Relevant bibliographies by topics / Paradifferential calculus with parameters

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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 'Paradifferential calculus with parameters'

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Published: 14 March 2023

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Journal articles on the topic "Paradifferential calculus with parameters"

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Hua, Chen, and Luigi Rodino. "Paradifferential calculus in Gevrey classes." Journal of Mathematics of Kyoto University 41, no. 1 (2001): 1–31. http://dx.doi.org/10.1215/kjm/1250517647.

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Xiang, Zhaoyin, and Wei Yan. "On the Well-Posedness of the Boussinesq Equation in the Triebel-Lizorkin-Lorentz Spaces." Abstract and Applied Analysis 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/573087.

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We establish the local well-posedness and obtain a blow-up criterion of smooth solutions for the Boussinesq equations in the framework of Triebel-Lizorkin-Lorentz spaces. The main ingredients of our proofs are Littlewood-Paley decomposition and the paradifferential calculus.
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Sango, Mamadou, and Tesfalem Abate Tegegn. "Harmonic analysis tools for stochastic magnetohydrodynamics equations in Besov spaces." International Journal of Modern Physics B 30, no. 28n29 (November 10, 2016): 1640025. http://dx.doi.org/10.1142/s0217979216400257.

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We establish a regularity result for stochastic heat equations in probabilistic evolution spaces of Besov type and we use it to prove a global in time existence and uniqueness of solution to a stochastic magnetohydrodynamics equation. The existence result holds with a positive probability which can be made arbitrarily close to one. The work is carried out by blending harmonic analysis tools such as Littlewood–Paley decomposition, Jean–Micheal Bony paradifferential calculus and stochastic calculus. The law of large numbers is a key tool in our investigation. Our global existence result is new in three-dimensional spaces.
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Fons-Badal, Carla, Antonio Fons-Font, Carlos Labaig-Rueda, M. Fernanda Solá-Ruiz, Eduardo Selva-Otaolaurruchi, and Rubén Agustín-Panadero. "Analysis of Predisposing Factors for Rapid Dental Calculus Formation." Journal of Clinical Medicine 9, no. 3 (March 20, 2020): 858. http://dx.doi.org/10.3390/jcm9030858.

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Background: Calculus accumulation varies widely between individuals. Dental calculus has been associated with the principal periodontal diseases. The aim of this study was to analyze individual characteristics, and salivary and microbiological parameters among patients considered to be rapid calculus formers and patients who form calculus slowly. Methods: Individual characteristics were recorded in a sample of 74 patients (age, sex, smoking, periodontal diagnosis, and dental crowding), as well as salivary parameters (unstimulated saliva flow, pH, and biochemical analysis of saliva) and microbiological parameters (by means of semi-quantitative polymerase chain reaction (PCR) analysis). Results: A statistically significant association (p = 0.002) was found between the rate of calculus formation and the diagnosis of periodontal disease. A greater presence of dental crowding was observed among the group of rapid calculus formers. Urea and phosphorus levels were higher among rapid calculus formers. Regarding microbiological parameters, differences were found in Streptococcus mutans, this being higher in the group of slow formers. Conclusions: Rapid calculus formation appears to be linked to patients diagnosed with more severe periodontal diseases. Rapid calculus-forming patients present more dental crowding and a lower proportion of S. mutans.
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Corless, Robert M., David J. Jeffrey, and David R. Stoutemyer. "Integrals of functions containing parameters." Mathematical Gazette 104, no. 561 (October 8, 2020): 412–26. http://dx.doi.org/10.1017/mag.2020.96.

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Calculus students are taught that an indefinite integral is defined only up to an additive constant, and as a consequence generations of students have assiduously added ‘+C’ to their calculus homework. Although ubiquitous, these constants rarely garner much attention, and typically loiter without intent around the ends of equations, feeling neglected. There is, however, useful work they can do, work which is particularly relevant in the contexts of integral tables and computer algebra systems. We begin, therefore, with a discussion of the context, before returning to coax the constants out of the shadows and assign them their tasks.
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Năstăsescu, Vasile, and Gheorghe Bârsan. "SPH method in numerical calculus of detonation parameters." Journal of Engineering Sciences and Innovation 4, no. 1 (March 5, 2019): 1–16. http://dx.doi.org/10.56958/jesi.2019.4.1.1.

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This paper presents some of our results in using of the Smoothed Particles Hydrodynamics (SPH) method for the numerical modelling of the detonation phenomena. The study of the detonation is very important for evaluation of different explosives and even for their design. The paper also presents, in a synthetically way, some fundamentals of the detonation. The numerical modelling of the detonation can be made by Finite Element Method (FEM), but using of the SPH method brings some important advantages because the large deformations, large distortions occur. If the FEM can be used in Arbitrary Lagrangian-Eulerian (ALE) formulation, the SPH method can easily works and next to it, some specific parameters (density variation, specific energy etc.) can be obtained and analyzed by post-processing. The numerical results (by FEM and by SPH method) are compared with theoretical results. The numerical study allowed us to analyse the influence of some explosive characteristics and of the circumstances (non confined and confined explosive) upon detonation parameters.
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Hackbusch, Wolfgang. "Numerical tensor calculus." Acta Numerica 23 (May 2014): 651–742. http://dx.doi.org/10.1017/s0962492914000087.

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The usual large-scale discretizations are applied to two or three spatial dimensions. The standard methods fail for higher dimensions because the data size increases exponentially with the dimension. In the case of a regular grid withngrid points per direction, a spatial dimensiondyieldsndgrid points. A grid function defined on such a grid is an example of a tensor of orderd. Here, suitable tensor formats help, since they try to approximate these huge objects by a much smaller number of parameters, which increases only linearly ind. In this way, data of sizend= 10001000can also be treated.This paper introduces the algebraic and analytical aspects of tensor spaces. The main part concerns the numerical representation of tensors and the numerical performance of tensor operations.
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Sarkar, Jyotirmoy, and Mamunur Rashid. "Estimating the Parameters of a Simple Linear Regression Model Without Using Differential Calculus." Journal of Probability and Statistical Science 20, no. 1 (October 3, 2022): 191–203. http://dx.doi.org/10.37119/jpss2022.v20i1.645.

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To estimate the parameters of a simple linear regression model, students who already know calculus can minimize the total squared deviations by setting its first-order partial derivatives to zero and solving simultaneously. For students who do not know calculus, most teachers/textbooks simply state the formulas without justifying them. Students accept the formulas on faith; and for given data, they evaluate the estimates using a calculator or a statistical software. In this paper, we justify the formulas without invoking calculus. We hope the users of statistics will benefit from our proposed justifications.
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Pena, Andra Elena, Florea Dorel Anania, and Miron Zapciu. "Research Regarding Software Developing for Machining Parameters Optimization Calculus." Applied Mechanics and Materials 656 (October 2014): 192–99. http://dx.doi.org/10.4028/www.scientific.net/amm.656.192.

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Establish of efficient machining parameters has been a problem that has confronted manufacturing industries for nearly a century, and is still the subject of many studies. Optimum machining parameters are of great concern in manufacturing environments, where economy of machining operation plays a key role in competitiveness in the market. The aim of this paper is to present a method to integrate advanced technology issues into a simple and intuitive application for machining parameters calculus. The goal is the development of a program easy to use in industry for CAM engineers and machine operators, that optimize the cutting parameters (in ways that diminish the defects – vibrations, cutting tool wear, machine tools wear – and reduce the power consumption) depending on a number of parameters determined by experimental and analytical calculation. The program will integrate calculus algorithms based on experimental data and analytical results with a simple and friendly user interface.
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AWAI, I., Y. ZHANG, T. ISHIDA, and T. SUZUKI. "Principles of Time Domain Calculus of Microwave Resonator Parameters." IEICE Transactions on Electronics E90-C, no. 12 (December 1, 2007): 2198–204. http://dx.doi.org/10.1093/ietele/e90-c.12.2198.

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Dissertations / Theses on the topic "Paradifferential calculus with parameters"

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Enfeldt, Viktor. "Real-Time Ray Tracing With Polarization Parameters." Thesis, Blekinge Tekniska Högskola, Institutionen för datavetenskap, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-19667.

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Background. The real-time renderers used in video games and similar graphics applications do not model the polarization aspect of light. Polarization parameters have previously been incorporated in some offline ray-traced renderers to simulate polarizing filters and various optical effects. As ray tracing is becoming more and more prevalent in real-time renderers, these polarization techniques could potentially be used to simulate polarization and its optical effects in real-time applications as well. Objectives. This thesis aims to determine if an existing polarization technique from offline renderers is, from a performance standpoint, viable to use in real-time ray-traced applications to simulate polarizing filters, or if further optimizations and simplifications would be needed. Methods. Three ray-traced renderers were implemented using the DirectX RayTracing API: one polarization-less Baseline version; one Polarization version using an existing polarization technique; and one optimized Hybrid version, which is a combination of the other two. Their performance was measured and compared in terms of frametimes and VRAM usage in three different scenes and with five different ray counts. Results. The Polarization renderer is ca. 30% slower than the Baseline in the two more complex scenes, and the Hybrid version is around 5–15% slower than the Baseline in all tested scenes. The VRAM usage of the Polarization version was higher than the Baseline one in the tests with higher ray counts, but only by negligible amounts. Conclusions.  The Hybrid version has the potential to be used in real-time applications where high frame rates are important, but not paramount (such as the commonly featured photo modes in video games). The performance impact of the Polarization renderer's implementation is greater, but it could potentially be used as well. Due to limitations in the measurement process and the scale of the test application, no conclusions could be made about the implementations' impact on VRAM usage.
Bakgrund. Realtidsrenderarna som används i videospel och liknande grafikapplikationer simulerar inte ljusets polarisering. Polariseringsinformation har tidigare implementerats i vissa stålföljningsbaserade (ray-traced) offline-renderare för att simulera polariseringsfilter och diverse optiska effekter. Eftersom strålföljning har blivit allt vanligare i realtidsrenderare så kan dessa polariseringstekniker potentiellt också användas för att simulera polarisering och dess optiska effekter i sådana program. Syfte. Syftet med denna rapport är att avgöra om en befintlig polariseringsteknik från offline-renderare, från en prestandasynpunkt, är lämplig att använda för att simulera polariseringsfilter i stålföljningsbaserade realtidsapplikationer, eller om ytterligare optimeringar och förenklingar behövs. Metod. DirectX RayTracing API:et har använts för att implementera tre stålföljningsbaserade realtidsrenderare: en polarisationsfri Baseline-version; en Polarization-version med en befintlig polariseringsteknik; och en optimerad Hybrid-version, som är en kombination av de andra två. Deras prestanda mättes och jämfördes med avseende på frametime och VRAM-användning i tre olika scener och med fem olika antal strålar per pixel. Resultat. Polarization-versionen är ca 30% långsammare än Baseline-versionen i de två mest komplexa scenerna, och Hybrid-versionen är ca 5–15% långsammare än Baseline-versionen i alla testade scener. Polarization-versionens VRAM-användningen var högre än Baseline-versions i testerna med högre strålantal, men endast med försumbara mängder. Slutsatser. Hybrid-versionen har potential att användas i realtidsapplikationer där höga bildhastigheter är viktiga, men inte absolut nödvändiga (exempelvis de vanligt förekommande fotolägena i videospel). Polarization-versionens implementation hade sämre prestanda, men även den skulle potentiellt kunna användas i sådana applikationer. På grund av mätprocessens begränsningar och testapplikationens omfattning så kunde inga slutsatser dras gällande implementeringarnas påverkan på VRAM-användning.
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Fanelli, Francesco. "Mathematical analysis of models of non-homogeneous fluids and of hyperbolic equations with low regularity coefficients." Phd thesis, Université Paris-Est, 2012. http://tel.archives-ouvertes.fr/tel-00794508.

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The present thesis is devoted both to the study of strictly hyperbolic operators with low regularity coefficients and of the density-dependent incompressible Euler system. On the one hand, we show a priori estimates for a second order strictly hyperbolic operator whose highest order coefficients satisfy a log-Zygmund continuity condition in time and a log-Lipschitz continuity condition with respect to space. Such an estimate involves a time increasing loss of derivatives. Nevertheless, this is enough to recover well-posedness for the associated Cauchy problem in the space $H^infty$ (for suitably smooth second order coefficients).In a first time, we consider acomplete operator in space dimension $1$, whose first order coefficients were assumed Hölder continuous and that of order $0$only bounded. Then, we deal with the general case of any space dimension, focusing on a homogeneous second order operator: the step to higher dimension requires a really different approach. On the other hand, we consider the density-dependent incompressible Euler system. We show its well-posedness in endpoint Besov spaces embedded in the class of globally Lipschitz functions, producing also lower bounds for the lifespan of the solution in terms of initial data only. This having been done, we prove persistence of geometric structures, such as striated and conormal regularity, for solutions to this system. In contrast with the classical case of constant density, even in dimension $2$ the vorticity is not transported by the velocity field. Hence, a priori one can expect to get only local in time results. For the same reason, we also have to dismiss the vortex patch structure. Littlewood-Paley theory and paradifferential calculus allow us to handle these two different problems .A new version of paradifferential calculus, depending on a parameter $ggeq1$, is also needed in dealing with hyperbolic operators with nonregular coefficients. The general framework is that of Besov spaces, which includes in particular Sobolev and Hölder sets. Intermediate classes of functions, of logaritmic type, come into play as well
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Nguyen, Van Tri. "Adjoint-based approach for estimation & sensor location on 1D hyperbolic systems with applications in hydrology & traffic." Thesis, Université Grenoble Alpes (ComUE), 2016. http://www.theses.fr/2016GREAT063/document.

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Ce travail de thèse propose une approche générique pour l'estimation de l'état/ des paramètres et pour le placement de capteurs de systèmes hyperboliques non linéaires en dimension infinie. Le travail est donc divisé en deux parties principales : une partie consacrée à l'estimation optimale et une partie dédiée au placement optimal de capteurs. La méthode d'estimation optimale utilise une approche par calcul des variations et utilise la méthode des multiplicateurs de Lagrange. Ces multiplicateurs jouent un rôle important en donnant accès aux sensibilités des mesures par rapport aux variables qui doivent être estimées. Ces sensibilités, décrites par les équations adjointes, sont aussi à l'origine d'une nouvelle approche, dite méthode de l'adjoint, pour le placement optimal de capteurs. Divers exemples, construits sur la base de simulations mais également de données réelles et pour différents scénarios, sont aussi étudiées afin d'illustrer l'efficacité des approches développées. Ces exemples concernent les écoulements à surface libre (en hydrologie des bassins versants) et le trafic routier représentés par des équations aux dérivées partielles hyperboliques non linéaires
The thesis proposes a general framework for both state/parameters estimation and sensor placement in nonlinear infinite dimensional hyperbolic systems. The work is therefore divided into two main parts: a first part devoted to the optimal estimation and a second one to optimal sensor location. The estimation method is based on the calculus of variations and the use of Lagrange multipliers. The Lagrange multipliers play an important role in giving access to the sensitivities of the measurements with respect to the variables to be estimated. These sensitivities, described by the adjoint equations, are also the key idea of a new approach, so-called the adjoint-based approach, for the optimal sensor placement. Various examples, either based on some simulations with synthetic measurements or real data sets and for different scenarios, are also studied to illustrate the effectiveness of the developed approaches. Theses examples concern the overland flow systems and the traffic flow, which are both governed by nonlinear hyperbolic partial differential equations
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Books on the topic "Paradifferential calculus with parameters"

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Lyndon B. Johnson Space Center., ed. On the optimal use of fictitious time in variation of parameters methods with application to BG14. Houston, Tex: National Aeronautics and Space Administration, Lyndon B. Johnson Space Center, 1991.

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Fonseca, Carlos M. da. A panorama of mathematics: Pure and applied : Conference on Mathematics and Its Applications, November 14-17, 2014, Kuwait University, Safat, Kuwait. Providence, Rhode Island: American Mathematical Society, 2016.

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Ninul, Anatolij Sergeevič. Tensor Trigonometry. Moscow, Russia: Fizmatlit Publisher, 2021.

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Ninul, Anatolij Sergeevič. Tenzornaja trigonometrija: Teorija i prilozenija / Theory and Applications /. Moscow, Russia: Mir Publisher, 2004.

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Book chapters on the topic "Paradifferential calculus with parameters"

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Berti, Massimiliano, and Jean-Marc Delort. "Paradifferential Calculus." In Lecture Notes of the Unione Matematica Italiana, 31–91. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-99486-4_3.

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Morgan, Carroll. "Procedures, Parameters, and Abstraction: Separate Concerns." In On the Refinement Calculus, 47–58. London: Springer London, 1988. http://dx.doi.org/10.1007/978-1-4471-3273-8_3.

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Chakraverty, Snehashish, Rajarama Mohan Jena, and Subrat Kumar Jena. "Preliminaries to Fractional Calculus." In Time-Fractional Order Biological Systems with Uncertain Parameters, 1–12. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-031-02423-8_1.

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Nummelin, Visa, Alexander Bentkamp, Sophie Tourret, and Petar Vukmirović. "Superposition with First-class Booleans and Inprocessing Clausification." In Automated Deduction – CADE 28, 378–95. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-79876-5_22.

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AbstractWe present a complete superposition calculus for first-order logic with an interpreted Boolean type. Our motivation is to lay the foundation for refutationally complete calculi in more expressive logics with Booleans, such as higher-order logic, and to make superposition work efficiently on problems that would be obfuscated when using clausification as preprocessing. Working directly on formulas, our calculus avoids the costly axiomatic encoding of the theory of Booleans into first-order logic and offers various ways to interleave clausification with other derivation steps. We evaluate our calculus using the Zipperposition theorem prover, and observe that, with no tuning of parameters, our approach is on a par with the state-of-the-art approach.
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Cioffi, Claudio. "Nabladot Analysis of Hybrid Theories in International Relations." In Studi e saggi, 31–53. Florence: Firenze University Press, 2022. http://dx.doi.org/10.36253/978-88-5518-595-0.04.

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Scientific research in International Relations has produced a growing corpus of empirically grounded formal theoretical models of phenomena ranging from deterrence to systemic polarity, from conditions of peace to the onset of war. Many of these important theories contain a mix of continuous and discrete dimensions, causal variables, and parameters. Analysis and understanding of this fundamental and intriguing class of theories containing functions with a mix of continuous and discrete variables has puzzled generations of social scientists and applied mathematicians. This challenging and longstanding puzzle now has a solution. Here we demonstrate how the recently created calculus with nabladot operators is beginning to uncover previously unknown properties of hybrid international phenomena. Results include new concepts and precise principles on causal relationships, previously unknown political features, and fundamental properties of probabilistic causality, demonstrated through nabladot analysis of international events, crisis dynamics, and warfare.
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La Camera, Giancarlo. "The Mean Field Approach for Populations of Spiking Neurons." In Advances in Experimental Medicine and Biology, 125–57. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-89439-9_6.

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AbstractMean field theory is a device to analyze the collective behavior of a dynamical system comprising many interacting particles. The theory allows to reduce the behavior of the system to the properties of a handful of parameters. In neural circuits, these parameters are typically the firing rates of distinct, homogeneous subgroups of neurons. Knowledge of the firing rates under conditions of interest can reveal essential information on both the dynamics of neural circuits and the way they can subserve brain function. The goal of this chapter is to provide an elementary introduction to the mean field approach for populations of spiking neurons. We introduce the general idea in networks of binary neurons, starting from the most basic results and then generalizing to more relevant situations. This allows to derive the mean field equations in a simplified setting. We then derive the mean field equations for populations of integrate-and-fire neurons. An effort is made to derive the main equations of the theory using only elementary methods from calculus and probability theory. The chapter ends with a discussion of the assumptions of the theory and some of the consequences of violating those assumptions. This discussion includes an introduction to balanced and metastable networks and a brief catalogue of successful applications of the mean field approach to the study of neural circuits.
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La Camera, Giancarlo. "The Mean Field Approach for Populations of Spiking Neurons." In Advances in Experimental Medicine and Biology, 125–57. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-89439-9_6.

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AbstractMean field theory is a device to analyze the collective behavior of a dynamical system comprising many interacting particles. The theory allows to reduce the behavior of the system to the properties of a handful of parameters. In neural circuits, these parameters are typically the firing rates of distinct, homogeneous subgroups of neurons. Knowledge of the firing rates under conditions of interest can reveal essential information on both the dynamics of neural circuits and the way they can subserve brain function. The goal of this chapter is to provide an elementary introduction to the mean field approach for populations of spiking neurons. We introduce the general idea in networks of binary neurons, starting from the most basic results and then generalizing to more relevant situations. This allows to derive the mean field equations in a simplified setting. We then derive the mean field equations for populations of integrate-and-fire neurons. An effort is made to derive the main equations of the theory using only elementary methods from calculus and probability theory. The chapter ends with a discussion of the assumptions of the theory and some of the consequences of violating those assumptions. This discussion includes an introduction to balanced and metastable networks and a brief catalogue of successful applications of the mean field approach to the study of neural circuits.
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Dias Rasteiro, Deolinda M. L., and Nelson Chibeles-Martins. "Random variables as arc parameters when solving shortest path problems." In Calculus for Engineering Students, 197–219. Elsevier, 2020. http://dx.doi.org/10.1016/b978-0-12-817210-0.00017-5.

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Khalil, Hammad, Tehseen Zahra, Zaffer Elahi, and Azeem Shahzad. "Effect of Titanium Oxide Nanofluid over Cattaneo-Christov Model." In Functional Calculus - Recent Advances and Development [Working Title]. IntechOpen, 2022. http://dx.doi.org/10.5772/intechopen.106900.

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The proposed chapter deals with the study of heat transfer development of titanium oxide nanofluid of platelet shape nanoparticles over a vertical stretching cylinder. The set of nonlinear equations is obtained using suitable transformation on the governing equations that are then solved with numerical scheme BVP4C. The obtained results are interpreted graphically and numerically. The effects of Prandtl, Eckert, and unsteadiness parameters on temperature distribution are depicted. Moreover the skin friction and Nusselt number are also computed.
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Baishya, Chandrali, Sindhu J. Achar, and P. Veeresha. "Mathematical Analysis of a Rumor Spreading Model within the Frame of Fractional Derivative." In Fractional Calculus: New Applications in Understanding Nonlinear Phenomena, 186–209. BENTHAM SCIENCE PUBLISHERS, 2022. http://dx.doi.org/10.2174/9789815051933122030011.

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Rumor spreading is a trivial social practice, which has a long history of affecting society both in a positive and negative way, and modelling of transmission of rumors has been an attractive area for social and, of late, for physical scientists. In this chapter, we have modified the rumor-spreading model by incorporating fractional derivatives in the Caputo sense. To analyze the spread of rumors in social as well as virtual networks, we have considered four populations, namely, ignorant, spreader, recaller, and stifler. The existence and uniqueness, and boundedness of the solutions of the present model have been exhibited theoretically. Numerically, we have experimented with the effect of fractional derivatives and the density of one population on the other population by demonstrating the impact of rumor spread with the change of various parameters.
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Conference papers on the topic "Paradifferential calculus with parameters"

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Awai, Ikuo, Tetsuya Ishida, and Yangjun Zhang. "Efficient time domain calculus of microwave resonator parameters." In 2006 Asia-Pacific Microwave Conference. IEEE, 2006. http://dx.doi.org/10.1109/apmc.2006.4429529.

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Grosz, Steven A., Rebeca Pereira, Matthew W. Urban, Tom Humphrey, and Robert J. McGough. "Measured Fractional Calculus Parameters for Shear Waves in Swine Liver." In 2018 IEEE International Ultrasonics Symposium (IUS). IEEE, 2018. http://dx.doi.org/10.1109/ultsym.2018.8580193.

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Miron, Nicolae, and Dan G. Sporea. "Calculus of the corrections for the atmospheric parameters in laser interferometry." In ROMOPTP '94: 4th Conference on Optics, edited by Valentin I. Vlad. SPIE, 1995. http://dx.doi.org/10.1117/12.203475.

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Promyslov, Vitaly, and Kirill Semenkov. "The Estimation of Control System Parameters in “Network Calculus” from Experimental Data." In 2021 International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM). IEEE, 2021. http://dx.doi.org/10.1109/icieam51226.2021.9446290.

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Barbosa, Ramiro S., J. A. Tenreiro Machado, and Isabel M. Ferreira. "A Fractional Calculus Perspective of PID Tuning." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48375.

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This paper gives an interpretation of the classical PID controller tuning based on the fractional calculus theory. The PID parameters are calculated according with the specifications of an elementary system whose open-loop transfer function is a fractional order integrator (FOI). The performances of the two systems are compared and illustrated through the frequency and time responses.
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Balyuba, Ivan, and Evgeniy Konopatskiy. "Point calculus. Historical background and basic definitions." In International Conference "Computing for Physics and Technology - CPT2020". ANO «Scientific and Research Center for Information in Physics and Technique», 2020. http://dx.doi.org/10.30987/conferencearticle_5fd755c0adb1d9.27038265.

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The paper describes the history of the origin and formation the mathematical apparatus «Point calculus», as one of the scientific directions of the Melitopol school of applied geometry. A brief description of point calculus as a mathematical device that operates within an arithmetic, coordinate affine space, equipped with a topological structure. The basic definitions of point calculus are presented, including point parameters and point equations, space simplex and global coordinate system, independent and current points.
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Sun, Caiyun, Genyin Cheng, and Ming Gao. "Application of calculus equation in solving thermal decomposition kinetics parameters of flame retardant flexible polyurethane foam." In 2016 6th International Conference on Machinery, Materials, Environment, Biotechnology and Computer. Paris, France: Atlantis Press, 2016. http://dx.doi.org/10.2991/mmebc-16.2016.385.

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Wood, K. L., E. K. Antonsson, and J. L. Beck. "Comparing Fuzzy and Probability Calculus for Representing Imprecision in Preliminary Engineering Design." In ASME 1989 Design Technical Conferences. American Society of Mechanical Engineers, 1989. http://dx.doi.org/10.1115/detc1989-0012.

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Abstract A technique to perform design calculations on imprecise representations of parameters using the calculus of fuzzy sets has been previously developed [17]. An analogous approach to representing and manipulating uncertainty in choosing among alternatives (imprecision) using probability calculus is presented and compared with the fuzzy calculus technique. We find that the fuzzy calculus is well suited to representing and manipulating the imprecision aspect of uncertainty, and probability is best used to represent stochastic uncertainty.
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9

Bonneau, Olivier, Victor Lucas, and Jean Frene. "Influence of Geometric Parameters on Annular Fluid Seal Characteristics." 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/detc1995-0511.

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Abstract The numerical prediction of the dynamical behavior of turbopumps is very important. The space technology and the field of energy products are in constant development and it is necessary to quantify the influence of each component. The dynamical characteristics of annular seals must be calculated with accuracy. The aim of this work is to quantify the influence of geometric parameters on the dynamical behavior of the shaft. Three parameters will be studied: the duct loss parameter (at the seal entrance), a conical seal, and a misaligned seal. The two last geometrical defects have a direct influence on the film thickness. It is important to insist on the influence of the entrance duct loss which governs, in large part, the stiffness calculus (and then the stability). The most difficult problem is to evaluate this duct loss which depends on the seal geometry, Reynolds number and fluid characteristics... This study shows the important rôle played by geometrical parameter of a seal. The conicity and the misalignment modify the dynamical behavior of the shaft. These effects are essentially due to the axial flow which generates a pressure field due to axial film geometry. It should be noted that in the case of predominant circumferential flow these conclusions are totally different.
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10

Radulescu, A. V. "Theoretical Calculus Model for the Finite Length Rayleigh Step Bearings Lubricated with Greases." In BALTTRIB 2015. Aleksandras Stulginskis University, 2015. http://dx.doi.org/10.15544/balttrib.2015.18.

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The present paper proposes a calculus methodology for the finite length Rayleigh step bearings (3D case), lubricated with greases. In the case of a Rayleigh step bearing, the main problem involved is the presence of the stagnant core of grease into the region of the step. The shape of the stagnant core is obtained by finite element method, applied for solving the Navier-Stokes equations. Once established the dimensions of the stagnant core, the characteristic parameters of the bearing (pressure distribution, load, flow capacity and apparent friction coefficient) will be numerically determined, using the finite differences method.
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Reports on the topic "Paradifferential calculus with parameters"

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Zarrieß, Benjamin, and Jens Claßen. Decidable Verification of Golog Programs over Non-Local Effect Actions. Technische Universität Dresden, 2015. http://dx.doi.org/10.25368/2022.224.

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The Golog action programming language is a powerful means to express high-level behaviours in terms of programs over actions defined in a Situation Calculus theory. In particular for physical systems, verifying that the program satisfies certain desired temporal properties is often crucial, but undecidable in general, the latter being due to the language’s high expressiveness in terms of first-order quantification and program constructs. So far, approaches to achieve decidability involved restrictions where action effects either had to be contextfree (i.e. not depend on the current state), local (i.e. only affect objects mentioned in the action’s parameters), or at least bounded (i.e. only affect a finite number of objects). In this paper, we present a new, more general class of action theories (called acyclic) that allows for context-sensitive, non-local, unbounded effects, i.e. actions that may affect an unbounded number of possibly unnamed objects in a state-dependent fashion. We contribute to the further exploration of the boundary between decidability and undecidability for Golog, showing that for acyclic theories in the two-variable fragment of first-order logic, verification of CTL properties of programs over ground actions is decidable
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