Exact Search Directions for Optimization of Linear and Nonlinear Models Based on Generalized Orthonormal Functions

A novel technique for selecting the poles of orthonormal basis functions (OBF) in Volterra models of any order is presented. It is well-known that the usual large number of parameters required to describe the Volterra kernels can be significantly reduced by representing each kernel using an appropriate basis of orthonormal functions. Such a representation results in the so-called OBF Volterra model, which has a Wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a nonlinear static mapping given by the Volterra polynomial series. Aiming at optimizing the poles that fully parameterize the orthonormal bases, the exact gradients of the outputs of the orthonormal filters with respect to their poles are computed analytically by using a back-propagation-through-time technique. The expressions relative to the Kautz basis and to generalized orthonormal bases of functions (GOBF) are addressed; the ones related to the Laguerre basis follow straightforwardly as a particular case. The main innovation here is that the dynamic nature of the OBF filters is fully considered in the gradient computations. These gradients provide exact search directions for optimizing the poles of a given orthonormal basis. Such search directions can, in turn, be used as part of an optimization procedure to locate the minimum of a cost-function that takes into account the error of estimation of the system output. The Levenberg-Marquardt algorithm is adopted here as the optimization procedure. Unlike previous related work, the proposed approach relies solely on input-output data measured from the system to be modeled, i.e., no information about the Volterra kernels is required. Examples are presented to illustrate the application of this approach to the modeling of dynamic systems, including a real magnetic levitation system with nonlinear oscillatory behavior.

Semiclassical evolution of dissipative Markovian systems

A semiclassical approximation for an evolving density operator, driven by a `closed` Hamiltonian operator and `open` Markovian Lindblad operators, is obtained. The theory is based on the chord function, i.e. the Fourier transform of the Wigner function. It reduces to an exact solution of the Lindblad master equation if the Hamiltonian operator is a quadratic function and the Lindblad operators are linear functions of positions and momenta. Initially, the semiclassical formulae for the case of Hermitian Lindblad operators are reinterpreted in terms of a (real) double phase space, generated by an appropriate classical double Hamiltonian. An extra `open` term is added to the double Hamiltonian by the non-Hermitian part of the Lindblad operators in the general case of dissipative Markovian evolution. The particular case of generic Hamiltonian operators, but linear dissipative Lindblad operators, is studied in more detail. A Liouville-type equivariance still holds for the corresponding classical evolution in double phase space, but the centre subspace, which supports the Wigner function, is compressed, along with expansion of its conjugate subspace, which supports the chord function. Decoherence narrows the relevant region of double phase space to the neighbourhood of a caustic for both the Wigner function and the chord function. This difficulty is avoided by a propagator in a mixed representation, so that a further `small-chord` approximation leads to a simple generalization of the quadratic theory for evolving Wigner functions.

A linear optimization approach to the combined production planning model

Two fundamental processes usually arise in the production planning of many industries. The first one consists of deciding how many final products of each type have to be produced in each period of a planning horizon, the well-known lot sizing problem. The other process consists of cutting raw materials in stock in order to produce smaller parts used in the assembly of final products, the well-studied cutting stock problem. In this paper the decision variables of these two problems are dependent of each other in order to obtain a global optimum solution. Setups that are typically present in lot sizing problems are relaxed together with integer frequencies of cutting patterns in the cutting problem. Therefore, a large scale linear optimizations problem arises, which is exactly solved by a column generated technique. It is worth noting that this new combined problem still takes the trade-off between storage costs (for final products and the parts) and trim losses (in the cutting process). We present some sets of computational tests, analyzed over three different scenarios. These results show that, by combining the problems and using an exact method, it is possible to obtain significant gains when compared to the usual industrial practice, which solve them in sequence. (C) 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Large Changes of Static Electric Properties Induced by Hydrogen Bonding: An ab Initio Study of Linear HCN Oligomers

We report the partitioning of the interaction-induced static electronic dipole (hyper)polarizabilities for linear hydrogen cyanide complexes into contributions arising from various interaction energy terms. We analyzed the nonadditivities of the studied properties and used these data to predict the electric properties of an infinite chain. The interaction-induced static electric dipole properties and their nonadditivities were analyzed using an approach based on numerical differentiation of the interaction energy components estimated in an external electric field. These were obtained using the hybrid variational-perturbational interaction energy decomposition scheme, augmented with coupled-cluster calculations, with singles, doubles, and noniterative triples. Our results indicate that the interaction-induced dipole moments and polarizabilities are primarily electrostatic in nature; however, the composition of the interaction hyperpolarizabilities is much more complex. The overlap effects substantially quench the contributions due to electrostatic interactions, and therefore, the major components are due to the induction and exchange induction terms, as well as the intramolecular electron-correlation corrections. A particularly intriguing observation is that the interaction first hyperpolarizability in the studied systems not only is much larger than the corresponding sum of monomer properties, but also has the opposite sign. We show that this effect can be viewed as a direct consequence of hydrogen-bonding interactions that lead to a decrease of the hyperpolarizability of the proton acceptor and an increase of the hyperpolarizability of the proton donor. In the case of the first hyperpolarizability, we also observed the largest nonadditivity of interaction properties (nearly 17%) which further enhances the effects of pairwise interactions.

Fock space for fermion-like lattices and the linear Glauber model

The concept of Fock space representation is developed to deal with stochastic spin lattices written in terms of fermion operators. A density operator is introduced in order to follow in parallel the developments of the case of bosons in the literature. Some general conceptual quantities for spin lattices are then derived, including the notion of generating function and path integral via Grassmann variables. The formalism is used to derive the Liouvillian of the d-dimensional Linear Glauber dynamics in the Fock-space representation. Then the time evolution equations for the magnetization and the two-point correlation function are derived in terms of the number operator. (C) 2008 Elsevier B.V. All rights reserved.

Augmented Lagrangian methods under the constant positive linear dependence constraint qualification

Two Augmented Lagrangian algorithms for solving KKT systems are introduced. The algorithms differ in the way in which penalty parameters are updated. Possibly infeasible accumulation points are characterized. It is proved that feasible limit points that satisfy the Constant Positive Linear Dependence constraint qualification are KKT solutions. Boundedness of the penalty parameters is proved under suitable assumptions. Numerical experiments are presented.

Skew-normal linear calibration: a Bayesian perspective

In this paper, we present a Bayesian approach for estimation in the skew-normal calibration model, as well as the conditional posterior distributions which are useful for implementing the Gibbs sampler. Data transformation is thus avoided by using the methodology proposed. Model fitting is implemented by proposing the asymmetric deviance information criterion, ADIC, a modification of the ordinary DIC. We also report an application of the model studied by using a real data set, related to the relationship between the resistance and the elasticity of a sample of concrete beams. Copyright (C) 2008 John Wiley & Sons, Ltd.

Reaction-diffusion systems coupled at the boundary and the Morse-Smale property

We study an one-dimensional nonlinear reaction-diffusion system coupled on the boundary. Such system comes from modeling problems of temperature distribution on two bars of same length, jointed together, with different diffusion coefficients. We prove the transversality property of unstable and stable manifolds assuming all equilibrium points are hyperbolic. To this end, we write the system as an equation with noncontinuous diffusion coefficient. We then study the nonincreasing property of the number of zeros of a linearized nonautonomous equation as well as the Sturm-Liouville properties of the solutions of a linear elliptic problem. (C) 2008 Elsevier Inc. All rights reserved.

Linear dimensional changes in plaster die models using different elastomeric materials

Dental impression is an important step in the preparation of prostheses since it provides the reproduction of anatomic and surface details of teeth and adjacent structures. The objective of this study was to evaluate the linear dimensional alterations in gypsum dies obtained with different elastomeric materials, using a resin coping impression technique with individual shells. A master cast made of stainless steel with fixed prosthesis characteristics with two prepared abutment teeth was used to obtain the impressions. References points (A, B, C, D, E and F) were recorded on the occlusal and buccal surfaces of abutments to register the distances. The impressions were obtained using the following materials: polyether, mercaptan-polysulfide, addition silicone, and condensation silicone. The transfer impressions were made with custom trays and an irreversible hydrocolloid material and were poured with type IV gypsum. The distances between identified points in gypsum dies were measured using an optical microscope and the results were statistically analyzed by ANOVA (p < 0.05) and Tukey's test. The mean of the distances were registered as follows: addition silicone (AB = 13.6 µm, CD=15.0 µm, EF = 14.6 µm, GH=15.2 µm), mercaptan-polysulfide (AB = 36.0 µm, CD = 36.0 µm, EF = 39.6 µm, GH = 40.6 µm), polyether (AB = 35.2 µm, CD = 35.6 µm, EF = 39.4 µm, GH = 41.4 µm) and condensation silicone (AB = 69.2 µm, CD = 71.0 µm, EF = 80.6 µm, GH = 81.2 µm). All of the measurements found in gypsum dies were compared to those of a master cast. The results demonstrated that the addition silicone provides the best stability of the compounds tested, followed by polyether, polysulfide and condensation silicone. No statistical differences were obtained between polyether and mercaptan-polysulfide materials.

Influence of different adhesive systems on the pull-out bond strength of glass fiber posts

This in vitro study evaluated the tensile bond strength of glass fiber posts (Reforpost - Angelus-Brazil) cemented to root dentin with a resin cement (RelyX ARC - 3M/ESPE) associated with two different adhesive systems (Adper Single Bond - 3M/ESPE and Adper Scotchbond Multi Purpose (MP) Plus - 3M/ESPE), using the pull-out test. Twenty single-rooted human teeth with standardized root canals were randomly assigned to 2 groups (n=10): G1- etching with 37% phosphoric acid gel (3M/ESPE) + Adper Single Bond + #1 post (Reforpost - Angelus) + four #1 accessory posts (Reforpin - Angelus) + resin cement; G2- etching with 37% phosphoric acid gel + Adper Scotchbond MP Plus + #1 post + four #1 accessory posts + resin cement. The specimens were stored in distilled water at 37°C for 7 days and submitted to the pull-out test in a universal testing machine (EMIC) at a crosshead speed of 0.5 mm/min. The mean values of bond strength (kgf) and standard deviation were: G1- 29.163 ± 7.123; G2- 37.752 ±13.054. Statistical analysis (Student's t-test; a=0.05 showed no statistically significant difference (p<0.05) between the groups. Adhesive bonding failures between resin cement and root canal dentin surface were observed in both groups, with non-polymerized resin cement in the apical portion of the post space when Single Bond was used (G1). The type of adhesive system employed on the fiber post cementation did not influence the pull-out bond strength.

Correlation between metal-ceramic bond strength and coefficient of linear thermal expansion difference

The purpose of this study was to evaluate the metal-ceramic bond strength (MCBS) of 6 metal-ceramic pairs (2 Ni-Cr alloys and 1 Pd-Ag alloy with 2 dental ceramics) and correlate the MCBS values with the differences between the coefficients of linear thermal expansion (CTEs) of the metals and ceramics. Verabond (VB) Ni-Cr-Be alloy, Verabond II (VB2), Ni-Cr alloy, Pors-on 4 (P), Pd-Ag alloy, and IPS (I) and Duceram (D) ceramics were used for the MCBS test and dilatometric test. Forty-eight ceramic rings were built around metallic rods (3.0 mm in diameter and 70.0 mm in length) made from the evaluated alloys. The rods were subsequently embedded in gypsum cast in order to perform a tensile load test, which enabled calculating the CMBS. Five specimens (2.0 mm in diameter and 12.0 mm in length) of each material were made for the dilatometric test. The chromel-alumel thermocouple required for the test was welded into the metal test specimens and inserted into the ceramics. ANOVA and Tukey's test revealed significant differences (p=0.01) for the MCBS test results (MPa), with PI showing higher MCBS (67.72) than the other pairs, which did not present any significant differences. The CTE (10-6 oC-1) differences were: VBI (0.54), VBD (1.33), VB2I (-0.14), VB2D (0.63), PI (1.84) and PD (2.62). Pearson's correlation test (r=0.17) was performed to evaluate of correlation between MCBS and CTE differences. Within the limitations of this study and based on the obtained results, there was no correlation between MCBS and CTE differences for the evaluated metal-ceramic pairs.

Shear bond strength of self-etch and total-etch bonding systems at different dentin depths

The purpose of this study was to evaluate the dentin shear bond strength of four adhesive systems (Adper Single Bond 2, Adper Prompt L-Pop, Magic Bond DE and Self Etch Bond) in regards to buccal and lingual surfaces and dentin depth. Forty extracted third molars had roots removed and crowns bisected in the mesiodistal direction. The buccal and lingual surfaces were fixed in a PVC/acrylic resin ring and were divided into buccal and lingual groups assigned to each selected adhesive. The same specimens prepared for the evaluation of superficial dentin shear resistance were used to evaluate the different depths of dentin. The specimens were identified and abraded at depths of 0.5, 1.0, 1.5 and 2.0 mm. Each depth was evaluated by ISO TR 11405 using an EMIC-2000 machine regulated at 0.5 mm/min with a 200 Kgf load cell. We performed statistical analyses on the results (ANOVA, Tukey and Scheffé tests). Data revealed statistical differences (p < 0.01) in the adhesive and depth variation as well as adhesive/depth interactions. The Adper Single Bond 2 demonstrated the highest mean values of shear bond strength. The Prompt L-Pop product, a self-etching adhesive, revealed higher mean values compared with Magic Bond DE and Self Etch Bond adhesives, a total and self-etching adhesive respectively. It may be concluded that the shear bond strength of dentin is dependent on material (adhesive system), substrate depth and adhesive/depth interaction.

Comparative study of chemical and mechanical retentive systems for bonding of indirect composite resin to commercially pure titanium

This study evaluated the effect of chemical and mechanical surface treatments for cast metal alloys on the bond strength of an indirect composite resin (Artglass) to commercially pure titanium (cpTi). Thirty cylindrical metal rods (3 mm diameter x 60 mm long) were cast in grade-1 cpTi and randomly assigned to 6 groups (n=5) according to the received surface treatment: sandblasting; chemical treatment; mechanical treatment - 0.4 mm beads; mechanical treatment - 0.6 mm beads; chemical/mechanical treatment - 0.4 mm; and chemical/mechanical treatment - 0.6 mm beads. Artglass rings (6.0 mm diameter x 2.0 mm thick) were light cured around the cpTi rods, according manufacturer's specifications. The specimens were invested in hard gypsum and their bond strength (in MPa) to the rods was measured at fracture with a universal testing machine at a crosshead speed of 2.0 mm/min and 500 kgf load cell. Data were analyzed statistically by one-way ANOVA and Tukey test (a=5%). The surface treatments differed significantly from each other (p<0.05) regarding the recorded bond strengths. Chemical retention and sandblasting showed statistically similar results to each other (p=0.139) and both had significantly lower bond strengths (p<0.05) than the other treatments. In conclusion, mechanical retention, either associated or not to chemical treatment, provided higher bond strength of the indirect composite resin to cpTi.

Bond strength of a pit-and-fissure sealant associated to etch-and-rinse and self-etching adhesive systems to saliva-contaminated enamel: individual vs. simultaneous light curing

This study evaluated in vitro the shear bond strength (SBS) of a resin-based pit-and-fissure sealant [Fluroshield (F), Dentsply/Caulk] associated with either an etch-and-rinse [Adper Single Bond 2 (SB), 3M/ESPE] or a self-etching adhesive system [Clearfil S3 Bond (S3), Kuraray Co., Ltd.] to saliva-contaminated enamel, comparing two curing protocols: individual light curing of the adhesive system and the sealant or simultaneous curing of both materials. Mesial and distal enamel surfaces from 45 sound third molars were randomly assigned to 6 groups (n=15), according to the bonding technique: I - F was applied to 37% phosphoric acid etched enamel. The other groups were contaminated with fresh human saliva (0.01 mL; 10 s) after acid etching: II - SB and F were light cured separately; III - SB and F were light cured together; IV - S3 and F were light cured separately; V - S3 and F were light cured simultaneously; VI - F was applied to saliva-contaminated, acid-etched enamel without an intermediate bonding agent layer. SBS was tested to failure in a universal testing machine at 0.5 mm/min. Data were analyzed by one-way ANOVA and Fisher's test (α=0.05).The debonded specimens were examined with a stereomicroscope to assess the failure modes. Three representative specimens from each group were observed under scanning electron microscopy for a qualitative analysis. Mean SBS in MPa were: I-12.28 (±4.29); II-8.57 (±3.19); III-7.97 (±2.16); IV-12.56 (±3.11); V-11.45 (±3.77); and VI-7.47 (±1.99). In conclusion, individual or simultaneous curing of the intermediate bonding agent layer and the resin sealant did not seem to affect bond strength to saliva-contaminated enamel. S3/F presented significantly higher SBS than the that of the groups treated with SB etch-and-rinse adhesive system and similar SBS to that of the control group, in which the sealant was applied under ideal dry, noncontaminated conditions.

Influence of light-curing unit systems on shear bond strength and marginal microleakage of composite resin restorations

The aim of the present study was to evaluate the influence of different photopolymerization (halogen, halogen soft-start and LED) systems on shear bond strength (SBS) and marginal microleakage of composite resin restorations. Forty Class V cavities (enamel and dentin margins) were prepared for microleakage assessment, and 160 enamel and dentin fragments were prepared for the SBS test, and divided into 4 groups. Kruskal-Wallis and Wilcoxon tests showed statistically significant difference in microleakage between the margins (p < 0.01) with incisal margins presenting the lowest values. Among the groups, it was observed that, only at the cervical margin, halogen soft-start photo polymerization presented statistically significant higher microleakage values. For SBS test, ANOVA showed no statistical difference (p > 0.05) neither between substrates nor among groups. It was concluded that Soft-Start technique with high intensity end-light influenced negatively the cervical marginal sealing, but the light-curing systems did not influence adhesion.