Relevant bibliographies by topics / Perturbation methods

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Perturbation methods'

Author: Grafiati
Published: 4 June 2021
Last updated: 15 June 2025

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Journal articles on the topic "Perturbation methods"

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Hinch, E. J., and Edward G. Harris. "Perturbation Methods." American Journal of Physics 60, no. 11 (1992): 1052–53. http://dx.doi.org/10.1119/1.16992.

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Heinrichs, Wilhelm. "Spectral methods for singular perturbation problems." Applications of Mathematics 39, no. 3 (1994): 161–88. http://dx.doi.org/10.21136/am.1994.134251.

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Cha, Philip D., and Austin Shin. "Perturbation Methods for the Eigencharacteristics of Symmetric and Asymmetric Systems." Shock and Vibration 2018 (October 17, 2018): 1–25. http://dx.doi.org/10.1155/2018/8609138.

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Dynamic analysis for a vibratory system typically begins with an evaluation of its eigencharacteristics. However, when design changes are introduced, the eigensolutions of the system change and thus must be recomputed. In this paper, three different methods based on the eigenvalue perturbation theory are introduced to analyze the effects of modifications without performing a potentially time-consuming and costly reanalysis. They will be referred to as the straightforward perturbation method, the incremental perturbation method, and the triple product method. In the straightforward perturbation method, the eigenvalue perturbation theory is used to formulate a first-order and a second-order approximation of the eigensolutions of symmetric and asymmetric systems. In the incremental perturbation method, the straightforward approach is extended to analyze systems with large perturbations using an iterative scheme. Finally, in the triple product method, the accuracy of the approximate eigenvalues is significantly improved by exploiting the orthogonality conditions of the perturbed eigenvectors. All three methods require only the eigensolutions of the nominal or unperturbed system, and in application, they involve simple matrix multiplications. Numerical experiments show that the proposed methods achieve accurate results for systems with and without damping and for systems with symmetric and asymmetric system matrices.
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Riley, N. "Perturbation methods, 1992." Journal of Fluids and Structures 6, no. 4 (1992): 523–24. http://dx.doi.org/10.1016/0889-9746(92)90029-3.

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Huang, Wei, Lei Zhang, Zizhou Wang, and Yan Wang. "GapMatch: Bridging Instance and Model Perturbations for Enhanced Semi-Supervised Medical Image Segmentation." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 16 (2025): 17458–66. https://doi.org/10.1609/aaai.v39i16.33919.

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Medical image segmentation provides detailed understanding and aids in diagnosis, treatment planning, and monitoring of diseases. Due to the high cost of acquiring labeled data in the field of medical image analysis, semi-supervised segmentation methods have garnered increasing attention. Benefiting from their simplicity and effectiveness, consistency regularization-based methods have emerged as a significant research focus by utilizing perturbations. However, existing methods typically consider perturbation strategies from only a single perspective: either instance perturbation or model perturbation, thus ignoring the potential benefit of effectively combining both. In response, we propose a unified perturbation framework named GapMatch, which bridges instance and model perturbations to broaden the perturbation space and employs dual perturbation to impose consistency regularization on the model. Specifically, GapMatch involves using instance perturbation to update the decision boundary and model perturbation to further optimize it. These two steps mutually reinforce each other in an iterative manner, effectively pushing the decision boundary towards low-density regions while maximizing the class margin. Extensive experimental results on two popular medical image benchmarks demonstrate the effectiveness and generality of the proposed method.
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Duan, Jiale, Linyao Qiu, Guangjun He, Ling Zhao, Zhenshi Zhang, and Haifeng Li. "A Region-Adaptive Local Perturbation-Based Method for Generating Adversarial Examples in Synthetic Aperture Radar Object Detection." Remote Sensing 16, no. 6 (2024): 997. http://dx.doi.org/10.3390/rs16060997.

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In synthetic aperture radar (SAR) imaging, intelligent object detection methods are facing significant challenges in terms of model robustness and application security, which are posed by adversarial examples. The existing adversarial example generation methods for SAR object detection can be divided into two main types: global perturbation attacks and local perturbation attacks. Due to the dynamic changes and irregular spatial distribution of SAR coherent speckle backgrounds, the attack effectiveness of global perturbation attacks is significantly reduced by coherent speckle. In contrast, by focusing on the image objects, local perturbation attacks achieve targeted and effective advantages over global perturbations by minimizing interference from the SAR coherent speckle background. However, the adaptability of conventional local perturbations is limited because they employ a fixed size without considering the diverse sizes and shapes of SAR objects under various conditions. This paper presents a framework for region-adaptive local perturbations (RaLP) specifically designed for SAR object detection tasks. The framework consists of two modules. To address the issue of coherent speckle noise interference in SAR imagery, we develop a local perturbation generator (LPG) module. By filtering the original image, this module reduces the speckle features introduced during perturbation generation. It then superimposes adversarial perturbations in the form of local perturbations on areas of the object with weaker speckles, thereby reducing the mutual interference between coherent speckles and adversarial perturbation. To address the issue of insufficient adaptability in terms of the size variation in local adversarial perturbations, we propose an adaptive perturbation optimizer (APO) module. This optimizer adapts the size of the adversarial perturbations based on the size and shape of the object, effectively solving the problem of adaptive perturbation size and enhancing the universality of the attack. The experimental results show that RaLP reduces the detection accuracy of the YOLOv3 detector by 29.0%, 29.9%, and 32.3% on the SSDD, SAR-Ship, and AIR-SARShip datasets, respectively, and the model-to-model and dataset-to-dataset transferability of RaLP attacks are verified.
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Li, Mengyang, Fengguang Su, Ou Wu, and Ji Zhang. "Logit Perturbation." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 2 (2022): 1359–66. http://dx.doi.org/10.1609/aaai.v36i2.20024.

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Features, logits, and labels are the three primary data when a sample passes through a deep neural network. Feature perturbation and label perturbation receive increasing attention in recent years. They have been proven to be useful in various deep learning approaches. For example, (adversarial) feature perturbation can improve the robustness or even generalization capability of learned models. However, limited studies have explicitly explored for the perturbation of logit vectors. This work discusses several existing methods related to logit perturbation. Based on a unified viewpoint between positive/negative data augmentation and loss variations incurred by logit perturbation, a new method is proposed to explicitly learn to perturb logits. A comparative analysis is conducted for the perturbations used in our and existing methods. Extensive experiments on benchmark image classification data sets and their long-tail versions indicated the competitive performance of our learning method. In addition, existing methods can be further improved by utilizing our method.
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Kuić, Domagoj, Alemka Knapp, and Diana Šaponja-Milutinović. "Finite Time Path Field Theory Perturbative Methods for Local Quantum Spin Chain Quenches." Universe 10, no. 10 (2024): 384. http://dx.doi.org/10.3390/universe10100384.

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We discuss local magnetic field quenches using perturbative methods of finite time path field theory (FTPFT) in the following spin chains: Ising and XY in a transverse magnetic field. Their common characteristics are: (i) they are integrable via mapping to a second quantized noninteracting fermion problem; and (ii) when the ground state is nondegenerate (true for finite chains except in special cases), it can be represented as a vacuum of Bogoliubov fermions. By switching on a local magnetic field perturbation at finite time, the problem becomes nonintegrable and must be approached via numeric or perturbative methods. Using the formalism of FTPFT based on Wigner transforms (WTs) of projected functions, we show how to: (i) calculate the basic “bubble” diagram in the Loschmidt echo (LE) of a quenched chain to any order in the perturbation; and (ii) resum the generalized Schwinger–Dyson equation for the fermion two-point retarded functions in the “bubble” diagram, hence achieving the resummation of perturbative expansion of LE for a wide range of perturbation strengths under certain analyticity assumptions. Limitations of the assumptions and possible generalizations beyond it and also for other spin chains are further discussed.
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Murdock, James. "Book Review: Perturbation methods." Bulletin of the American Mathematical Society 28, no. 2 (1993): 418–22. http://dx.doi.org/10.1090/s0273-0979-1993-00378-1.

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Chacon, Monique Revoredo, and Michael C. Zerner. "Perturbation-variational methods revisited." International Journal of Quantum Chemistry 47, no. 2 (1993): 103–18. http://dx.doi.org/10.1002/qua.560470202.

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Dissertations / Theses on the topic "Perturbation methods"

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Elago, David. "Robust computational methods for two-parameter singular perturbation problems." Thesis, University of the Western Cape, 2010. http://etd.uwc.ac.za/index.php?module=etd&action=viewtitle&id=gen8Srv25Nme4_1693_1308039217.

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<p>This thesis is concerned with singularly perturbed two-parameter problems. We study a tted nite difference method as applied on two different meshes namely a piecewise mesh (of Shishkin type) and a graded mesh (of Bakhvalov type) as well as a tted operator nite di erence method. We notice that results on Bakhvalov mesh are better than those on Shishkin mesh. However, piecewise uniform meshes provide a simpler platform for analysis and computations. Fitted operator methods are even simpler in these regards due to the ease of operating on uniform meshes. Richardson extrapolation is applied on one of the tted mesh nite di erence method (those based on Shishkin mesh) as well as on the tted operator nite di erence method in order to improve the accuracy and/or the order of convergence. This is our main contribution to this eld and in fact we have achieved very good results after extrapolation on the tted operator finitete difference method. Extensive numerical computations are carried out on to confirm the theoretical results.</p>
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Young, Caroline Jane. "Methods of geographical perturbation for disclosure control." Thesis, University of Southampton, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.486433.

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Disclosure control methods are used to protect the confidentiality of individuals and households in aggregate census data. With growth in computational power, the disclosure control problem has been rapidly transformed. Increased analytical power has stimulated user demand for more detailed information for smaller geographic areas and to customized geographical boundaries. However, the possibility of allowing census users to create their own aggregates from census microdata, and for small areas, can lead to problems of disclosure by differencing. Traditionally, methods of statistical disclosure control have been aspatial in nature. This thesis describes a new framework of geographical perturbation methods designed to deal with the spatial nature of disclosure risk. The research offers several new contributions, specifically; . (1) Aframework of new geographical perturbation methods is defined, based on creating uncertainty around geographical location. Zone-independent methods are designed for protection in a flexibletabulation scenario'and to account for the spatial dimension of risk. • (2) Techniques for implementation of t~ese methods are tested on a synthetic census dataset which· show comparable risk-utility outcomes to RRS (an existing method used for the US and UK Censuses). The advantages and disadvantages of the proposed methods are discussed with regard to ease of implementation and flexibility of parameter values. (3) One of these new methods; LOS, is then explored in more detail showing a significant improvement over RRS in terms of the risk-utility outcome. Risk reduction is illustrated in a geographical differencing scenario and distortion to utility explored in a spatial context of typical census users' analyses.
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Munyakazi, Justin Bazimaziki. "Higher Order Numerical Methods for Singular Perturbation Problems." Thesis, Online Access, 2009. http://etd.uwc.ac.za/usrfiles/modules/etd/docs/etd_gen8Srv25Nme4_6335_1277251056.pdf.

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Kateregga, Michael. "Perturbation methods in derivatives pricing under stochastic volatility." Thesis, Stellenbosch : Stellenbosch University, 2012. http://hdl.handle.net/10019.1/71708.

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Thesis (MSc)--Stellenbosch University, 2012.<br>ENGLISH ABSTRACT: This work employs perturbation techniques to price and hedge financial derivatives in a stochastic volatility framework. Fouque et al. [44] model volatility as a function of two processes operating on different time-scales. One process is responsible for the fast-fluctuating feature of volatility and corresponds to the slow time-scale and the second is for slowfluctuations or fast time-scale. The former is an Ergodic Markov process and the latter is a strong solution to a Lipschitz stochastic differential equation. This work mainly involves modelling, analysis and estimation techniques, exploiting the concept of mean reversion of volatility. The approach used is robust in the sense that it does not assume a specific volatility model. Using singular and regular perturbation techniques on the resulting PDE a first-order price correction to Black-Scholes option pricing model is derived. Vital groupings of market parameters are identified and their estimation from market data is extremely efficient and stable. The implied volatility is expressed as a linear (affine) function of log-moneyness-tomaturity ratio, and can be easily calibrated by estimating the grouped market parameters from the observed implied volatility surface. Importantly, the same grouped parameters can be used to price other complex derivatives beyond the European and American options, which include Barrier, Asian, Basket and Forward options. However, this semi-analytic perturbative approach is effective for longer maturities and unstable when pricing is done close to maturity. As a result a more accurate technique, the decomposition pricing approach that gives explicit analytic first- and second-order pricing and implied volatility formulae is discussed as one of the current alternatives. Here, the method is only employed for European options but an extension to other options could be an idea for further research. The only requirements for this method are integrability and regularity of the stochastic volatility process. Corrections to [3] remarkable work are discussed here.<br>AFRIKAANSE OPSOMMING: Hierdie werk gebruik steuringstegnieke om finansiële afgeleide instrumente in ’n stogastiese wisselvalligheid raamwerk te prys en te verskans. Fouque et al. [44] gemodelleer wisselvalligheid as ’n funksie van twee prosesse wat op verskillende tyd-skale werk. Een proses is verantwoordelik vir die vinnig-wisselende eienskap van die wisselvalligheid en stem ooreen met die stadiger tyd-skaal en die tweede is vir stadig-wisselende fluktuasies of ’n vinniger tyd-skaal. Die voormalige is ’n Ergodiese-Markov-proses en die laasgenoemde is ’n sterk oplossing vir ’n Lipschitz stogastiese differensiaalvergelyking. Hierdie werk behels hoofsaaklik modellering, analise en skattingstegnieke, wat die konsep van terugkeer to die gemiddelde van die wisseling gebruik. Die benadering wat gebruik word is rubuust in die sin dat dit nie ’n aanname van ’n spesifieke wisselvalligheid model maak nie. Deur singulêre en reëlmatige steuringstegnieke te gebruik op die PDV kan ’n eerste-orde pryskorreksie aan die Black-Scholes opsie-waardasiemodel afgelei word. Belangrike groeperings van mark parameters is geïdentifiseer en hul geskatte waardes van mark data is uiters doeltreffend en stabiel. Die geïmpliseerde onbestendigheid word uitgedruk as ’n lineêre (affiene) funksie van die log-geldkarakter-tot-verval verhouding, en kan maklik gekalibreer word deur gegroepeerde mark parameters te beraam van die waargenome geïmpliseerde wisselvalligheids vlak. Wat belangrik is, is dat dieselfde gegroepeerde parameters gebruik kan word om ander komplekse afgeleide instrumente buite die Europese en Amerikaanse opsies te prys, dié sluit in Barrier, Asiatiese, Basket en Stuur opsies. Hierdie semi-analitiese steurings benadering is effektief vir langer termyne en onstabiel wanneer pryse naby aan die vervaldatum beraam word. As gevolg hiervan is ’n meer akkurate tegniek, die ontbinding prys benadering wat eksplisiete analitiese eerste- en tweede-orde pryse en geïmpliseerde wisselvalligheid formules gee as een van die huidige alternatiewe bespreek. Hier word slegs die metode vir Europese opsies gebruik, maar ’n uitbreiding na ander opsies kan’n idee vir verdere navorsing wees. Die enigste vereistes vir hierdie metode is integreerbaarheid en reëlmatigheid van die stogastiese wisselvalligheid proses. Korreksies tot [3] se noemenswaardige werk word ook hier bespreek.
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Ahmed, Samah. "Perturbation field theory methods for calculating expectation values." Thesis, University of Cape Town, 2016. http://hdl.handle.net/11427/26214.

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Tronko, Natalia. "Hamiltonian Perturbation Methods for Magnetically Confined Fusion Plasmas." Thesis, Aix-Marseille 2, 2010. http://www.theses.fr/2010AIX22088/document.

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Les effets auto-consistantes sont omniprésents dans les plasmas de fusion. Ils sont dus au fait que les équations de Maxwell qui décrivent l’évolution des champs électromagnétiques contiennent la densité de charge et de courant des particules.D’autre côté à son tour les trajectoires des particules sont influencés par les champs à travers les équations de mouvement ( où l’équation de Vlasov). Le résultat decette interaction auto-consistente se résume dans un effet cumulatif qui peut causer le déconfinement de plasma à l’intérieur d’une machine de fusion. Ce travail de thèse traite les problèmes liés à l’amélioration de confinement de plasma de fusion dans le cadre des approches hamiltonienne et lagrangien par le contrôle de transport turbulent et la création des barrières de transport. Les fluctuations auto-consistantes de champs électromagnétiques et de densités des particules sont à l’origine de l’apparition des instabilités de plasma qui sont à son tour liés aux phénomènes de transport. Dans la perspective de comprendre les mécanismes de la turbulence sousjacente,on considère ici l’application des méthodes hamiltoniennes pour des plasmasnon-collisionnelles<br>This thesis deals with dynamicla investigation of magnetically confined fusion plasmas by using Lagrangian and Hamilton formalisms. It consists of three parts. The first part is devoted to the investigation of barrier formation for the EXB drift model by means of the Hamiltonian control method. The strong magnetic field approach is relevant for magnetically confined fusion plasmas ; this is why at the first approximation one can consider the dynamics of particles driven by constant and uniform magnetic field. In this case only the electrostatic turbulence is taken into account. During this study the expressions for the control term (quadratic in perturbation amplitude) additive to the electrostatic potential, has been obtained. The effeciency of such a control for stopping turbulent diffusion has been shown analytically abd numerically. The second and the third parts of this thesis are devoted to study of self consistent phenomena in magnetized plasmas through the Maxwell-Vlasov model. In particular, the second part of this thesis treats the problem of the monumentum transport by derivation of its conservation law. the Euler-Poincare variational principle (with constrained variations) as well as Noether's theorem is apllied here. this derivation is realized in two cases : first, in electromagnetic turbulence case for the full Maxwell-Vlasov system, and then in electrostatic turbulence case for the gyrokinetic Maxwell-Vlasov system. Then the intrinsic mechanisms reponsible for the intrinsic plama rotation, that can give an important in plasma stabilization, are identified. The last part of this thesis deals with dynamicla reduction for the Maxwell-Vlaslov model. More particularly; the intrisic formulation for the guiding center model is derived. Here the term 'intrinsis" means that no fixed frame was used during its construction. Due to that not any problem related to the gyrogauge dependence of dynamics appears. The study of orbits of trapped particles is considered as one of the possible for illustration of the first step of such a dynamical reduction
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Hwang, Ho-yon. "Identification methods for physical parameters in structures." Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/15652.

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Pulya, Ravishankar Sandheep. "Device Modelling of Perovskite Solar Cells using Small Perturbation Methods." Doctoral thesis, Universitat Jaume I, 2019. http://hdl.handle.net/10803/667627.

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Perovskite solar cells (PSC) have emerged as an important player in the search for producing c1ean and renewable energy at high efficiencies. However, there exist several bottlenecks to maximise their efficiency and stability. This thesis explores the physical mechanisms related to these limitations in operation and provides a deeper understanding as to how to overcome them. Through systematic experiments based on the small perturbation methods of Impedance Spectroscopy (IS) and Intensity Modulated Photocurrent Spectroscopy (IMPS), the perovskite/selective contact interfaces are identified as a critical factor that controls charge accumulation, recombination ando extraction. Therefore, these interfaces require to be carefully tuned in order to gain control over the device operation. Based on these insights, a robust equivalent circuit of the PSC is developed that provides a strong foundation for further development of these solar cells.<br>Las células solares de perovskite (PSC) se han convertido en un jugador importante en la búsqueda de producir energía limpia y renovable con altas eficiencias. Sin embargo, existen varios cuellos de botella para maximizar su eficiencia y estabilidad. Esta tesis explora los mecanismos físicos relacionados con estas limitaciones en la operación y proporciona una comprensión más profunda de cómo superarlas. A través de experimentos sistemáticos basados en los pequeños métodos de perturbación de la espectroscopia de impedancia (IS) y la espectroscopia de fotocorriente modulada de intensidad (IMPS), las interfaces de contacto perovskita / selectiva se identifican como un factor crítico que controla la acumulación de carga, la recombinación y la extracción. Por lo tanto, estas interfaces deben ajustarse con cuidado para poder controlar el funcionamiento del dispositivo. Sobre la base de estas ideas, se desarrolla un sólido circuito equivalente del PSC que proporciona una base sólida para el desarrollo posterior de estas células solares.
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Fung, Jimmy Jr. "Parameter Identification of Nonlinear Systems Using Perturbation Methods and Higher-Order Statistics." Thesis, Virginia Tech, 1998. http://hdl.handle.net/10919/36921.

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A parametric identification procedure is proposed that combines the method of multiple scales and higher-order statistics to efficiently and accurately model nonlinear systems. A theoretical background for the method of multiple scales and higher-order statistics is given. Validation of the procedure is performed through applying it to numerical simulations of two nonlinear systems. The results show how the procedure can successfully characterize the system damping and nonlinearities and determine the corresponding parameters. The procedure is then applied to experimental measurements from two structural systems, a cantilevered beam and a three-beam frame. The results show that quadratic damping should be accounted for in both systems. Moreover, for the three-beam frame, the parametric excitation is much more important than the direct excitation. To show the flexibility of the procedure, numerical simulations of ship motion under parametric excitation are used to determine nonlinear parameters govening the relation between pitch, heave, and roll motions. The results show a high level of agreement between the numerical simulation and the mathematical model with the identified parameters.<br>Master of Science
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Sabouri, Pouya. "Application of perturbation theory methods to nuclear data uncertainty propagation using the collision probability method." Thesis, Grenoble, 2013. http://www.theses.fr/2013GRENI071/document.

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Dans cette thèse, nous présentons une étude rigoureuse des barres d'erreurs et des sensibilités de paramètres neutroniques (tels le keff) aux données nucléaires de base utilisées pour les calculer. Notre étude commence au niveau fondamental, i.e. les fichiers de données ENDF et leurs incertitudes, fournies sous la forme de matrices de variance/covariance, et leur traitement. Lorsqu'un calcul méthodique et consistant des sensibilités est consenti, nous montrons qu'une approche déterministe utilisant des formalismes bien connus est suffisante pour propager les incertitudes des bases de données avec un niveau de précision équivalent à celui des meilleurs outils disponibles sur le marché, comme les codes Monte-Carlo de référence. En appliquant notre méthodologie à trois exercices proposés par l'OCDE, dans le cadre des Benchmarks UACSA, nous donnons des informations, que nous espérons utiles, sur les processus physiques et les hypothèses sous-jacents aux formalismes déterministes utilisés dans cette étude<br>This dissertation presents a comprehensive study of sensitivity/uncertainty analysis for reactor performance parameters (e.g. the k-effective) to the base nuclear data from which they are computed. The analysis starts at the fundamental step, the Evaluated Nuclear Data File and the uncertainties inherently associated with the data they contain, available in the form of variance/covariance matrices. We show that when a methodical and consistent computation of sensitivity is performed, conventional deterministic formalisms can be sufficient to propagate nuclear data uncertainties with the level of accuracy obtained by the most advanced tools, such as state-of-the-art Monte Carlo codes. By applying our developed methodology to three exercises proposed by the OECD (UACSA Benchmarks), we provide insights of the underlying physical phenomena associated with the used formalisms
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Books on the topic "Perturbation methods"

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Hinch, E. J. Perturbation methods. Cambridge University Press, 1991.

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Wang, C. Y. Essential Perturbation Methods. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-26545-7.

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Holmes, Mark H. Introduction to Perturbation Methods. Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4612-5347-1.

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Holmes, Mark H. Introduction to Perturbation Methods. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-5477-9.

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Holmes, Mark H. Introduction to Perturbation Methods. 2nd ed. Springer New York, 2013.

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Shivamoggi, Bhimsen K. Perturbation Methods for Differential Equations. Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-0047-5.

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1958-, Allman Mark C., ed. Modernastrodynamics: Fundamentals and perturbation methods. Princeton University Press, 1996.

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He, Ji-Huan. Perturbation methods: Basic and beyond. Elsevier, 2006.

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Luongo, Angelo, Daniele Zulli, Manuel Ferretti, and Francesco D’Annibale. Perturbation Methods and Nonlinear Phenomena. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-49397-3.

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Bensoussan, Alain. Perturbation methods in optimal control. Gauthier-Villars, 1988.

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Book chapters on the topic "Perturbation methods"

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Ginsberg, Jerry H. "Perturbation Methods." In Nonlinear Acoustics. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-58963-8_10.

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AbstractPerturbation methods yield approximate analytical solutions that provide physical insight into finite-amplitude sound and benchmarks for computational methods. The acoustic Mach number is employed as the small parameter for the perturbation expansions. The first method presented is the regular perturbation technique leading to a straightforward expansion of the solution in powers of the small parameter, but which is not uniformly valid. Two methods are presented for rendering the solutions uniformly valid, the method of multiple scales and the method of renormalization. Analysis of radiation from a vibrating plate is provided as an example of a multidimensional problem solved by perturbation.
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Witelski, Thomas, and Mark Bowen. "Perturbation Methods." In Methods of Mathematical Modelling. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-23042-9_6.

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Kelley, Walter G., and Allan C. Peterson. "Perturbation Methods." In The Theory of Differential Equations. Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-5783-2_4.

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Murdock, James. "Perturbation Methods." In Mathematical Tools for Physicists. Wiley-VCH Verlag GmbH & Co. KGaA, 2006. http://dx.doi.org/10.1002/3527607773.ch11.

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Holmes, Mark H. "Perturbation Methods." In Texts in Applied Mathematics. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-24261-9_2.

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Carrier, George F. "Perturbation Methods." In Handbook of Applied Mathematics. Springer US, 1990. http://dx.doi.org/10.1007/978-1-4684-1423-3_14.

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Holmes, Mark H. "Perturbation Methods." In Texts in Applied Mathematics. Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-87765-5_2.

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Jorba, Àngel. "Computational Methods in Perturbation Theory." In Perturbation Theory. Springer US, 2022. http://dx.doi.org/10.1007/978-1-0716-2621-4_758.

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Gentile, Guido. "Diagrammatic Methods in Classical Perturbation Theory." In Perturbation Theory. Springer US, 2009. http://dx.doi.org/10.1007/978-1-0716-2621-4_122.

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Hoppensteadt, Frank C. "Regular Perturbation Methods." In Applied Mathematical Sciences. Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4757-2275-8_5.

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Conference papers on the topic "Perturbation methods"

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Lu, Yuhang, and Touradj Ebrahimi. "Improving perturbation-based explanation methods with application to face recognition." In Applications of Digital Image Processing XLVII, edited by Andrew G. Tescher and Touradj Ebrahimi. SPIE, 2024. http://dx.doi.org/10.1117/12.3030872.

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Fisher, Jillian, Skyler Hallinan, Ximing Lu, Mitchell L. Gordon, Zaid Harchaoui, and Yejin Choi. "StyleRemix: Interpretable Authorship Obfuscation via Distillation and Perturbation of Style Elements." In Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing. Association for Computational Linguistics, 2024. http://dx.doi.org/10.18653/v1/2024.emnlp-main.241.

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Salim, Saiful Islam, Rubin Yuchan Yang, Alexander Cooper, Suryashree Ray, Saumya Debray, and Sazzadur Rahaman. "Impeding LLM-assisted Cheating in Introductory Programming Assignments via Adversarial Perturbation." In Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing. Association for Computational Linguistics, 2024. http://dx.doi.org/10.18653/v1/2024.emnlp-main.27.

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De Paolis, Niccolò, and Paolo Milazzo. "Towards a New Method for Perturbation Analysis in Biochemical Pathways Based on Network Propagation." In 16th International Conference on Bioinformatics Models, Methods and Algorithms. SCITEPRESS - Science and Technology Publications, 2025. https://doi.org/10.5220/0013384200003911.

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Ghanati, Elaheh, and Miranda van Iersel. "Laguerre-Gaussian Beam Propagation through Anisotropic Turbulence: A Comparison of the Extended Huygens-Fresnel Principle and Perturbation Method." In Applications of Lasers for Sensing and Free Space Communications. Optica Publishing Group, 2024. https://doi.org/10.1364/lsc.2024.lsth1c.3.

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A Laguerre-Gaussian beam is propagated through anisotropic atmospheric turbulence using the extended-Huygens-Fresnel principle and perturbation method. The normalized intensity profile and spot size are calculated using both methods and compared.
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Li, Ze-guang, Kan Wang, and Gang-lin Yu. "Research on Monte Carlo Perturbation Calculation Methods Applied in Reactor Physics." In 17th International Conference on Nuclear Engineering. ASMEDC, 2009. http://dx.doi.org/10.1115/icone17-75584.

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In the reactor design and analysis, there is often a need to calculate the effects caused by perturbations of temperature, components and even structure of reactors on reactivity. And in sensitivity studies, uncertainty analysis of target quantities and unclear data adjustment, perturbation calculations are also widely used. To meet the need of different types of reactors (complex, multidimensional systems), Monte Carlo perturbation methods have been developed. In this paper, several kinds of perturbation methods are investigated. Specially, differential operator sampling method and correlated tracking method are discussed in details. MCNP’s perturbation calculation capability is discussed by calculating certain problems, from which some conclusions are obtained on the capabilities of the differential operator sampling method used in the perturbation calculation model of MCNP. Also, a code using correlated tracking method has been developed to solve certain problems with cross-section changes, and the results generated by this code agree with the results generated by straightforward Monte Carlo techniques.
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Andrienko, Yu A., M. S. Dubovikov, and A. D. Gladun. "Refraction in interferometric tomography: perturbation approach." In Analytical Methods for Optical Tomography, edited by Gennady G. Levin. SPIE, 1992. http://dx.doi.org/10.1117/12.131889.

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Wong, C. N., W. D. Zhu, and G. Y. Xu. "On an Iterative General-Order Perturbation Method for Multiple Structural Damage Detection." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-33946.

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A general-order perturbation method involving multiple perturbation parameters is developed for eigenvalue problems with changes in the stiffness parameters. The perturbation solutions and eigenparameter sensitivities of all orders are derived explicitly. The perturbation method is used iteratively in conjunction with an optimization method in a robust damage detection algorithm. The generalized inverse method is used efficiently with the first order perturbations, and the gradient and quasi-Newton methods are used with the higher-order perturbations. Numerical simulations demonstrated the effectiveness of the algorithm in detecting the locations and extents of small to large levels of damage.
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Kamegawa, Tomoki, Masaomi Kimura, Imam Mukhlash, and Mohammad Iqbal. "A method to generate adversarial examples based on color variety of adjacent pixels." In AHFE 2023 Hawaii Edition. AHFE International, 2023. http://dx.doi.org/10.54941/ahfe1004184.

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Deep neural networks have improved the performance of large-scale learning tasks such as image recognition and speech recognition. However, neural networks also have vulnerabilities. Adversarial examples are generated by adding perturbations to images to cause incorrect predictions of image classifiers. The well-known perturbation attack is JSMA, which is relatively fast to generate perturbation and requires only simple procedures and is widely used in cybersecurity, anomaly detection and intrusion detection. However, there are problems with the way to perturb pixels. JSMA’s perturbations are easily perceivable by the human eyes because JSAM adds large perturbations to pixels. Some previous methods to generate adversarial examples did not assume that adversarial examples are checked by human eyes and allow larger perturbation to be adding to a single pixel. However, in situations where a deep learning model causes significant damage if it misrecognizes an input, a visual check by a human is necessary. In such cases, adversarial examples should not only cause misclassification in the image classifier system but also require less perturbation to avoid human perception of the perturbation. We propose methods to improve the JSMA problems. Specifically, it adjusts the amount of perturbation by calculating the variance between the value of the pixel to be perturbed and its surrounding pixels. If a large perturbation is added to the area of an image with a large pixel value variation, the perturbation will be imperceptible. In such case, perceivability does not increase significantly with a slightly larger perturbation. In contrast, if the large perturbation is added to the area of an image with small pixel value variation, the perturbation will be more perceptible. In such case, perturbations must be small. In our previous study, we assumed thresholds to classify the perturbations into two classes, large perturbation and small perturbation. If the variance was larger than the threshold, a larger perturbation was added; if the variance was smaller than the threshold, a smaller perturbation was added, which achieved a reduction in the amount of perturbation. However, there were still rooms of improvements of the perturbation to reduce the perceptibility. In this study, we focused on that there were differences in the perception of perturbations depending on the color of the pixel. The amount of perturbation should vary from pixel to pixel, not a fixed amount. Not only the variance of the surrounding pixels but also the variance of a larger area is calculated. By using these ratios, the amount of perturbation is varied from pixel to pixel. Experimental results using cifar-10 showed that the proposed method reduced the amount of perturbation to pixels with a misclassification success rate comparable to that of JSMA and our past method. We also confirmed that the reduced perturbation made the perturbation less perceptible.
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Pulkkinen, Aki, Aleksi Leino, Tuomas Lunttila, Meghdoot Mozumder, and Tanja Tarvainen. "Perturbation Monte Carlo in quantitative photoacoustic tomography." In Opto-Acoustic Methods and Applications in Biophotonics, edited by Roger J. Zemp, Chulhong Kim, and Jan Laufer. SPIE, 2021. http://dx.doi.org/10.1117/12.2615870.

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Reports on the topic "Perturbation methods"

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Becher, Thomas G. Continuum methods in lattice perturbation theory. Office of Scientific and Technical Information (OSTI), 2002. http://dx.doi.org/10.2172/808671.

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Foerster, Andrew, Juan Rubio-Ramírez, Daniel Waggoner, and Tao Zha. Perturbation Methods for Markov-Switching DSGE Models. National Bureau of Economic Research, 2014. http://dx.doi.org/10.3386/w20390.

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Downar, T. J. Advanced depletion perturbation methods and waste transmutation in the IFR. Office of Scientific and Technical Information (OSTI), 1991. http://dx.doi.org/10.2172/6090382.

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Clifton, Kelly, and Steven Gehrke. Wider Dissemination of Household Travel Survey Data Using Geographical Perturbation Methods. Portland State University Library, 2014. http://dx.doi.org/10.15760/trec.116.

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Fardad, Makan, and Bassam Bamieh. Perturbation Methods in Stability and Norm Analysis of Spatially Periodic Systems. Defense Technical Information Center, 2006. http://dx.doi.org/10.21236/ada458858.

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Downar, T. J. Advanced depletion perturbation methods and waste transmutation in the IFR. Final report. Office of Scientific and Technical Information (OSTI), 1991. http://dx.doi.org/10.2172/10105995.

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Collin, R. E. Comparative Evaluation of Kirchhoff, Perturbation, and Full Wave Methods for Rough Surface Scattering. Defense Technical Information Center, 1993. http://dx.doi.org/10.21236/ada271198.

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Balderson, Keith A., and Jeffrey T. Weathers. Comparison of Frequency Response and Perturbation Methods to Extract Linear Models from a Nonlinear Simulation. Defense Technical Information Center, 1994. http://dx.doi.org/10.21236/ada284115.

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Swanson and Kilman. L51506 Development of Improved Methods for Inspecting Gas Storage Well Downhole Casing. Pipeline Research Council International, Inc. (PRCI), 1986. http://dx.doi.org/10.55274/r0010199.

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Casing corrosion in storage wells is a matter of considerable concern to the gas storage industry. Such wells are typically flowed through the casing rather than through production tubing, to facilitate high flow capacities. When failures occur, gas leakage to surrounding formations, freshwater zones and to the surface can pose a sizable economic loss as well as a serious safety hazard. For these reasons, monitoring corrosion in down-hole casing in gas storage fields has become a major concern of many storage field operators, and the in situ detection and assessment of corrosion damage by means of logging instruments is a significant part of this effort. The study reported in this document has sought to investigate in detail the objectives, methods and results of currently available commercial logging devices as a first step in determining whether down-hole corrosion damage can be more accurately characterized by improved logging methods. Of the several methods potentially capable of meeting the through-wall measurement requirement, only two form the basis for current commercial corrosion logs: the flux leakage, or magnetic perturbation technique, and the remote field eddy current approach. In seeking to provide reasonably short term performance improvements to the industry, it was decided in this project to pursue refinements of magnetic perturbation logs for two reasons: first, the shortcomings evidenced by present logs of this type appear to be amenable to relatively simple improvement, and second, the remote field eddy current approach, while useful as an adjunct to damage assessment, offers little promise of sizing individual corrosion flaws.
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Landwehr, Philipp, Paulius Cebatarauskas, Csaba Rosztoczy, Santeri Röpelinen, and Maddalena Zanrosso. Inverse Methods In Freeform Optics. Technische Universität Dresden, 2023. http://dx.doi.org/10.25368/2023.148.

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Traditional methods in optical design like ray tracing suffer from slow convergence and are not constructive, i.e., each minimal perturbation of input parameters might lead to “chaotic” changes in the output. However, so-called inverse methods can be helpful in designing optical systems of reflectors and lenses. The equations in R2 become ordinary differential equations, while in R3 the equations become partial differential equations. These equations are then used to transform source distributions into target distributions, where the distributions are arbitrary, though assumed to be positive and integrable. In this project, we derive the governing equations and solve them numerically, for the systems presented by our instructor Martijn Anthonissen [Anthonissen et al. 2021]. Additionally, we show how point sources can be derived as a special case of a interval source with di- rected source interval, i.e., with each point in the source interval there is also an associated unit direction vector which could be derived from a system of two interval sources in R2. This way, it is shown that connecting source distributions with target distributions can be classified into two instead of three categories. The resulting description of point sources as a source along an interval with directed rays could potentially be extended to three dimensions, leading to interpretations of point sources as directed sources on convex or star-shaped sets.
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