Relevant bibliographies by topics / Perturbation

Contents

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

Academic literature on the topic 'Perturbation'

Author: Grafiati
Published: 4 June 2021
Last updated: 21 September 2024

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Journal articles on the topic "Perturbation"

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Huang, Pei, Yuting Yang, Fuqi Jia, Minghao Liu, Feifei Ma, and Jian Zhang. "Word Level Robustness Enhancement: Fight Perturbation with Perturbation." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 10 (June 28, 2022): 10785–93. http://dx.doi.org/10.1609/aaai.v36i10.21324.

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State-of-the-art deep NLP models have achieved impressive improvements on many tasks. However, they are found to be vulnerable to some perturbations. Before they are widely adopted, the fundamental issues of robustness need to be addressed. In this paper, we design a robustness enhancement method to defend against word substitution perturbation, whose basic idea is to fight perturbation with perturbation. We find that: although many well-trained deep models are not robust in the setting of the presence of adversarial samples, they satisfy weak robustness. That means they can handle most non-crafted perturbations well. Taking advantage of the weak robustness property of deep models, we utilize non-crafted perturbations to resist the adversarial perturbations crafted by attackers. Our method contains two main stages. The first stage is using randomized perturbation to conform the input to the data distribution. The second stage is using randomized perturbation to eliminate the instability of prediction results and enhance the robustness guarantee. Experimental results show that our method can significantly improve the ability of deep models to resist the state-of-the-art adversarial attacks while maintaining the prediction performance on the original clean data.
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Malamud, M., and H. Neidhardt. "Perturbation determinants for singular perturbations." Russian Journal of Mathematical Physics 21, no. 1 (March 2014): 55–98. http://dx.doi.org/10.1134/s1061920814010051.

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DINKLER, DIETER, and JENS PONTOW. "EVALUATION OF THE PERTURBATION SENSITIVITY OF COMPOSITE LAMINATED SHELLS." International Journal of Structural Stability and Dynamics 10, no. 04 (October 2010): 779–90. http://dx.doi.org/10.1142/s0219455410003737.

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Imperfection sensitivity and its influence on the limit loads of shells are widely discussed phenomena. Both phenomena may be classified with respect to the type of imperfection, which may be generalized to a perturbation. As perturbations influence the stability of shells, the identification of unfavorable perturbations is essential for the design of shells. The perturbation energy concept enables one to identify unfavorable perturbations of different kinds and to evaluate the sensitivity of fundamental states against buckling by the perturbation energy. This paper discusses the perturbation sensitivity of unstiffened composite laminated cylindrical shells consisting of unidirectional layers. Moreover, an approach for a load-level-specific modification of the perturbation sensitivity is introduced.
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Bessa, Pedro, Ruth Durrer, and Dennis Stock. "Perturbations of cosmological redshift drift." Journal of Cosmology and Astroparticle Physics 2023, no. 11 (November 1, 2023): 093. http://dx.doi.org/10.1088/1475-7516/2023/11/093.

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Abstract In this paper we calculate the linear perturbations of the cosmological redshift drift. We show explicitly that our expressions are gauge-invariant and compute the power spectrum of the redshift drift perturbations and its correlations with galaxy number counts within linear perturbation theory. Our findings show that the perturbations are small, and that the peculiar velocity and acceleration terms are dominating and cannot be neglected when modeling the full perturbative expression for the redshift drift. We also find that the cross-correlations with galaxy number count fluctuations might increase the detectability of the effect and can help to separate the perturbative effects from the background cosmological redshift drift signal.
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Jiang, Aojun, Francis M. Grover, Mary Bucklin, Jasjit Deol, Anna Shafer, and Keith E. Gordon. "Prior uncertainty impedes discrete locomotor adaptation." PLOS ONE 19, no. 2 (February 16, 2024): e0291284. http://dx.doi.org/10.1371/journal.pone.0291284.

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The impact of environmental uncertainty on locomotor adaptation remains unclear. Environmental uncertainty could either aid locomotor adaptation by prompting protective control strategies that stabilize movements to assist learning or impede adaptation by reducing error sensitivity and fostering hesitance to pursue corrective movements. To explore this, we investigated participants’ adaptation to a consistent force field after experiencing environmental uncertainty in the form of unpredictable balance perturbations. We compared the performance of this group (Perturbation) to the adaptive performance of a group that did not experience any unpredictable perturbations (Non-Perturbation). Perturbations were delivered using a cable-driven robotic device applying lateral forces to the pelvis. We assessed whole-body center of mass (COM) trajectory (COM signed deviation), anticipatory postural adjustments (COM lateral offset), and first step width. The Perturbation group exhibited larger disruptions in COM trajectory (greater COM signed deviations) than the Non-Perturbation group when first walking in the force field. While the COM signed deviations of both groups decreased towards baseline values, only the Non-Perturbation group returned to baseline levels. The Perturbation groups COM signed deviations remained higher, indicating they failed to fully adapt to the force field before the end. The Perturbation group also did not adapt their COM lateral offset to counter the predictable effects of the force field as the Non-Perturbation group did, and their first step width increased more slowly. Our findings suggest that exposure to unpredictable perturbations impeded future sensorimotor adaptations to consistent perturbations.
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Wu, Zhenqing, Zhejun Huang, Sijin Wu, Ziying Yu, Liuxin Zhu, and Lili Yang. "Accelerating Convergence of Langevin Dynamics via Adaptive Irreversible Perturbations." Mathematics 12, no. 1 (December 29, 2023): 118. http://dx.doi.org/10.3390/math12010118.

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Irreversible perturbations in Langevin dynamics have been widely recognized for their role in accelerating convergence in simulations of multi-modal distributions π(θ). A commonly used and easily computed standard irreversible perturbation is J∇logπ(θ), where J is a skew-symmetric matrix. However, Langevin dynamics employing a fixed-scale standard irreversible perturbation encounter a trade-off between local exploitation and global exploration, associated with small and large scales of standard irreversible perturbation, respectively. To address this trade-off, we introduce the adaptive irreversible perturbations Langevin dynamics, where the scale of the standard irreversible perturbation changes adaptively. Through numerical examples, we demonstrate that adaptive irreversible perturbations in Langevin dynamics can enhance performance compared to fixed-scale irreversible perturbations.
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Fallahtafti, Farahnaz, Sjoerd Bruijn, Arash Mohammadzadeh Gonabadi, Mohammad Sangtarashan, Julie Blaskewicz Boron, Carolin Curtze, Ka-Chun Siu, Sara A. Myers, and Jennifer Yentes. "Trunk Velocity Changes in Response to Physical Perturbations Are Potential Indicators of Gait Stability." Sensors 23, no. 5 (March 5, 2023): 2833. http://dx.doi.org/10.3390/s23052833.

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Response to challenging situations is important to avoid falls, especially after medial perturbations, which require active control. There is a lack of evidence on the relationship between the trunk’s motion in response to perturbations and gait stability. Eighteen healthy adults walked on a treadmill at three speeds while receiving perturbations of three magnitudes. Medial perturbations were applied by translating the walking platform to the right at left heel contact. Trunk velocity changes in response to the perturbation were calculated and divided into the initial and the recovery phases. Gait stability after a perturbation was assessed using the margin of stability (MOS) at the first heel contact, MOS mean, and standard deviation for the first five strides after the perturbation onset. Faster speed and smaller perturbations led to a lower deviation of trunk velocity from the steady state, which can be interpreted as an improvement in response to the perturbation. Recovery was quicker after small perturbations. The MOS mean was associated with the trunk’s motion in response to perturbations during the initial phase. Increasing walking speed may increase resistance to perturbations, while increasing the magnitude of perturbation leads to greater trunk motions. MOS is a useful marker of resistance to perturbations.
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Churchland, Anne K., and Stephen G. Lisberger. "Gain Control in Human Smooth-Pursuit Eye Movements." Journal of Neurophysiology 87, no. 6 (June 1, 2002): 2936–45. http://dx.doi.org/10.1152/jn.2002.87.6.2936.

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In previous experiments, on-line modulation of the gain of visual-motor transmission for pursuit eye movements was demonstrated in monkeys by showing that the response to a brief perturbation of target motion was strongly enhanced during pursuit relative to during fixation. The present paper elaborates the properties of on-line gain control by recording the smooth-pursuit eye movements of human subjects during tracking of a spot target. When perturbations consisted of one cycle of a 5-Hz sine wave, responses were significantly larger during pursuit than during fixation. Furthermore, responses grew as a function of eye/target velocity at the time of the perturbation and of perturbation amplitude. Thus human pursuit, like monkey pursuit, is modulated by on-line gain control. For larger perturbations consisting of a single sine wave at 2.8 Hz, ±19°/s, the degree of enhancement depended strongly on the phase of the perturbation. Enhancement was present when “peak-first” perturbations caused the target speed to increase first and was attenuated when “peak-last” perturbations caused target speed to decrease first. This effect was most profound when the perturbation was 2.8 Hz, ±19°/s but was also present when the amplitude of the peak-last perturbation was ±5o/s. For peak-last perturbations, the eye velocity evoked by the later peak of the perturbation was inversely related to that evoked by the preceding trough of the perturbation. We interpret these effects of perturbation phase as evidence that peak-last perturbations cause a decrease in the on-line gain of visual-motor transmission for pursuit. We conclude that gain control is modulated dynamically as behavioral conditions change. Finally, when perturbations were presented as a sequence of three large, peak-last sine waves starting at the onset of target motion at 10°/s, repeating the conditions used in prior studies on humans, we were able to replicate the prior finding that the response to the perturbations was equal during pursuit and fixation. We conclude that on-line gain control modulates human pursuit and that it can be probed most reliably with small, brief perturbations that do not affect the on-line gain themselves.
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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 (March 12, 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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Zanto, Theodore P., Edward W. Large, Armin Fuchs, and J. A. Scott Kelso. "Gamma-Band Responses to Perturbed Auditory Sequences: Evidence for Synchronization of Perceptual Processes." Music Perception 22, no. 3 (2005): 531–47. http://dx.doi.org/10.1525/mp.2005.22.3.531.

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We measured modulations of neuroelectric gamma-band activity (GBA) as subjects listened to isochronous pure-tone sequences with embedded temporal perturbations. Perturbations occurred every 6�10 tones, and at the locus of the perturbation, tones occurred early, on time, or late. In the absence of perturbations, induced (non�phase-locked) GBA reached maximum power simultaneously with the occurrence of tone onsets, whereas evoked (phase-locked) GBA peaks were observed after onsets. During late perturbation trials, peaks in induced activity tended to precede tone onsets, and during early perturbation trials, induced peaks followed tone onsets. Induced peaks returned to synchrony after both types of perturbations. Early tones resulted in a marked increase in evoked GBA power at the locus of the perturbation. The latency of evoked GBA relative to tone onset, as well as some other features of the response, depended asymmetrically on the direction of the perturbation. The current results provide evidence for the synchronization of GBA during the perception of auditory rhythms, thus supporting the role of GBA in temporal expectancy.
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Dissertations / Theses on the topic "Perturbation"

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Garioud, Renaud. "When perturbation theory goes non-perturbative : applications to strongly-correlated systems." Electronic Thesis or Diss., Institut polytechnique de Paris, 2023. http://www.theses.fr/2023IPPAX052.

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Cette thèse concerne le développement et l’utilisation de nouveaux algorithmes pour l’étude théorique de systèmes quantiques fortement corrélés. Il s’agit de systèmes dans lesquels les interactions, par exemple l’interaction de Coulomb répulsive entre les électrons d’un matériau, induisent des phénomènes physiques remarquables (comme la supraconductivité à haute température critique) qui ne peuvent être décrits dans le cadre d’une théorie standard à un corps. Pour comprendre l’origine de ces phénomènes, il est indispensable de traiter l’ensemble des particules et leurs interactions: on parle du problème à N -corps.Le projet de thèse consiste à continuer le développement, l’analyse et l’application des méthodes numériques dites diagrammatiques à ces systèmes. Si des progrès ont été faits, il reste beaucoup de questions fondamentales ouvertes quant à l’utilisation de méthodes perturbatives pour décrire un système qui est,par nature, dans un régime non-perturbatif. Quelles sont les limites de ces approches? Comment se manifestent les effets des corrélations dans la structure des séries perturbatives?Les développements algorithmiques seront utilisés pour l’étude de modèles de systèmes fortement corrélés, comme le modèle de Hubbard, ce qui permettra d’aborder des questions physiques d’intérêt actuel, en particulier en relation avec la physique des corrélations magnétiques et du pseudo-gap dans les cuprates supraconducteurs ou avec l’existence d’une transition de Mott sans phase ordonnée préemptive telle qu’elle est observée dans des expériences récentes sur des composés organiques
This thesis focuses on developing new algorithms for the study of strongly correlated materials. They are quantum systems in which interactions between electrons, such as the Coulomb repulsion, play a major role and give rise to remarkable physical properties (like high temperature superconductivity) which can't be described using a one-body formalism. To fully understand these phenomenon one has to treat the full system of many particles and their interactions : this is the many body problem.The project of this thesis is developing, analyzing and applying numerical methods called diagrammatic to these systems. A lots of fundamental questions remain unanswered about the using of perturbative methods to describe a system which is, by definition, in a non-perturbative regime. What are the limits of these approaches? How do correlations effects control the structure of the perturbative series ?Algorithmic developments will be applied to the study of strongly correlated systems, such as the Hubbard model, which will allow to cope with current topics of interest in condensed matter physics, in particular with the physics of correlated magnetism and of the pseudo gap in cuprate superconductors, or with the existence of a Mott phase transition with no preexisting ordered phase as it has been recently observed in experiments on organic materials
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Brechet, Sylvain David. "Cosmological perturbation theory." Thesis, University of Cambridge, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.611602.

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Ali, Saad Ahmad. "A unitary perturbation theory /." Thesis, McGill University, 2000. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=33373.

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The use of ordinary perturbation theory is ubiquitous in modern physics. However, it violates probability conservation, one of the fundamental laws of physics. In this thesis a unitarized perturbation theory is briefly described and its predictions for the behaviour of a number of simple systems are compared with those of ordinary perturbation theory. It is found that the new technique performs just as well as the usual perturbative approach in the regime where the latter is valid and provides improved results where perturbation theory fails. In particular, in the cases studied, the new method is found to reproduce the exact result at resonance.
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Lovett-Turner, Charles. "Resumming QCD perturbation series." Thesis, Durham University, 1995. http://etheses.dur.ac.uk/5375/.

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Since the advent of Quantum Field Theory (QFT) in the late 1940's, perturbation theory has become one of the most developed and successful means of extracting phenomenologically useful information from a QFT. In the ever- increasing enthusiasm for new phenomenological predictions, the mechanics of perturbation theory itself have often taken a back seat. It is in this light that this thesis aims to investigate some of the more fundamental properties of perturbation theory. The benefits of resumming perturbative series are highlighted by the explicit calculation of the three-jet rate in e+e- annihilation, resummed to all orders in leading and next-to-leading large logarithms. It is found that the result can be expressed simply in terms of exponentials and error functions. In general it is found that perturbative expansions in QED and QCD diverge at large orders. The nature of these divergences has been explored and found to come from two sources. The first are instanton singularities, which correspond to the combinatoric factors involved in counting Feynman diagrams at large orders. The second are renormalon singularities, which are closely linked to non-perturbative effects through the operator product expansion (OPE).By using Borel transform techniques, the singularity structure in the Borel plane for the QCD vacuum polarization is studied in detail. The renormalon singularity structure is as expected from OPE considerations. These results and existing exact large-A^/ results for the QCD Adler D-function and Deep Inelastic Scattering sum rules are used to resum to all orders the portion of the QCD perturbative coefficients which is leading in b, the first coefficient of the QCD beta-function. This part is expected asymptotically to dominate the coefficients in a large-Nj expansion. Resummed results are also obtained for the e+e- R-ratio and the r-lepton decay ratio. The renormalization scheme dependence of these resummed results is discussed in some detail.
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Barclay, David Thomas. "Topics in perturbation theory." Thesis, Durham University, 1992. http://etheses.dur.ac.uk/6006/.

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In providing a means of progressively improving an initial estimate, perturbation series have become a ubiquitous tool in modern physics. However, and mainly because this stepwise process of improvement rapidly becomes increasingly involved, surprisingly little is known about the formal properties of the series obtained. This thesis therefore investigates some aspects of these properties and how they effect the application of these techniques, with an emphasis on quantum field theory and the phenomenology of e+e(^-) colliders. One of the better understood examples of a perturbative series is the WKB one which is widely used to approximate the energy levels of quantum mechanical systems. Recently much interest has centred on a modification of this, the SWKB series. Apart from (possibly) offering an improvement on the original, this is intrinsically interesting in being related to the supersymmetry of field theory. Furthermore, as Chapter 1 explains, there is a close connection between the cases where the initial estimate requires no correction and an important set of quantum mechanical problems (the "shape invariant" ones) which can be solved elegantly and completely. The situation in field theory is more complicated, not least because the series for any particular problem is no longer unique. While this presents few theoretical difficulties, it has serious consequences when attempts are made to compare predictions with experiment. This obstacle is particularly severe in Quantum Chromodynamics and its fundamental constant (A(_QCD)) is therefore only roughly known at present. It will be argued that current responses to this are all imperfect, but that tests of the theory can be envisaged that circumvent the problem. This leads into questions concerning the origin of the divergences in the perturbation series - for although it may initially provide usefully improved estimates, the series probably breaks down eventually. Existing arguments about this topic are critically reviewed - and in one case substantially simplified - before an alternative one is proposed in some detail. By concentrating on a particularly restricted situation, the Common Effective Charge Approach simplifies matters to the extent that issues such as non-analyticity of functions and the potential accuracy of perturbative techniques in realistic applications can be conveniently investigated.
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Amery, Gareth. "Causal cosmological perturbation theory." Thesis, University of Cambridge, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.619761.

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Akin, Osman Caglar. "Perturbation of renewal processes." Thesis, University of North Texas, 2008. https://digital.library.unt.edu/ark:/67531/metadc6140/.

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Renewal theory began development in the early 1940s, as the need for it in the industrial engineering sub-discipline operations research had risen. In time, the theory found applications in many stochastic processes. In this thesis I investigated the effect of seasonal effects on Poisson and non-Poisson renewal processes in the form of perturbations. It was determined that the statistical analysis methods developed at UNT Center for Nonlinear Science can be used to detect the effects of seasonality on the data obtained from Poisson/non-Poisson renewal systems. It is proved that a perturbed Poisson process can serve as a paradigmatic model for a case where seasonality is correlated to the noise and that diffusion entropy method can be utilized in revealing this relation. A renewal model making a connection with the stochastic resonance phenomena is used to analyze a previous neurological experiment, and it was shown that under the effect of a nonlinear perturbation, a non-Poisson system statistics may make a transition and end up in the of Poisson basin of statistics. I determine that nonlinear perturbation of the power index for a complex system will lead to a change in the complexity characteristics of the system, i.e., the system will reach a new form of complexity.
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Akin, Osman Caglar Grigolini Paolo. "Perturbation of renewal processes." [Denton, Tex.] : University of North Texas, 2008. http://digital.library.unt.edu/permalink/meta-dc-6140.

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Borinsky, Michael. "Graphs in perturbation theory." Doctoral thesis, Humboldt-Universität zu Berlin, 2018. http://dx.doi.org/10.18452/19201.

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Inhalt dieser Arbeit ist eine Erweiterung der Hopfalgebrastruktur der Feynmangraphen und Renormierung von Connes und Kreimer. Zusätzlich wird eine Struktur auf faktoriell wachsenden Potenzreihen eingeführt, die deren asymptotisches Wachstum beschreibt und die kompatibel mit der Hopfalgebrastruktur ist. Die Hopfalgebrastruktur auf Graphen erlaubt die explizite Enumeration von Graphen mit Einschränkungen in Bezug auf die erlaubten Untergraphen. Im Fall der Feynmangraphen wird zusätzlich eine algebraische Verbandstruktur eingeführt, die weitere eindeutige Eigenschaften von physikalischen Quantenfeldtheorien aufdeckt. Der Differenzialring der faktoriell divergenten Potenzreihen erlaubt es asymptotische Resultate von implizit definierten Potenzreihen mit verschwindendem Konvergenzradius zu extrahieren. In Kombination ergeben beide Strukturen eine algebraische Formulierung großer Graphen mit Einschränkungen für die erlaubten Untergraphen. Diese Strukturen sind motiviert von null-dimensionaler Quantenfeldtheorie and werden zur Analyse ebendieser benutzt. Als reine Anwendung der Hopfalgebrastruktur wird eine hopfalgebraische Formulierung der Legendretransformation in Quantenfeldtheorien formuliert. Der Differenzialring der faktoriell divergenten Potenzreihen wird dazu benutzt zwei asymptotische Enumerationsprobleme zu lösen: Die asymptotische Anzahl der verbundenen Chorddiagramme und die asymptotische Anzahl der simplen Permutationen. Für beide asymptotischen Lösungen werden vollständige asymptotische Entwicklungen in Form von geschlossenen Erzeugendenfunktionen berechnet. Kombiniert werden beide Strukturen zur Anwendung an null-dimensionaler Quantenfeldtheorie. Zahlreiche Größen werden in den null-dimensionalen Varianten von phi^3, phi^4, QED, quenched QED and Yukawatheorie mit ihren kompletten asymptotischen Entwicklungen berechnet.
This thesis provides an extension of the work of Dirk Kreimer and Alain Connes on the Hopf algebra structure of Feynman graphs and renormalization to general graphs. Additionally, an algebraic structure of the asymptotics of formal power series with factorial growth, which is compatible with the Hopf algebraic structure, will be introduced. The Hopf algebraic structure on graphs permits the explicit enumeration of graphs with constraints for the allowed subgraphs. In the case of Feynman diagrams a lattice structure, which will be introduced, exposes additional unique properties for physical quantum field theories. The differential ring of factorially divergent power series allows the extraction of asymptotic results of implicitly defined power series with vanishing radius of convergence. Together both structures provide an algebraic formulation of large graphs with constraints on the allowed subgraphs. These structures are motivated by and used to analyze renormalized zero-dimensional quantum field theory at high orders in perturbation theory. As a pure application of the Hopf algebra structure, an Hopf algebraic interpretation of the Legendre transformation in quantum field theory is given. The differential ring of factorially divergent power series will be used to solve two asymptotic counting problems in combinatorics: The asymptotic number of connected chord diagrams and the number of simple permutations. For both asymptotic solutions, all order asymptotic expansions are provided as generating functions in closed form. Both structures are combined in an application to zero-dimensional quantum field theory. Various quantities are explicitly given asymptotically in the zero-dimensional version of phi^3, phi^4, QED, quenched QED and Yukawa theory with their all order asymptotic expansions.
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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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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.

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Books on the topic "Perturbation"

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Lampersberg, Gerhard. Perturbation. Klagenfurt: Ritter, 1987.

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

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Skinner, Lindsay A. Singular Perturbation Theory. Boston, MA: Springer US, 2011. http://dx.doi.org/10.1007/978-1-4419-9958-0.

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Ferraz-Mello, Sylvio. Canonical Perturbation Theories. New York, NY: Springer New York, 2007. http://dx.doi.org/10.1007/978-0-387-38905-9.

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Stewart, G. W. Matrix perturbation theory. Boston: Academic Press, 1990.

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Criminale, W. O. Vortex perturbation dynamics. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1995.

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

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Borinsky, Michael. Graphs in Perturbation Theory. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-03541-9.

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

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Book chapters on the topic "Perturbation"

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Hislop, P. D., and I. M. Sigal. "Perturbation Theory: Relatively Bounded Perturbations." In Introduction to Spectral Theory, 149–59. New York, NY: Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4612-0741-2_15.

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Wang, Rui-Sheng. "Perturbation." In Encyclopedia of Systems Biology, 1680–81. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4419-9863-7_385.

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Weik, Martin H. "perturbation." In Computer Science and Communications Dictionary, 1254. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/1-4020-0613-6_13873.

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Gallavotti, Giovanni. "Perturbation Theory." In Perturbation Theory, 1–14. New York, NY: Springer US, 2009. http://dx.doi.org/10.1007/978-1-0716-2621-4_396.

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Fassò, Francesco. "Perturbation of Superintegrable Hamiltonian Systems." In Perturbation Theory, 307–37. New York, NY: Springer US, 2022. http://dx.doi.org/10.1007/978-1-0716-2621-4_757.

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Bambusi, Dario. "Perturbation Theory for PDEs." In Perturbation Theory, 229–46. New York, NY: Springer US, 2009. http://dx.doi.org/10.1007/978-1-0716-2621-4_401.

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Celletti, Alessandra. "Perturbation Theory in Celestial Mechanics." In Perturbation Theory, 339–55. New York, NY: Springer US, 2022. http://dx.doi.org/10.1007/978-1-0716-2621-4_397.

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Sacchetti, Andrea. "Semiclassical Perturbation Theory." In Perturbation Theory, 391–407. New York, NY: Springer US, 2009. http://dx.doi.org/10.1007/978-1-0716-2621-4_403.

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Chierchia, Luigi, and Michela Procesi. "Kolmogorov-Arnold-Moser (KAM) Theory for Finite and Infinite Dimensional Systems." In Perturbation Theory, 247–89. New York, NY: Springer US, 2022. http://dx.doi.org/10.1007/978-1-0716-2621-4_302.

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Pucacco, Giuseppe. "Perturbation Theory and the Method of Detuning." In Perturbation Theory, 141–52. New York, NY: Springer US, 2022. http://dx.doi.org/10.1007/978-1-0716-2621-4_761.

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Conference papers on the topic "Perturbation"

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Parker, Robert G. "Stability of Continuous Gyroscopic Systems Using Perturbation Analysis." In ASME 1996 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/imece1996-1071.

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Abstract Continuous gyroscopic system eigenvalues and stability are analytically calculable in only a limited set of cases. This paper presents an eigenvalue perturbation analysis to determine approximate eigenvalue loci and stability conclusions in the vicinity of critical speeds and zero speed. The perturbation analysis relies on a formulation of the general continuous gyroscopic system eigenvalue problem in terms of matrix differential operators and vector eigenfunctions. The eigenvalue λ appears only as λ2 in the formulation, and the smoothness of λ2 at the critical speeds and zero speed is the essential feature required for the perturbatton. First order eigenvalue perturbations are determined at the critical speeds and zero speed. The derived eigenvalue perturbations are simple expressions in terms of the original mass, gyroscopic, and stiffness operators and the critical speed/stationary system eigenfunctions. Prediction of whether an eigenvalue passes to or from a region of divergence instability is determined by the sign of the eigenvalue perturbation. Additionally, perturbation of the critical speed/stationary system yields approximations for the eigenvalue loci at speeds away from these. The results provide analytical means for estimating continuous gyroscopic system eigenvalues and stability near critical speeds without numerical computation. The results are limited to systems having one independent eigenfunction associated with each critical speed and each stationary system eigenvalue. The techniques also apply to discrete gyroscopic systems. Examples are presented for an axially-moving, tensioned beam and a rotating rigid body and comparisons with known solutions are given.
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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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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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Tang, Liaoyuan, Zheng Wang, Guanxiong He, Rong Wang, and Feiping Nie. "Perturbation Guiding Contrastive Representation Learning for Time Series Anomaly Detection." In Thirty-Third International Joint Conference on Artificial Intelligence {IJCAI-24}. California: International Joint Conferences on Artificial Intelligence Organization, 2024. http://dx.doi.org/10.24963/ijcai.2024/548.

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Time series anomaly detection is a critical task with applications in various domains. Due to annotation challenges, self-supervised methods have become the mainstream approach for time series anomaly detection in recent years. However, current contrastive methods categorize data perturbations into binary classes, normal or anomaly, which lack clarity on the specific impact of different perturbation methods. Inspired by the hypothesis that "the higher the probability of misclassifying perturbation types, the higher the probability of anomalies", we propose PCRTA, our approach firstly devises a perturbation classifier to learn the pseudo-labels of data perturbations. Furthermore, for addressing "class collapse issue" in contrastive learning, we propose a perturbation guiding positive and negative samples selection strategy by introducing learnable perturbation classification networks. Extensive experiments on six realworld datasets demonstrate the significant superiority of our model over thirteen state-of-the-art competitors, and obtains average 5.14%, 8.24% improvement in F1 score and AUC-PR, respectively.
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Degasperis, A., and G. Gaeta. "Symmetry and Perturbation Theory." In International Workshop on Symmetry and Perturbation Theory. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812833037.

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Parker, R. G., and C. D. Mote. "Exact Perturbation for the Vibration of Almost Annular or Circular Plates." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0647.

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Abstract Using perturbation analysis, the eigensolutions for plate vibration problems on nearly annular or circular domains are determined. The irregular domain eigensolutions are calculated as perturbations of the corresponding annular or circular domain eigensolutions. These perturbations are determined exactly. The simplicity of these exact solutions allows the perturbation to be carried through third order for distinct unperturbed eigenvalues and through second order for degenerate unperturbed eigenvalues. Furthermore, this simplicity allows the resulting orthonormalized eigenfunctions to be readily incorporated into response, system identification, and control analyses. The clamped, nearly circular plate is studied in detail, and the exact eigensolution perturbations are derived for an arbitrary boundary shape deviation. Rules governing the splitting of degenerate unperturbed eigenvalues at both first and second orders of perturbation are presented. These rules, which apply for arbitrary shape deviation, generalize those obtained in previous works where specific, discrete asymmetries and first order splitting are examined. The eigensolution perturbations and splitting rules reduce to simple, algebraic formulae in the Fourier coefficients of the boundary shape asymmetry. Elliptical plate eigensolutions are calculated and compared to finite element analysis and, for the fundamental eigenvalue, to the exact solution given by Shibaoka (1956).
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Parker, Robert G., and Xionghua Wu. "Structured Eigensolution Properties of Planetary Gears With Elastically Deformable Ring Gears." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87340.

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The distinctive modal properties of equally spaced planetary gears with elastic ring gears are studied through perturbation and a candidate mode method. All eigenfunctions fall into one of four mode types whose structured properties are derived analytically. Two perturbations are used to obtain closed-form expressions of all the eigenfunctions. In the Discrete Planetary Perturbation (DPP), the unperturbed system is a discrete planetary gear with a rigid ring. The stiffness of the ring is perturbed from infinite to a finite number. In the Elastic Ring Perturbation (ERP), the unperturbed system is an elastic ring supported by the ring-planet mesh springs; the sun, planet and carrier motions are treated as small perturbations. A subsequent candidate mode method analysis proves the perturbation results and removes any reliance on perturbation parameters being small. All vibration modes are classified into rotational, translational, planet and purely ring modes. The well defined properties of each type of mode are analytically determined. All modal properties are verified numerically.
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Ho, Yu-Chi. "Perturbation analysis." In the 24th conference. New York, New York, USA: ACM Press, 1992. http://dx.doi.org/10.1145/167293.167340.

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Akavia, Adi, and Ramarathnam Venkatesan. "Perturbation codes." In 2008 46th Annual Allerton Conference on Communication, Control, and Computing. IEEE, 2008. http://dx.doi.org/10.1109/allerton.2008.4797725.

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Šimić, Ilija, Vedran Sabol, and Eduardo Veas. "Perturbation Effect." In CIKM '22: The 31st ACM International Conference on Information and Knowledge Management. New York, NY, USA: ACM, 2022. http://dx.doi.org/10.1145/3511808.3557418.

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Reports on the topic "Perturbation"

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Liu, Zhenyue, and Norman Bleistein. Velocity Analysis by Perturbation. Fort Belvoir, VA: Defense Technical Information Center, May 1993. http://dx.doi.org/10.21236/ada272537.

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Meissner, U. G. Chiral perturbation theory with nucleons. Office of Scientific and Technical Information (OSTI), September 1991. http://dx.doi.org/10.2172/10107296.

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Edmunds, T. Base case and perturbation scenarios. Office of Scientific and Technical Information (OSTI), October 1998. http://dx.doi.org/10.2172/3845.

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Meissner, U. G. Chiral perturbation theory with nucleons. Office of Scientific and Technical Information (OSTI), September 1991. http://dx.doi.org/10.2172/6095581.

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Wright, Adam, Marija Milacic, Karen Rothfels, Joel Weiser, Quang Trinh, Bijay Jassal, Robin Haw, and Lincoln Stein. Evaluating the Predictive Accuracy of Reactome's Curated Biological Pathways. Reactome, November 2022. http://dx.doi.org/10.3180/poster/20221109wright.

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Reactome is a database of human biological pathways manually curated from the primary literature and peer-reviewed by experts. To evaluate the utility of Reactome pathways for predicting functional consequences of genetic perturbations, we compared predictions of perturbation effects based on Reactome pathways against published empirical observations. Ten cancer-relevant Reactome pathways, representing diverse biological processes such as signal transduction, cell division, DNA repair, and transcriptional regulation, were selected for testing. For each pathway, root input nodes and key pathway outputs were defined. We then used pathway-diagram-derived logic graphs to predict, either by inspection by biocurators or using a novel algorithm MP-BioPath, the effects of bidirectional perturbations (upregulation/activation or downregulation/inhibition) of single root inputs on the status of key outputs. These predictions were then compared to published empirical tests.
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Langnau, Alex. Perturbation theory in light-cone quantization. Office of Scientific and Technical Information (OSTI), January 1992. http://dx.doi.org/10.2172/10134550.

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Weinstein, Marvin. Adaptive Perturbation Theory I: Quantum Mechanics. Office of Scientific and Technical Information (OSTI), October 2005. http://dx.doi.org/10.2172/878047.

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

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Omohundro, S. M. Geometric perturbation theory and plasma physics. Office of Scientific and Technical Information (OSTI), April 1985. http://dx.doi.org/10.2172/5171541.

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Langnau, A. Perturbation theory in light-cone quantization. Office of Scientific and Technical Information (OSTI), January 1992. http://dx.doi.org/10.2172/5609121.

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