Stable multivariate rational interpolation for parameter-dependent aerospace models

A multivariate, robust, rational interpolation method for propagating uncertainties in several dimensions is presented. The algorithm for selecting numerator and denominator polynomial orders is based on recent work that uses a singular value decomposition approach. In this paper we extend this algorithm to higher dimensions and demonstrate its efficacy in terms of convergence and accuracy, both as a method for response suface generation and interpolation. To obtain stable approximants for continuous functions, we use an L2 error norm indicator to rank optimal numerator and denominator solutions. For discontinous functions, a second criterion setting an upper limit on the approximant value is employed. Analytical examples demonstrate that, for the same stencil, rational methods can yield more rapid convergence compared to pseudospectral or collocation approaches for certain problems. © 2012 AIAA.

Testing of the multi-objective alliance algorithm on benchmark functions

A new version of the Multi-objective Alliance Algorithm (MOAA) is described. The MOAA's performance is compared with that of NSGA-II using the epsilon and hypervolume indicators to evaluate the results. The benchmark functions chosen for the comparison are from the ZDT and DTLZ families and the main classical multi-objective (MO) problems. The results show that the new MOAA version is able to outperform NSGA-II on almost all the problems.

A coupled hydro-mechanical analysis for prediction of hydraulic fracture propagation in saturated porous media using EFG mesh-less method

The details of the Element Free Galerkin (EFG) method are presented with the method being applied to a study on hydraulic fracturing initiation and propagation process in a saturated porous medium using coupled hydro-mechanical numerical modelling. In this EFG method, interpolation (approximation) is based on nodes without using elements and hence an arbitrary discrete fracture path can be modelled.The numerical approach is based upon solving two governing partial differential equations of equilibrium and continuity of pore water simultaneously. Displacement increment and pore water pressure increment are discretized using the same EFG shape functions. An incremental constrained Galerkin weak form is used to create the discrete system of equations and a fully implicit scheme is used for discretization in the time domain. Implementation of essential boundary conditions is based on the penalty method. In order to model discrete fractures, the so-called diffraction method is used.Examples are presented and the results are compared to some closed-form solutions and FEM approximations in order to demonstrate the validity of the developed model and its capabilities. The model is able to take the anisotropy and inhomogeneity of the material into account. The applicability of the model is examined by simulating hydraulic fracture initiation and propagation process from a borehole by injection of fluid. The maximum tensile strength criterion and Mohr-Coulomb shear criterion are used for modelling tensile and shear fracture, respectively. The model successfully simulates the leak-off of fluid from the fracture into the surrounding material. The results indicate the importance of pore fluid pressure in the initiation and propagation pattern of fracture in saturated soils. © 2013 Elsevier Ltd.

Low-rank optimization with trace norm penalty

The paper addresses the problem of low-rank trace norm minimization. We propose an algorithm that alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is characterized by an efficient factorization that makes the trace norm differentiable in the search space and the computation of duality gap numerically tractable. The search space is nonlinear but is equipped with a Riemannian structure that leads to efficient computations. We present a second-order trust-region algorithm with a guaranteed quadratic rate of convergence. Overall, the proposed optimization scheme converges superlinearly to the global solution while maintaining complexity that is linear in the number of rows and columns of the matrix. To compute a set of solutions efficiently for a grid of regularization parameters we propose a predictor-corrector approach that outperforms the naive warm-restart approach on the fixed-rank quotient manifold. The performance of the proposed algorithm is illustrated on problems of low-rank matrix completion and multivariate linear regression. © 2013 Society for Industrial and Applied Mathematics.

Designing folding rings using polynomial continuation

© 2014 by ASME. Two types of foldable rings are designed using polynomial continuation. The first type of ring, when deployed, forms regular polygons with an even number of sides and is designed by specifying a sequence of orientations which each bar must attain at various stages throughout deployment. A design criterion is that these foldable rings must fold with all bars parallel in the stowed position. At first, all three Euler angles are used to specify bar orientations, but elimination is also used to reduce the number of specified Euler angles to two, allowing greater freedom in the design process. The second type of ring, when deployed, forms doubly plane-symmetric (irregular) polygons. The doubly symmetric rings are designed using polynomial continuation, but in this example a series of bar end locations (in the stowed position) is used as the design criterion with focus restricted to those rings possessing eight bars.

Monolithic MZI-SOA hybrid switch for low-power and low-penalty operation.

We report the first experimental demonstration of a monolithically integrated hybrid dilated 2×2 modular optical switch using Mach-Zehnder modulators as low-loss 1×2 switching elements and short semiconductor optical amplifiers to provide additional extinction and gain. An excellent 40 dB cross-talk/extinction ratio is recorded with data-modulated signal-to-noise ratios of up to 44 dB in a 0.1 nm bandwidth. A switching time of 3 ns is demonstrated. Bit error rate studies show extremely low subsystem penalties of less than 0.1 dB, and studies indicate that, by using this hybrid switch building block, an 8×8 port switch could be achieved with 14 dB input power dynamic range for subsystem penalties of less than 0.5 dB.

Effects of the "all-fish" growth hormone transgene expression on non-specific immune functions of common carp, Cyprinus carpio L.

This study investigated non-specific immune functions of the F-2 generation of "all-fish" growth hormone transgenic carp, Cyprinus carpio L. Lysozyme activity was 145.0 (+/- 30.7) U ml(-1) in the transgenic fish serum and 105.0 (+/- 38.7) U ml(-1) in age-matched non-transgenic control fish serum, a significant difference (P < 0.01). The serum bactericidal activity in the transgenics was significantly higher than that in the controls (P < 0.05), with the percentage serum killing of 59.5% (6.83%) and 50.8% (8.67%), respectively. Values for leukocrit and phagocytic percent of macrophages in head kidney were higher in transgenics than controls (P < 0.05). However, the phagocytic indices in the transgenics and the controls were not different. In addition, the mean body weight of the transgenics was 63.4 (6.65) g, much higher than that of the controls [39.2 (+/- 3.30) g, P < 0.01]. The absolute weight of spleen of the transgenics [0.13 (+/- 0.03) g] was higher than that of the controls [0.08 (+/- 0.02) g, P < 0.01]. However, there was no difference in the relative weight of spleen between the transgenics and the controls, with the spleen mass index being 0.21% (+/- 0.02%) and 0.20% (+/- 0.03%), respectively. This study suggests that the "all-fish" growth hormone transgene expression could stimulate not only the growth but also the non-specific immune functions of carp. (c) 2006 Published by Elsevier B.V.

Effects of intraperitoneal injection of cortisol on nonspecific immune functions of Ctenopharyngodon idella

After grass carps Ctenopharyngodon idellus were injected with cortisol, with (CBC) and without (C) a cocoa butter carrier, the effects of both slowly and rapidly acting exogenous cortisol oil their non-specific immune functions were investigated. On the one hand, after injection with CBC, the cortisol concentration and lysozyme activity in fish serum were enhanced and were sustained at high levels for a long period (30 days). The killing activity in the serum declined with time, and phagocytosis of head kidney macrophages diminished significantly (P < 0.05 or P < 0.01). The leukocrit values in the high dose group (31-8 mg cortisol fish(-1)) increased over time, however, with the maximum average being 5.6% at day 30. The spleen mass index in the high dose group was 0.93 x 10(-3) after 30 days, notably lower (P < 0.05) than that in the control group. In addition, a decrease in resistance to Aeronionas hydrophilo infection in cortisol-treated fish was shown, with the final cumulative mortalities being 54.5 and 66.7% in the low and high dose groups, respectively. On the other hand, there was a decrease in both serum cortisol concentration and lysozyme activity of the experimental fish within 2 weeks after injection with C, where plasma bactericidal activities in the high dose group (31-8 mg cortisol fish(-1)) were remarkably lower (P < 0.01) than those in the control group at each sampling, but were increased slightly over time. The results of which were different from those in the CBC trial. Phagocytic activity of head kidney macrophages and spleen mass index decreased significantly (P < 0.05), while there were increases in leukocrit value and cumulative mortality due to A. hydrophila. The results of which were similar to those in the CBC trial. This study indicated that the injection of cortisol depressed the non-specific immune functions of the grass carp and increased its susceptibility to disease. (c) 2005 The Fisheries Society of the British Isles.

Predictive entropy search for efficient global optimization of black-box functions

We propose a novel information-theoretic approach for Bayesian optimization called Predictive Entropy Search (PES). At each iteration, PES selects the next evaluation point that maximizes the expected information gained with respect to the global maximum. PES codifies this intractable acquisition function in terms of the expected reduction in the differential entropy of the predictive distribution. This reformulation allows PES to obtain approximations that are both more accurate and efficient than other alternatives such as Entropy Search (ES). Furthermore, PES can easily perform a fully Bayesian treatment of the model hyperparameters while ES cannot. We evaluate PES in both synthetic and real-world applications, including optimization problems in machine learning, finance, biotechnology, and robotics. We show that the increased accuracy of PES leads to significant gains in optimization performance.

Silica-based 64-channel arrayed waveguide gratings with double functions

Silica-based 64-channel arrayed waveguide gratings (AWGs) with double functions and 0.4 nm (50 GHz) channel spacing have been designed and fabricated. On the same component, Gauss and flat-top output response spectra are obtained simultaneously. The test results show that when the insertion loss ranges from 3.5 dB to 6 dB,the crosstalk is better than -34 dB, the 1 dB bandwidth is 0.12 nm, the 3 dB bandwidth is 0,218 nm, and the polarization-dependent loss (PDL) is less than 0.5 dB for Gauss response. When the insertion loss ranges,from 5.8 dB to 7.8 dB, the crosstalk is better than -30 dB, the 1 dB bandwidth is 0.24 nm, the 3 dB bandwidth is 0.33 nm, and the PDL is less than 0.2 dB for flat-top response.

When Does a Polynomial Over a Finite Field Permute the Elements of the Field?

We present a class of indecomposable polynomials of non prime-power degree over the finite field of two elements which are permutation polynomials on infinitely many finite extensions of the field. The associated geometric monodromy groups are the simple ...

practical type checking of functions defined on context-free languages

A type checking method for the functional language LFC is presented. A distinct feature of LFC is that it uses Context-Free (CF) languages as data types to represent compound data structures. This makes LFC a dynamically typed language. To improve efficiency, a practical type checking method is presented, which consists of both static and dynamic type checking. Although the inclusion relation of CF.languages is not decidable,a special subset of the relation is decidable, i.e., the sentential form relation, which can be statically checked.Moreover, most of the expressions in actual LFC programs appear to satisfy this relation according to the statistic data of experiments. So, despite that the static type checking is not complete, it undertakes most of the type checking task. Consequently the run-time efficiency is effectively improved. Another feature of the type checking is that it converts the expressions with implicit structures to structured representation. Structure reconstruction technique is presented.

pattern matching compilation of functions defined in context-free languages

LFC is a functional language based on recursive functions defined in context-free languages. In this paper, a new pattern matching algorithm for LFC is presented, which can represent a sequence of patterns as an integer by an encoding method. It is a rather simple method and produces efficient case-expressions for pattern matching definitions of LFC. The algorithm can also be used for other functional languages, but for nested patterns it may become complicated and further studies are needed.

facilitating formal specification acquisition by using recursive functions on context-free languages

Although formal specification techniques are very useful in software development, the acquisition of formal specifications is a difficult task. This paper presents the formal specification language LFC, which is designed to facilitate the acquisition and validation of formal specifications. LFC uses context-free languages for syntactic aspect and relies on a new kind of recursive functions, i.e. recursive functions on context-free languages, for semantic aspect of specifications. Construction and validation of LFC specifications are machine-aided. The basic ideas behind LFC, the main aspects of LFC, and the use of LFC and illustrative examples are described.