Modified Laplace transformation method and its application to the anharmonic oscillator

We apply a recently proposed approximation method to the evaluation of non-Gaussian integral and anharmonic oscillator. The method makes use of the truncated perturbation series by recasting it via the modified Laplace integral representation. The modification of the Laplace transformation is such that the upper limit of integration is cut off and an extra term is added for the compensation. For the non-Gaussian integral, we find that the perturbation series can give accurate result and the obtained approximation converges to the exact result in the $N \to \infty$ limit ($N$ denotes the order of perturbation expansion). In the case of anharmonic oscillator, we show that several order result yields good approximation of the ground state energy over the entire parameter space. The large order aspect is also investigated for the anharmonic oscillator.Comment: 26 pages including tables, Late

Free jet feasibility study of a thermal acoustic shield concept for AST/VCE application: Single stream nozzles

A technology base for the thermal acoustic shield concept as a noise suppression device for single stream exhaust nozzles was developed. Acoustic data for 314 test points for 9 scale model nozzle configurations were obtained. Five of these configurations employed an unsuppressed annular plug core jet and the remaining four nozzles employed a 32 chute suppressor core nozzle. Influence of simulated flight and selected geometric and aerodynamic flow variables on the acoustic behavior of the thermal acoustic shield was determined. Laser velocimeter and aerodynamic measurements were employed to yield valuable diagnostic information regarding the flow field characteristics of these nozzles. An existing theoretical aeroacoustic prediction method was modified to predict the acoustic characteristics of partial thermal acoustic shields

Neural networks for variational problems in engineering

In this work a conceptual theory of neural networks (NNs) from the perspective of functional analysis and variational calculus is presented. Within this formulation, the learning problem for the multilayer perceptron lies in terms of finding a function, which is an extremal for some functional. Therefore, a variational formulation for NNs provides a direct method for the solution of variational problems. This proposed method is then applied to distinct types of engineering problems. In particular a shape design, an optimal control and an inverse problem are considered. The selected examples can be solved analytically, which enables a fair comparison with the NN results. Copyright © 2008 John Wiley & Sons, Ltd

Experimental Investigation of Shock-Cell Noise Reduction for Single Stream Nozzles in Simulated Flight

Seven single stream model nozzles were tested in the Anechoic Free-Jet Acoustic Test Facility to evaluate the effectiveness of convergent divergent (C-D) flowpaths in the reduction of shock-cell noise under both static and mulated flight conditions. The test nozzles included a baseline convergent circular nozzle, a C-D circular nozzle, a convergent annular plug nozzle, a C-D annular plug nozzle, a convergent multi-element suppressor plug nozzle, and a C-D multi-element suppressor plug nozzle. Diagnostic flow visualization with a shadowgraph and aerodynamic plume measurements with a laser velocimeter were performed with the test nozzles. A theory of shock-cell noise for annular plug nozzles with shock-cells in the vicinity of the plug was developed. The benefit of these C-D nozzles was observed over a broad range of pressure ratiosin the vicinity of their design conditions. At the C-D design condition, the C-D annual nozzle was found to be free of shock-cells on the plug

GenSSI: a software toolbox for structural identifiability analysis of biological models

Summary: Mathematical modeling has a key role in systems biology. Model building is often regarded as an iterative loop involving several tasks, among which the estimation of unknown parameters of the model from a certain set of experimental data is of central importance. This problem of parameter estimation has many possible pitfalls, and modelers should be very careful to avoid them. Many of such difficulties arise from a fundamental (yet often overlooked) property: the so-called structural (or a priori) identifiability, which considers the uniqueness of the estimated parameters. Obviously, the structural identifiability of any tentative model should be checked at the beginning of the model building loop. However, checking this property for arbitrary non-linear dynamic models is not an easy task. Here we present a software toolbox, GenSSI (Generating Series for testing Structural Identifiability), which enables non-expert users to carry out such analysis. The toolbox runs under the popular MATLAB environment and is accompanied by detailed documentation and relevant examples

DOTcvpSB, a software toolbox for dynamic optimization in systems biology

<p>Abstract</p> <p>Background</p> <p>Mathematical optimization aims to make a system or design as effective or functional as possible, computing the quality of the different alternatives using a mathematical model. Most models in systems biology have a dynamic nature, usually described by sets of differential equations. Dynamic optimization addresses this class of systems, seeking the computation of the optimal time-varying conditions (control variables) to minimize or maximize a certain performance index. Dynamic optimization can solve many important problems in systems biology, including optimal control for obtaining a desired biological performance, the analysis of network designs and computer aided design of biological units.</p> <p>Results</p> <p>Here, we present a software toolbox, DOTcvpSB, which uses a rich ensemble of state-of-the-art numerical methods for solving continuous and mixed-integer dynamic optimization (MIDO) problems. The toolbox has been written in MATLAB and provides an easy and user friendly environment, including a graphical user interface, while ensuring a good numerical performance. Problems are easily stated thanks to the compact input definition. The toolbox also offers the possibility of importing SBML models, thus enabling it as a powerful optimization companion to modelling packages in systems biology. It serves as a means of handling generic black-box models as well.</p> <p>Conclusion</p> <p>Here we illustrate the capabilities and performance of DOTcvpSB by solving several challenging optimization problems related with bioreactor optimization, optimal drug infusion to a patient and the minimization of intracellular oscillations. The results illustrate how the suite of solvers available allows the efficient solution of a wide class of dynamic optimization problems, including challenging multimodal ones. The toolbox is freely available for academic use.</p

AMIGO2, a toolbox for dynamic modeling, optimization and control in systems biology

3 páginas, 1 figura.-- This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly citedMotivation: Many problems of interest in dynamic modeling and control of biological systems can be posed as non-linear optimization problems subject to algebraic and dynamic constraints. In the context of modeling, this is the case of, e.g. parameter estimation, optimal experimental design and dynamic flux balance analysis. In the context of control, model-based metabolic engineering or drug dose optimization problems can be formulated as (multi-objective) optimal control problems. Finding a solution to those problems is a very challenging task which requires advanced numerical methods. Results: This work presents the AMIGO2 toolbox: the first multiplatform software tool that automatizes the solution of all those problems, offering a suite of state-of-the-art (multi-objective) global optimizers and advanced simulation approachesEU FP7 project NICHE [ITN grant number 289384], Spanish MINECO/ FEDER projects IMPROWINE [grant number AGL2015-67504-C3-2-R] and SYNBIOFACTORY [DPI2014-55276-C5-2-R]Peer reviewe

On the relationship between sloppiness and identifiability

25 páginas, 11 figuras, 2 tablasDynamic models of biochemical networks are often formulated as sets of non-linear ordinary differential equations, whose states are the concentrations or abundances of the network components. They typically have a large number of kinetic parameters, which must be determined by calibrating the model with experimental data. In recent years it has been suggested that dynamic systems biology models are universally sloppy, meaning that the values of some parameters can be perturbed by several orders of magnitude without causing significant changes in the model output. This observation has prompted calls for focusing on model predictions rather than on parameters. In this work we examine the concept of sloppiness, investigating its links with the long-established notions of structural and practical identifiability. By analysing a set of case studies we show that sloppiness is not equivalent to lack of identifiability, and that sloppy models can be identifiable. Thus, using sloppiness to draw conclusions about the possibility of estimating parameter values can be misleading. Instead, structural and practical identifiability analyses are better tools for assessing the confidence in parameter estimates. Furthermore, we show that, when designing new experiments to decrease parametric uncertainty, designs that optimize practical identifiability criteria are more informative than those that minimize sloppinessThis project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 686282 (“CANPATHPRO”) and from the Spanish government (MINECO) and the European Regional Development Fund (ERDF) through the projects “SYNBIOFACTORY” (grant number DPI2014-55276-C5-2-R), and “IMPROWINE” (grant number AGL2015-67504-C3-2-R)N

Structural Identifiability of Systems Biology Models: A Critical Comparison of Methods

Analysing the properties of a biological system through in silico experimentation requires a satisfactory mathematical representation of the system including accurate values of the model parameters. Fortunately, modern experimental techniques allow obtaining time-series data of appropriate quality which may then be used to estimate unknown parameters. However, in many cases, a subset of those parameters may not be uniquely estimated, independently of the experimental data available or the numerical techniques used for estimation. This lack of identifiability is related to the structure of the model, i.e. the system dynamics plus the observation function. Despite the interest in knowing a priori whether there is any chance of uniquely estimating all model unknown parameters, the structural identifiability analysis for general non-linear dynamic models is still an open question. There is no method amenable to every model, thus at some point we have to face the selection of one of the possibilities. This work presents a critical comparison of the currently available techniques. To this end, we perform the structural identifiability analysis of a collection of biological models. The results reveal that the generating series approach, in combination with identifiability tableaus, offers the most advantageous compromise among range of applicability, computational complexity and information provided