Stable linearization using multilayer neural networks

The main limitation of linearization theory that prevents its application in practical problems is the need for an exact knowledge of the plant. This requirement is eliminated and it is shown that a multilayer network can synthesise the state feedback coefficients that linearize a nonlinear control affine plant. The stability of the linearizing closed loop can be guaranteed if the autonomous plant is asymptotically stable and the state feedback is bounded.

Optimal linearization trajectories for tangent linear models

We examine differential equations where nonlinearity is a result of the advection part of the total derivative or the use of quadratic algebraic constraints between state variables (such as the ideal gas law). We show that these types of nonlinearity can be accounted for in the tangent linear model by a suitable choice of the linearization trajectory. Using this optimal linearization trajectory, we show that the tangent linear model can be used to reproduce the exact nonlinear error growth of perturbations for more than 200 days in a quasi-geostrophic model and more than (the equivalent of) 150 days in the Lorenz 96 model. We introduce an iterative method, purely based on tangent linear integrations, that converges to this optimal linearization trajectory. The main conclusion from this article is that this iterative method can be used to account for nonlinearity in estimation problems without using the nonlinear model. We demonstrate this by performing forecast sensitivity experiments in the Lorenz 96 model and show that we are able to estimate analysis increments that improve the two-day forecast using only four backward integrations with the tangent linear model. Copyright © 2011 Royal Meteorological Society

Precision of fit and retention force of cast non-precious-crowns on standard titanium implant-abutment with different design and height

OBJECTIVE The cost-effectiveness of cast nonprecious frameworks has increased their prevalence in cemented implant crowns. The purpose of this study was to assess the effect of the design and height of the retentive component of a standard titanium implant abutment on the fit, possible horizontal rotation and retention forces of cast nonprecious alloy crowns prior to cementation. MATERIALS AND METHODS Two abutment designs were examined: Type A with a 6° taper and 8 antirotation planes (Straumann Tissue-Level RN) and Type B with a 7.5° taper and 1 antirotation plane (SICace implant). Both types were analyzed using 60 crowns: 20 with a full abutment height (6 mm), 20 with a medium abutment height (4 mm), and 20 with a minimal (2.5 mm) abutment height. The marginal and internal fit and the degree of possible rotation were evaluated by using polyvinylsiloxane impressions under a light microscope (magnification of ×50). To measure the retention force, a custom force-measuring device was employed. STATISTICAL ANALYSIS one-sided Wilcoxon rank-sum tests with Bonferroni-Holm corrections, Fisher's exact tests, and Spearman's rank correlation coefficient. RESULTS Type A exhibited increased marginal gaps (primary end-point: 55 ± 20 μm vs. 138 ± 59 μm, P < 0.001) but less rotation (P < 0.001) than Type B. The internal fit was also better for Type A than for Type B (P < 0.001). The retention force of Type A (2.49 ± 3.2 N) was higher (P = 0.019) than that of Type B (1.27 ± 0.84 N). Reduction in abutment height did not affect the variables observed. CONCLUSION Less-tapered abutments with more antirotation planes provide an increase in the retention force, which confines the horizontal rotation but widens the marginal gaps of the crowns. Thus, casting of nonprecious crowns with Type A abutments may result in clinically unfavorable marginal gaps.

Exact Unification and Admissibility

A new hierarchy of "exact" unification types is introduced, motivated by the study of admissible rules for equational classes and non-classical logics. In this setting, unifiers of identities in an equational class are preordered, not by instantiation, but rather by inclusion over the corresponding sets of unified identities. Minimal complete sets of unifiers under this new preordering always have a smaller or equal cardinality than those provided by the standard instantiation preordering, and in significant cases a dramatic reduction may be observed. In particular, the classes of distributive lattices, idempotent semigroups, and MV-algebras, which all have nullary unification type, have unitary or finitary exact type. These results are obtained via an algebraic interpretation of exact unification, inspired by Ghilardi's algebraic approach to equational unification.

Laminar counterflow parallel-plate heat exchangers: Exact and approximate solutions

Multilayered, counterflow, parallel-plate heat exchangers are analyzed numerically and theoretically. The analysis, carried out for constant property fluids, considers a hydrodynamically developed laminar flow and neglects longitudinal conduction both in the fluid and in the plates. The solution for the temperature field involves eigenfunction expansions that can be solved in terms of Whittaker functions using standard symbolic algebra packages, leading to analytical expressions that provide the eigenvalues numerically. It is seen that the approximate solution obtained by retaining the first two modes in the eigenfunction expansion provides an accurate representation for the temperature away from the entrance regions, specially for long heat exchangers, thereby enabling simplified expressions for the wall and bulk temperatures, local heat-transfer rate, overall heat-transfer coefficient, and outlet bulk temperatures. The agreement between the numerical and theoretical results suggests the possibility of using the analytical solutions presented herein as benchmark problems for computational heat-transfer codes.

Introducing the Logarithmic finite element method: a geometrically exact planar Bernoulli beam element

We propose a novel finite element formulation that significantly reduces the number of degrees of freedom necessary to obtain reasonably accurate approximations of the low-frequency component of the deformation in boundary-value problems. In contrast to the standard Ritz–Galerkin approach, the shape functions are defined on a Lie algebra—the logarithmic space—of the deformation function. We construct a deformation function based on an interpolation of transformations at the nodes of the finite element. In the case of the geometrically exact planar Bernoulli beam element presented in this work, these transformation functions at the nodes are given as rotations. However, due to an intrinsic coupling between rotational and translational components of the deformation function, the formulation provides for a good approximation of the deflection of the beam, as well as of the resultant forces and moments. As both the translational and the rotational components of the deformation function are defined on the logarithmic space, we propose to refer to the novel approach as the “Logarithmic finite element method”, or “LogFE” method.

Quantum integrability as a new method for exact results on N=2 supersymmetric gauge theories and black holes

In this thesis I show a triple new connection we found between quantum integrability, N=2 supersymmetric gauge theories and black holes perturbation theory. I use the approach of the ODE/IM correspondence between Ordinary Differential Equations (ODE) and Integrable Models (IM), first to connect basic integrability functions - the Baxter’s Q, T and Y functions - to the gauge theory periods. This fundamental identification allows several new results for both theories, for example: an exact non linear integral equation (Thermodynamic Bethe Ansatz, TBA) for the gauge periods; an interpretation of the integrability functional relations as new exact R-symmetry relations for the periods; new formulas for the local integrals of motion in terms of gauge periods. This I develop in all details at least for the SU(2) gauge theory with Nf=0,1,2 matter flavours. Still through to the ODE/IM correspondence, I connect the mathematically precise definition of quasinormal modes of black holes (having an important role in gravitational waves’ obervations) with quantization conditions on the Q, Y functions. In this way I also give a mathematical explanation of the recently found connection between quasinormal modes and N=2 supersymmetric gauge theories. Moreover, it follows a new simple and effective method to numerically compute the quasinormal modes - the TBA - which I compare with other standard methods. The spacetimes for which I show these in all details are in the simplest Nf=0 case the D3 brane in the Nf=1,2 case a generalization of extremal Reissner-Nordström (charged) black holes. Then I begin treating also the Nf=3,4 theories and argue on how our integrability-gauge-gravity correspondence can generalize to other types of black holes in either asymptotically flat (Nf=3) or Anti-de-Sitter (Nf=4) spacetime. Finally I begin to show the extension to a 4-fold correspondence with also Conformal Field Theory (CFT), through the renowned AdS/CFT correspondence.

Biased Random-key Genetic Algorithms For The Winner Determination Problem In Combinatorial Auctions.

Abstract In this paper, we address the problem of picking a subset of bids in a general combinatorial auction so as to maximize the overall profit using the first-price model. This winner determination problem assumes that a single bidding round is held to determine both the winners and prices to be paid. We introduce six variants of biased random-key genetic algorithms for this problem. Three of them use a novel initialization technique that makes use of solutions of intermediate linear programming relaxations of an exact mixed integer-linear programming model as initial chromosomes of the population. An experimental evaluation compares the effectiveness of the proposed algorithms with the standard mixed linear integer programming formulation, a specialized exact algorithm, and the best-performing heuristics proposed for this problem. The proposed algorithms are competitive and offer strong results, mainly for large-scale auctions.

A Feasibility Study Of Fricke Dosimetry As An Absorbed Dose To Water Standard For 192ir Hdr Sources.

High dose rate brachytherapy (HDR) using 192Ir sources is well accepted as an important treatment option and thus requires an accurate dosimetry standard. However, a dosimetry standard for the direct measurement of the absolute dose to water for this particular source type is currently not available. An improved standard for the absorbed dose to water based on Fricke dosimetry of HDR 192Ir brachytherapy sources is presented in this study. The main goal of this paper is to demonstrate the potential usefulness of the Fricke dosimetry technique for the standardization of the quantity absorbed dose to water for 192Ir sources. A molded, double-walled, spherical vessel for water containing the Fricke solution was constructed based on the Fricke system. The authors measured the absorbed dose to water and compared it with the doses calculated using the AAPM TG-43 report. The overall combined uncertainty associated with the measurements using Fricke dosimetry was 1.4% for k = 1, which is better than the uncertainties reported in previous studies. These results are promising; hence, the use of Fricke dosimetry to measure the absorbed dose to water as a standard for HDR 192Ir may be possible in the future.

Nasal Potential Difference In Cystic Fibrosis Considering Severe Cftr Mutations.

The gold standard for diagnosing cystic fibrosis (CF) is a sweat chloride value above 60 mEq/L. However, this historical and important tool has limitations; other techniques should be studied, including the nasal potential difference (NPD) test. CFTR gene sequencing can identify CFTR mutations, but this method is time-consuming and too expensive to be used in all CF centers. The present study compared CF patients with two classes I-III CFTR mutations (10 patients) (G1), CF patients with classes IV-VI CFTR mutations (five patients) (G2), and 21 healthy subjects (G3). The CF patients and healthy subjects also underwent the NPD test. A statistical analysis was performed using the Mann-Whitney, Kruskal-Wallis, χ(2), and Fisher's exact tests, α = 0.05. No differences were observed between the CF patients and healthy controls for the PDMax, Δamiloride, and Δchloride + free + amiloride markers from the NPD test. For the finger value, a difference between G2 and G3 was described. The Wilschanski index values were different between G1 and G3. In conclusion, our data showed that NPD is useful for CF diagnosis when classes I-III CFTR mutations are screened. However, if classes IV-VI are considered, the NPD test showed an overlap in values with healthy subjects.

Linearization of Chains and Sideward Movement

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Sensitivity and specificity of machine learning classifiers for glaucoma diagnosis using Spectral Domain OCT and standard automated perimetry

PURPOSE: To evaluate the sensitivity and specificity of machine learning classifiers (MLCs) for glaucoma diagnosis using Spectral Domain OCT (SD-OCT) and standard automated perimetry (SAP). METHODS: Observational cross-sectional study. Sixty two glaucoma patients and 48 healthy individuals were included. All patients underwent a complete ophthalmologic examination, achromatic standard automated perimetry (SAP) and retinal nerve fiber layer (RNFL) imaging with SD-OCT (Cirrus HD-OCT; Carl Zeiss Meditec Inc., Dublin, California). Receiver operating characteristic (ROC) curves were obtained for all SD-OCT parameters and global indices of SAP. Subsequently, the following MLCs were tested using parameters from the SD-OCT and SAP: Bagging (BAG), Naive-Bayes (NB), Multilayer Perceptron (MLP), Radial Basis Function (RBF), Random Forest (RAN), Ensemble Selection (ENS), Classification Tree (CTREE), Ada Boost M1(ADA),Support Vector Machine Linear (SVML) and Support Vector Machine Gaussian (SVMG). Areas under the receiver operating characteristic curves (aROC) obtained for isolated SAP and OCT parameters were compared with MLCs using OCT+SAP data. RESULTS: Combining OCT and SAP data, MLCs' aROCs varied from 0.777(CTREE) to 0.946 (RAN).The best OCT+SAP aROC obtained with RAN (0.946) was significantly larger the best single OCT parameter (p<0.05), but was not significantly different from the aROC obtained with the best single SAP parameter (p=0.19). CONCLUSION: Machine learning classifiers trained on OCT and SAP data can successfully discriminate between healthy and glaucomatous eyes. The combination of OCT and SAP measurements improved the diagnostic accuracy compared with OCT data alone.

Study of C- and O-glycosylflavones in sugarcane extracts using liquid chromatography: exact mass measurement mass spectrometry

The flavonoids present in sugarcane (Saccharum officinarum) extracts were analyzed by liquid chromatography - mass spectrometry (LC-MS), and a study of the fragmentation patterns of selected flavonoids was conducted using orthogonal acceleration time-of-flight electrospray ionization mass spectrometry (ESI-oa-ToF MS). Seven C- and O-glycosylflavones were identified in the extracts, namely, schaftoside, isoschaftoside, luteolin-8-C-(rhamnosylglucoside), vitexin, orientin, tricin-7-O-neohesperidoside and tricin-7-O-glucoside. Of these, five were identified in the absence of direct comparison with their respective standards. The described method also permitted the differentiation of the 6-C and 8-C isomeric flavones, schaftoside and isoschaftoside. The combination of fragmentation data and exact mass measurement showed to be complimentary to the HPLC-UV-MS techniques previously utilized for isomers discrimination in sugarcane studies.

Exact time-dependent solutions for a self-regulating gene

The exact time-dependent solution for the stochastic equations governing the behavior of a binary self-regulating gene is presented. Using the generating function technique to rephrase the master equations in terms of partial differential equations, we show that the model is totally integrable and the analytical solutions are the celebrated confluent Heun functions. Self-regulation plays a major role in the control of gene expression, and it is remarkable that such a microscopic model is completely integrable in terms of well-known complex functions.