Linear minimum mean square filter for discrete-time linear systems with Markov jumps and multiplicative noises

In this paper we obtain the linear minimum mean square estimator (LMMSE) for discrete-time linear systems subject to state and measurement multiplicative noises and Markov jumps on the parameters. It is assumed that the Markov chain is not available. By using geometric arguments we obtain a Kalman type filter conveniently implementable in a recurrence form. The stationary case is also studied and a proof for the convergence of the error covariance matrix of the LMMSE to a stationary value under the assumption of mean square stability of the system and ergodicity of the associated Markov chain is obtained. It is shown that there exists a unique positive semi-definite solution for the stationary Riccati-like filter equation and, moreover, this solution is the limit of the error covariance matrix of the LMMSE. The advantage of this scheme is that it is very easy to implement and all calculations can be performed offline. (c) 2011 Elsevier Ltd. All rights reserved.

Echocardiographic assessment of the different left ventricular geometric patterns in hypertensive patients

OBJECTIVE: To identiy left ventricular geometric patterns in hypertensive patients on echocardiography, and to correlate those patterns with casual blood pressure measurements and with the parameters obtained on a 24-hour ambulatory blood pressure monitoring. METHODS: We studied sixty hypertensive patients, grouped according to the Joint National Committee stages of hypertension.. Using the single- and two-dimensional Doppler Echocardiography, we analyzed the left ventricular mass and the geometric patterns through the correlation of left ventricular mass index and relative wall thickness. On ambulatory blood pressure monitoring we assessed the means and pressure loads in the different geometric patterns detected on echocardiography RESULTS: We identified three left ventricular geometric patterns: 1) concentric hypertrophy, in 25% of the patients; 2) concentric remodeling, in 25%; and 3) normal geometry, in 50%. Casual systolic blood pressure was higher in the group with concentric hypertrophy than in the other groups (p=0.001). Mean systolic pressure in the 24h, daytime and nighttime periods was also higher in patients with concentric hypertrophy, as compared to the other groups (p=0.003, p=0.004 and p=0.007). Daytime systolic load and nighttime diastolic load were higher in patients with concentric hypertrophy ( p=0.004 and p=0.01, respectively). CONCLUSIONS: Left ventricular geometric patterns show significant correlation with casual systolic blood pressure, and with means and pressure loads on ambulatory blood pressure monitoring.

Geometric and long run aspects of Granger causality

This paper extends multivariate Granger causality to take into account the subspacesalong which Granger causality occurs as well as long run Granger causality. The propertiesof these new notions of Granger causality, along with the requisite restrictions, are derivedand extensively studied for a wide variety of time series processes including linear invertibleprocess and VARMA. Using the proposed extensions, the paper demonstrates that: (i) meanreversion in L2 is an instance of long run Granger non-causality, (ii) cointegration is a specialcase of long run Granger non-causality along a subspace, (iii) controllability is a special caseof Granger causality, and finally (iv) linear rational expectations entail (possibly testable)Granger causality restriction along subspaces.

Nanocrystalline M-type hexaferrite powders: preparation, geometric and magnetic propertiess

Co-Ti-Sn-Ge substituted M-type bariumhexaferrite powders with mean grain sizes between about 10 nm and about 1 ¿m and a narrow size distribution were prepared reproducibly by means of a modified glass crystallization method. At annealing temperatures between 560 and 580°C of the amorphous flakes nanocrystalline particles grow. They behave superparamagnetically at room temperature and change into stable magnetic single domains at lower temperatures. The magnetic volume of the powders is considerably less than the geometric one. However, the effective anisotropy fields are larger by a Factor of two to three.

Nanocrystalline M-type hexaferrite powders: preparation, geometric and magnetic propertiess

Co-Ti-Sn-Ge substituted M-type bariumhexaferrite powders with mean grain sizes between about 10 nm and about 1 ¿m and a narrow size distribution were prepared reproducibly by means of a modified glass crystallization method. At annealing temperatures between 560 and 580°C of the amorphous flakes nanocrystalline particles grow. They behave superparamagnetically at room temperature and change into stable magnetic single domains at lower temperatures. The magnetic volume of the powders is considerably less than the geometric one. However, the effective anisotropy fields are larger by a Factor of two to three.

Searching for the perfect surface area normalizing term - a comparison of BET surface area-, geometric surface area- and mass-normalized dissolution rates of anorthite and biotite

Dissolution rates were calculated for a range of grain sizes of anorthite and biotite dissolved under far from equilibrium conditions at pH 3, T = 20 degrees C. Dissolution rates were normalized to initial and final BET surface area, geometric surface area, mass and (for biotite only) geometric edge surface area. Constant (within error) dissolution rates were only obtained by normalizing to initial BET surface area for biotite. The normalizing term that gave the smallest variation about the mean for anorthite was initial BET surface area. In field studies, only current (final) surface area is measurable. In this study, final geometric surface area gave the smallest variation for anorthite dissolution rates and final geometric edge surface area for biotite dissolution rates. (c) 2005 Published by Elsevier B.V.

Near-optimal mean value estimates for multidimensional Weyl sums

We obtain sharp estimates for multidimensional generalisations of Vinogradov’s mean value theorem for arbitrary translation-dilation invariant systems, achieving constraints on the number of variables approaching those conjectured to be the best possible. Several applications of our bounds are discussed.

The complementary exponential geometric distribution: Model, properties, and a comparison with its counterpart

In this paper, we proposed a new two-parameter lifetime distribution with increasing failure rate, the complementary exponential geometric distribution, which is complementary to the exponential geometric model proposed by Adamidis and Loukas (1998). The new distribution arises on a latent complementary risks scenario, in which the lifetime associated with a particular risk is not observable; rather, we observe only the maximum lifetime value among all risks. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulas for its reliability and failure rate functions, moments, including the mean and variance, variation coefficient, and modal value. The parameter estimation is based on the usual maximum likelihood approach. We report the results of a misspecification simulation study performed in order to assess the extent of misspecification errors when testing the exponential geometric distribution against our complementary one in the presence of different sample size and censoring percentage. The methodology is illustrated on four real datasets; we also make a comparison between both modeling approaches. (C) 2011 Elsevier B.V. All rights reserved.

Geometric parameters of shoreface profiles of Laptev Sea erosion coast (Table 1)

Field investigations of the Laptev Sea shoreface morphology were carried out (1) off erosional shores composed of unconsolidated sediments, (2) off the modern delta shores of the Lena River, and (3) off rocky shores. It was found that profiles off erosional shores had a concave shape. This shape is not well described by commonly applied power functions, a feature, which is in disagreement with the generally accepted concept of the equilibrium shape of shoreface profiles. The position of the lower shoreface boundary is determined by the elevation of the coastal lowland inundated during the last transgression (at -5 to -10 m) and may easily be recognized by a sharp, an order of magnitude decrease in the mean inclination of the sea floor. The mean shoreface inclination depends on sediment grain-size and ranges from 0.0022 to 0.033. The concave shape of the shoreface did not change substantially during the last 20-30 years, which indicates that shoreline retreat did not slow down and hence suggests continued intensive coastal erosion in the 21st century. The underwater part of the Lena River delta extends up to 35 km offshore. Its upper part is formed by a shallow and up to 18-km wide bench, which reaches depths of 2-3 m along the outer edge. The evolution of the delta was irregular. Whereas some parts of the delta are advancing rapidly (58 m/year), other parts are eroding. Comparison of measured profiles with older bathymetric data gave an opportunity to evaluate the changes of the underwater delta over past decades. Bathymetric surveys of the seabed around the delta can thus contribute towards a quantification of the sediment budget of the river-sea system. In addition, some sections of the Laptev Sea coast are composed of bedrock that has a comparatively low resistance to wave erosion. These sections may supply a considerable amount of sediment, especially if the cliffs are high. This source must therefore also be taken into account when assessing the contribution of shore erosion to the Laptev Sea sediment budget.

Einstein-like geometric structures on surfaces

An AH (affine hypersurface) structure is a pair comprising a projective equivalence class of torsion-free connections and a conformal structure satisfying a compatibility condition which is automatic in two dimensions. They generalize Weyl structures, and a pair of AH structures is induced on a co-oriented non-degenerate immersed hypersurface in flat affine space. The author has defined for AH structures Einstein equations, which specialize on the one hand to the usual Einstein Weyl equations and, on the other hand, to the equations for affine hyperspheres. Here these equations are solved for Riemannian signature AH structures on compact orientable surfaces, the deformation spaces of solutions are described, and some aspects of the geometry of these structures are related. Every such structure is either Einstein Weyl (in the sense defined for surfaces by Calderbank) or is determined by a pair comprising a conformal structure and a cubic holomorphic differential, and so by a convex flat real projective structure. In the latter case it can be identified with a solution of the Abelian vortex equations on an appropriate power of the canonical bundle. On the cone over a surface of genus at least two carrying an Einstein AH structure there are Monge-Amp`ere metrics of Lorentzian and Riemannian signature and a Riemannian Einstein K"ahler affine metric. A mean curvature zero spacelike immersed Lagrangian submanifold of a para-K"ahler four-manifold with constant para-holomorphic sectional curvature inherits an Einstein AH structure, and this is used to deduce some restrictions on such immersions.

Analysis of the geometric altimetry to support aircraft optimal trajectories within the future 4d trajectory management

Over the past few years, the common practice within air traffic management has been that commercial aircraft fly by following a set of predefined routes to reach their destination. Currently, aircraft operators are requesting more flexibility to fly according to their prefer- ences, in order to achieve their business objectives. Due to this reason, much research effort is being invested in developing different techniques which evaluate aircraft optimal trajectory and traffic synchronisation. Also, the inefficient use of the airspace using barometric altitude overall in the landing and takeoff phases or in Continuous Descent Approach (CDA) trajectories where currently it is necessary introduce the necessary reference setting (QNH or QFE). To solve this problem and to permit a better airspace management born the interest of this research. Where the main goals will be to evaluate the impact, weakness and strength of the use of geometrical altitude instead of the use of barometric altitude. Moreover, this dissertation propose the design a simplified trajectory simulator which is able to predict aircraft trajectories. The model is based on a three degrees of freedom aircraft point mass model that can adapt aircraft performance data from Base of Aircraft Data, and meteorological information. A feature of this trajectory simulator is to support the improvement of the strategic and pre-tactical trajectory planning in the future Air Traffic Management. To this end, the error of the tool (aircraft Trajectory Simulator) is measured by comparing its performance variables with actual flown trajectories obtained from Flight Data Recorder information. The trajectory simulator is validated by analysing the performance of different type of aircraft and considering different routes. A fuel consumption estimation error was identified and a correction is proposed for each type of aircraft model. In the future Air Traffic Management (ATM) system, the trajectory becomes the fundamental element of a new set of operating procedures collectively referred to as Trajectory-Based Operations (TBO). Thus, governmental institutions, academia, and industry have shown a renewed interest for the application of trajectory optimisation techniques in com- mercial aviation. The trajectory optimisation problem can be solved using optimal control methods. In this research we present and discuss the existing methods for solving optimal control problems focusing on direct collocation, which has received recent attention by the scientific community. In particular, two families of collocation methods are analysed, i.e., Hermite-Legendre-Gauss-Lobatto collocation and the pseudospectral collocation. They are first compared based on a benchmark case study: the minimum fuel trajectory problem with fixed arrival time. For the sake of scalability to more realistic problems, the different meth- ods are also tested based on a real Airbus 319 El Cairo-Madrid flight. Results show that pseudospectral collocation, which has shown to be numerically more accurate and computa- tionally much faster, is suitable for the type of problems arising in trajectory optimisation with application to ATM. Fast and accurate optimal trajectory can contribute properly to achieve the new challenges of the future ATM. As atmosphere uncertainties are one of the most important issues in the trajectory plan- ning, the final objective of this dissertation is to have a magnitude order of how different is the fuel consumption under different atmosphere condition. Is important to note that in the strategic phase planning the optimal trajectories are determined by meteorological predictions which differ from the moment of the flight. The optimal trajectories have shown savings of at least 500 [kg] in the majority of the atmosphere condition (different pressure, and temperature at Mean Sea Level, and different lapse rate temperature) with respect to the conventional procedure simulated at the same atmosphere condition.This results show that the implementation of optimal profiles are beneficial under the current Air traffic Management (ATM).

A novel phantom and method for comprehensive 3-dimensional measurement and correction of geometric distortion in magnetic resonance imaging

A phantom that can be used for mapping geometric distortion in magnetic resonance imaging (MRI) is described. This phantom provides an array of densely distributed control points in three-dimensional (3D) space. These points form the basis of a comprehensive measurement method to correct for geometric distortion in MR images arising principally from gradient field non-linearity and magnet field inhomogeneity. The phantom was designed based on the concept that a point in space can be defined using three orthogonal planes. This novel design approach allows for as many control points as desired. Employing this novel design, a highly accurate method has been developed that enables the positions of the control points to be measured to sub-voxel accuracy. The phantom described in this paper was constructed to fit into a body coil of a MRI scanner, (external dimensions of the phantom were: 310 mm x 310 mm x 310 mm), and it contained 10,830 control points. With this phantom, the mean errors in the measured coordinates of the control points were on the order of 0.1 mm or less, which were less than one tenth of the voxel's dimensions of the phantom image. The calculated three-dimensional distortion map, i.e., the differences between the image positions and true positions of the control points, can then be used to compensate for geometric distortion for a full image restoration. It is anticipated that this novel method will have an impact on the applicability of MRI in both clinical and research settings. especially in areas where geometric accuracy is highly required, such as in MR neuro-imaging. (C) 2004 Elsevier Inc. All rights reserved.

Geometric distortion in clinical MRI systems - Part II: correction using a 3D phantom

In this paper, we present the correction of the geometric distortion measured in the clinical magnetic resonance imaging (MRI) systems reported in the preceding paper (Part 1) using a 3D method based on the phantom-mapped geometric distortion data. This method allows the correction to be made on phantom images acquired without or with the vendor correction applied. With the vendor's 2D correction applied, the method corrects for both the residual geometric distortion still present in the plane in which the correction method was applied (the axial plane) and the uncorrected geometric distortion along the axis non-nal to the plane. The evaluation of the effectiveness of the correction using this new method was carried out through analyzing the residual geometric distortion in the corrected phantom images. The results show that the new method can restore the distorted images in 3D nearly to perfection. For all the MRI systems investigated, the mean absolute deviations in the positions of the control points (along x-, y- and z-axes) measured on the corrected phantom images were all less than 0.2 mm. The maximum absolute deviations were all below similar to0.8 mm. As expected, the correction of the phantom images acquired with the vendor's correction applied in the axial plane performed equally well. Both the geometric distortion still present in the axial plane after applying the vendor's correction and the uncorrected distortion along the z-axis have all been restored. (C) 2004 Elsevier Inc. All rights reserved.

Local geometric changes in left ventricular remodeling post-infarction can lead to apparent reduction in scar thickness

Serial reduction in scar thickness has been shown in animal models. We sought whether this reduction in scar thickness may be a result of dilatation of the left ventricle (LV) with stretching and thinning of the wall. Contrast enhanced magnetic resonance imaging (CMRI) was performed to delineate radial scar thickness in 25 patients (age 63±10, 21 men) after myocardial infarction. The LV was divided into 16 segts and the absolute radial scar thickness (ST) and percentage scar to total wall thickness (%ST) were measured. Regional end diastolic (EDV) and end systolic volumes (ESV) of corresponding segments were measured on CMRI. All patients underwent revascularization and serial changes in ST, %ST, and regional volumes were assessed with a mean follow up of 15±5 months. CMRI identified a total of 93 scar segments. An increase in EDV or ESV was associated with a serial reduction inST(versusEDV, r =−0.3, p = 0.01; versusESV, r =−0.3, p = 0.005) and%ST(versusEDV, r =−0.2, p = 0.04; versus ESV, r =−0.3, p = 0.001). For segts associated with a positive increase in EDV (group I) or ESV (group II) there was a significant decrease in ST and %ST, but in those segts with stable EDV (group III) or ESV (group IV) there were no significant changes in ST and %ST (Table).

Information geometric measurements of generalisation

Neural networks can be regarded as statistical models, and can be analysed in a Bayesian framework. Generalisation is measured by the performance on independent test data drawn from the same distribution as the training data. Such performance can be quantified by the posterior average of the information divergence between the true and the model distributions. Averaging over the Bayesian posterior guarantees internal coherence; Using information divergence guarantees invariance with respect to representation. The theory generalises the least mean squares theory for linear Gaussian models to general problems of statistical estimation. The main results are: (1)~the ideal optimal estimate is always given by average over the posterior; (2)~the optimal estimate within a computational model is given by the projection of the ideal estimate to the model. This incidentally shows some currently popular methods dealing with hyperpriors are in general unnecessary and misleading. The extension of information divergence to positive normalisable measures reveals a remarkable relation between the dlt dual affine geometry of statistical manifolds and the geometry of the dual pair of Banach spaces Ld and Ldd. It therefore offers conceptual simplification to information geometry. The general conclusion on the issue of evaluating neural network learning rules and other statistical inference methods is that such evaluations are only meaningful under three assumptions: The prior P(p), describing the environment of all the problems; the divergence Dd, specifying the requirement of the task; and the model Q, specifying available computing resources.