Relevant bibliographies by topics / Differential equations, Nonlinear Data processing

Academic literature on the topic 'Differential equations, Nonlinear Data processing'

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Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Differential equations, Nonlinear Data processing"

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Enciso-Salas, Luis, Gustavo Pérez-Zuñiga, and Javier Sotomayor-Moriano. "Fault Diagnosis via Neural Ordinary Differential Equations." Applied Sciences 11, no. 9 (April 22, 2021): 3776. http://dx.doi.org/10.3390/app11093776.

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Implementation of model-based fault diagnosis systems can be a difficult task due to the complex dynamics of most systems, an appealing alternative to avoiding modeling is to use machine learning-based techniques for which the implementation is more affordable nowadays. However, the latter approach often requires extensive data processing. In this paper, a hybrid approach using recent developments in neural ordinary differential equations is proposed. This approach enables us to combine a natural deep learning technique with an estimated model of the system, making the training simpler and more efficient. For evaluation of this methodology, a nonlinear benchmark system is used by simulation of faults in actuators, sensors, and process. Simulation results show that the proposed methodology requires less processing for the training in comparison with conventional machine learning approaches since the data-set is directly taken from the measurements and inputs. Furthermore, since the model used in the essay is only a structural approximation of the plant; no advanced modeling is required. This approach can also alleviate some pitfalls of training data-series, such as complicated data augmentation methodologies and the necessity for big amounts of data.
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Lazarev, Alexander. "THE TECHNOLOGY OF WINTER CONCRETING OF MONOLITHIC FRAME STRUCTURES WITH SUBSTANTIATION OF HEAT TREATMENT MODES BY SOLUTIONS OF THE DIFFERENTIAL EQUATION OF THERMAL CONDUCTIVITY OBTAINED BY THE METHOD OF GROUP ANALYSIS." International Journal for Computational Civil and Structural Engineering 17, no. 4 (December 26, 2021): 115–22. http://dx.doi.org/10.22337/2587-9618-2021-17-4-115-122.

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An innovative method for calculating thermal fields inside monolithic structures has been developed, based on the use and analysis of nonlinear differential equations. The innovativeness of the method lies in the approach to the analysis of nonlinear physical processes using nonlinear differential equations. Thanks to the method of group analysis, 13 expressions are obtained from complex mathematical equations, which are easy to use and depend on several empirical coefficients. It is assumed that this calculation method is a priori more accurate than the existing ones, as well as available to people at a construction site without higher mathematical education, which makes it a priority for research. The applicability of this method must be proven by linking empirical coefficients and variables to the conditions of the experiments, while obtaining reliable data that will turn out to be more accurate than the existing calculation methods. This article demonstrates a systematic approach to establishing the suitability of using the method of group analysis of differential equations for problems of winter concreting on the basis of laboratory experiments under stationary conditions. The equations were subject to verification, which, according to the physical description, correspond to the real conditions of the course of thermal processes inside monolithic structures. Based on the obtained processing results, it was decided that it was necessary to further study the innovative method in the conditions of the construction site, but only for some expressions that showed the best results at the stage of laboratory tests.
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Borgese, G., S. Vena, P. Pantano, C. Pace, and E. Bilotta. "Simulation, Modeling, and Analysis of Soliton Waves Interaction and Propagation in CNN Transmission Lines for Innovative Data Communication and Processing." Discrete Dynamics in Nature and Society 2015 (2015): 1–13. http://dx.doi.org/10.1155/2015/139238.

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We present an innovative approach to study the interaction between oblique solitons, using nonlinear transmission lines, based on Cellular Neural Network (CNN) paradigm. A single transmission line consists of a 1D array of cells that interact with neighboring cells, through both linear and nonlinear connections. Each cell is controlled by a nonlinear Ordinary Differential Equation, in particular the Korteweg de Vries equation, which defines the cell status and behavior. Two typologies of CNN transmission lines are modelled: crisscross and ring lines. In order to solve KdV equations two different methods are used: 4th-order Runge-Kutta and Forward Euler methods. This is done to evaluate their accuracy and stability with the purpose of implementing CNN transmission lines on embedded systems such as FPGA and microcontrollers. Simulation/analysis Graphic User Interface platforms are designed to conduct numerical simulations and to display elaboration results. From this analysis it is possible both to identify the presence and the propagation of soliton waves on the transmission lines and to highlight the interaction between solitons and rich nonlinear dynamics. With this approach it is possible to simulate and develop the transmission and processing of information within large brain networks and high density sensor systems.
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Zaręba, Mateusz, and Tomasz Danek. "Nonlinear anisotropic diffusion techniques for seismic signal enhancing - Carpathian Foredeep study." E3S Web of Conferences 66 (2018): 01016. http://dx.doi.org/10.1051/e3sconf/20186601016.

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The use of nonlinear anisotropic diffusion algorithm for advanced seismic signal processing in the complicated geological region of Carpathian Foredeep was examined. This technique allows for an improvement of seismic data quality and for more accurate interpretation by the recovery of a significant amount of structural information in the form of a correlating seismic reflections and by preserving true DHI indicators. It also allows searching for more subtle geological structures. Anisotropic diffusion is an iterative image processing algorithm that removes noise by modifying the data by solving partial differential equations. Moreover, it can reduce image noise without blurring the edges between regions of different chrominance or brightness. This filter preserves edges, lines, or other features relevant to the seismic structural and stratigraphic interpretation. The algorithm also enables noise reduction without removing significant information from a seismic section even for high dips values. For a better estimation of anisotropic diffusion structure tensor, the parameterization is done using the depth field and the calculations in the two-way travel time field. The presented research shows the results of using an anisotropic diffusion algorithm for post-stack and migration processing of seismic 3D data collected in Carpathian reservoir rocks of southern Poland.
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Dyvak, M., V. Manzhula, A. Melnyk, and V. Tymchyshyn. "A System for Monitoring Air Pollution by Motor Vehicles Based on an Autonomous Air-Mobile Measuring Complex." Optoelectronic Information-Power Technologies 42, no. 2 (October 26, 2022): 73–83. http://dx.doi.org/10.31649/1681-7893-2021-42-2-73-83.

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The article proposes an approach to constructing a system of complex and uninterrupted monitoring of harmful emissions of motor vehicles into the air. The architecture of the environmental monitoring system for measuring and forecasting the distribution of pollutant concentrations in motor vehicle exhaust gases, among which mainly CO, SO₂, NO₂, and СО₂, is presented. The mobile information and measurement complex Sniffer4D Hyper-local Air Quality Analyzer and a charging station based on solar batteries are used as the hardware. For modeling and forecasting the distribution of concentrations of harmful emissions, mathematical models of the dynamics of the distribution of concentrations of pollutants due to harmful emissions in the exhaust gases of motor vehicles are proposed in the form of differential equations that are analogs of differential equations in partial derivatives, as models of turbulent diffusion and interval models of the distribution of the background level of pollution concentration in the form of nonlinear algebraic equations. Implemented software for data collection, processing (model learning and prediction), and visualization.
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Dyvak, M., V. Manzhula, A. Melnyk, and V. Tymchyshyn. "A System for Monitoring Air Pollution by Motor Vehicles Based on an Autonomous Air-Mobile Measuring Complex." Optoelectronic Information-Power Technologies 42, no. 2 (October 26, 2022): 73–83. http://dx.doi.org/10.31649/1681-7893-2021-41-1-73-83.

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The article proposes an approach to constructing a system of complex and uninterrupted monitoring of harmful emissions of motor vehicles into the air. The architecture of the environmental monitoring system for measuring and forecasting the distribution of pollutant concentrations in motor vehicle exhaust gases, among which mainly CO, SO₂, NO₂, and СО₂, is presented. The mobile information and measurement complex Sniffer4D Hyper-local Air Quality Analyzer and a charging station based on solar batteries are used as the hardware. For modeling and forecasting the distribution of concentrations of harmful emissions, mathematical models of the dynamics of the distribution of concentrations of pollutants due to harmful emissions in the exhaust gases of motor vehicles are proposed in the form of differential equations that are analogs of differential equations in partial derivatives, as models of turbulent diffusion and interval models of the distribution of the background level of pollution concentration in the form of nonlinear algebraic equations. Implemented software for data collection, processing (model learning and prediction), and visualization.
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Gandham, Rajesh, David Medina, and Timothy Warburton. "GPU Accelerated Discontinuous Galerkin Methods for Shallow Water Equations." Communications in Computational Physics 18, no. 1 (July 2015): 37–64. http://dx.doi.org/10.4208/cicp.070114.271114a.

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AbstractWe discuss the development, verification, and performance of a GPU accelerated discontinuous Galerkin method for the solutions of two dimensional nonlinear shallow water equations. The shallow water equations are hyperbolic partial differential equations and are widely used in the simulation of tsunami wave propagations. Our algorithms are tailored to take advantage of the single instruction multiple data (SIMD) architecture of graphic processing units. The time integration is accelerated by local time stepping based on a multi-rate Adams-Bashforthscheme. A total variational bounded limiter is adopted for nonlinear stability of the numerical scheme. This limiter is coupled with a mass and momentum conserving positivity preserving limiter for the special treatment of a dry or partially wet element in the triangulation. Accuracy, robustness and performance are demonstrated with the aid of test cases. Furthermore, we developed a unified multi-threading model OCCA. The kernels expressed in OCCA model can be cross-compiled with multi-threading models OpenCL, CUDA, and OpenMP. We compare the performance of the OCCA kernels when cross-compiled with these models.
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Bhatti, Muhammad Mubashir, Anwar Shahid, Tehseen Abbas, Sultan Z. Alamri, and Rahmat Ellahi. "Study of Activation Energy on the Movement of Gyrotactic Microorganism in a Magnetized Nanofluids Past a Porous Plate." Processes 8, no. 3 (March 11, 2020): 328. http://dx.doi.org/10.3390/pr8030328.

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The present study deals with the swimming of gyrotactic microorganisms in a nanofluid past a stretched surface. The combined effects of magnetohydrodynamics and porosity are taken into account. The mathematical modeling is based on momentum, energy, nanoparticle concentration, and microorganisms’ equation. A new computational technique, namely successive local linearization method (SLLM), is used to solve nonlinear coupled differential equations. The SLLM algorithm is smooth to establish and employ because this method is based on a simple univariate linearization of nonlinear functions. The numerical efficiency of SLLM is much powerful as it develops a series of equations which can be subsequently solved by reutilizing the data from the solution of one equation in the next one. The convergence was improved through relaxation parameters in the study. The accuracy of SLLM was assured through known methods and convergence analysis. A comparison of the proposed method with the existing literature has also been made and found an excellent agreement. It is worth mentioning that the successive local linearization method was found to be very stable and flexible for resolving the issues of nonlinear magnetic materials processing transport phenomena.
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Xu, Qingzhen. "A Novel Machine Learning Strategy Based on Two-Dimensional Numerical Models in Financial Engineering." Mathematical Problems in Engineering 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/659809.

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Machine learning is the most commonly used technique to address larger and more complex tasks by analyzing the most relevant information already present in databases. In order to better predict the future trend of the index, this paper proposes a two-dimensional numerical model for machine learning to simulate major U.S. stock market index and uses a nonlinear implicit finite-difference method to find numerical solutions of the two-dimensional simulation model. The proposed machine learning method uses partial differential equations to predict the stock market and can be extensively used to accelerate large-scale data processing on the history database. The experimental results show that the proposed algorithm reduces the prediction error and improves forecasting precision.
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Wu, Jianhong, Hossein Zivari-Piran, John D. Hunter, and John G. Milton. "Projective Clustering Using Neural Networks with Adaptive Delay and Signal Transmission Loss." Neural Computation 23, no. 6 (June 2011): 1568–604. http://dx.doi.org/10.1162/neco_a_00124.

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We develop a new neural network architecture for projective clustering of data sets that incorporates adaptive transmission delays and signal transmission information loss. The resultant selective output signaling mechanism does not require the addition of multiple hidden layers but instead is based on the assumption that the signal transmission velocity between input processing neurons and clustering neurons is proportional to the similarity between the input pattern and the feature vector (the top-down weights) of the clustering neuron. The mathematical model governing the evolution of the signal transmission delay, the short-term memory traces, and the long-term memory traces represents a new class of large-scale delay differential equations where the evolution of the delay is described by a nonlinear differential equation involving the similarity measure already noted. We give a complete description of the computational performance of the network for a wide range of parameter values.
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Dissertations / Theses on the topic "Differential equations, Nonlinear Data processing"

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Cereijo, Martinez Maria. "A new parallel technique for the solution of sparse nonlinear equations." FIU Digital Commons, 1994. http://digitalcommons.fiu.edu/etd/2097.

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Solving nonlinear systems of equations is a central problem in numerical analysis, with enormous significance for science and engineering. A special case, sparse systems of equations, occurs frequently in various applications. Sparsity occurs in the analysis of many types of complex systems because of the local nature of the dependence or connectivity among system components. One such system which may be modeled by a nonlinear sparse set of equations is the power system load flow analysis. This is a mathematical study performed by electrical utilities to monitor the electrical power system. The data from system components are used to create a set of nonlinear equations. These equations are then solved to find the voltage profile of the power network. With these data, control and security of the power system are achieved. Solving problems of this type is very time consuming when the system is large. This dissertation proposes a highly parallel computer architecture for solving large sets of nonlinear sparse equations. The goal of this architecture is to reduce the processing time required to solve this type of problem. In particular, the load flow problem is analyzed and implemented on this architecture. For the FPL network, the speed is increased by a factor of about 2000.
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Jakubowski, Volker G. "Nonlinear elliptic parabolic integro differential equations with L-data existence, uniqueness, asymptotic /." [S.l.] : [s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=966250141.

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He, Chuan. "Numerical solutions of differential equations on FPGA-enhanced computers." [College Station, Tex. : Texas A&M University, 2007. http://hdl.handle.net/1969.1/ETD-TAMU-1248.

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Zhang, Chun Yang. "A second order ADI method for 2D parabolic equations with mixed derivative." Thesis, University of Macau, 2012. http://umaclib3.umac.mo/record=b2592940.

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Sheng, Shan Liang. "Classical and Bayesian approaches to nonlinear models based on human in vivo cadmium data." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0001/NQ42878.pdf.

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Karasev, Peter A. "Feedback augmentation of pde-based image segmentation algorithms using application-specific exogenous data." Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/50257.

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This thesis is divided into five chapters. The scope of problems considered is defined in chapter I. Next, chapter II provides background material on image processing with partial differential equations and a review of prior work in the field. Chapter III covers the medical imaging portion of the research; the key contribution is a control-based algorithm for interactive image segmentation. Applications of the feedback-augmented level set method to fracture reconstruction and surgical planning are shown. Problems in vision-based control are considered in Chapters IV and V. A method of improving performance in closed-loop target tracking using level set segmentation is developed, with unmanned aerial vehicle or next-generation missile guidance being the primary applications of interest. Throughout this thesis, the two application types are connected into a unified viewpoint of open-loop systems that are augmented by exogenous data.
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Challa, Subhash. "Nonlinear state estimation and filtering with applications to target tracking problems." Thesis, Queensland University of Technology, 1998.

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Lazcano, Vanel. "Some problems in depth enhanced video processing." Doctoral thesis, Universitat Pompeu Fabra, 2016. http://hdl.handle.net/10803/373917.

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In this thesis we tackle two problems, namely, the data interpolation prob- lem in the context of depth computation both for images and for videos, and the problem of the estimation of the apparent movement of objects in image sequences. The rst problem deals with completion of depth data in a region of an image or video where data are missing due to occlusions, unreliable data, damage or lost of data during acquisition. In this thesis we tackle it in two ways. First, we propose a non-local gradient-based energy which is able to complete planes locally. We consider this model as an extension of the bilateral lter to the gradient domain. We have successfully evaluated our model to complete synthetic depth images and also incomplete depth maps provided by a Kinect sensor. The second approach to tackle the problem is an experimental study of the Biased Absolutely Minimizing Lipschitz Extension (biased AMLE in short) for anisotropic interpolation of depth data to big empty regions without informa- tion. The AMLE operator is a cone interpolator, but the biased AMLE is an exponential cone interpolator which makes it more addapted to depth maps of real scenes that usually present soft convex or concave surfaces. Moreover, the biased AMLE operator is able to expand depth data to huge regions. By con- sidering the image domain endowed with an anisotropic metric, the proposed method is able to take into account the underlying geometric information in order not to interpolate across the boundary of objects at di erent depths. We have proposed a numerical model to compute the solution of the biased AMLE which is based on the eikonal operators. Additionally, we have extended the proposed numerical model to video sequences. The second problem deals with the motion estimation of the objects in a video sequence. This problem is known as the optical ow computation. The Optical ow problem is one of the most challenging problems in computer vision. Traditional models to estimate it fail in presence of occlusions and non-uniform illumination. To tackle these problems we proposed a variational model to jointly estimate optical ow and occlusion. Moreover, the proposed model is able to deal with the usual drawback of variational methods in dealing with fast displacements of objects in the scene which are larger than the object it- self. The addition of a term that balance gradient and intensities increases the robustness to illumination changes of the proposed model. The inclusions of a supplementary matches given by exhaustive search in speci cs locations helps to follow large displacements.
En esta tesis se abordan dos problemas: interpolación de datos en el contexto del cálculo de disparidades tanto para imágenes como para video, y el problema de la estimación del movimiento aparente de objetos en una secuencia de imágenes. El primer problema trata de la completación de datos de profundidad en una región de la imagen o video dónde los datos se han perdido debido a oclusiones, datos no confiables, datos dañados o pérdida de datos durante la adquisición. En esta tesis estos problemas se abordan de dos maneras. Primero, se propone una energía basada en gradientes no-locales, energía que puede (localmente) completar planos. Se considera este modelo como una extensión del filtro bilateral al dominio del gradiente. Se ha evaluado en forma exitosa el modelo para completar datos sintéticos y también mapas de profundidad incompletos de un sensor Kinect. El segundo enfoque, para abordar el problema, es un estudio experimental del biased AMLE (Biased Absolutely Minimizing Lipschitz Extension) para interpolación anisotrópica de datos de profundidad en grandes regiones sin información. El operador AMLE es un interpolador de conos, pero el operador biased AMLE es un interpolador de conos exponenciales lo que lo hace estar más adaptado a mapas de profundidad de escenas reales (las que comunmente presentan superficies convexas, concavas y suaves). Además, el operador biased AMLE puede expandir datos de profundidad a regiones grandes. Considerando al dominio de la imagen dotado de una métrica anisotrópica, el método propuesto puede tomar en cuenta información geométrica subyacente para no interpolar a través de los límites de los objetos a diferentes profundidades. Se ha propuesto un modelo numérico, basado en el operador eikonal, para calcular la solución del biased AMLE. Adicionalmente, se ha extendido el modelo numérico a sequencias de video. El cálculo del flujo óptico es uno de los problemas más desafiantes para la visión por computador. Los modelos tradicionales fallan al estimar el flujo óptico en presencia de oclusiones o iluminación no uniforme. Para abordar este problema se propone un modelo variacional para conjuntamente estimar flujo óptico y oclusiones. Además, el modelo propuesto puede tolerar, una limitación tradicional de los métodos variacionales, desplazamientos rápidos de objetos que son más grandes que el tamaño objeto en la escena. La adición de un término para el balance de gradientes e intensidades aumenta la robustez del modelo propuesto ante cambios de iluminación. La inclusión de correspondencias adicionales (obtenidas usando búsqueda exhaustiva en ubicaciones específicas) ayuda a estimar grandes desplazamientos.
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Michel, Thomas. "Analyse mathématique et calibration de modèles de croissance tumorale." Thesis, Bordeaux, 2016. http://www.theses.fr/2016BORD0222/document.

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Cette thèse présente des travaux sur l’étude et la calibration de modèles d’équations aux dérivées partielles pour la croissance tumorale. La première partie porte sur l’analyse d’un modèle de croissance tumorale pour le cas de métastases au foie de tumeurs gastro-intestinales (GIST). Le modèle est un système d’équations aux dérivées partielles couplées et prend en compte plusieurs traitements dont un traitement anti-angiogénique. Le modèle permet de reproduire des données cliniques. La première partie de ce travail concerne la preuve d’existence/unicité de la solution du modèle. La seconde partie du travail porte sur l’étude du comportement asymptotique de la solution du modèle lorsqu’un paramètre du modèle, décrivant la capacité de la tumeur à évacuer la nécrose, converge vers 0. La seconde partie de la thèse concerne le développement d’un modèle de croissance pour des sphéroïdes tumoraux ainsi que sur la calibration de ce modèle à partir de données expérimentales in vitro. L’objectif est de développer un modèle permettant de reproduire quantitativement la distribution des cellules proliférantes à l’intérieur d’un sphéroïde en fonction de la concentration en nutriments. Le travail de modélisation et de calibration du modèle a été effectué à partir de données expérimentales permettant d’obtenir la répartition spatiale de cellules proliférantes dans un sphéroïde tumoral
In this thesis, we present several works on the study and the calibration of partial differential equations models for tumor growth. The first part is devoted to the mathematical study of a model for tumor drug resistance in the case of gastro-intestinal tumor (GIST) metastases to the liver. The model we study consists in a coupled partial differential equations system and takes several treatments into account, such as a anti-angiogenic treatment. This model is able to reproduce clinical data. In a first part, we present the proof of the existence/uniqueness of the solution to this model. Then, in a second part, we study the asymptotic behavior of the solution when a parameter of this model, describing the capacity of the tumor to evacuate the necrosis, goes to 0. In the second part of this thesis, we present the development of model for tumor spheroids growth. We also present the model calibration thanks to in vitro experimental data. The main objective of this work is to reproduce quantitatively the proliferative cell distribution in a spheroid, as a function of the concentration of nutrients. The modeling and calibration of this model have been done thanks to experimental data consisting of proliferative cells distribution in a spheroid
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Antelo, Junior Ernesto Willams Molina. "Estimação conjunta de atraso de tempo subamostral e eco de referência para sinais de ultrassom." Universidade Tecnológica Federal do Paraná, 2017. http://repositorio.utfpr.edu.br/jspui/handle/1/2616.

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CAPES
Em ensaios não destrutivos por ultrassom, o sinal obtido a partir de um sistema de aquisição de dados real podem estar contaminados por ruído e os ecos podem ter atrasos de tempo subamostrais. Em alguns casos, esses aspectos podem comprometer a informação obtida de um sinal por um sistema de aquisição. Para lidar com essas situações, podem ser utilizadas técnicas de estimativa de atraso temporal (Time Delay Estimation ou TDE) e também técnicas de reconstrução de sinais, para realizar aproximações e obter mais informações sobre o conjunto de dados. As técnicas de TDE podem ser utilizadas com diversas finalidades na defectoscopia, como por exemplo, para a localização precisa de defeitos em peças, no monitoramento da taxa de corrosão em peças, na medição da espessura de um determinado material e etc. Já os métodos de reconstrução de dados possuem uma vasta gama de aplicação, como nos NDT, no imageamento médico, em telecomunicações e etc. Em geral, a maioria das técnicas de estimativa de atraso temporal requerem um modelo de sinal com precisão elevada, caso contrário, a localização dessa estimativa pode ter sua qualidade reduzida. Neste trabalho, é proposto um esquema alternado que estima de forma conjunta, uma referência de eco e atrasos de tempo para vários ecos a partir de medições ruidosas. Além disso, reinterpretando as técnicas utilizadas a partir de uma perspectiva probabilística, estendem-se suas funcionalidades através de uma aplicação conjunta de um estimador de máxima verossimilhança (Maximum Likelihood Estimation ou MLE) e um estimador máximo a posteriori (MAP). Finalmente, através de simulações, resultados são apresentados para demonstrar a superioridade do método proposto em relação aos métodos convencionais.
Abstract (parágrafo único): In non-destructive testing (NDT) with ultrasound, the signal obtained from a real data acquisition system may be contaminated by noise and the echoes may have sub-sample time delays. In some cases, these aspects may compromise the information obtained from a signal by an acquisition system. To deal with these situations, Time Delay Estimation (TDE) techniques and signal reconstruction techniques can be used to perform approximations and also to obtain more information about the data set. TDE techniques can be used for a number of purposes in the defectoscopy, for example, for accurate location of defects in parts, monitoring the corrosion rate in pieces, measuring the thickness of a given material, and so on. Data reconstruction methods have a wide range of applications, such as NDT, medical imaging, telecommunications and so on. In general, most time delay estimation techniques require a high precision signal model, otherwise the location of this estimate may have reduced quality. In this work, an alternative scheme is proposed that jointly estimates an echo model and time delays for several echoes from noisy measurements. In addition, by reinterpreting the utilized techniques from a probabilistic perspective, its functionalities are extended through a joint application of a maximum likelihood estimator (MLE) and a maximum a posteriori (MAP) estimator. Finally, through simulations, results are presented to demonstrate the superiority of the proposed method over conventional methods.
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Books on the topic "Differential equations, Nonlinear Data processing"

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Methods for solving systems of nonlinear equations. 2nd ed. Philadelphia: Society for Industrial and Applied Mathematics, 1998.

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Carlos, Lizárraga-Celaya, ed. Solving nonlinear partial differential equations with Maple and Mathematica. Wien: Springer, 2011.

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M, Kytmanov A., Lazman M. Z, and Aĭzenberg Lev Abramovich 1937-, eds. Metody iskli͡u︡chenii͡a︡ v kompʹi͡u︡ternoĭ algebre mnogochlenov. Novosibirsk: "Nauka," Sibirskoe otd-nie, 1991.

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Bykov, V. I. Elimination methods in polynomial computer algebra. Dordrecht: Kluwer Academic Publishers, 1998.

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Lang, Jens. Adaptive multilevel solution of nonlinear parabolic PDE systems: Theory, algorithm, and applications. Berlin: Springer, 2001.

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Elimination practice: Software tools and applications. London: Imperial College Press, 2004.

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1963-, Kunoth Angela, and SpringerLink (Online service), eds. Multiscale, Nonlinear and Adaptive Approximation: Dedicated to Wolfgang Dahmen on the Occasion of his 60th Birthday. Berlin, Heidelberg: Springer-Verlag Berlin Heidelberg, 2009.

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Meurer, Thomas. Control of Higher–Dimensional PDEs: Flatness and Backstepping Designs. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013.

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Tikhonenko, A. V. Integrirovanie uravneniĭ dvizhenii︠a︡ zari︠a︡zhennykh chastit︠s︡ v MAPLE: Monografii︠a︡. Obninsk: IATĖ, 2007.

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1955-, Coombes Kevin Robert, ed. Differential equations with Maple. New York: Wiley, 1996.

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Book chapters on the topic "Differential equations, Nonlinear Data processing"

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Zobitz, John M. "Systems of Nonlinear Differential Equations." In Exploring Modeling with Data and Differential Equations Using R, 203–14. Boca Raton: Chapman and Hall/CRC, 2022. http://dx.doi.org/10.1201/9781003286974-16.

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Kreinovich, Vladik, Anatoly Lakeyev, Jiří Rohn, and Patrick Kahl. "Solving Differential Equations." In Computational Complexity and Feasibility of Data Processing and Interval Computations, 219–23. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4757-2793-7_20.

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Astuti, P., M. Corless, and D. Williamson. "On the Convergence of Sampled Data Nonlinear Systems." In Differential Equations Theory, Numerics and Applications, 201–10. Dordrecht: Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-011-5157-3_10.

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Clarenz, Ulrich, Gerhard Dziuk, and Martin Rumpf. "On Generalized Mean Curvature Flow in Surface Processing." In Geometric Analysis and Nonlinear Partial Differential Equations, 217–48. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-55627-2_14.

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Horbelt, Werner, Thorsten Müller, Jens Timmer, Werner Melzer, and Karl Winkler. "Analysis of Nonlinear Differential Equations: Parameter Estimation and Model Selection." In Medical Data Analysis, 152–59. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/3-540-39949-6_19.

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Hubený, Jan, Pavel Matula, Petr Matula, and Michal Kozubek. "Improved 3D Reconstruction of Interphase Chromosomes Based on Nonlinear Diffusion Filtering." In Image Processing Based on Partial Differential Equations, 163–72. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-33267-1_10.

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Chan, Tony F., Ke Chen, and Xue-Cheng Tai. "Nonlinear Multilevel Schemes for Solving the Total Variation Image Minimization Problem." In Image Processing Based on Partial Differential Equations, 265–88. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-33267-1_15.

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Kamimura, Yutaka. "Inverse Problems of Determining Nonlinear Terms in Ordinary Differential Equations." In Inverse Problems, Tomography, and Image Processing, 87–94. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4020-7975-7_6.

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Villegas, Rossmary, Oliver Dorn, Miguel Moscoso, and Manuel Kindelan. "Shape Reconstruction from Two-Phase Incompressible Flow Data using Level Sets." In Image Processing Based on Partial Differential Equations, 381–401. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-33267-1_21.

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Mahalov, A., B. Nicolaenko, C. Bardos, and F. Golse. "Regularity of Euler Equations for a Class of Three-Dimensional Initial Data." In Progress in Nonlinear Differential Equations and Their Applications, 161–85. Basel: Birkhäuser Basel, 2005. http://dx.doi.org/10.1007/3-7643-7317-2_13.

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Conference papers on the topic "Differential equations, Nonlinear Data processing"

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Liu, Zeyi, Zhong Liu, Yanghe Feng, Qing Cheng, Xingxing Liang, Rongxiao Wang, Yuling Yang, Naifu Xu, and Yan Li. "Quasi-Spectral Method for Nonlinear Partial Differential KdV Equation in Image Processing." In 2019 5th International Conference on Big Data and Information Analytics (BigDIA). IEEE, 2019. http://dx.doi.org/10.1109/bigdia.2019.8802837.

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Крысько, Вадим, Vadim Krys'ko, Ирина Папкова, Irina Papkova, Екатерина Крылова, Ekaterina Krylova, Антон Крысько, and Anton Krysko. "Visualization of Transition's Scenarios from Harmonic to Chaotic Flexible Nonlinear-elastic Nano Beam's Oscillations." In 29th International Conference on Computer Graphics, Image Processing and Computer Vision, Visualization Systems and the Virtual Environment GraphiCon'2019. Bryansk State Technical University, 2019. http://dx.doi.org/10.30987/graphicon-2019-2-62-65.

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In this study, a mathematical model of the nonlinear vibrations of a nano-beam under the action of a sign-variable load and an additive white noise was constructed and visualized. The beam is heterogeneous, isotropic, elastic. The physical nonlinearity of the nano-beam was taken into account. The dependence of stress intensity on deformations intensity for aluminum was taken into account. Geometric non-linearity according to Theodore von Karman’s theory was applied. The equations of motion, the boundary and initial conditions of the Hamilton-Ostrogradski principle with regard to the modified couple stress theory were obtained. The system of nonlinear partial differential equations to the Cauchy problem by the method of finite differences was reduced. The Cauchy problem by the finite-difference method in the time coordinate was solved. The Birger variable method was used. Data visualization is carried out from the standpoint of the qualitative theory of differential equations and nonlinear dynamics were carried out. Using a wide range of tools visualization allowed to established that the transition from ordered vibrations to chaos is carried out according to the scenario of Ruelle-Takens-Newhouse. With an increase of the size-dependent parameter, the zone of steady and regular vibrations increases. The transition from regular to chaotic vibrations is accompanied by a tough dynamic loss of stability. The proposed method is universal and can be extended to solve a wide class of various problems of mechanics of shells.
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Mahmoodi, S. Nima, Amin Salehi-Khojin, and Mehdi Ahmadian. "Nonlinear Force Analysis of Atomic Force Microscopy." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48482.

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The objective of this work is to highlight and discuss some critical conditions in which the imprecision of atomic force microscopy (AFM) system will be intensified. To precisely address these issues, we developed a complete close form solution for a non-linear motion of AFM system subjected to non-linear contact and van der Waals forces. Galerkin method and multiple time scale approach are used to solve the governing non-linear differential equation of the AFM system. A nonlinear frequency-response equation is then obtained as a function of displacement excitation, resonance frequency and associated response amplitude. By simulation of the AFM response under different tip-sample interaction force and distance, it is shown that jump phenomenon takes place due to the non-linear motion of microcantilever at certain operating frequencies. This case can be avoided via operating the AFM in a right frequency region; however the error associated with it must be compensated by a post-processing of collected data.
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Яковлева, Татьяна, Tat'yana Yakovleva, Валентин Баженов, Valentin Bazhenov, Вадим Крысько, and Vadim Krys'ko. "Mathematical Modeling of the Contact Interaction of Plate and Beam in Color Noise Field." In 29th International Conference on Computer Graphics, Image Processing and Computer Vision, Visualization Systems and the Virtual Environment GraphiCon'2019. Bryansk State Technical University, 2019. http://dx.doi.org/10.30987/graphicon-2019-1-113-115.

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A mathematical model and data visualization of contact interaction between a plate and a beam under the action of external transverse load and external additive color noise is constructed. The construction is in a stationary temperature field, the effect of which is taken into account according to the theory of Duhamel Neumann by solving the three-dimensional and two-dimensional heat conduction equations by the finite difference method, the heat exchange between the plate and the beam is not taken into account. The plate is subject to the Kirchhoff model, and the beam to the Euler- Bernoulli model. The mathematical model takes into account the physical nonlinearity of the elastically deformable material. Contact interaction is taken into account according to the theory of Kantor. The system of differential equations is reduced to the Cauchy problem by the Bubnov-Galerkin method in higher approximations in spatial variables. The Cauchy problem is solved by the Runge-Kutta method of the fourth order of accuracy. To solve the physically nonlinear problem, at each time step, an Birger iterative procedure was applied. The visualization of the results of a numerical experiment was carried out using the methods of nonlinear dynamics and using wavelet analysis. The numerical results of the effect of color noise on the contact interaction between the plate and the beam are given. It has been established that red additive noise has a more significant effect on the oscillation pattern of the lamellar-beam structure in comparison with pink and white noise.
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RAUTELA, MAHINDRA, MANISH RAUT, and S. GOPALAKRISHNAN. "SIMULATION OF GUIDED WAVES FOR STRUCTURAL HEALTH MONITORING USING PHYSICS-INFORMED NEURAL NETWORKS." In Structural Health Monitoring 2021. Destech Publications, Inc., 2022. http://dx.doi.org/10.12783/shm2021/36297.

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Guided wave propagation is a valuable and reliable technique for structural health monitoring (SHM) of aerospace structures. Along with its higher sensitivity towards small damages, it offers advantages in traveling long distances with minimum attenuation. Simulation of guided wave propagation is essential to understand wave behavior, and calculating the dispersion relations forms an integral part of the procedure. Application of the current numerical techniques for complex media is highly involved and faces issues related to accuracy, stability, and computational resources. Development in the field of machine learning and graphical processing units (GPUs) leads to the implementation of a faster, automated, and scalable deep neural networks-based learning approach for such problems. Most of the implementation in the field is based on data collection and uses neural networks for nonlinear mapping from input space to target space. However, a large amount of prior information in the form of a governing differential equation is not utilized. In this paper, we have used Physics-Informed Neural Networks (PINNs), in which neural networks are utilized to solve governing partial differential equations. PINNs are implemented to obtain the solution of a one-dimensional wave equation with Dirichlet boundary conditions. The exact solutions and predicted responses match closely with lower mean square error in limited computational time. We have also conducted a detailed comparison of the effect of neural architecture on the mean square error and the training time. This study shows the merit of deep neural networks leveraging the available physical information to simulate the wave phenomenon for SHM efficiently.
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Chen, Yu, JinRong Wang, and XiaoKai Cao. "Iterative Learning Control for Nonlinear Stieltjes Differential Equations." In 2019 IEEE 8th Data Driven Control and Learning Systems Conference (DDCLS). IEEE, 2019. http://dx.doi.org/10.1109/ddcls.2019.8908903.

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Sarkka, Simo. "On Sequential Monte Carlo Sampling of Discretely Observed Stochastic Differential Equations." In 2006 IEEE Nonlinear Statistical Signal Processing Workshop. IEEE, 2006. http://dx.doi.org/10.1109/nsspw.2006.4378811.

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Cheng, Jun, and Jeffrey M. Falzarano. "System Identification of Nonlinear Coupled Ship/Offshore Platform Dynamics in Beam Seas." In ASME 2003 22nd International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2003. http://dx.doi.org/10.1115/omae2003-37336.

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The Mobile Offshore Base (MOB) is designed to transit to anywhere in the world in the required time frame. This means that the MOB must be able to transit in severe environmental conditions. In these extreme sea conditions, a primary cause for concern is the large accelerations that the vessel motions might experience due to the high static stability of the MOB at Transit Draft. Furthermore, since the vessel has minimum freeboard in this condition, it is exposed to green water over the pontoon tops. The submergence of the pontoon deck causes a considerable loss in the vessel’s restoring moment. These concerns have warranted a study by the Office of Naval Research into the Transit Draft Dynamics of the MOB. During the research of MOB dynamical properties, a nonlinear system modeling and optimization tool utilizing Reverse MI/SO (Multiple-Input / Single Output) techniques was developed and applied to different aspects of MOB dynamics analysis. MISO is based on statistical signal processing of the recorded time histories of the excitation and response of the non-linear multi-degree-of-freedom system. This method of analysis is functional and reliable in identifying an optimum representation of the linear and non-linear parameters of the system under consideration. In this paper, we analyze the model testing data in beam seas using the Reverse MISO technique. We expected to identify significant nonlinear roll damping for the nonlinear integro-differential equation as is the case with ships. Instead, a significant nonlinear heave damping related with the nonlinear relative heave velocity has been found during the analysis. This reminds us again that due to the strong nonlinearity of MOB motions in the severe sea ways, nonlinear analysis methods such as Reverse MISO are important and need to be applyed in order to fully identify the dynamics of the MOB motion.
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Han, Xizhen, and Zhao Jian. "A nonlinear image enhancement algorithm based on partial differential equations." In 2010 10th International Conference on Signal Processing (ICSP 2010). IEEE, 2010. http://dx.doi.org/10.1109/icosp.2010.5655875.

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Luo, Juan, Zhimin Luo, and He Qingyan. "On the Asymptotic Behavior of Second Order Nonlinear Differential Equations." In 2010 International Symposium on Intelligence Information Processing and Trusted Computing (IPTC). IEEE, 2010. http://dx.doi.org/10.1109/iptc.2010.57.

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Reports on the topic "Differential equations, Nonlinear Data processing"

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Osher, Stanley, and Leonid Rudin. Feature-Oriented Signal Processing Under Nonlinear Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, January 1992. http://dx.doi.org/10.21236/ada259951.

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