Randomness-efficient curve sampling

Curve samplers are sampling algorithms that proceed by viewing the domain as a vector space over a finite field, and randomly picking a low-degree curve in it as the sample. Curve samplers exhibit a nice property besides the sampling property: the restriction of low-degree polynomials over the domain to the sampled curve is still low-degree. This property is often used in combination with the sampling property and has found many applications, including PCP constructions, local decoding of codes, and algebraic PRG constructions.

The randomness complexity of curve samplers is a crucial parameter for its applications. It is known that (non-explicit) curve samplers using O(log N + log(1/δ)) random bits exist, where N is the domain size and δ is the confidence error. The question of explicitly constructing randomness-efficient curve samplers was first raised in [TU06] where they obtained curve samplers with near-optimal randomness complexity.

In this thesis, we present an explicit construction of low-degree curve samplers with optimal randomness complexity (up to a constant factor) that sample curves of degree (m log_q(1/δ))^O(1) in F_q^m. Our construction is a delicate combination of several components, including extractor machinery, limited independence, iterated sampling, and list-recoverable codes.

Phase-step calibration technique based on a two-run-times-two-frame phase-shift method

A novel phase-step calibration technique is presented on the basis of a two-run-times-two-frame phase-shift method. First the symmetry factor M is defined to describe the distribution property of the distorted phase due to phase-shifter miscalibration; then the phase-step calibration technique, in which two sets of two interferograms with a straight fringe pattern are recorded and the phase step is obtained by calculating M of the wrapped phase map, is developed. With this technique, a good mirror is required, but no uniform illumination is needed and no complex mathematical operation is involved. This technique can be carried out in situ and is applicable to any phase shifter, whether linear or nonlinear. (c) 2006 Optical Society of America.

Calibration of Grassholme Channels, 1982

Adjustment of experimental channels to give any specified pattern of water depth or velocity is complex and tedious because it involves a number of variables. Since some variables are not controllable and variables may interact, valve settings of the Grassholme channels were initially determined on an ad hoc basis to suit individual experiments. This method was used during 1982 but additional observations were made in order to gain more detailed understanding of the channel system and, as far as possible, to develop a guide to future short-cuts in attaining suitable channel settings for any given purpose. This report describes calibration of the Grassholme channels (using water of the Grassholme Reservoir) for the biological experiments of spring - summer 1982. The main variables that are discussed are valve turns and discharge and velocity and depth. It also seeks to establish relationships which will be of value in future managment of the channels for experimental purposes.

Acoplamento de técnicas espectrométricas com métodos quimiométricos de classificação e calibração multivariada em alimentos

Este trabalho de pesquisa descreve três estudos de utilização de métodos quimiométricos para a classificação e caracterização de óleos comestíveis vegetais e seus parâmetros de qualidade através das técnicas de espectrometria de absorção molecular no infravermelho médio com transformada de Fourier e de espectrometria no infravermelho próximo, e o monitoramento da qualidade e estabilidade oxidativa do iogurte usando espectrometria de fluorescência molecular. O primeiro e segundo estudos visam à classificação e caracterização de parâmetros de qualidade de óleos comestíveis vegetais utilizando espectrometria no infravermelho médio com transformada de Fourier (FT-MIR) e no infravermelho próximo (NIR). O algoritmo de Kennard-Stone foi usado para a seleção do conjunto de validação após análise de componentes principais (PCA). A discriminação entre os óleos de canola, girassol, milho e soja foi investigada usando SVM-DA, SIMCA e PLS-DA. A predição dos parâmetros de qualidade, índice de refração e densidade relativa dos óleos, foi investigada usando os métodos de calibração multivariada dos mínimos quadrados parciais (PLS), iPLS e SVM para os dados de FT-MIR e NIR. Vários tipos de pré-processamentos, primeira derivada, correção do sinal multiplicativo (MSC), dados centrados na média, correção do sinal ortogonal (OSC) e variação normal padrão (SNV) foram utilizados, usando a raiz quadrada do erro médio quadrático de validação cruzada (RMSECV) e de predição (RMSEP) como parâmetros de avaliação. A metodologia desenvolvida para determinação de índice de refração e densidade relativa e classificação dos óleos vegetais é rápida e direta. O terceiro estudo visa à avaliação da estabilidade oxidativa e qualidade do iogurte armazenado a 4C submetido à luz direta e mantido no escuro, usando a análise dos fatores paralelos (PARAFAC) na luminescência exibida por três fluoróforos presentes no iogurte, onde pelo menos um deles está fortemente relacionado com as condições de armazenamento. O sinal fluorescente foi identificado pelo espectro de emissão e excitação das substâncias fluorescentes puras, que foram sugeridas serem vitamina A, triptofano e riboflavina. Modelos de regressão baseados nos escores do PARAFAC para a riboflavina foram desenvolvidos usando os escores obtidos no primeiro dia como variável dependente e os escores obtidos durante o armazenamento como variável independente. Foi visível o decaimento da curva analítica com o decurso do tempo da experimentação. Portanto, o teor de riboflavina pode ser considerado um bom indicador para a estabilidade do iogurte. Assim, é possível concluir que a espectroscopia de fluorescência combinada com métodos quimiométricos é um método rápido para monitorar a estabilidade oxidativa e a qualidade do iogurte

Calibration method for a photoelastic modulator with a peak retardation of less than a half-wavelength

A new calibration method for a photoelastic modulator is proposed. The calibration includes a coarse calibration and a fine calibration. In the coarse calibration, the peak retardation of the photoelastic modulator is set near 1.841 rad. In the fine calibration, the value of the zeroth Bessel function is obtained. The zeroth Bessel function is approximated as a linear equation to directly calculate the peak retardation. In experiments, the usefulness of the calibration method is verified and the calibration error is less than 0.014 rad. The calibration is immune to the intensity fluctuation of the light source and independent of the circuit parameters. The method specially suits the calibration of a photoelastic modulator with a peak retardation of less than a half-wavelength. (c) 2007 Optical Society of America.

Estimation of the growth curve parameters in Macrobrachium rosenbergii

Growth is one of the most important characteristics of cultured species. The objective of this study was to determine the fitness of linear, log linear, polynomial, exponential and Logistic functions to the growth curves of Macrobrachium rosenbergii obtained by using weekly records of live weight, total length, head length, claw length, and last segment length from 20 to 192 days of age. The models were evaluated according to the coefficient of determination (R2), and error sum off square (ESS) and helps in formulating breeders in selective breeding programs. Twenty full-sib families consisting 400 PLs each were stocked in 20 different hapas and reared till 8 weeks after which a total of 1200 animals were transferred to earthen ponds and reared up to 192 days. The R2 values of the models ranged from 56 – 96 in case of overall body weight with logistic model being the highest. The R2 value for total length ranged from 62 to 90 with logistic model being the highest. In case of head length, the R2 value ranged between 55 and 95 with logistic model being the highest. The R2 value for claw length ranged from 44 to 94 with logistic model being the highest. For last segment length, R2 value ranged from 55 – 80 with polynomial model being the highest. However, the log linear model registered low ESS value followed by linear model for overall body weight while exponential model showed low ESS value followed by log linear model in case of head length. For total length the low ESS value was given by log linear model followed by logistic model and for claw length exponential model showed low ESS value followed by log linear model. In case of last segment length, linear model showed lowest ESS value followed by log linear model. Since, the model that shows highest R2 value with low ESS value is generally considered as the best fit model. Among the five models tested, logistic model, log linear model and linear models were found to be the best models for overall body weight, total length and head length respectively. For claw length and last segment length, log linear model was found to be the best model. These models can be used to predict growth rates in M. rosenbergii. However, further studies need to be conducted with more growth traits taken into consideration