Multidimensional Scaling Analysis of Stock Market Indexes

This paper applies multidimensional scaling techniques and Fourier transform for visualizing possible time-varying correlations between 25 stock market values. The method is useful for observing clusters of stock markets with similar behavior.

Dynamical Analysis of Non-Repetitive Trajectories in Robotic Manipulation

A new method for the study and optimization of manu«ipulator trajectories is developed. The novel feature resides on the modeling formulation. Standard system desciptions are based on a set of differential equations which, in general, require laborious computations and may be difficult to analyze. Moreover, the derived algorithms are suited to "deterministic" tasks, such as those appearing in a repetitivework, and are not well adapted to a "random" operation that occurs in intelligent systems interacting with a non-structured and changing environment. These facts motivate the development of alternative models based on distinct concepts. The proposed embedding of statistics and Fourier trasnform gives a new perspective towards the calculation and optimization of the robot trajectories in manipulating tasks.

Analysis of Natural and Artificial Phenomena Using Signal Processing and Fractional Calculus

In this paper we study several natural and man-made complex phenomena in the perspective of dynamical systems. For each class of phenomena, the system outputs are time-series records obtained in identical conditions. The time-series are viewed as manifestations of the system behavior and are processed for analyzing the system dynamics. First, we use the Fourier transform to process the data and we approximate the amplitude spectra by means of power law functions. We interpret the power law parameters as a phenomenological signature of the system dynamics. Second, we adopt the techniques of non-hierarchical clustering and multidimensional scaling to visualize hidden relationships between the complex phenomena. Third, we propose a vector field based analogy to interpret the patterns unveiled by the PL parameters.

On the analysis of data emerging in non-linear and complex systemscomparison of two X-Ray prony spectra

New arguments proving that successive (repeated) measurements have a memory and actually remember each other are presented. The recognition of this peculiarity can change essentially the existing paradigm associated with conventional observation in behavior of different complex systems and lead towards the application of an intermediate model (IM). This IM can provide a very accurate fit of the measured data in terms of the Prony's decomposition. This decomposition, in turn, contains a small set of the fitting parameters relatively to the number of initial data points and allows comparing the measured data in cases where the “best fit” model based on some specific physical principles is absent. As an example, we consider two X-ray diffractometers (defined in paper as A- (“cheap”) and B- (“expensive”) that are used after their proper calibration for the measuring of the same substance (corundum a-Al2O3). The amplitude-frequency response (AFR) obtained in the frame of the Prony's decomposition can be used for comparison of the spectra recorded from (A) and (B) - X-ray diffractometers (XRDs) for calibration and other practical purposes. We prove also that the Fourier decomposition can be adapted to “ideal” experiment without memory while the Prony's decomposition corresponds to real measurement and can be fitted in the frame of the IM in this case. New statistical parameters describing the properties of experimental equipment (irrespective to their internal “filling”) are found. The suggested approach is rather general and can be used for calibration and comparison of different complex dynamical systems in practical purposes.

Analysis, testing and development of safe cleaning methods of rusted stone material

Three different treatments were applied on several specimens of dolomitic and calcitic marble, properly stained with rust to mimic real situations (the stone specimens were exposed to the natural environment for about six months in contact with rusted iron). Thirty six marble specimens, eighteen calcitic and eighteen dolomitic, were characterized before and after treatment and monitored throughout the cleaning tests. The specimens were characterized by SEM-EDS (Scanning Electron Microscopy coupled with Energy Dispersion System), XRD (XRay Diffraction), XRF (X-Ray Fluorescence), FTIR (Fourier Transform Infrared Spectroscopy) and color measurements. It was also made a microscopic and macroscopic analysis of the stone surface along with the tests of short and long term capillary absorption. A series of test trials were conducted in order to understand which concentrations and contact times best suits to this purpose, to confirm what had been written to date in the literature. We sought to develop new methods of treatment application, skipping the usual methods of applying chemical treatments on stone substrates, with the use of cellulose poultice, resorting to the agar, a gel already used in many other areas, being something new in this area, which possesses great applicability in the field of conservation of stone materials. After the application of the best methodology for cleaning, specimens were characterized again in order to understand which treatment was more effective and less harmful, both for the operator and the stone material. Very briefly conclusions were that for a very intense and deep penetration into the stone, a solution of 3.5% of SDT buffered with ammonium carbonate to pH around 7 applied with agar support would be indicated. For rust stains in its initial state, the use of Ammonium citrate at a concentration of 5% buffered with ammonium to pH 7 could be applied more than once until satisfactory results appear.

Spectral Analysis Related to Bare-Metal and Drug-Eluting Coronary Stent Implantation

Background: The autonomic nervous system plays a central role in cardiovascular regulation; sympathetic activation occurs during myocardial ischemia. Objective: To assess the spectral analysis of heart rate variability during stent implantation, comparing the types of stent. Methods: This study assessed 61 patients (mean age, 64.0 years; 35 men) with ischemic heart disease and indication for stenting. Stent implantation was performed under Holter monitoring to record the spectral analysis of heart rate variability (Fourier transform), measuring the low-frequency (LF) and high-frequency (HF) components, and the LF/HF ratio before and during the procedure. Results: Bare-metal stent was implanted in 34 patients, while the others received drug-eluting stents. The right coronary artery was approached in 21 patients, the left anterior descending, in 28, and the circumflex, in 9. As compared with the pre-stenting period, all patients showed an increase in LF and HF during stent implantation (658 versus 185 ms2, p = 0.00; 322 versus 121, p = 0.00, respectively), with no change in LF/HF. During stent implantation, LF was 864 ms2 in patients with bare-metal stents, and 398 ms2 in those with drug-eluting stents (p = 0.00). The spectral analysis of heart rate variability showed no association with diabetes mellitus, family history, clinical presentation, beta-blockers, age, and vessel or its segment. Conclusions: Stent implantation resulted in concomitant sympathetic and vagal activations. Diabetes mellitus, use of beta-blockers, and the vessel approached showed no influence on the spectral analysis of heart rate variability. Sympathetic activation was lower during the implantation of drug-eluting stents.

Transmission Fourier transform infrared microspectroscopy allows simultaneous assessment of cutin and cell-wall polysaccharides of Arabidopsis petals.

A procedure for the simultaneous analysis of cell-wall polysaccharides, amides and aliphatic polyesters by transmission Fourier transform infrared microspectroscopy (FTIR) has been established for Arabidopsis petals. The combination of FTIR imaging with spectra derivatization revealed that petals, in contrast to other organs, have a characteristic chemical zoning with high amount of aliphatic compounds and esters in the lamina and of polysaccharides in the stalk of the petal. The hinge region of petals was particular rich in amides as well as in vibrations potentially associated with hemicellulose. In addition, a number of other distribution patterns have been identified. Analyses of mutants in cutin deposition confirmed that vibrations of aliphatic compounds and esters present in the lamina were largely associated with the cuticular polyester. Calculation of spectrotypes, including the standard deviation of intensities, allowed detailed comparison of the spectral features of various mutants. The spectrotypes not only revealed differences in the amount of polyesters in cutin mutants, but also changes in other compound classes. For example, in addition to the expected strong deficiencies in polyester content, the long-chain acyl CoA synthase 2 mutant showed increased intensities of vibrations in a wavelength range that is typical for polysaccharides. Identical spectral features were observed in quasimodo2, a cell-wall mutant of Arabidopsis with a defect in pectin formation that exhibits increased cellulose synthase activity. FTIR thus proved to be a convenient method for the identification and characterization of mutants affected in the deposition of cutin in petals.

Spectral analysis of the luteinizing hormone in the blood samples

Generally, medicine books are concentrated almost exclusively in explaining methodology that analyzes fixed measures, measures done in a certain moment, nevertheless the evolution of the measurement and correct interpretation of the missed values are very important and sometimes can give the key information of the results obtained. Thus, the analysis of the temporary series and spectral analysis or analysis of the time series in the dominion of frequencies can be regarded as an appropriate tool for this kind of studies.In this work the frequency of the pulsating secretion of luteinizing hormone LH (thatregulates the fertile life of women) were analyzed in order to determine the existence of the significant frequencies obtained by analysis of Fourier. Detection of the frequencies, with which the pulsating secretion of the LH takes place, is a quite difficult question due topresence of the random errors in measures and samplings, i.e. that pulsating secretions of small amplitude are not detected and disregarded. In physiology it is accepted that cyclical patterns in the secretion of the LH exist and in the results of this research confirm this pattern and determine its frequency presented in the corresponded periodograms to each of studied cycle. The obtained results can be used as key pattern for future sampling frequencies in order to ¿catch¿ the significant picks of the luteinizing hormone and reflect on time forproductivity treatment of women.

Bi-planar 2D-to-3D registration in Fourier domain for stereoscopic X-ray motion tracking

In this paper we present a new method to track bonemovements in stereoscopic X-ray image series of the kneejoint. The method is based on two different X-ray imagesets: a rotational series of acquisitions of the stillsubject knee that will allow the tomographicreconstruction of the three-dimensional volume (model),and a stereoscopic image series of orthogonal projectionsas the subject performs movements. Tracking the movementsof bones throughout the stereoscopic image series meansto determine, for each frame, the best pose of everymoving element (bone) previously identified in the 3Dreconstructed model. The quality of a pose is reflectedin the similarity between its simulated projections andthe actual radiographs. We use direct Fourierreconstruction to approximate the three-dimensionalvolume of the knee joint. Then, to avoid the expensivecomputation of digitally rendered radiographs (DRR) forpose recovery, we reformulate the tracking problem in theFourier domain. Under the hypothesis of parallel X-raybeams, we use the central-slice-projection theorem toreplace the heavy 2D-to-3D registration of projections inthe signal domain by efficient slice-to-volumeregistration in the Fourier domain. Focusing onrotational movements, the translation-relevant phaseinformation can be discarded and we only consider scalarFourier amplitudes. The core of our motion trackingalgorithm can be implemented as a classical frame-wiseslice-to-volume registration task. Preliminary results onboth synthetic and real images confirm the validity ofour approach.

Applications of Fourier transform infrared spectroscopy

This article summarizes the basic principles of Fourier Transform Infrared Spectroscopy, with examples of methodologies and applications to different field sciences.

On the inverse windowed Fourier transform

The inversion problem concerning the windowed Fourier transform is considered. It is shown that, out of the infinite solutions that the problem admits, the windowed Fourier transform is the "optimal" solution according to a maximum-entropy selection criterion.

Methods for the analysis of two dimensional measurement data of paper web

This work is devoted to the problem of reconstructing the basis weight structure at paper web with black{box techniques. The data that is analyzed comes from a real paper machine and is collected by an o®-line scanner. The principal mathematical tool used in this work is Autoregressive Moving Average (ARMA) modelling. When coupled with the Discrete Fourier Transform (DFT), it gives a very flexible and interesting tool for analyzing properties of the paper web. Both ARMA and DFT are independently used to represent the given signal in a simplified version of our algorithm, but the final goal is to combine the two together. Ljung-Box Q-statistic lack-of-fit test combined with the Root Mean Squared Error coefficient gives a tool to separate significant signals from noise.

Otolith shape analysis as a tool for population discrimination of the white grunt (Haemulon plumieri) stock in the northern coast of the Yucatan Peninsula, Mexico

In this study, the population structure of the white grunt (Haemulon plumieri) from the northern coast of the Yucatan Peninsula was determined through an otolith shape analysis based on the samples collected in three locations: Celestún (N 20°49",W 90°25"), Dzilam (N 21°23", W 88°54") and Cancún (N 21°21",W 86°52"). The otolith outline was based on the elliptic Fourier descriptors, which indicated that the H. plumieri population in the northern coast of the Yucatan Peninsula is composed of three geographically delimited units (Celestún, Dzilam, and Cancún). Significant differences were observed in mean otolith shapes among all samples (PERMANOVA; F2, 99 = 11.20, P = 0.0002), and the subsequent pairwise comparisons showed that all samples were significantly differently from each other. Samples do not belong to a unique white grunt population, and results suggest that they might represent a structured population along the northern coast of the Yucatan Peninsula

Particle shape and orientation in laser diffraction and static image analysis size distribution analysis of micrometer sized rectangular particles

Laser diffraction (LD) and static image analysis (SIA) of rectangular particles [United States Pharmacopeia, USP30-NF25, General Chapter <776>, Optical Miroscopy.] have been systematically studied. To rule out sample dispersion and particle orientation as the root cause of differences in size distribution profiles, we immobilize powder samples on a glass plate by means of a dry disperser. For a defined region of the glass plate, we measure the diffraction pattern as induced by the dispersed particles, and the 2D dimensions of the individual particles using LD and optical microscopy, respectively. We demonstrate a correlation between LD and SIA, with the scattering intensity of the individual particles as the dominant factor. In theory, the scattering intensity is related to the square of the projected area of both spherical and rectangular particles. In traditional LD the size distribution profile is dominated by the maximum projected area of the particles (A). The diffraction diameters of a rectangular particle with length L and breadth B as measured by the LD instrument approximately correspond to spheres of diameter ØL and ØB respectively. Differences in the scattering intensity between spherical and rectangular particles suggest that the contribution made to the overall LD volume probability distribution by each rectangular particle is proportional to A2/L and A2/B. Accordingly, for rectangular particles the scattering intensity weighted diffraction diameter (SIWDD) explains an overestimation of their shortest dimension and an underestimation of their longest dimension. This study analyzes various samples of particles whose length ranges from approximately 10 to 1000 μm. The correlation we demonstrate between LD and SIA can be used to improve validation of LD methods based on SIA data for a variety of pharmaceutical powders all with a different rectangular particle size and shape.

Wavelets in real-time paper web analysis

Online paper web analysis relies on traversing scanners that criss-cross on top of a rapidly moving paper web. The sensors embedded in the scanners measure many important quality variables of paper, such as basis weight, caliper and porosity. Most of these quantities are varying a lot and the measurements are noisy at many different scales. The zigzagging nature of scanning makes it difficult to separate machine direction (MD) and cross direction (CD) variability from one another. For improving the 2D resolution of the quality variables above, the paper quality control team at the Department of Mathematics and Physics at LUT has implemented efficient Kalman filtering based methods that currently use 2D Fourier series. Fourier series are global and therefore resolve local spatial detail on the paper web rather poorly. The target of the current thesis is to study alternative wavelet based representations as candidates to replace the Fourier basis for a higher resolution spatial reconstruction of these quality variables. The accuracy of wavelet compressed 2D web fields will be compared with corresponding truncated Fourier series based fields.