Modelos não lineares resultantes da soma de regressões lineares ponderadas por funções distribuição acumulada

Os controladores eletrônicos de pulverização visam minimizar a variação das taxas de insumos aplicadas no campo. Eles fazem parte de um sistema de controle, e permitem a compensação da variação de velocidade de deslocamento do pulverizador durante a operação. Há vários tipos de controladores eletrônicos de pulverização disponíveis no mercado e uma das formas de selecionar qual o mais eficiente nas mesmas condições, ou seja, em um mesmo sistema de controle, é quantificar o tempo de resposta do sistema para cada controlador específico. O objetivo desse trabalho foi estimar os tempos de resposta para mudanças de velocidade de um sistema eletrônico de pulverização via modelos de regressão não lineares, estes, resultantes da soma de regressões lineares ponderadas por funções distribuição acumulada. Os dados foram obtidos no Laboratório de Tecnologia de Aplicação, localizado no Departamento de Engenharia de Biossistemas da Escola Superior de Agricultura \"Luiz de Queiroz\", Universidade de São Paulo, no município de Piracicaba, São Paulo, Brasil. Os modelos utilizados foram o logístico e de Gompertz, que resultam de uma soma ponderada de duas regressões lineares constantes com peso dado pela função distribuição acumulada logística e Gumbell, respectivamente. Reparametrizações foram propostas para inclusão do tempo de resposta do sistema de controle nos modelos, com o objetivo de melhorar a interpretação e inferência estatística dos mesmos. Foi proposto também um modelo de regressão não linear difásico que resulta da soma ponderada de regressões lineares constantes com peso dado pela função distribuição acumulada Cauchy seno hiperbólico exponencial. Um estudo de simulação foi feito, utilizando a metodologia de Monte Carlo, para avaliar as estimativas de máxima verossimilhança dos parâmetros do modelo.

Excitation spectra of the spin-1/2 triangular-lattice Heisenberg antiferromagnet

We use series expansion methods to calculate the dispersion relation of the one-magnon excitations for the spin-(1)/(2) triangular-lattice nearest-neighbor Heisenberg antiferromagnet above a three-sublattice ordered ground state. Several striking features are observed compared to the classical (large-S) spin-wave spectra. Whereas, at low energies the dispersion is only weakly renormalized by quantum fluctuations, significant anomalies are observed at high energies. In particular, we find rotonlike minima at special wave vectors and strong downward renormalization in large parts of the Brillouin zone, leading to very flat or dispersionless modes. We present detailed comparison of our calculated excitation energies in the Brillouin zone with the spin-wave dispersion to order 1/S calculated recently by Starykh, Chubukov, and Abanov [Phys. Rev. B74, 180403(R) (2006)]. We find many common features but also some quantitative and qualitative differences. We show that at temperatures as low as 0.1J the thermally excited rotons make a significant contribution to the entropy. Consequently, unlike for the square lattice model, a nonlinear sigma model description of the finite-temperature properties is only applicable at temperatures < 0.1J. Finally, we review recent NMR measurements on the organic compound kappa-(BEDT-TTF)(2)Cu-2(CN)(3). We argue that these are inconsistent with long-range order and a description of the low-energy excitations in terms of interacting magnons, and that therefore a Heisenberg model with only nearest-neighbor exchange does not offer an adequate description of this material.

Adiabatic soliton laser

The key to generating stable optical pulses is mastery of nonlinear light dynamics in laser resonators. Modern techniques to control the buildup of laser pulses are based on nonlinear science and include classical solitons, dissipative solitons, parabolic pulses (similaritons) and various modifications and blending of these methods. Fiber lasers offer remarkable opportunities to apply one-dimensional nonlinear science models for the design and optimization of very practical laser systems. Here, we propose a new concept of a laser based on the adiabatic amplification of a soliton pulse in the cavity - the adiabatic soliton laser. The adiabatic change of the soliton parameters during evolution in the resonator relaxes the restriction on the pulse energy inherent in traditional soliton lasers. Theoretical analysis is confirmed by extensive numerical modeling.

Does money matter in inflation forecasting?

This paper provides the most fully comprehensive evidence to date on whether or not monetary aggregates are valuable for forecasting US inflation in the early to mid 2000s. We explore a wide range of different definitions of money, including different methods of aggregation and different collections of included monetary assets. In our forecasting experiment we use two nonlinear techniques, namely, recurrent neural networks and kernel recursive least squares regressiontechniques that are new to macroeconomics. Recurrent neural networks operate with potentially unbounded input memory, while the kernel regression technique is a finite memory predictor. The two methodologies compete to find the best fitting US inflation forecasting models and are then compared to forecasts from a nave random walk model. The best models were nonlinear autoregressive models based on kernel methods. Our findings do not provide much support for the usefulness of monetary aggregates in forecasting inflation. Beyond its economic findings, our study is in the tradition of physicists' long-standing interest in the interconnections among statistical mechanics, neural networks, and related nonparametric statistical methods, and suggests potential avenues of extension for such studies. © 2010 Elsevier B.V. All rights reserved.

Evaluation of One-Dimensional Seismic Site Response Analyses at Small to Large Strain Levels

Thesis (Master's)--University of Washington, 2016-08

Effects of Wingwall Configurations on the Behavior of Integral Abutment Bridges

This research includes parametric studies performed with the use of three-dimensional nonlinear finite element models in order to investigate the effects of cantilever wingwall configurations on the behavior of integral abutment bridges located on straight alignment and zero skew. The parametric studies include all three types of cantilever wingwalls; inline, flared, and U-shaped wingwalls. Bridges analyzed vary in length from 100 to 1200 feet. Soil-structure and soil-pile interaction are included in the analysis. Loadings include dead load in combination with temperature loads in both rising and falling temperatures. Plasticity in the integral abutment piles is investigated by means of nonlinear plasticity models. Cracking in the abutments and stresses in the reinforcing steel are investigated by means of nonlinear concrete models. The effects of wingwall configurations are assessed in terms of stresses in the integral abutment piles, cracking in the abutment walls, stresses in the reinforcing steel of abutment walls, and axial forces induced in the steel girders. The models developed are analyzed for three types of soil behind the abutments and wingwalls; dense sand, medium dense sand, and loose sand. In addition, the models consider both the case of presence and absence of predrilled holes at the top nine feet of piles. The soil around the piles below the predrilled holes consists of very stiff clay. The results indicate that for the stresses in the piles, the critical load is temperature contraction and the most critical parameter is the use of predrilled holes. However, for both the stresses in the reinforcing steel and the axial forces induced in the girders, the critical load is temperature expansion and the critical parameter is the bridge length. In addition, the results indicate that the use of cantilever wingwalls in integral abutment bridges results in an increase in the magnitude of axial forces in the steel girders during temperature expansion and generation of pile plasticity at shorter bridge lengths compared to bridges built without cantilever wingwalls.

An analytical method to solve a general class of nonlinear reactive transport models

Three recent papers published in Chemical Engineering Journal studied the solution of a model of diffusion and nonlinear reaction using three different methods. Two of these studies obtained series solutions using specialized mathematical methods, known as the Adomian decomposition method and the homotopy analysis method. Subsequently it was shown that the solution of the same particular model could be written in terms of a transcendental function called Gauss’ hypergeometric function. These three previous approaches focused on one particular reactive transport model. This particular model ignored advective transport and considered one specific reaction term only. Here we generalize these previous approaches and develop an exact analytical solution for a general class of steady state reactive transport models that incorporate (i) combined advective and diffusive transport, and (ii) any sufficiently differentiable reaction term R(C). The new solution is a convergent Maclaurin series. The Maclaurin series solution can be derived without any specialized mathematical methods nor does it necessarily involve the computation of any transcendental function. Applying the Maclaurin series solution to certain case studies shows that the previously published solutions are particular cases of the more general solution outlined here. We also demonstrate the accuracy of the Maclaurin series solution by comparing with numerical solutions for particular cases.

A general method to determine sampling windows for nonlinear mixed effects models with an application to population pharmacokinetic studies

Optimal design methods have been proposed to determine the best sampling times when sparse blood sampling is required in clinical pharmacokinetic studies. However, the optimal blood sampling time points may not be feasible in clinical practice. Sampling windows, a time interval for blood sample collection, have been proposed to provide flexibility in blood sampling times while preserving efficient parameter estimation. Because of the complexity of the population pharmacokinetic models, which are generally nonlinear mixed effects models, there is no analytical solution available to determine sampling windows. We propose a method for determination of sampling windows based on MCMC sampling techniques. The proposed method attains a stationary distribution rapidly and provides time-sensitive windows around the optimal design points. The proposed method is applicable to determine sampling windows for any nonlinear mixed effects model although our work focuses on an application to population pharmacokinetic models.

Towards Bayesian experimental design for nonlinear models that require a large number of sampling times

The use of Bayesian methodologies for solving optimal experimental design problems has increased. Many of these methods have been found to be computationally intensive for design problems that require a large number of design points. A simulation-based approach that can be used to solve optimal design problems in which one is interested in finding a large number of (near) optimal design points for a small number of design variables is presented. The approach involves the use of lower dimensional parameterisations that consist of a few design variables, which generate multiple design points. Using this approach, one simply has to search over a few design variables, rather than searching over a large number of optimal design points, thus providing substantial computational savings. The methodologies are demonstrated on four applications, including the selection of sampling times for pharmacokinetic and heat transfer studies, and involve nonlinear models. Several Bayesian design criteria are also compared and contrasted, as well as several different lower dimensional parameterisation schemes for generating the many design points.

Exploring new and emerging models for nonlinear performative works

This dissertation seeks to define and classify potential forms of Nonlinear structure and explore the possibilities they afford for the creation of new musical works. It provides the first comprehensive framework for the discussion of Nonlinear structure in musical works and provides a detailed overview of the rise of nonlinearity in music during the 20th century. Nonlinear events are shown to emerge through significant parametrical discontinuity at the boundaries between regions of relatively strong internal cohesion. The dissertation situates Nonlinear structures in relation to linear structures and unstructured sonic phenomena and provides a means of evaluating Nonlinearity in a musical structure through the consideration of the degree to which the structure is integrated, contingent, compressible and determinate as a whole. It is proposed that Nonlinearity can be classified as a three dimensional space described by three continuums: the temporal continuum, encompassing sequential and multilinear forms of organization, the narrative continuum encompassing processual, game structure and developmental narrative forms and the referential continuum encompassing stylistic allusion, adaptation and quotation. The use of spectrograms of recorded musical works is proposed as a means of evaluating Nonlinearity in a musical work through the visual representation of parametrical divergence in pitch, duration, timbre and dynamic over time. Spectral and structural analysis of repertoire works is undertaken as part of an exploration of musical nonlinearity and the compositional and performative features that characterize it. The contribution of cultural, ideological, scientific and technological shifts to the emergence of Nonlinearity in music is discussed and a range of compositional factors that contributed to the emergence of musical Nonlinearity is examined. The evolution of notational innovations from the mobile score to the screen score is plotted and a novel framework for the discussion of these forms of musical transmission is proposed. A computer coordinated performative model is discussed, in which a computer synchronises screening of notational information, provides temporal coordination of the performers through click-tracks or similar methods and synchronises the audio processing and synthesized elements of the work. It is proposed that such a model constitutes a highly effective means of realizing complex Nonlinear structures. A creative folio comprising 29 original works that explore nonlinearity is presented, discussed and categorised utilising the proposed classifications. Spectrograms of these works are employed where appropriate to illustrate the instantiation of parametrically divergent substructures and examples of structural openness through multiple versioning.

Model-predictive control and closed-loop stability considerations for nonlinear plants described by local ARX-type models

In this paper, a model-predictive control (MPC) method is detailed for the control of nonlinear systems with stability considerations. It will be assumed that the plant is described by a local input/output ARX-type model, with the control potentially included in the premise variables, which enables the control of systems that are nonlinear in both the state and control input. Additionally, for the case of set point regulation, a suboptimal controller is derived which has the dual purpose of ensuring stability and enabling finite-iteration termination of the iterative procedure used to solve the nonlinear optimization problem that is used to determine the control signal.

Damping structure selection in nonlinear ship manoeuvring models

This paper presents the application of a statistical method for model structure selection of lift-drag and viscous damping components in ship manoeuvring models. The damping model is posed as a family of linear stochastic models, which is postulated based on previous work in the literature. Then a nested test of hypothesis problem is considered. The testing reduces to a recursive comparison of two competing models, for which optimal tests in the Neyman sense exist. The method yields a preferred model structure and its initial parameter estimates. Alternatively, the method can give a reduced set of likely models. Using simulated data we study how the selection method performs when there is both uncorrelated and correlated noise in the measurements. The first case is related to instrumentation noise, whereas the second case is related to spurious wave-induced motion often present during sea trials. We then consider the model structure selection of a modern high-speed trimaran ferry from full scale trial data.

Building macroscale models from microscale probabilistic models : a general probabilistic approach for nonlinear diffusion and multispecies phenomena

A discrete agent-based model on a periodic lattice of arbitrary dimension is considered. Agents move to nearest-neighbor sites by a motility mechanism accounting for general interactions, which may include volume exclusion. The partial differential equation describing the average occupancy of the agent population is derived systematically. A diffusion equation arises for all types of interactions and is nonlinear except for the simplest interactions. In addition, multiple species of interacting subpopulations give rise to an advection-diffusion equation for each subpopulation. This work extends and generalizes previous specific results, providing a construction method for determining the transport coefficients in terms of a single conditional transition probability, which depends on the occupancy of sites in an influence region. These coefficients characterize the diffusion of agents in a crowded environment in biological and physical processes.

Linear and weakly nonlinear stability analyses of cooperative car-following models

Stability analyses have been widely used to better understand the mechanism of traffic jam formation. In this paper, we consider the impact of cooperative systems (a.k.a. connected vehicles) on traffic dynamics and, more precisely, on flow stability. Cooperative systems are emerging technologies enabling communication between vehicles and/or with the infrastructure. In a distributed communication framework, equipped vehicles are able to send and receive information to/from other equipped vehicles. Here, the effects of cooperative traffic are modeled through a general bilateral multianticipative car-following law that improves cooperative drivers' perception of their surrounding traffic conditions within a given communication range. Linear stability analyses are performed for a broad class of car-following models. They point out different stability conditions in both multianticipative and nonmultianticipative situations. To better understand what happens in unstable conditions, information on the shock wave structure is studied in the weakly nonlinear regime by the mean of the reductive perturbation method. The shock wave equation is obtained for generic car-following models by deriving the Korteweg de Vries equations. We then derive traffic-state-dependent conditions for the sign of the solitary wave (soliton) amplitude. This analytical result is verified through simulations. Simulation results confirm the validity of the speed estimate. The variation of the soliton amplitude as a function of the communication range is provided. The performed linear and weakly nonlinear analyses help justify the potential benefits of vehicle-integrated communication systems and provide new insights supporting the future implementation of cooperative systems.