On the Filtering Problem for Continuous-Time Markov Jump Linear Systems with no Observation of the Markov Chain

We consider in this paper the optimal stationary dynamic linear filtering problem for continuous-time linear systems subject to Markovian jumps in the parameters (LSMJP) and additive noise (Wiener process). It is assumed that only an output of the system is available and therefore the values of the jump parameter are not accessible. It is a well known fact that in this setting the optimal nonlinear filter is infinite dimensional, which makes the linear filtering a natural numerically, treatable choice. The goal is to design a dynamic linear filter such that the closed loop system is mean square stable and minimizes the stationary expected value of the mean square estimation error. It is shown that an explicit analytical solution to this optimal filtering problem is obtained from the stationary solution associated to a certain Riccati equation. It is also shown that the problem can be formulated using a linear matrix inequalities (LMI) approach, which can be extended to consider convex polytopic uncertainties on the parameters of the possible modes of operation of the system and on the transition rate matrix of the Markov process. As far as the authors are aware of this is the first time that this stationary filtering problem (exact and robust versions) for LSMJP with no knowledge of the Markov jump parameters is considered in the literature. Finally, we illustrate the results with an example.

Some remarks on static-feedback linearization for time-varying systems

This work summarizes some results about static state feedback linearization for time-varying systems. Three different necessary and sufficient conditions are stated in this paper. The first condition is the one by [Sluis, W. M. (1993). A necessary condition for dynamic feedback linearization. Systems & Control Letters, 21, 277-283]. The second and the third are the generalizations of known results due respectively to [Aranda-Bricaire, E., Moog, C. H., Pomet, J. B. (1995). A linear algebraic framework for dynamic feedback linearization. IEEE Transactions on Automatic Control, 40, 127-132] and to [Jakubczyk, B., Respondek, W. (1980). On linearization of control systems. Bulletin del` Academie Polonaise des Sciences. Serie des Sciences Mathematiques, 28, 517-522]. The proofs of the second and third conditions are established by showing the equivalence between these three conditions. The results are re-stated in the infinite dimensional geometric approach of [Fliess, M., Levine J., Martin, P., Rouchon, P. (1999). A Lie-Backlund approach to equivalence and flatness of nonlinear systems. IEEE Transactions on Automatic Control, 44(5), 922-937]. (C) 2008 Elsevier Ltd. All rights reserved.

Pitfalls driven by the sole use of local updates in dynamical

The recent claim that the exit probability (EP) of a slightly modified version of the Sznadj model is a continuous function of the initial magnetization is questioned. This result has been obtained analytically and confirmed by Monte Carlo simulations, simultaneously and independently by two different groups (EPL, 82 (2008) 18006; 18007). It stands at odds with an earlier result which yielded a step function for the EP (Europhys. Lett., 70 (2005) 705). The dispute is investigated by proving that the continuous shape of the EP is a direct outcome of a mean-field treatment for the analytical result. As such, it is most likely to be caused by finite-size effects in the simulations. The improbable alternative would be a signature of the irrelevance of fluctuations in this system. Indeed, evidence is provided in support of the stepwise shape as going beyond the mean-field level. These findings yield new insight in the physics of one-dimensional systems with respect to the validity of a true equilibrium state when using solely local update rules. The suitability and the significance to perform numerical simulations in those cases is discussed. To conclude, a great deal of caution is required when applying updates rules to describe any system especially social systems. Copyright (C) EPLA, 2011

Violet ZnSe/ZnS as an Alternative to Green CdSe/ZnS in Nanocrystal-Fluorescent Protein FRET Systems

Fluorescent proteins from the green fluorescent protein family strongly interact with CdSe/ZnS and ZnSe/ZnS nanocrystals at neutral pH. Green emitting CdSe/ZnS nanocrystals and red emitting fluorescent protein dTomato constitute a 72% efficiency FRET system with the largest alteration of the overall photoluminescence profile, following complex formation, observed so far. The substitution of ZnSe/ZnS for CdSe/ZnS nanocrystals as energy donors enabled the use of a green fluorescent protein, GFP5, as energy acceptor. Violet emitting ZnSe/ZnS nanocrystals and green GFP5 constitute a system with 43% FRET efficiency and an unusually strong sensitized emission. ZnSe/ZnS-GFP5 provides a cadmium-free, high-contrast FRET system that covers only the high-energy part of the visible spectrum, leaving room for simultaneous use of the yellow and red color channels. Anisotropic fluorescence measurements confirmed the depolarization of GFP5 sensitized emission.

Penetration of Quantum Dot Particles Through Human Skin

The skin is a large and accessible area of the body, offering the possibility to be used as an alternative route for drug delivery. In the last few years strong progress has been made on the developing of nanoparticulate systems for specific applications. The interaction of such small particles with human skin and their possible penetration attracted some interest from toxicological as well as from drug delivery perspectives. As size is assumed to play a key role, the aim of the present work was to investigate the penetration profile of very small model particles (similar to 4 nm) into excised human skin under conditions chosen to mimic the in vivo situation. Possible application procedures such as massaging the formulation (5 to 10 minutes) were analyzed by non-invasive multiphoton- and confocal laser scanning microscopy (MPM, CLSM). Furthermore, the application on damaged skin was taken into account by deliberately removing parts of the stratum corneum. Although it was clearly observed that the mechanical actions affected the distribution pattern of the QDs on the skin surface, there was no evidence of penetration into the skin in all cases tested. QDs could be found in deeper layers only after massaging of damaged skin for 10 min. Taking these data into account, obtained on the gold standard human skin, the potential applications of nanoparticulate systems to act as carrier delivering drugs into intact skin might be limited and are only of interest for partly damaged skin.

Asymptotic behaviour of two-dimensional time-delayed Navier-Stokes equations

We consider the two-dimensional Navier-Stokes equations with a time-delayed convective term and a forcing term which contains some hereditary features. Some results on existence and uniqueness of solutions are established. We discuss the asymptotic behaviour of solutions and we also show the exponential stability of stationary solutions.

Loss of Ergodicity in the Transition from Annealed to Quenched Disorder in a Finite Kinetic Ising Model

We consider a kinetic Ising model which represents a generic agent-based model for various types of socio-economic systems. We study the case of a finite (and not necessarily large) number of agents N as well as the asymptotic case when the number of agents tends to infinity. The main ingredient are individual decision thresholds which are either fixed over time (corresponding to quenched disorder in the Ising model, leading to nonlinear deterministic dynamics which are generically non-ergodic) or which may change randomly over time (corresponding to annealed disorder, leading to ergodic dynamics). We address the question how increasing the strength of annealed disorder relative to quenched disorder drives the system from non-ergodic behavior to ergodicity. Mathematically rigorous analysis provides an explicit and detailed picture for arbitrary realizations of the quenched initial thresholds, revealing an intriguing ""jumpy"" transition from non-ergodicity with many absorbing sets to ergodicity. For large N we find a critical strength of annealed randomness, above which the system becomes asymptotically ergodic. Our theoretical results suggests how to drive a system from an undesired socio-economic equilibrium (e. g. high level of corruption) to a desirable one (low level of corruption).

Standard Values for Real-Time Transthoracic Three-Dimensional Echocardiographic Dyssynchrony Indexes in a Normal Population

Background: There is a paucity of information describing the real-time 3-dimensional echocardiography (RT3DE) and dyssynchrony indexes (DIs) of a normal population. We evaluate the RT3DE DIs in a population with normal electrocardiograms and 2- and 3-dimensional echocardiographic analyses. This information is relevant for cardiac resynchronization therapy. Methods: We evaluated 131 healthy volunteers (73 were male, aged 46 +/- 14 years) who were referred for routine echocardiography; who presented normal cardiac structure on electrocardiography, 2-dimensional echocardiography, and RT3DE; and who had no history of cardiac diseases. We analyzed 3-dimensional left ventricular ejection fraction, left ventricle end-diastolic volume, left ventricle end-systolic volume, and left ventricular systolic DI% (6-, 12-, and 16-segment models). RT3DE data were analyzed by quantifying the statistical distribution (mean, median, standard deviation [SD], relative SD, coefficient of skewness, coefficient of kurtosis, Kolmogorov-Smirnov test, D`Agostino-Pearson test, percentiles, and 95% confidence interval). Results: Left ventricular ejection fraction ranged from 50% to 80% (66.1% +/- 7.1%); left ventricle end-diastolic volume ranged from 39.8 to 145 mL (79.1 +/- 24.9 mL); left ventricle end-systolic volume ranged from 12.9 to 66 mL (27 +/- 12.1 mL); 6-segment DI% ranged from 0.20% to 3.80% (1.21% +/- 0.66%), median: 1.06, relative SD: 0.5482, coefficient of skewness: 1.2620 (P < .0001), coefficient of Kurtosis: 1.9956 (P = .0039); percentile 2.5%: 0.2900, percentile 97.5%: 2.8300; 12-segment DI% ranged from 0.22% to 4.01% (1.29% +/- 0.71%), median: 1.14, relative SD: 0.95, coefficient of skewness: 1.1089 (P < .0001), coefficient of Kurtosis: 1.6372 (P = .0100), percentile 2.5%: 0.2850, percentile 97.5%: 3.0700; and 16-segment DI% ranged from 0.29% to 4.88% (1.59 +/- 0.99), median: 1.39, relative SD: 0.56, coefficient of skewness: 1.0792 (P < .0001), coefficient of Kurtosis: 0.9248 (P = .07), percentile 2.5%: 0.3750, percentile 97.5%: 3.750. Conclusion: This study allows for the quantification of RT3DE DIs in normal subjects, providing a comparison for patients with heart failure who may be candidates for cardiac resynchronization therapy. (J Am Soc Echocardiogr 2008; 21: 1229-1235)

Value of real time three-dimensional echocardiography in patients with hypertrophic cardiomyopathy: Comparison with two-dimensional echocardiography and magnetic resonance imaging

Real time three-dimensional echocardiography (RT3DE) has been demonstrated to be an accurate technique to quantify left ventricular (LV) volumes and function in different patient populations. We sought to determine the value of RT3DE for evaluating patients with hypertrophic cardiomyopathy (HCM), in comparison with cardiac magnetic resonance imaging (MRI). Methods: We studied 20 consecutive patients with HCM who underwent two-dimensional echocardiography (2DE), RT3DE, and MRI. Parameters analyzed by echocardiography and MRI included: wall thickness, LV volumes, ejection fraction (LVEF), mass, geometric index, and dyssynchrony index. Statistical analysis was performed by Lin agreement coefficient, Pearson linear correlation and Bland-Altman model. Results: There was excellent agreement between 2DE and RT3DE (Rc = 0.92), 2DE and MRI (Rc = 0.85), and RT3DE and MRI (Rc = 0.90) for linear measurements. Agreement indexes for LV end-diastolic and end-systolic volumes were Rc = 0.91 and Rc = 0.91 between 2DE and RT3DE, Rc = 0.94 and Rc = 0.95 between RT3DE and MRI, and Rc = 0.89 and Rc = 0.88 between 2DE and MRI, respectively. Satisfactory agreement was observed between 2DE and RT3DE (Rc = 0.75), RT3DE and MRI (Rc = 0.83), and 2DE and MRI (Rc = 0.73) for determining LVEF, with a mild underestimation of LVEF by 2DE, and smaller variability between RT3DE and MRI. Regarding LV mass, excellent agreement was observed between RT3DE and MRI (Rc = 0.96), with bias of -6.3 g (limits of concordance = 42.22 to -54.73 g). Conclusion: In patients with HCM, RT3DE demonstrated superior performance than 2DE for the evaluation of myocardial hypertrophy, LV volumes, LVEF, and LV mass.

Three-dimensional electrical impedance, tomography: A topology optimization approach

Electrical impedance tomography is a technique to estimate the impedance distribution within a domain, based on measurements on its boundary. In other words, given the mathematical model of the domain, its geometry and boundary conditions, a nonlinear inverse problem of estimating the electric impedance distribution can be solved. Several impedance estimation algorithms have been proposed to solve this problem. In this paper, we present a three-dimensional algorithm, based on the topology optimization method, as an alternative. A sequence of linear programming problems, allowing for constraints, is solved utilizing this method. In each iteration, the finite element method provides the electric potential field within the model of the domain. An electrode model is also proposed (thus, increasing the accuracy of the finite element results). The algorithm is tested using numerically simulated data and also experimental data, and absolute resistivity values are obtained. These results, corresponding to phantoms with two different conductive materials, exhibit relatively well-defined boundaries between them, and show that this is a practical and potentially useful technique to be applied to monitor lung aeration, including the possibility of imaging a pneumothorax.

One-dimensional point interaction with three complex parameters

For a pair of non-Hermitian Hamiltonian H and its Hermitian adjoint H(dagger), there are situations in which their eigenfunctions form a biorthogonal system. We illustrate such a situation by means of a one-particle system with a one-dimensional point interaction in the form of the Fermi pseudo-potential. The interaction consists of three terms with three strength parameters g(i) (i = 1, 2 and 3), which are all complex. This complex point interaction is neither Hermitian nor PT-invariant in general. The S-matrix for the transmission reflection problem constructed with H (or with H(dagger)) in the usual manner is not unitary, but it conforms to the pseudo-unitarity that we define. The pseudounitarity is closely related to the biorthogonality of the eigenfunctions. The eigenvalue spectrum of H with the complex interaction is generally complex but there are cases where the spectrum is real. In such a case H and H(dagger) form a pseudo-Hermitian pair.

Renormalizing the kinetic energy operator in elementary quantum mechanics

In this paper, we consider solutions to the three-dimensional Schrodinger equation of the form psi(r) = u(r)/r, where u(0) not equal 0. The expectation value of the kinetic energy operator for such wavefunctions diverges. We show that it is possible to introduce a potential energy with an expectation value that also diverges, exactly cancelling the kinetic energy divergence. This renormalization procedure produces a self-adjoint Hamiltonian. We solve some problems with this new Hamiltonian to illustrate its usefulness.

Measuring Bond Strength Between Fiber Post and Root Dentin: A Comparison of Different Tests

Purpose The aim of this study was to evaluate the ability of bond strength tests to accurately measure the bond strength of fiber posts luted into root canals Materials and Methods The test methods studied were hourglass microtensile (HM), push-out (PS), modified push out (MP) and pull out (PL) The evaluated parameters were bond strength values, reliability (using Weibull analysis), failure mode (using confocal microscopy), and stress distribution (using finite element analysis) Forty human intact single rooted and endodontically treated teeth were divided into four groups Each group was assigned one of the test methods The samples in the HM and PS groups were 1 0 +/- 0 1 mm thick, the HM samples were hourglass shaped and the PS samples were disk shaped For the PL and MP groups, each 1 mm dentin slice was luted with a fiber post piece Three dimensional models of each group were made and stress was analyzed based on Von Mises criteria Results PL provided the highest values of bond strength followed by MP both of which also had greater amounts of adhesive failures PS showed the highest frequency of cohesive failures MP showed a more homogeneous stress distribution and a higher Weibull modulus Conclusion The specimen design directly influences the biomechanical behavior of bond strength tests

Vertical Root Fracture in Upper Premolars with Endodontic Posts: Finite Element Analysis

Upper premolars restored with endodontic posts present a high incidence of vertical root fracture (VRF). Two hypotheses were tested: (1) the smaller mesiodistal diameter favors stress concentration in the root and (2) the lack of an effective bonding between root and post increases the risk of VRF. Using finite element analysis, maximum principal stress was analyzed in 3-dimensional intact upper second premolar models. From the intact models, new models were built including endodontic posts of different elastic modulus (E = 37 or E = 200 GPa) with circular or oval cross-section, either bonded or nonbonded to circular or oval cross-section root canals. The first hypothesis was partially confirmed because the conditions involving nonbonded, low-modulus posts showed lower tensile stress for oval canals compared to circular canals. Tensile stress peaks for the nonbonded models were approximately three times higher than for the bonded or intact models, therefore confirming the second hypothesis. (J Endod 2009;35:117-120)

The suitability of different FEA models for studying root fractures caused by wedge effect

Finite element analysis (FEA) utilizing models with different levels of complexity are found in the literature to study the tendency to vertical root fracture caused by post intrusion (""wedge effect""). The objective of this investigation was to verify if some simplifications used in bi-dimensional FEA models are acceptable regarding the analysis of stresses caused by wedge effect. Three plane strain (PS) and two axisymmtric (Axi) models were studied. One PS model represented the apical third of the root entirely, in dentin (PS-nG). The other models included gutta-percha in the apical third, and differed regarding dentin-post relationship: bonded (PS-B and Axi-B) or nonbonded (PS-nB and Axi-nB). Mesh discretization and material properties were similar for all cases. Maximum principal stress (sigma(max)) was analyzed as a response to a 165 N longitudinal load. Stress magnitude and orientation varied widely (PS-nG: 10.3 MPa; PS-B: 0.8 MPa; PS-nB: 10.4 MPa; Axi-13: 0.2 MPa, Axi-nB: 10.8 MPa). Axi-nB was the only model where all (sigma(max) vectors at the apical third were perpendicular to the model plane. Therefore, it is adequate to demonstrate the tendency to vertical root fractures caused by wedge effect. Axi-13 showed only part of the (sigma(max) perpendicular to the model plane while PS models showed sigma(max) on the model plane. In these models, sigma(max) orientation did not represent a situation where vertical root fracture would occur due to wedge effect. Adhesion between post and dentin significantly reduced (c) 2007 Wiley Periodicals, Inc.