Analysis of financial data series using fractional Fourier transform and multidimensional scaling

The goal of this study is the analysis of the dynamical properties of financial data series from worldwide stock market indexes during the period 2000–2009. We analyze, under a regional criterium, ten main indexes at a daily time horizon. The methods and algorithms that have been explored for the description of dynamical phenomena become an effective background in the analysis of economical data. We start by applying the classical concepts of signal analysis, fractional Fourier transform, and methods of fractional calculus. In a second phase we adopt the multidimensional scaling approach. Stock market indexes are examples of complex interacting systems for which a huge amount of data exists. Therefore, these indexes, viewed from a different perspectives, lead to new classification patterns.

Cálculo Integral y Series de Fourier.

En este libro, se desarrollan los conceptos fundamentales del cálculo integral y de las series de Fourier. Cada uno de estos apartados constituyen dos campos de las matemáticas aplicadas en que las conexiones con los problemas de física y de la ingeniería son más evidentes. Cada capítulo consta de un desarrollo teórico el cual va acompañado con ejercicios de aplicación de las teorías expuestas, asimismo al finalixar cada capítulo se recojen una serie de ejercicios resueltos así como de ejercicios propuestos. Se concluye el libro con un apéndice, en el cual se hace uso del paquete de cálculo simbólico 'Mathemática', para la resolución de algunos ejercicios, así como dar una visión gráfica de algunos de los ejercicios previstos.

Partial lateralization of the nasopalatine nerve at the incisive foramen for ridge augmentation in the anterior maxilla prior to placement of dental implants: a retrospective case series evaluating self-reported data and neurosensory testing

The objective of this study was to assess implant therapy after a staged guided bone regeneration procedure in the anterior maxilla by lateralization of the nasopalatine nerve and vessel bundle. Neurosensory function following augmentative procedures and implant placement, assessed using a standardized questionnaire and clinical examination, were the primary outcome variables measured. This retrospective study included patients with a bone defect in the anterior maxilla in need of horizontal and/or vertical ridge augmentation prior to dental implant placement. The surgical sites were allowed to heal for at least 6 months before placement of dental implants. All patients received fixed implant-supported restorations and entered into a tightly scheduled maintenance program. In addition to the maintenance program, patients were recalled for a clinical examination and to fill out a questionnaire to assess any changes in the neurosensory function of the nasopalatine nerve at least 6 months after function. Twenty patients were included in the study from February 2001 to December 2010. They received a total of 51 implants after augmentation of the alveolar crest and lateralization of the nasopalatine nerve. The follow-up examination for questionnaire and neurosensory assessment was scheduled after a mean period of 4.18 years of function. None of the patients examined reported any pain, they did not have less or an altered sensation, and they did not experience a "foreign body" feeling in the area of surgery. Overall, 6 patients out of 20 (30%) showed palatal sensibility alterations of the soft tissues in the region of the maxillary canines and incisors resulting in a risk for a neurosensory change of 0.45 mucosal teeth regions per patient after ridge augmentation with lateralization of the nasopalatine nerve. Regeneration of bone defects in the anterior maxilla by horizontal and/or vertical ridge augmentation and lateralization of the nasopalatine nerve prior to dental implant placement is a predictable surgical technique. Whether or not there were clinically measurable impairments of neurosensory function, the patients did not report them or were not bothered by them.

A new algorithm to accelerate harmonic analysis of time series

The Lomb periodogram has been traditionally a tool that allows us to elucidate if a frequency turns out to be important for explaining the behaviour of a given time series. Many linear and nonlinear reiterative harmonic processes that are used for studying the spectral content of a time series take into account this periodogram in order to avoid including spurious frequencies in their models due to the leakage problem of energy from one frequency to others. However, the estimation of the periodogram requires long computation time that makes the harmonic analysis slower when we deal with certain time series. Here we propose an algorithm that accelerates the extraction of the most remarkable frequencies from the periodogram, avoiding its whole estimation of the harmonic process at each iteration. This algorithm allows the user to perform a specific analysis of a given scalar time series. As a result, we obtain a functional model made of (1) a trend component, (2) a linear combination of Fourier terms, and (3) the so-called mixed secular terms by reducing the computation time of the estimation of the periodogram.

Mixed human saliva, its variations in composition and amylolytic power and the action of its freed enzyme, a series of observations and experiments from a chemical standpoint; submitted in partial fulfillment of the requirements for the degree of M.S. [in the] University of California.

Type-written manuscript.

Quantification of hydroxycinnamic acids and lignin in perennial forage and energy grasses by Fourier-transform infrared spectroscopy and partial least squares regression

Levels of lignin and hydroxycinnamic acid wall components in three genera of forage grasses (Lolium,Festuca and Dactylis) have been accurately predicted by Fourier-transform infrared spectroscopy using partial least squares models correlated to analytical measurements. Different models were derived that predicted the concentrations of acid detergent lignin, total hydroxycinnamic acids, total ferulate monomers plus dimers, p-coumarate and ferulate dimers in independent spectral test data from methanol extracted samples of perennial forage grass with accuracies of 92.8%, 86.5%, 86.1%, 59.7% and 84.7% respectively, and analysis of model projection scores showed that the models relied generally on spectral features that are known absorptions of these compounds. Acid detergent lignin was predicted in samples of two species of energy grass, (Phalaris arundinacea and Pancium virgatum) with an accuracy of 84.5%.

On generalized orlicz sequence spaces of Fourier coefficients for trigonometric gap series. I.

We investigate the operator associating with a function fєLp2π, 1Fourier coefficients of ƒ with respect to a trigonometric gap system, as well as an operator from a modular space X ρs(ϕ) to the generalized Orlicz sequence space lϕ.

Rapid quantification of methamphetamine: using Attenuated Total Reflectance Fourier Transform Infrared Spectroscopy (ATR-FTIR) and Chemometrics

In Australia and increasingly worldwide, methamphetamine is one of the most commonly seized drugs analysed by forensic chemists. The current well-established GC/MS methods used to identify and quantify methamphetamine are lengthy, expensive processes, but often rapid analysis is requested by undercover police leading to an interest in developing this new analytical technique. Ninety six illicit drug seizures containing methamphetamine (0.1% - 78.6%) were analysed using Fourier Transform Infrared Spectroscopy with an Attenuated Total Reflectance attachment and Chemometrics. Two Partial Least Squares models were developed, one using the principal Infrared Spectroscopy peaks of methamphetamine and the other a Hierarchical Partial Least Squares model. Both of these models were refined to choose the variables that were most closely associated with the methamphetamine % vector. Both of the models were excellent, with the principal peaks in the Partial Least Squares model having Root Mean Square Error of Prediction 3.8, R2 0.9779 and lower limit of quantification 7% methamphetamine. The Hierarchical Partial Least Squares model had lower limit of quantification 0.3% methamphetamine, Root Mean Square Error of Prediction 5.2 and R2 0.9637. Such models offer rapid and effective methods for screening illicit drug samples to determine the percentage of methamphetamine they contain.

Exact series solutions of reactive transport models with general initial conditions

Exact solutions of partial differential equation models describing the transport and decay of single and coupled multispecies problems can provide insight into the fate and transport of solutes in saturated aquifers. Most previous analytical solutions are based on integral transform techniques, meaning that the initial condition is restricted in the sense that the choice of initial condition has an important impact on whether or not the inverse transform can be calculated exactly. In this work we describe and implement a technique that produces exact solutions for single and multispecies reactive transport problems with more general, smooth initial conditions. We achieve this by using a different method to invert a Laplace transform which produces a power series solution. To demonstrate the utility of this technique, we apply it to two example problems with initial conditions that cannot be solved exactly using traditional transform techniques.

Partial intervertebral fusion secures successful outcomes after thoracoscopic anterior scoliosis correction: A low-dose computed tomography study

Study Design Retrospective review of prospectively collected data. Objectives To analyze intervertebral (IV) fusion after thoracoscopic anterior spinal fusion (TASF) and explore the relationship between fusion scores and key clinical variables. Summary of Background Information TASF provides comparable correction with some advantages over posterior approaches but reported mechanical complications, and their relationship to non-union and graft material is unclear. Similarly, the optimal combination of graft type and implant stiffness for effecting successful radiologic union remains undetermined. Methods A subset of patients from a large single-center series who had TASF for progressive scoliosis underwent low-dose computed tomographic scans 2 years after surgery. The IV fusion mass in the disc space was assessed using the 4-point Sucato scale, where 1 indicates <50% and 4 indicates 100% bony fusion of the disc space. The effects of rod diameter, rod material, graft type, fusion level, and mechanical complications on fusion scores were assessed. Results Forty-three patients with right thoracic major curves (mean age 14.9 years) participated in the study. Mean fusion scores for patient subgroups ranged from 1.0 (IV levels with rod fractures) to 2.2 (4.5-mm rod with allograft), with scores tending to decrease with increasing rod size and stiffness. Graft type (autograft vs. allograft) did not affect fusion scores. Fusion scores were highest in the middle levels of the rod construct (mean 2.52), dropping off by 20% to 30% toward the upper and lower extremities of the rod. IV levels where a rod fractured had lower overall mean fusion scores compared to levels without a fracture. Mean total Scoliosis Research Society (SRS) questionnaire scores were 98.9 from a possible total of 120, indicating a good level of patient satisfaction. Conclusions Results suggest that 100% radiologic fusion of the entire disc space is not necessary for successful clinical outcomes following thoracoscopic anterior selective thoracic fusion.

A novel method for the age estimation of Saddletail snapper (Lutjanus malabaricus) using Fourier Transform-near infrared (FT-NIR) spectroscopy

Near infrared (NIR) spectroscopy was investigated as a potential rapid method of estimating fish age from whole otoliths of Saddletail snapper (Lutjanus malabaricus). Whole otoliths from 209 Saddletail snapper were extracted and the NIR spectral characteristics were acquired over a spectral range of 800–2780 nm. Partial least-squares models (PLS) were developed from the diffuse reflectance spectra and reference-validated age estimates (based on traditional sectioned otolith increments) to predict age for independent otolith samples. Predictive models developed for a specific season and geographical location performed poorly against a different season and geographical location. However, overall PLS regression statistics for predicting a combined population incorporating both geographic location and season variables were: coefficient of determination (R2) = 0.94, root mean square error of prediction (RMSEP) = 1.54 for age estimation, indicating that Saddletail age could be predicted within 1.5 increment counts. This level of accuracy suggests the method warrants further development for Saddletail snapper and may have potential for other fish species. A rapid method of fish age estimation could have the potential to reduce greatly both costs of time and materials in the assessment and management of commercial fisheries.