Variational ensemble Kalman filtering applied to data assimilation problems in computational fluid dynamics

One challenge on data assimilation (DA) methods is how the error covariance for the model state is computed. Ensemble methods have been proposed for producing error covariance estimates, as error is propagated in time using the non-linear model. Variational methods, on the other hand, use the concepts of control theory, whereby the state estimate is optimized from both the background and the measurements. Numerical optimization schemes are applied which solve the problem of memory storage and huge matrix inversion needed by classical Kalman filter methods. Variational Ensemble Kalman filter (VEnKF), as a method inspired the Variational Kalman Filter (VKF), enjoys the benefits from both ensemble methods and variational methods. It avoids filter inbreeding problems which emerge when the ensemble spread underestimates the true error covariance. In VEnKF this is tackled by resampling the ensemble every time measurements are available. One advantage of VEnKF over VKF is that it needs neither tangent linear code nor adjoint code. In this thesis, VEnKF has been applied to a two-dimensional shallow water model simulating a dam-break experiment. The model is a public code with water height measurements recorded in seven stations along the 21:2 m long 1:4 m wide flume’s mid-line. Because the data were too sparse to assimilate the 30 171 model state vector, we chose to interpolate the data both in time and in space. The results of the assimilation were compared with that of a pure simulation. We have found that the results revealed by the VEnKF were more realistic, without numerical artifacts present in the pure simulation. Creating a wrapper code for a model and DA scheme might be challenging, especially when the two were designed independently or are poorly documented. In this thesis we have presented a non-intrusive approach of coupling the model and a DA scheme. An external program is used to send and receive information between the model and DA procedure using files. The advantage of this method is that the model code changes needed are minimal, only a few lines which facilitate input and output. Apart from being simple to coupling, the approach can be employed even if the two were written in different programming languages, because the communication is not through code. The non-intrusive approach is made to accommodate parallel computing by just telling the control program to wait until all the processes have ended before the DA procedure is invoked. It is worth mentioning the overhead increase caused by the approach, as at every assimilation cycle both the model and the DA procedure have to be initialized. Nonetheless, the method can be an ideal approach for a benchmark platform in testing DA methods. The non-intrusive VEnKF has been applied to a multi-purpose hydrodynamic model COHERENS to assimilate Total Suspended Matter (TSM) in lake Säkylän Pyhäjärvi. The lake has an area of 154 km2 with an average depth of 5:4 m. Turbidity and chlorophyll-a concentrations from MERIS satellite images for 7 days between May 16 and July 6 2009 were available. The effect of the organic matter has been computationally eliminated to obtain TSM data. Because of computational demands from both COHERENS and VEnKF, we have chosen to use 1 km grid resolution. The results of the VEnKF have been compared with the measurements recorded at an automatic station located at the North-Western part of the lake. However, due to TSM data sparsity in both time and space, it could not be well matched. The use of multiple automatic stations with real time data is important to elude the time sparsity problem. With DA, this will help in better understanding the environmental hazard variables for instance. We have found that using a very high ensemble size does not necessarily improve the results, because there is a limit whereby additional ensemble members add very little to the performance. Successful implementation of the non-intrusive VEnKF and the ensemble size limit for performance leads to an emerging area of Reduced Order Modeling (ROM). To save computational resources, running full-blown model in ROM is avoided. When the ROM is applied with the non-intrusive DA approach, it might result in a cheaper algorithm that will relax computation challenges existing in the field of modelling and DA.

Implementação da rotina de unfolding para determinação de distribuição de tamanho de grãos esféricos via distribuição de interceptos lineares e de área de seção

Na unfolding method of linear intercept distributions and secction área distribution was implemented for structures with spherical grains. Although the unfolding routine depends on the grain shape, structures with spheroidal grains can also be treated by this routine. Grains of non-spheroidal shape can be treated only as approximation. A software was developed with two parts. The first part calculates the probability matrix. The second part uses this matrix and minimizes the chi-square. The results are presented with any number of size classes as required. The probability matrix was determined by means of the linear intercept and section area distributions created by computer simulation. Using curve fittings the probability matrix for spheres of any sizes could be determined. Two kinds of tests were carried out to prove the efficiency of the Technique. The theoretical tests represent ideal cases. The software was able to exactly find the proposed grain size distribution. In the second test, a structure was simulated in computer and images of its slices were used to produce the corresponding linear intercept the section area distributions. These distributions were then unfolded. This test simulates better reality. The results show deviations from the real size distribution. This deviations are caused by statistic fluctuation. The unfolding of the linear intercept distribution works perfectly, but the unfolding of section area distribution does not work due to a failure in the chi-square minimization. The minimization method uses a matrix inversion routine. The matrix generated by this procedure cannot be inverted. Other minimization method must be used

A principal component approach to space-based gravitational wave astronomy

The current approach to data analysis for the Laser Interferometry Space Antenna (LISA) depends on the time delay interferometry observables (TDI) which have to be generated before any weak signal detection can be performed. These are linear combinations of the raw data with appropriate time shifts that lead to the cancellation of the laser frequency noises. This is possible because of the multiple occurrences of the same noises in the different raw data. Originally, these observables were manually generated starting with LISA as a simple stationary array and then adjusted to incorporate the antenna's motions. However, none of the observables survived the flexing of the arms in that they did not lead to cancellation with the same structure. The principal component approach is another way of handling these noises that was presented by Romano and Woan which simplified the data analysis by removing the need to create them before the analysis. This method also depends on the multiple occurrences of the same noises but, instead of using them for cancellation, it takes advantage of the correlations that they produce between the different readings. These correlations can be expressed in a noise (data) covariance matrix which occurs in the Bayesian likelihood function when the noises are assumed be Gaussian. Romano and Woan showed that performing an eigendecomposition of this matrix produced two distinct sets of eigenvalues that can be distinguished by the absence of laser frequency noise from one set. The transformation of the raw data using the corresponding eigenvectors also produced data that was free from the laser frequency noises. This result led to the idea that the principal components may actually be time delay interferometry observables since they produced the same outcome, that is, data that are free from laser frequency noise. The aims here were (i) to investigate the connection between the principal components and these observables, (ii) to prove that the data analysis using them is equivalent to that using the traditional observables and (ii) to determine how this method adapts to real LISA especially the flexing of the antenna. For testing the connection between the principal components and the TDI observables a 10x 10 covariance matrix containing integer values was used in order to obtain an algebraic solution for the eigendecomposition. The matrix was generated using fixed unequal arm lengths and stationary noises with equal variances for each noise type. Results confirm that all four Sagnac observables can be generated from the eigenvectors of the principal components. The observables obtained from this method however, are tied to the length of the data and are not general expressions like the traditional observables, for example, the Sagnac observables for two different time stamps were generated from different sets of eigenvectors. It was also possible to generate the frequency domain optimal AET observables from the principal components obtained from the power spectral density matrix. These results indicate that this method is another way of producing the observables therefore analysis using principal components should give the same results as that using the traditional observables. This was proven by fact that the same relative likelihoods (within 0.3%) were obtained from the Bayesian estimates of the signal amplitude of a simple sinusoidal gravitational wave using the principal components and the optimal AET observables. This method fails if the eigenvalues that are free from laser frequency noises are not generated. These are obtained from the covariance matrix and the properties of LISA that are required for its computation are the phase-locking, arm lengths and noise variances. Preliminary results of the effects of these properties on the principal components indicate that only the absence of phase-locking prevented their production. The flexing of the antenna results in time varying arm lengths which will appear in the covariance matrix and, from our toy model investigations, this did not prevent the occurrence of the principal components. The difficulty with flexing, and also non-stationary noises, is that the Toeplitz structure of the matrix will be destroyed which will affect any computation methods that take advantage of this structure. In terms of separating the two sets of data for the analysis, this was not necessary because the laser frequency noises are very large compared to the photodetector noises which resulted in a significant reduction in the data containing them after the matrix inversion. In the frequency domain the power spectral density matrices were block diagonals which simplified the computation of the eigenvalues by allowing them to be done separately for each block. The results in general showed a lack of principal components in the absence of phase-locking except for the zero bin. The major difference with the power spectral density matrix is that the time varying arm lengths and non-stationarity do not show up because of the summation in the Fourier transform.

Fast, scalable master equation solution algorithms. IV. Lanczos iteration with diffusion approximation preconditioned iterative inversion

In this paper we propose a second linearly scalable method for solving large master equations arising in the context of gas-phase reactive systems. The new method is based on the well-known shift-invert Lanczos iteration using the GMRES iteration preconditioned using the diffusion approximation to the master equation to provide the inverse of the master equation matrix. In this way we avoid the cubic scaling of traditional master equation solution methods while maintaining the speed of a partial spectral decomposition. The method is tested using a master equation modeling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long-lived isomerizing intermediates. (C) 2003 American Institute of Physics.

Local re-inversion coronary MR angiography: arterial spin-labeling without the need for subtraction.

PURPOSE: To implement a double-inversion bright-blood coronary MR angiography sequence using a cylindrical re-inversion prepulse for selective visualization of the coronary arteries. MATERIALS AND METHODS: Local re-inversion bright-blood magnetization preparation was implemented using a nonselective inversion followed by a cylindrical aortic re-inversion prepulse. After an inversion delay that allows for in-flow of the labeled blood-pool into the coronary arteries, three-dimensional radial steady-state free-precession (SSFP) imaging (repetition/echo time, 7.2/3.6 ms; flip angle, 120 degrees, 16 profiles per RR interval; field of view, 360 mm; matrix, 512, twelve 3-mm slices) is performed. Coronary MR angiography was performed in three healthy volunteers and in one patient on a commercial 1.5 Tesla whole-body MR System. RESULTS: In all subjects, coronary arteries were selectively visualized with positive contrast. In addition, a middle-grade stenosis of the proximal right coronary artery was seen in one patient. CONCLUSION: A novel T1 contrast-enhancement strategy is presented for selective visualization of the coronary arteries without extrinsic contrast medium application. In comparison to former arterial spin-labeling schemes, the proposed magnetization preparation obviates the need for a second data set and subtraction.

Affinity distribution functions in multicomponent heterogeneous adsorption. Analytical inversion of isotherms to obtain affinity spectra

An analytical approach for the interpretation of multicomponent heterogeneous adsorption or complexation isotherms in terms of multidimensional affinity spectra is presented. Fourier transform, applied to analyze the corresponding integral equation, leads to an inversion formula which allows the computation of the multicomponent affinity spectrum underlying a given competitive isotherm. Although a different mathematical methodology is used, this procedure can be seen as the extension to multicomponent systems of the classical Sips’s work devoted to monocomponent systems. Furthermore, a methodology which yields analytical expressions for the main statistical properties (mean free energies of binding and covariance matrix) of multidimensional affinity spectra is reported. Thus, the level of binding correlation between the different components can be quantified. It has to be highlighted that the reported methodology does not require the knowledge of the affinity spectrum to calculate the means, variances, and covariance of the binding energies of the different components. Nonideal competitive consistent adsorption isotherm, widely used in metal/proton competitive complexation to environmental macromolecules, and Frumkin competitive isotherms are selected to illustrate the application of the reported results. Explicit analytical expressions for the affinity spectrum as well as for the matrix correlation are obtained for the NICCA case. © 2004 American Institute of Physics.

Natural gradient matrix momentum

Natural gradient learning is an efficient and principled method for improving on-line learning. In practical applications there will be an increased cost required in estimating and inverting the Fisher information matrix. We propose to use the matrix momentum algorithm in order to carry out efficient inversion and study the efficacy of a single step estimation of the Fisher information matrix. We analyse the proposed algorithm in a two-layer network, using a statistical mechanics framework which allows us to describe analytically the learning dynamics, and compare performance with true natural gradient learning and standard gradient descent.

Key Agreement Protocol Using Elliptic Curve Matrix Power Function

* Work is partially supported by the Lithuanian State Science and Studies Foundation.

Quantitative Proteomic Analysis Reveals Metabolic Alterations, Calcium Dysregulation, And Increased Expression Of Extracellular Matrix Proteins In Laminin α2 Chain-deficient Muscle.

Congenital muscular dystrophy with laminin α2 chain deficiency (MDC1A) is one of the most severe forms of muscular disease and is characterized by severe muscle weakness and delayed motor milestones. The genetic basis of MDC1A is well known, yet the secondary mechanisms ultimately leading to muscle degeneration and subsequent connective tissue infiltration are not fully understood. In order to obtain new insights into the molecular mechanisms underlying MDC1A, we performed a comparative proteomic analysis of affected muscles (diaphragm and gastrocnemius) from laminin α2 chain-deficient dy(3K)/dy(3K) mice, using multidimensional protein identification technology combined with tandem mass tags. Out of the approximately 700 identified proteins, 113 and 101 proteins, respectively, were differentially expressed in the diseased gastrocnemius and diaphragm muscles compared with normal muscles. A large portion of these proteins are involved in different metabolic processes, bind calcium, or are expressed in the extracellular matrix. Our findings suggest that metabolic alterations and calcium dysregulation could be novel mechanisms that underlie MDC1A and might be targets that should be explored for therapy. Also, detailed knowledge of the composition of fibrotic tissue, rich in extracellular matrix proteins, in laminin α2 chain-deficient muscle might help in the design of future anti-fibrotic treatments. All MS data have been deposited in the ProteomeXchange with identifier PXD000978 (http://proteomecentral.proteomexchange.org/dataset/PXD000978).

Matrix Metalloproteinases And Left Ventricular Function And Structure In Spinal Cord Injured Subjects.

Subjects with spinal cord injury (SCI) exhibit impaired left ventricular (LV) diastolic function, which has been reported to be attenuated by regular physical activity. This study investigated the relationship between circulating matrix metalloproteinases (MMPs) and tissue inhibitors of MMPs (TIMPs) and echocardiographic parameters in SCI subjects and the role of physical activity in this regard. Forty-two men with SCI [19 sedentary (S-SCI) and 23 physically-active (PA-SCI)] were evaluated by clinical, anthropometric, laboratory, and echocardiographic analysis. Plasmatic pro-MMP-2, MMP-2, MMP-8, pro-MMP-9, MMP-9, TIMP-1 and TIMP-2 levels were determined by enzyme-linked immunosorbent assay and zymography. PA-SCI subjects presented lower pro-MMP-2 and pro-MMP-2/TIMP-2 levels and improved markers of LV diastolic function (lower E/Em and higher Em and E/A values) than S-SCI ones. Bivariate analysis showed that pro-MMP-2 correlated inversely with Em and directly with E/Em, while MMP-9 correlated directly with LV mass index and LV end-diastolic diameter in the whole sample. Following multiple regression analysis, pro-MMP-2, but not physical activity, remained associated with Em, while MMP-9 was associated with LV mass index in the whole sample. These findings suggest differing roles for MMPs in LV structure and function regulation and an interaction among pro-MMP-2, diastolic function and physical activity in SCI subjects.

Identification Of Corynebacterium Spp. Isolated From Bovine Intramammary Infections By Matrix-assisted Laser Desorption Ionization-time Of Flight Mass Spectrometry.

Corynebacterium species (spp.) are among the most frequently isolated pathogens associated with subclinical mastitis in dairy cows. However, simple, fast, and reliable methods for the identification of species of the genus Corynebacterium are not currently available. This study aimed to evaluate the usefulness of matrix-assisted laser desorption ionization/mass spectrometry (MALDI-TOF MS) for identifying Corynebacterium spp. isolated from the mammary glands of dairy cows. Corynebacterium spp. were isolated from milk samples via microbiological culture (n=180) and were analyzed by MALDI-TOF MS and 16S rRNA gene sequencing. Using MALDI-TOF MS methodology, 161 Corynebacterium spp. isolates (89.4%) were correctly identified at the species level, whereas 12 isolates (6.7%) were identified at the genus level. Most isolates that were identified at the species level with 16 S rRNA gene sequencing were identified as Corynebacterium bovis (n=156; 86.7%) were also identified as C. bovis with MALDI-TOF MS. Five Corynebacterium spp. isolates (2.8%) were not correctly identified at the species level with MALDI-TOF MS and 2 isolates (1.1%) were considered unidentified because despite having MALDI-TOF MS scores >2, only the genus level was correctly identified. Therefore, MALDI-TOF MS could serve as an alternative method for species-level diagnoses of bovine intramammary infections caused by Corynebacterium spp.

Inactivation Of Ampk Mediates High Phosphate-induced Extracellular Matrix Accumulation Via Nox4/tgfß-1 Signaling In Human Mesangial Cells.

High phosphate (Pi) levels and extracellular matrix (ECM) accumulation are associated with chronic kidney disease progression. However, how high Pi levels contribute to ECM accumulation in mesangial cells is unknown. The present study investigated the role and mechanism of high Pi levels in ECM accumulation in immortalized human mesangial cells (iHMCs). iHMCs were exposed to normal (0.9 mM) or increasing Pi concentrations (2.5 and 5 mM) with or without diferent blockers or activators. NOX4, phosphorylated AMPK (p-AMPK), phosphorylated SMAD3 (p-SMAD3), fibronectin (F/N), collagen IV (C-IV) and alpha-smooth muscle actin (α-SMA) expression was assessed via western blot and immunofluorescence. Lucigenin-enhanced chemiluminescence, and dihydroethidium (DHE) assessed NADPH oxidase activity and superoxide (SO), respectively. In iHMCs, a Pi transporter blocker (PFA) abrogated high Pi-induced AMPK inactivation, increase in NADPH oxidase-induced reactive oxygen species (ROS) levels, NOX4, p-SMAD3, α-SMA and C-IV expression. AMPK activation by AICAR, NOX4 silencing or NADPH oxidase blocker prevented high Pi-induced DHE levels, p-SMAD3, F/N, C-IV and α-SMA expression. AMPK inactivation with NOX4-induced ROS formation and transforming growth factor ß-1 (TGFß-1) signaling activation mediates high Pi-induced ECM accumulation in iHMCs. Maneuvers increasing AMPK or reducing NOX4 activity may contribute to renal protection under hyperphosphatemia.

A Metabolomic Protocol For Plant Systematics By Matrix-assisted Laser-desorption/ionization Time-of Flight Mass Spectrometry.

Matrix-assisted laser desorption/ionization time-of flight mass spectrometry (MALDI-TOF MS) has been widely used for the identification and classification of microorganisms based on their proteomic fingerprints. However, the use of MALDI-TOF MS in plant research has been very limited. In the present study, a first protocol is proposed for metabolic fingerprinting by MALDI-TOF MS using three different MALDI matrices with subsequent multivariate data analysis by in-house algorithms implemented in the R environment for the taxonomic classification of plants from different genera, families and orders. By merging the data acquired with different matrices, different ionization modes and using careful algorithms and parameter selection, we demonstrate that a close taxonomic classification can be achieved based on plant metabolic fingerprints, with 92% similarity to the taxonomic classifications found in literature. The present work therefore highlights the great potential of applying MALDI-TOF MS for the taxonomic classification of plants and, furthermore, provides a preliminary foundation for future research.

Matrix Support And Institutional Support: Analyzing Their Construction.

This is an analysis of the theoretical and practical construction of the methodology of Matrix Support by means of studies on Paideia Support (Institutional and Matrix Support), which is an inter-professional work of joint care in recent literature and official documents of the Unified Health System (SUS). An attempt was made to describe methodological concepts and strategies. A comparative analysis of Institutional Support and Matrix Support was also conducted using the epistemological framework of Field and Core Knowledge and Practices.

Key Participants Of The Tumor Microenvironment Of The Prostate: An Approach Of The Structural Dynamic Of Cellular Elements And Extracellular Matrix Components During Epithelial-stromal Transition.

Cancer is a multistep process that begins with the transformation of normal epithelial cells and continues with tumor growth, stromal invasion and metastasis. The remodeling of the peritumoral environment is decisive for the onset of tumor invasiveness. This event is dependent on epithelial-stromal interactions, degradation of extracellular matrix components and reorganization of fibrillar components. Our research group has studied in a new proposed rodent model the participation of cellular and molecular components in the prostate microenvironment that contributes to cancer progression. Our group adopted the gerbil Meriones unguiculatus as an alternative experimental model for prostate cancer study. This model has presented significant responses to hormonal treatments and to development of spontaneous and induced neoplasias. The data obtained indicate reorganization of type I collagen fibers and reticular fibers, synthesis of new components such as tenascin and proteoglycans, degradation of basement membrane components and elastic fibers and increased expression of metalloproteinases. Fibroblasts that border the region, apparently participate in the stromal reaction. The roles of each of these events, as well as some signaling molecules, participants of neoplastic progression and factors that promote genetic reprogramming during epithelial-stromal transition are also discussed.