Hamilton Jacobi theory for constrained systems

We extend the HamiltonJacobi formulation to constrained dynamical systems. The discussion covers both the case of first-class constraints alone and that of first- and second-class constraints combined. The HamiltonDirac equations are recovered as characteristic of the system of partial differential equations satisfied by the HamiltonJacobi function.

Equivalence Between the Lagrangian and Hamiltonian Formalisms for Constrained Systems

The equivalence between the Lagrangian and Hamiltonian formalism is studied for constraint systems. A procedure to construct the Lagrangian constraints from the Hamiltonian constraints is given. Those Hamiltonian constraints that are first class with respect to the Hamiltonian constraints produce Lagrangian constraints that are FL-projectable.

Lee HWA Chung theorem for presympectic manifolds. Canonical transformations for constrained systems

We generalize the analogous of Lee Hwa Chungs theorem to the case of presymplectic manifolds. As an application, we study the canonical transformations of a canonical system (M, S, O). The role of Dirac brackets as a test of canonicity is clarified.

Hamilton-Jacobi theory for constrained systems

We extend the HamiltonJacobi formulation to constrained dynamical systems. The discussion covers both the case of first-class constraints alone and that of first- and second-class constraints combined. The HamiltonDirac equations are recovered as characteristic of the system of partial differential equations satisfied by the HamiltonJacobi function.

Accelerated Microstructure Imaging via Convex Optimization (AMICO) from diffusion MRI data.

Microstructure imaging from diffusion magnetic resonance (MR) data represents an invaluable tool to study non-invasively the morphology of tissues and to provide a biological insight into their microstructural organization. In recent years, a variety of biophysical models have been proposed to associate particular patterns observed in the measured signal with specific microstructural properties of the neuronal tissue, such as axon diameter and fiber density. Despite very appealing results showing that the estimated microstructure indices agree very well with histological examinations, existing techniques require computationally very expensive non-linear procedures to fit the models to the data which, in practice, demand the use of powerful computer clusters for large-scale applications. In this work, we present a general framework for Accelerated Microstructure Imaging via Convex Optimization (AMICO) and show how to re-formulate this class of techniques as convenient linear systems which, then, can be efficiently solved using very fast algorithms. We demonstrate this linearization of the fitting problem for two specific models, i.e. ActiveAx and NODDI, providing a very attractive alternative for parameter estimation in those techniques; however, the AMICO framework is general and flexible enough to work also for the wider space of microstructure imaging methods. Results demonstrate that AMICO represents an effective means to accelerate the fit of existing techniques drastically (up to four orders of magnitude faster) while preserving accuracy and precision in the estimated model parameters (correlation above 0.9). We believe that the availability of such ultrafast algorithms will help to accelerate the spread of microstructure imaging to larger cohorts of patients and to study a wider spectrum of neurological disorders.

Optimization of the sampling scheme for maps of physical and chemical properties estimated by kriging

The sampling scheme is essential in the investigation of the spatial variability of soil properties in Soil Science studies. The high costs of sampling schemes optimized with additional sampling points for each physical and chemical soil property, prevent their use in precision agriculture. The purpose of this study was to obtain an optimal sampling scheme for physical and chemical property sets and investigate its effect on the quality of soil sampling. Soil was sampled on a 42-ha area, with 206 geo-referenced points arranged in a regular grid spaced 50 m from each other, in a depth range of 0.00-0.20 m. In order to obtain an optimal sampling scheme for every physical and chemical property, a sample grid, a medium-scale variogram and the extended Spatial Simulated Annealing (SSA) method were used to minimize kriging variance. The optimization procedure was validated by constructing maps of relative improvement comparing the sample configuration before and after the process. A greater concentration of recommended points in specific areas (NW-SE direction) was observed, which also reflects a greater estimate variance at these locations. The addition of optimal samples, for specific regions, increased the accuracy up to 2 % for chemical and 1 % for physical properties. The use of a sample grid and medium-scale variogram, as previous information for the conception of additional sampling schemes, was very promising to determine the locations of these additional points for all physical and chemical soil properties, enhancing the accuracy of kriging estimates of the physical-chemical properties.

Computation of arbitrarily constrained synthetic discriminant functions

An algorithm for computing correlation filters based on synthetic discriminant functions that can be displayed on current spatial light modulators is presented. The procedure is nondivergent, computationally feasible, and capable of producing multiple solutions, thus overcoming some of the pitfalls of previous methods.

Use of information on the manufacture of samples for the optical characterization of multilayers through a global optimization

We present a procedure for the optical characterization of thin-film stacks from spectrophotometric data. The procedure overcomes the intrinsic limitations arising in the numerical determination of manyparameters from reflectance or transmittance spectra measurements. The key point is to use all theinformation available from the manufacturing process in a single global optimization process. The method is illustrated by a case study of solgel applications.

Computer-aided procedure for optimization of layer thickness uniformity in thermal evaporation physical vapor deposition chambers for lens coating

A computer-aided method to improve the thickness uniformity attainable when coating multiple substrates inside a thermal evaporation physical vapor deposition unit is presented. The study is developed for the classical spherical (dome-shaped) calotte and also for a plane sector reversible holder setup. This second arrangement is very useful for coating both sides of the substrate, such as antireflection multilayers on lenses. The design of static correcting shutters for both kinds of configurations is also discussed. Some results of using the method are presented as an illustration.

Optimization of preservation conditions of As (III) bioreporter bacteria.

Long-term preservation of bioreporter bacteria is essential for the functioning of cell-based detection devices, particularly when field application, e.g., in developing countries, is intended. We varied the culture conditions (i.e., the NaCl content of the medium), storage protection media, and preservation methods (vacuum drying vs. encapsulation gels remaining hydrated) in order to achieve optimal preservation of the activity of As (III) bioreporter bacteria during up to 12 weeks of storage at 4 degrees C. The presence of 2% sodium chloride during the cultivation improved the response intensity of some bioreporters upon reconstitution, particularly of those that had been dried and stored in the presence of sucrose or trehalose and 10% gelatin. The most satisfying, stable response to arsenite after 12 weeks storage was obtained with cells that had been dried in the presence of 34% trehalose and 1.5% polyvinylpyrrolidone. Amendments of peptone, meat extract, sodium ascorbate, and sodium glutamate preserved the bioreporter activity only for the first 2 weeks, but not during long-term storage. Only short-term stability was also achieved when bioreporter bacteria were encapsulated in gels remaining hydrated during storage.

Optimization of laser interferometers for the detection of gravitational waves from coalescing binaries

Coalescing compact binary systems are important sources of gravitational waves. Here we investigate the detectability of this gravitational radiation by the recently proposed laser interferometers. The spectral density of noise for various practicable configurations of the detector is also reviewed. This includes laser interferometers with delay lines and Fabry-Prot cavities in the arms, both in standard and dual recycling arrangements. The sensitivity of the detector in all those configurations is presented graphically and the signal-to-noise ratio is calculated numerically. For all configurations we find values of the detector's parameters which maximize the detectability of coalescing binaries, the discussion comprising Newtonian- as well as post-Newtonian-order effects. Contour plots of the signal-to-noise ratio are also presented in certain parameter domains which illustrate the interferometer's response to coalescing binary signals.

Lee HWA Chung theorem for presympectic manifolds. Canonical transformations for constrained systems

We generalize the analogous of Lee Hwa Chungs theorem to the case of presymplectic manifolds. As an application, we study the canonical transformations of a canonical system (M, S, O). The role of Dirac brackets as a test of canonicity is clarified.

Cost limitation through constrained oviposition site in a plant-pollinator/seed predator mutualism

Mutualism often involves reciprocal exploitation due to individual selection for increased benefits even at the expense of the partner. Therefore, stability and outcomes of such interactions crucially depend on cost limitation mechanisms. In the plant, pollinator /seed predator interaction between Silene latifolia (Caryophyllaceae) and Hadena bicruris (Lepidoptera: Noctuidae), moths generate pollination benefits as adults but impose seed predation costs as larvae. We examined whether floral morphology limits over-exploitation by constraining oviposition site. Oviposition site varies naturally inside vs. outside the corolla tube, but neither its determinants nor its effect on the interaction have been investigated. In a common garden with plants originating from eight populations, corolla tube length predicted oviposition site, but not egg presence or pollination efficiency, suggesting that long corolla tubes constrain the moth to lay eggs on petals. Egg position was also predicted by the combined effect of corolla tube and moth ovipositor lengths, with shorter ovipositor than corolla tube resulting in higher probability for eggs outside. Egg position on a given plant was repeatable over different exposure nights. When egg position was experimentally manipulated, eggs placed on the petal resulted in significantly fewer successful fruit attacks compared with eggs placed inside the corolla tube, suggesting differences in egg/larval mortality. Egg position also differently affected larval mass, fruit mass and fruit development. Our results indicate that constraining oviposition site through a long corolla tube reduces seed predation costs suffered by the plant without negatively affecting pollination efficiency and, hence may act to limit over-exploitation. However, the net effects of corolla tube depth variation on this interaction may fluctuate with extrinsic factors affecting egg mortality, and with patterns of gene flow affecting trait matching between the interacting species. The intermediate fitness costs incurred by both plant and insect associated with the different egg positions may reduce selective pressures for this interaction to evolve towards antagonism, favouring instead a mutualistic outcome. While a role for oviposition site variation in cost limitation is a novel finding in this system, it may apply more generally also to other mutualisms involving pollinating seed predators.

Evidence of a critical time in constrained Kinetic Ising models

We study the relaxational dynamics of the one-spin facilitated Ising model introduced by Fredrickson and Andersen. We show the existence of a critical time which separates an initial regime in which the relaxation is exponentially fast and aging is absent from a regime in which relaxation becomes slow and aging effects are present. The presence of this fast exponential process and its associated critical time is in agreement with some recent experimental results on fragile glasses.