGINEERING COMPUTATIONS
(2022)
Article
Mathematics, Applied
R. Prakash, M. Hrizi, A. A. Novotny
Summary: This paper presents a noniterative method for solving an inverse source problem governed by the two-dimensional time-fractional diffusion equation, using the topological derivative method to minimize a shape functional for reconstructing the geometrical support of the unknown source. The study results indicate that the proposed approach can efficiently and quickly reconstruct multiple anomalies of varying shapes and sizes, even when noisy data is taken into account.
Article
Computer Science, Interdisciplinary Applications
A. J. Torii, J. R. de Faria, A. A. Novotny
Summary: The main issue with existing constraint aggregation and regularization approaches is the significant bias that may affect the quality of the designs obtained, especially when dealing with a large number of active constraints. This paper proposes a novel probabilistic approach that overcomes such issues and allows for sharp regularization of extreme values even in the presence of closely spaced values. The proposed approach is compared with the p-norm regularization method and the results show that the proposed approach is more suitable for regularization and aggregation in such cases.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2022)
Article
Computer Science, Interdisciplinary Applications
A. A. M. da Silva, A. A. Novotny
Summary: In this work, a novel approach for solving a damage identification problem in plate structures is proposed, based on the topological derivative method. The method minimizes a shape function to determine the geometrical support of the unknown damage distribution, and represents the damage size and shape by minimizing the error between measured data and computed data.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2022)
Article
Engineering, Multidisciplinary
R. Mattoso, L. H. Gabrielli, A. A. Novotny
Summary: A novel topology optimization method for nanophotonic energy concentrators is proposed in this work. The method maximizes a shape functional to find the best material distribution that concentrates energy in a given target domain, using the topological derivative method. It avoids issues from eigen-mode calculations and can be applied to different design domains. The associated topological gradient is rigorously derived and used to devise a black/white binary topology design algorithm that conforms to practical fabrication constraints.
APPLIED MATHEMATICAL MODELLING
(2022)
Article
Mathematics, Applied
Mourad Hrizi, Antonio Andre Novotny, Maatoug Hassine
Summary: This paper discusses an inverse source problem governed by the Poisson equation and proposes a self-regularized topology optimization method to reconstruct multiple anomalies. It uses a least-square functional to measure the misfit between observation data and model values and applies the topological derivative method for the reconstruction process.
JOURNAL OF INVERSE AND ILL-POSED PROBLEMS
(2022)
Article
Mathematics
M. Hrizi, A. A. Novotny, R. Prakash
Summary: Time-fractional diffusion equations have attracted attention from mathematicians due to their wide applicability. This paper investigates a time-fractional inverse source problem, analyzing it through two interconnected streams. The identifiability of this inverse problem is established by proving the existence of a unique solution based on observed data. Furthermore, the problem is reformulated as a topology optimization problem with a quadratic mismatch functional and a regularization term, leading to the design of a noniterative reconstruction algorithm using the topological derivative method.
JOURNAL OF GEOMETRIC ANALYSIS
(2023)
Article
Engineering, Multidisciplinary
Jorge M. M. Luz Filho, Marcel Xavier, Antonio A. Novotny, Marcio A. Murad
Summary: We propose a new operator splitting scheme to describe fluid-driven brittle fracture propagation in a Biot medium. The scheme consists of two steps: in the injection step, a fixed stress split scheme is used to solve the hydrodynamic subsystem and the geomechanics, and in the fast time scale step, pore mechanics and fracture propagation are solved with frozen pore pressure and Darcy velocity fields. The evolution of the damaged zone is governed by the sensitivity of the associated shape functional with respect to the nucleation of a small damaged zone, which is computed using the topological derivative method.
INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
V Calisti, A. Lebee, A. A. Novotny, J. Sokolowski
Summary: The study investigates a multiscale elasticity model of solids with singular geometrical perturbations of microstructure for purposes such as optimum design. The homogenized linear elasticity tensors of first and second orders are considered in the framework of periodic Sobolev spaces. Sensitivity analysis of the second order homogenized elasticity tensor to topological microstructural changes is derived by introducing a small circular inclusion for topological perturbation of the microstructure.
JOURNAL OF ELASTICITY
(2021)