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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
11

Asymptotics of higher-order Painlevé equations

Morrison, Tegan Ann January 2009 (has links)
Doctor of Philosophy (PhD) / We undertake an asymptotic study of a second Painlevé hierarchy based on the Jimbo-Miwa Lax pair in the limit as the independent variable approaches infinity. The hierarchy is defined by an infinite sequence of non-linear ordinary differential equations, indexed by order, with the classical second Painlevé equation as the first member. We investigate general and special asymptotic behaviours admitted by each equation in the hierarchy. We show that the general asymptotic behaviour is described by two related hyperelliptic functions, where the genus of the functions increases with each member of the hierarchy, and we prove that there exist special families of solutions which are represented by algebraic formal power series. For specific values of the constants which appear in the higher-order second Painlevé equations, exact solutions are also constructed. Particular attention is given to the fourth-order analogue of the classical second Painlevé equation. In this case, the general asymptotic behaviour is given to leading-order by two related genus-2 hyperelliptic functions. These functions are characterised by four complex parameters which depend on the independent variable through the perturbation terms of the leading-order equations, and we investigate how these parameters change with respect to this variable. We also show that the fourth-order equation admits two classes of algebraic formal power series and that there exist families of true solutions with these behaviours in specified sectors of the complex plane, as well as unique solutions in extended sectors. To complement our asymptotic study of higher-order Painlevé equations, we consider a new setting in which classical Painlevé equations arise. We study reaction-diffusion equations with quadratic and cubic source terms, with a spatio-temporal dependence included in those terms, and show that solutions of these equations are given by first and second Painlevé transcendents.
12

Symmetry Analysis of General Rank-3 Pfaffian Systems in Five Variables

Strazzullo, Francesco 01 May 2009 (has links)
In this dissertation we applied geometric methods to study underdetermined second order scalar ordinary differential equations (called general Monge equations), nonlinear involutive systems of two scalar partial differential equations in two independent variables and one unknown and non-Monge-Ampere Goursat parabolic scalar PDE in the plane. These particular kinds of differential equations are related to general rank-3 Pfaffian systems in five variables. Cartan studied these objects in his 1910 paper. In this work Cartan provided normal forms only for some general rank-3 Pfaffian systems with 14-, 7-, and 6-dimensional symmetry algebra. We applied our normal forms to [i] sharpen Cartan's integration method of nonlinear involutive systems, [ii] classify all general Monge equations with a freely acting transverse 3-dimensional symmetry algebra, of which many new examples are presented, and [iii] provide a broad classification of non-Monge-Ampere Darboux integrable hyperbolic PDE in the plane. We developed a computer software, called FiveVariables, that classifies general rank-3 Pfaffian systems. FiveVariables runs in the environment DifferentialGeometry of Maple, version 11 and later.
13

An Ordinary Differential Equation Based Model For Clustering And Vector Quantization

Cheng, Jie 01 January 2009 (has links) (PDF)
This research focuses on the development of a novel adaptive dynamical system approach to vector quantization or clustering based on only ordinary differential equations (ODEs) with potential for a real-time implementation. The ODE-based approach has an advantage in making it possible real-time implementation of the system with either electronic or photonic analog devices. This dynamical system consists of a set of energy functions which create valleys for representing clusters. Each valley represents a cluster of similar input patterns. The proposed system includes a dynamic parameter, called vigilance parameter. This parameter approximately reflects the radius of the generated valleys. Through several examples of different pattern clusters, it is shown that the model can successfully quantize/cluster these types of input patterns. Also, a hardware implementation by photonic and/or electronic analog devices is given In addition, we analyze and study stability of our dynamical system. By discovering the equilibrium points for certain input patterns and analyzing their stability, we have shown the quantizing behavior of the system with respect to its parameters. We also extend our model to include competition mechanism and vigilance dynamics. The competition mechanism causes only one label to be assigned to a group of patterns. The vigilance dynamics adjust vigilance parameter so that the cluster size or the quantizing resolution can be adaptive to the density and distribution of the input patterns. This reduces the burden of re-tuning the vigilance parameter for a given input pattern set and also better represents the input pattern space. The vigilance parameter approximately reflects the radius of the generated valley for each cluster. Making this parameter dynamic allows the bigger cluster to have a bigger radius and as a result a better cluster. Furthermore, an alternative dynamical system to our proposed system is also introduced. This system utilizes sigmoid and competitive functions. Although the results of this system are encouraging, the use of sigmoid function makes analyze and study stability of the system extremely difficult.
14

Graph-based Multi-ODE Neural Networks for Spatio-Temporal Traffic Forecasting

Liu, Zibo 20 December 2022 (has links)
There is a recent surge in the development of spatio-temporal forecasting models in many applications, and traffic forecasting is one of the most important ones. Long-range traffic forecasting, however, remains a challenging task due to the intricate and extensive spatio-temporal correlations observed in traffic networks. Current works primarily rely on road networks with graph structures and learn representations using graph neural networks (GNNs), but this approach suffers from over-smoothing problem in deep architectures. To tackle this problem, recent methods introduced the combination of GNNs with residual connections or neural ordinary differential equations (NODEs). The existing graph ODE models are still limited in feature extraction due to (1) having bias towards global temporal patterns and ignoring local patterns which are crucial in case of unexpected events; (2) missing dynamic semantic edges in the model architecture; and (3) using simple aggregation layers that disregard the high-dimensional feature correlations. In this thesis, we propose a novel architecture called Graph-based Multi-ODE Neural Networks (GRAM-ODE) which is designed with multiple connective ODE-GNN modules to learn better representations by capturing different views of complex local and global dynamic spatio-temporal dependencies. We also add some techniques to further improve the communication between different ODE-GNN modules towards the forecasting task. Extensive experiments conducted on four real-world datasets demonstrate the outperformance of GRAM-ODE compared with state-of-the-art baselines as well as the contribution of different GRAM-ODE components to the performance. / Master of Science / There is a recent surge in the development of spatio-temporal forecasting models in many applications, and traffic forecasting is one of the most important ones. In traffic forecasting, current works limited in correctly capturing the key correlation of spatial and temporal patterns. In this thesis, we propose a novel architecture called Graph-based Multi-ODE Neural Networks (GRAM-ODE) to tackle the problem by using the separate ODE modules to deal with spatial and temporal patterns and further improve the communication between different modules. Extensive experiments conducted on four real-world datasets demonstrate the outperformance of GRAM-ODE compared with state-of-the-art baselines.
15

Self-Celebratory Musical Acts: Cecilian Odes and Other Sung Texts as a Means of Acknowledging the Place of Music within the Arts

Degott, Pierre 18 December 2020 (has links)
No description available.
16

Ode to the Temple of Sound, Floating World-Ukiyo and Meditation on Zeami: An Analysis of Three Works by Alan Hovhaness

Park, Chung Hoon 02 May 2008 (has links)
This essay, through a thorough examination of primary and secondary sources, presents analyses of three orchestral works from Hovhaness' "fourth-period," a period of time spanning approximately ten years, from 1960 to 1970. This essay focuses on three works from this period: Meditation on Zeami, Floating World, and Ode to the Temple of Sound, written in 1963, 1964 and 1965, respectively. This essay gathers information from various primary and secondary sources in order to provide performers who are preparing works from this period with a single source of information, bringing clarity to theoretical and musicological problems. Analyses of this sort are made all the more necessary by the fact that there are currently no extant recordings of any of the works being studied here, and that two of the works, Meditation on Zeami and Floating World, have never been commercially recorded. Without an aural precedent and guide to follow, analyses of these musics will be a welcome resource for the conductor preparing a performance.
17

Na senda tradutória da ode: Horácio e Filinto Elísio / On the translate pathway of ode: Horatius and Filinto Elísio

Teixeira, Francisco Diniz [UNESP] 28 May 2018 (has links)
Submitted by Francisco Diniz Teixeira (chicodinizteixeira@yahoo.com.br) on 2018-06-26T20:39:02Z No. of bitstreams: 1 Francisco Diniz Teixeira versão final(corrigida_06_2018).pdf: 3163926 bytes, checksum: deebaf70618706b5c83dc90e0d90641e (MD5) / Approved for entry into archive by Priscila Carreira B Vicentini null (priscila@fclar.unesp.br) on 2018-06-28T12:16:03Z (GMT) No. of bitstreams: 1 teixeira_fd_dr_arafcl.pdf: 2904732 bytes, checksum: 0ff3727a7a24bdb9c659c43b22c90fe2 (MD5) / Made available in DSpace on 2018-06-28T12:16:03Z (GMT). No. of bitstreams: 1 teixeira_fd_dr_arafcl.pdf: 2904732 bytes, checksum: 0ff3727a7a24bdb9c659c43b22c90fe2 (MD5) Previous issue date: 2018-05-28 / O trabalho que ora se encerra, tencionou ao longo do curso de doutoramento efetuar uma investigação acerca da ode enquanto gênero literário, na sua matriz latina a partir do estudo da poesia horaciana e das projeções desta na poesia de Francisco Manoel do Nascimento, poeta neoclássico conhecido pelo pseudônimo de Filinto Elísio. Para tornar isso possível, foi necessário fazer o levantamento da fortuna crítica, a partir de estudos que permitissem a compreensão da ode enquanto gênero ligado ao arquigênero, vislumbrado sob o conceito “Lírico”. Entendendo-se que a transposição de uma forma antiga para as literaturas vernáculas só se torna possível através da tradução, optou-se por delimitar o corpus de trabalho para as onze odes de Horácio que Filinto Elísio traduziu e que, juntamente com as odes de sua autoria, compõem o maior corpus de odes produzidas no Século das Luzes. O estudo de tradução levado a cabo se ancorou no referencial teórico encontrado nos escritos de Henri Meschonnic, Haroldo de Campos e Antony Pym. Evidentemente, o estudo proposto não se limitou aos referenciais teóricos necessários para o desvelamento da prática tradutória do poeta luso, sem que antes se resgatasse o peso de suas ideias estéticas, do contexto histórico-artístico em que ele se inseriu e da recepção de suas ideias e obras na história da literatura portuguesa. Ao fim do trabalho, concluiu-se que a criação artística prolífica entre os poetas neoclássicos, particularmente na obra de Filinto Elísio, se deve ao estudo e tradução – etapa fundamental – das Odes horacianas, tomadas como matriz do gênero e sinônimo de bom gosto no contexto intelectual do século XVIII. / El trabajo que se concluye acá, pretendió, a lo largo del curso de doctorado, efectuar una investigación acerca de la oda como género literario, en su matriz latina a partir del estudio de la poesía horaciana y sus proyecciones en la poesía de Francisco Manoel do Nascimento, poeta neoclásico portugués conocido por el pseudónimo de Filinto Elísio. Para hacerla posible, fue necesario investigar el acervo crítico acerca del tema, a partir de estudios que permitiesen la comprensión de la oda como género vinculado al archigénero, vislumbrado bajo el concepto "Lírico". Comprendiendo que la transposición de una forma antigua a las literaturas vernáculas sólo se hace posible a través de la traducción, se optó por delimitar el corpus de trabajo para las once odas de Horacio que Filinto Elísio tradujo y que junto a las odas de su autoría componen el mayor corpus de odas producidas en el Siglo de las Luces. El estudio de traducción llevado a cabo se ancló en el referencial teórico encontrado en los escritos de Henri Meschonnic, Haroldo de Campos y Antony Pym. Evidentemente, el estudio propuesto no se limitó a los referenciales teóricos necesarios para el desvelamiento de la práctica traductora del poeta luso sin antes se rescatar el peso de sus ideas estéticas, del contexto histórico-artístico en que se inserta y de la recepción de sus ideas y obras en la historia de la literatura portuguesa. Al final del trabajo se concluye que la creación artística prolífica de los poetas neoclásicos, particularmente en la obra de Filinto Elísio, se debe al estudio y traducción – etapa fundamental – de las Odas horacianas, tomadas como matriz del género y sinónimo de buen gusto en el contexto intelectual del siglo XVIII.
18

The Human Body is Not Designed for Ambivalence: Odes

Walker, Tammy 12 1900 (has links)
The critical analysis section of this dissertation seeks to define the ode using examples in translation from Greek and Latin odes and examples in English written from the 1500s to the 2000s. Although most definitions of the ode contend that this subgenre of the lyric is an occasional poem of praise that includes a meditative or mythological element, the ode is far more complex. An ode is an occasional poem, but it works to privilege rather than strictly praise its subject, allowing for the speaker's ambivalence toward the subject. Meditation is a key element of the ode, since the poet uses the subject as a means for moving to the meditation or as a conduit through which the meditation occurs. The meditation in the poem is also a way for the poet or speaker to negotiate the relationship between the subject and herself; thus, the ode is concerned with power, since the poet must place herself or the speaker in relation to the subject. Power thus may be granted to either the speaker or the subject; the poet names and speaks of the subject, and often the poet names and speaks of himself in relation to the subject. Additionally, odes usually contain some exhortation, generally directed to the subject if not to those surrounding the reader or capable of "listening in" to the performance of the poem. This definition, it should be noted, is intended to be fluid. In order for a poem to be relevant to its age, it must either adhere to or usefully challenge the contemporary concerns. Thus, while many of the odes discussed will contain the elements of this definition, others will work against the definition. In the remainder of the introduction, I examine ancient models and twentieth- and twenty-first century examples of the ode as a means of exploring what an ode is and how it can undermine the elements of the definition and still work as a poem of this subgenre. In the second section of the dissertation are lyric poems, many of which fit in varying degrees the definition laid out in the critical analysis.
19

Adaptive Numerical Methods for Large Scale Simulations and Data Assimilation

Constantinescu, Emil Mihai 07 July 2008 (has links)
Numerical simulation is necessary to understand natural phenomena, make assessments and predictions in various research and engineering fields, develop new technologies, etc. New algorithms are needed to take advantage of the increasing computational resources and utilize the emerging hardware and software infrastructure with maximum efficiency. Adaptive numerical discretization methods can accommodate problems with various physical, scale, and dynamic features by adjusting the resolution, order, and the type of method used to solve them. In applications that simulate real systems, the numerical accuracy of the solution is typically just one of the challenges. Measurements can be included in the simulation to constrain the numerical solution through a process called data assimilation in order to anchor the simulation in reality. In this thesis we investigate adaptive discretization methods and data assimilation approaches for large-scale numerical simulations. We develop and investigate novel multirate and implicit-explicit methods that are appropriate for multiscale and multiphysics numerical discretizations. We construct and explore data assimilation approaches for, but not restricted to, atmospheric chemistry applications. A generic approach for describing the structure of the uncertainty in initial conditions that can be applied to the most popular data assimilation approaches is also presented. We show that adaptive numerical methods can effectively address the discretization of large-scale problems. Data assimilation complements the adaptive numerical methods by correcting the numerical solution with real measurements. Test problems and large-scale numerical experiments validate the theoretical findings. Synergistic approaches that use adaptive numerical methods within a data assimilation framework need to be investigated in the future. / Ph. D.
20

MATLODE: A MATLAB ODE Solver and Sensitivity Analysis Toolbox

D'Augustine, Anthony Frank 04 May 2018 (has links)
Sensitivity analysis quantifies the effect that of perturbations of the model inputs have on the model's outputs. Some of the key insights gained using sensitivity analysis are to understand the robustness of the model with respect to perturbations, and to select the most important parameters for the model. MATLODE is a tool for sensitivity analysis of models described by ordinary differential equations (ODEs). MATLODE implements two distinct approaches for sensitivity analysis: direct (via the tangent linear model) and adjoint. Within each approach, four families of numerical methods are implemented, namely explicit Runge-Kutta, implicit Runge-Kutta, Rosenbrock, and single diagonally implicit Runge-Kutta. Each approach and family has its own strengths and weaknesses when applied to real world problems. MATLODE has a multitude of options that allows users to find the best approach for a wide range of initial value problems. In spite of the great importance of sensitivity analysis for models governed by differential equations, until this work there was no MATLAB ordinary differential equation sensitivity analysis toolbox publicly available. The two most popular sensitivity analysis packages, CVODES [8] and FATODE [10], are geared toward the high performance modeling space; however, no native MATLAB toolbox was available. MATLODE fills this need and offers sensitivity analysis capabilities in MATLAB, one of the most popular programming languages within scientific communities such as chemistry, biology, ecology, and oceanogra- phy. We expect that MATLODE will prove to be a useful tool for these communities to help facilitate their research and fill the gap between theory and practice. / Master of Science

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