Lanczos subspace filter diagonalization: Homogeneous recursive filtering and a low-storage method for the calculation of matrix elements

We develop a new iterative filter diagonalization (FD) scheme based on Lanczos subspaces and demonstrate its application to the calculation of bound-state and resonance eigenvalues. The new scheme combines the Lanczos three-term vector recursion for the generation of a tridiagonal representation of the Hamiltonian with a three-term scalar recursion to generate filtered states within the Lanczos representation. Eigenstates in the energy windows of interest can then be obtained by solving a small generalized eigenvalue problem in the subspace spanned by the filtered states. The scalar filtering recursion is based on the homogeneous eigenvalue equation of the tridiagonal representation of the Hamiltonian, and is simpler and more efficient than our previous quasi-minimum-residual filter diagonalization (QMRFD) scheme (H. G. Yu and S. C. Smith, Chem. Phys. Lett., 1998, 283, 69), which was based on solving for the action of the Green operator via an inhomogeneous equation. A low-storage method for the construction of Hamiltonian and overlap matrix elements in the filtered-basis representation is devised, in which contributions to the matrix elements are computed simultaneously as the recursion proceeds, allowing coefficients of the filtered states to be discarded once their contribution has been evaluated. Application to the HO2 system shows that the new scheme is highly efficient and can generate eigenvalues with the same numerical accuracy as the basic Lanczos algorithm.

Colour filtering in a-SiC : H based p-i-n-p-i-n cells: A trade-off between bias polarity and absorption regions

A large area colour imager optically addressed is presented. The colour imager consists of a thin wide band gap p-i-n a-SiC:H filtering element deposited on the top of a thick large area a-SiC:H(-p)/a-Si:H(-i)/a-SiC:H(-n) image sensor, which reveals itself an intrinsic colour filter. In order to tune the external applied voltage for full colour discrimination the photocurrent generated by a modulated red light is measured under different optical and electrical bias. Results reveal that the integrated device behaves itself as an imager and a filter giving information not only on the position where the optical image is absorbed but also on it wavelength and intensity. The amplitude and sign of the image signals are electrically tuneable. In a wide range of incident fluxes and under reverse bias, the red and blue image signals are opposite in sign and the green signal is suppressed allowing blue and red colour recognition. The green information is obtained under forward bias, where the blue signal goes down to zero and the red and green remain constant. Combining the information obtained at this two applied voltages a RGB colour image picture can be acquired without the need of the usual colour filters or pixel architecture. A numerical simulation supports the colour filter analysis.

Automatic front-crawl temporal phase detection using adaptive filtering of inertial signals

This study introduces a novel approach for automatic temporal phase detection and inter-arm coordination estimation in front-crawl swimming using inertial measurement units (IMUs). We examined the validity of our method by comparison against a video-based system. Three waterproofed IMUs (composed of 3D accelerometer, 3D gyroscope) were placed on both forearms and the sacrum of the swimmer. We used two underwater video cameras in side and frontal views as our reference system. Two independent operators performed the video analysis. To test our methodology, seven well-trained swimmers performed three 300 m trials in a 50 m indoor pool. Each trial was in a different coordination mode quantified by the index of coordination. We detected different phases of the arm stroke by employing orientation estimation techniques and a new adaptive change detection algorithm on inertial signals. The difference of 0.2 +/- 3.9% between our estimation and video-based system in assessment of the index of coordination was comparable to experienced operators' difference (1.1 +/- 3.6%). The 95% limits of agreement of the difference between the two systems in estimation of the temporal phases were always less than 7.9% of the cycle duration. The inertial system offers an automatic easy-to-use system with timely feedback for the study of swimming.

A new poly(ortho ester)-based drug delivery system as an adjunct treatment in filtering surgery.

PURPOSE: Pharmacologic modulation of wound healing after glaucoma filtering surgery remains a major clinical challenge in ophthalmology. Poly(ortho ester) (POE) is a bioerodible and biocompatible viscous polymer potentially useful as a sustained drug delivery system that allows the frequency of intraocular injections to be reduced. The purpose of this study was to determine the efficacy of POE containing a precise amount of 5-fluorouracil (5-FU) in an experimental model of filtering surgery in the rabbit. METHODS: Trabeculectomy was performed in pigmented rabbit eyes. An ointmentlike formulation of POE containing 1% wt/wt 5-FU was injected subconjunctivally at the site of surgery, during the procedure. Intraocular pressure (IOP), bleb persistence, and ocular inflammatory reaction were monitored until postoperative day 30. Quantitative analysis of 5-FU was performed in the anterior chamber. Histologic analysis was used to assess the appearance of the filtering fistula and the polymer's biocompatibility. RESULTS: The decrease in IOP from baseline and the persistence of the filtering bleb were significantly more marked in the 5-FU-treated eyes during postoperative days 9 through 28. Corneal toxicity triggered by 5-FU was significantly lower in the group that received 5-FU in POE compared with a 5-FU tamponade. Histopathologic evaluation showed that POE was well tolerated, and no fibrosis occurred in eyes treated with POE containing 5-FU. CONCLUSIONS: In this rabbit model of trabeculectomy, the formulation based on POE and containing a precise amount of 5-FU reduced IOP and prolonged bleb persistence in a way similar to the conventional method of a 5-FU tamponade, while significantly reducing 5-FU toxicity.

Estudi comparatiu dels filtres de Kalman i IMM per a navegació

Els sistemes híbrids de navegació integren mesures de posició i velocitat provinents de satèl·lits (GPS) i d’unitats de mesura inercials (IMU).Les dades d’aquests sensors s’han de fusionar i suavitzar, i per a aquest propòsit existeixen diversos algorismes de filtratge, que tracten les dades conjuntament o per separat. En aquest treball s’han codificat en Matlab els algorismes dels filtres de Kalman i IMM, i s’han comparat les seves prestacions en diverses trajectòries d’un vehicle. S’han avaluat quantitativament els errors dels dos filtres, i s’han sintonitzat els seus paràmetres per a minimitzar aquests errors. Amb una correcta sintonia dels filtres, s’ha comprovat que el filtre IMM és superior al filtre de Kalman, tant per maniobres brusques com per maniobres suaus, malgrat que la complexitat i el temps de càlcul requerit són majors.

Inversion and assimilation methods with applications in geophysical remote sensing

Stratospheric ozone can be measured accurately using a limb scatter remote sensing technique at the UV-visible spectral region of solar light. The advantages of this technique includes a good vertical resolution and a good daytime coverage of the measurements. In addition to ozone, UV-visible limb scatter measurements contain information about NO2, NO3, OClO, BrO and aerosols. There are currently several satellite instruments continuously scanning the atmosphere and measuring the UVvisible region of the spectrum, e.g., the Optical Spectrograph and Infrared Imager System (OSIRIS) launched on the Odin satellite in February 2001, and the Scanning Imaging Absorption SpectroMeter for Atmospheric CartograpHY (SCIAMACHY) launched on Envisat in March 2002. Envisat also carries the Global Ozone Monitoring by Occultation of Stars (GOMOS) instrument, which also measures limb-scattered sunlight under bright limb occultation conditions. These conditions occur during daytime occultation measurements. The global coverage of the satellite measurements is far better than any other ozone measurement technique, but still the measurements are sparse in the spatial domain. Measurements are also repeated relatively rarely over a certain area, and the composition of the Earth’s atmosphere changes dynamically. Assimilation methods are therefore needed in order to combine the information of the measurements with the atmospheric model. In recent years, the focus of assimilation algorithm research has turned towards filtering methods. The traditional Extended Kalman filter (EKF) method takes into account not only the uncertainty of the measurements, but also the uncertainty of the evolution model of the system. However, the computational cost of full blown EKF increases rapidly as the number of the model parameters increases. Therefore the EKF method cannot be applied directly to the stratospheric ozone assimilation problem. The work in this thesis is devoted to the development of inversion methods for satellite instruments and the development of assimilation methods used with atmospheric models.

Metabolism of diglycine and triglycine by non-filtering kidneys

We have studied the metabolism of diglycine and triglycine in the isolated non-filtering rat kidney. Kidneys from adult male Wistar Kyoto rats weighing 250-350 g were perfused with Krebs-Henseleit solution containing either 1 mM diglycine or triglycine. The analysis of the peptide residues and their components was performed using an amino acid microanalyzer utilizing ion exchange chromatography. Diglycine was degraded to a final concentration of 0.09 mM after 120 min (91%); this degradation occurred predominantly during the first hour, with a 56% reduction of the initial concentration. The metabolism of triglycine occurred similarly, with a final concentration of 0.18 mM (82%); during the first hour there was a 67% reduction of the initial concentration of the tripeptide. Both peptides produced glycine in increasing concentrations, but there was a slightly lower recovery of glycine, suggesting its utilization by the kidney as fuel. The hydrolysis of triglycine also produced diglycine, which was also hydrolyzed to glycine. The results of the present study show the existence of functional endothelial or contraluminal membrane peptidases which may be important during parenteral nutrition.

Adaptive Markov chain Monte Carlo and Bayesian filtering for state space models

This thesis is concerned with the state and parameter estimation in state space models. The estimation of states and parameters is an important task when mathematical modeling is applied to many different application areas such as the global positioning systems, target tracking, navigation, brain imaging, spread of infectious diseases, biological processes, telecommunications, audio signal processing, stochastic optimal control, machine learning, and physical systems. In Bayesian settings, the estimation of states or parameters amounts to computation of the posterior probability density function. Except for a very restricted number of models, it is impossible to compute this density function in a closed form. Hence, we need approximation methods. A state estimation problem involves estimating the states (latent variables) that are not directly observed in the output of the system. In this thesis, we use the Kalman filter, extended Kalman filter, Gauss–Hermite filters, and particle filters to estimate the states based on available measurements. Among these filters, particle filters are numerical methods for approximating the filtering distributions of non-linear non-Gaussian state space models via Monte Carlo. The performance of a particle filter heavily depends on the chosen importance distribution. For instance, inappropriate choice of the importance distribution can lead to the failure of convergence of the particle filter algorithm. In this thesis, we analyze the theoretical Lᵖ particle filter convergence with general importance distributions, where p ≥2 is an integer. A parameter estimation problem is considered with inferring the model parameters from measurements. For high-dimensional complex models, estimation of parameters can be done by Markov chain Monte Carlo (MCMC) methods. In its operation, the MCMC method requires the unnormalized posterior distribution of the parameters and a proposal distribution. In this thesis, we show how the posterior density function of the parameters of a state space model can be computed by filtering based methods, where the states are integrated out. This type of computation is then applied to estimate parameters of stochastic differential equations. Furthermore, we compute the partial derivatives of the log-posterior density function and use the hybrid Monte Carlo and scaled conjugate gradient methods to infer the parameters of stochastic differential equations. The computational efficiency of MCMC methods is highly depend on the chosen proposal distribution. A commonly used proposal distribution is Gaussian. In this kind of proposal, the covariance matrix must be well tuned. To tune it, adaptive MCMC methods can be used. In this thesis, we propose a new way of updating the covariance matrix using the variational Bayesian adaptive Kalman filter algorithm.

Modeling and Analysis of Some Heavy Tailed Time Series

The thesis has covered various aspects of modeling and analysis of finite mean time series with symmetric stable distributed innovations. Time series analysis based on Box and Jenkins methods are the most popular approaches where the models are linear and errors are Gaussian. We highlighted the limitations of classical time series analysis tools and explored some generalized tools and organized the approach parallel to the classical set up. In the present thesis we mainly studied the estimation and prediction of signal plus noise model. Here we assumed the signal and noise follow some models with symmetric stable innovations.We start the thesis with some motivating examples and application areas of alpha stable time series models. Classical time series analysis and corresponding theories based on finite variance models are extensively discussed in second chapter. We also surveyed the existing theories and methods correspond to infinite variance models in the same chapter. We present a linear filtering method for computing the filter weights assigned to the observation for estimating unobserved signal under general noisy environment in third chapter. Here we consider both the signal and the noise as stationary processes with infinite variance innovations. We derived semi infinite, double infinite and asymmetric signal extraction filters based on minimum dispersion criteria. Finite length filters based on Kalman-Levy filters are developed and identified the pattern of the filter weights. Simulation studies show that the proposed methods are competent enough in signal extraction for processes with infinite variance.Parameter estimation of autoregressive signals observed in a symmetric stable noise environment is discussed in fourth chapter. Here we used higher order Yule-Walker type estimation using auto-covariation function and exemplify the methods by simulation and application to Sea surface temperature data. We increased the number of Yule-Walker equations and proposed a ordinary least square estimate to the autoregressive parameters. Singularity problem of the auto-covariation matrix is addressed and derived a modified version of the Generalized Yule-Walker method using singular value decomposition.In fifth chapter of the thesis we introduced partial covariation function as a tool for stable time series analysis where covariance or partial covariance is ill defined. Asymptotic results of the partial auto-covariation is studied and its application in model identification of stable auto-regressive models are discussed. We generalize the Durbin-Levinson algorithm to include infinite variance models in terms of partial auto-covariation function and introduce a new information criteria for consistent order estimation of stable autoregressive model.In chapter six we explore the application of the techniques discussed in the previous chapter in signal processing. Frequency estimation of sinusoidal signal observed in symmetric stable noisy environment is discussed in this context. Here we introduced a parametric spectrum analysis and frequency estimate using power transfer function. Estimate of the power transfer function is obtained using the modified generalized Yule-Walker approach. Another important problem in statistical signal processing is to identify the number of sinusoidal components in an observed signal. We used a modified version of the proposed information criteria for this purpose.

Median filtering: structure analysis and application

Median filtering is a simple digital non—linear signal smoothing operation in which median of the samples in a sliding window replaces the sample at the middle of the window. The resulting filtered sequence tends to follow polynomial trends in the original sample sequence. Median filter preserves signal edges while filtering out impulses. Due to this property, median filtering is finding applications in many areas of image and speech processing. Though median filtering is simple to realise digitally, its properties are not easily analysed with standard analysis techniques,

Modelación estocástica y trading algorítmico del spread entre acciones mediante procesos de reversión a la media

Las estrategias de inversión pairs trading se basan en desviaciones del precio entre pares de acciones correlacionadas y han sido ampliamente implementadas por fondos de inversión tomando posiciones largas y cortas en las acciones seleccionadas cuando surgen divergencias y obteniendo utilidad cerrando la posición al converger. Se describe un modelo de reversión a la media para analizar la dinámica que sigue el diferencial del precio entre acciones ordinarias y preferenciales de una misma empresa en el mismo mercado. La media de convergencia en el largo plazo es obtenida con un filtro de media móvil, posteriormente, los parámetros del modelo de reversión a la media se estiman mediante un filtro de Kalman bajo una formulación de estado espacio sobre las series históricas. Se realiza un backtesting a la estrategia de pairs trading algorítmico sobre el modelo propuesto indicando potenciales utilidades en mercados financieros que se observan por fuera del equilibrio. Aplicaciones de los resultados podrían mostrar oportunidades para mejorar el rendimiento de portafolios, corregir errores de valoración y sobrellevar mejor periodos de bajos retornos.

Far-red light filtering by plastic film, greenhouse-cladding materials: effects on growth and flowering in Petunia and Impatiens

Photoselective plastic films with low transmission to far-red (FR) light (700-800 nm) are now available so that plants grown in greenhouses clad with such plastics exhibit reduced stem extension and, consequently, plant height. Here we compare the action of three FR-absorbing polythene films on extension growth of Petunia (Petunia X hybrida) cv. 'Express Blue' and Impatiens walleriana cv. 'Accent Deep Pink' with plants grown under a control polythene film (standard UVI/EVA film). Half of the plants under the control film were treated with a chemical plant growth regulator (PGR; diaminozide, B-Nine) and half were sprayed with water alone. Possible negative effects of such film plastics on flowering, and on fresh and dry weight accumulation, were also quantified. Plants were harvested destructively when all plants in each treatment had reached the first open flower stage. In Petunia, plant height was reduced by all three FR-filtering films and by PGR-treatment. The FR-filtering films giving the highest R:FR ratios also reduced plant height in Impatiens. Leaf number, leaf area and total dry Weight in both species. were greatest in the controls and smallest under films with the lowest PAR transmission. The film giving the highest R:FR ratio and PAR transmission also produced the most compact Petunia plants;, while the film. with. the lowest PAR transmission produced the least compact plants in both species. There was no significant effect of treatments on time to first flower in Impatiens. However, Petunia plants under low PAR transmission films took longer to flower. Plastic-films which filter out FR light to increase the R:FR ratio, combined With high PAR transmission, can therefore be used as an alternative to conventional PGRs.

On the Kalman-Bucy filter with specified input

In a recent paper, Vathsal suggested that a new configuration had been obtained for linear filtering problems, which was distinctly different from the Kalman-Bucy filter. It is shown that this in fact is merely a special case of the filter with a specified input.