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We study a non standard infinite horizon, infinite dimensional linear-quadratic control problem arising in the physics of non-stationary states (see e.g. \cite{BDGJL4,BertiniGabrielliLebowitz05}): finding the minimum energy to drive a given stationary state $\bar x=0$ (at time $t=-\infty$) into an arbitrary non-stationary state $x$ (at time $t=0$). This is the opposite to what is commonly studied in the literature on null controllability (where one drives a generic state $x$ into the equilibrium state $\bar x=0$). Consequently, the Algebraic Riccati Equation (ARE) associated to this problem is non-standard since the sign of the linear part is opposite to the usual one and since it is intrinsically unbounded. Hence the standard theory of AREs does not apply. The analogous finite horizon problem has been studied in the companion paper \cite{AcquistapaceGozzi17}. Here, similarly to such paper, we prove that the linear selfadjoint operator associated to the value function is a solution of the above mentioned ARE. Moreover, differently to \cite{AcquistapaceGozzi17}, we prove that such solution is the maximal one. The first main result (Theorem \ref{th:maximalARE}) is proved by approximating the problem with suitable auxiliary finite horizon problems (which are different from the one studied in \cite{AcquistapaceGozzi17}). Finally in the special case where the involved operators commute we characterize all solutions of the ARE (Theorem \ref{th:sol=proj}) and we apply this to the Landau-Ginzburg model., Comment: 31 pages, 0 figures

In this paper we address the problem of visualizing a set of individuals, which have attached a statistical value given as a proportion, and a dissimilarity measure. Each individual is represented as a region within the unit square, in such a way that the area of the regions represent the proportions and the distances between them represent the dissimilarities. To enhance the interpretability of the representation, the regions are required to satisfy two properties. First, they must form a partition of the unit square, namely, the portions in which it is divided must cover its area without overlapping. Second, the portions must be made of a connected union of rectangles which verify the so-called box-connectivity constraints, yielding a visualization map called Space-filling Box-connected Map (SBM). The construction of an SBM is formally stated as a mathematical optimization problem, which is solved heuristically by using the Large Neighborhood Search technique. The methodology proposed in this paper is applied to three real-world datasets: the first one concerning financial markets in Europe and Asia, the second one about the letters in the English alphabet, and finally the provinces of The Netherlands as a geographical application. HighlightsWe visualize the proportions and the dissimilarities attached to a set of individuals by using Space-filling Box-connected Maps (SBM), which are more flexible than the pie or fan charts.We propose a Mixed Integer Linear model to build SBMs.Large Neighborhood Search metaheuristic is shown to be capable of help visualizing complex sets.The methodology proposed in this paper is applicable to sets of different nature, as shown in our examples.

This paper presents selective coloring as a new paradigm for branch-and-bound exact maximum clique search. Approximate coloring has, in recent, years been at the heart of leading solvers in the field. Selective coloring proposes to relax coloring up to a certain threshold. The result is a less informed but lighter decision heuristic. Different operators for the remaining uncolored vertices give rise to algorithmic variants integrated in a new BBMCL framework. BBMCL allows for an interesting comparison between approximate coloring and degree-based decision heuristics. The paper also reports extensive empirical tests. Selective coloring algorithms are fastest for a large subset of the graphs considered. © 2013 Published by Elsevier Ltd., This work is funded by the Spanish Ministry of Economy and Competitiveness (ARABOT:DPI2010-21247-C02-01) and supervised by CACSA whose kindness we gratefully acknowledge. The authors would also like to thank Jorge Artieda for his help with the experiments during the reviewing process. Finally we express our gratitude to reviewers for their insightful suggestions and comments.

In this paper we present an algorithm to segment the nuclei of neuronal cells in confocal microscopy images, a key technical problem in many experimental studies in the field of neuroscience. We describe the whole procedure, from the original images to the segmented individual nuclei, paying particular attention to the binarization of the images, which is not straightforward due to the technical difficulties related to the visualization of nuclei as individual objects and incomplete and irregular staining. We have focused on the division of clusters of nuclei that appear frequently in these images. Thus we have developed a clump-splitting algorithm to separate touching or overlapping nuclei allowing us to accurate account for both the number and size of the nuclei. The results presented in the paper show that the proposed algorithm performs well on different sets of images from different layers of the cerebral cortex. © 2013 Elsevier Ltd. All rights reserved.

Due to copyright restrictions, the access to the full text of this article is only available via subscription. This paper investigates the budget variant of the discrete time/cost trade-off problem (DTCTP). This multi-mode project scheduling problem requires assigning modes to the activities of a project so that the total completion time is minimized and the budget and the precedence constraints are satisfied. This problem is often encountered in practice as timely completion of the projects without exceeding the budget is crucial. The contribution of this paper to the literatures is to describe an effective Benders Decomposition-based exact algorithm to solve the DTCTP instances of realistic sizes. Although Benders Decomposition often exhibits a very slow convergence, we have included several algorithmic features to enhance the performance of the proposed tailored approach. Computational results attest to the efficacy of the proposed algorithm, which can solve large-scale instances to optimality. Fatimah Alnijris’ Research Chair for Advanced Manufacturing Technology

This paper considers the feed-forward training problem from the numerical point of view, in particular the conditioning of the problem. It is well known that the feed-forward training problem is often ill-conditioned; this affects the behaviour of training algorithms, the choice of such algorithms and the quality of the solutions achieved. A geometric interpretation of ill-conditioning is explored and an example of function approximation is analysed in detail. This paper considers the feed-forward training problem from the numerical point of view, in particular the conditioning of the problem. It is well known that the feed-forward training problem is often ill-conditioned; this affects the behaviour of training algorithms, the choice of such algorithms and the quality of the solutions achieved. A geometric interpretation of ill-conditioning is explored and an example of function approximation is analyzed in detail

We study the existence and multiplicity of solutions for a class of fractional Schrodinger–Kirchhoff type equations with the Trudinger–Moser nonlinearity. More precisely, we consider M ( ‖ u ‖ N ∕ s ) ( − Δ ) N ∕ s s u + V ( x ) | u | N s − 1 u = f ( x , u ) + λ h ( x ) | u | p − 2 u in R N , ‖ u ‖ = ∬ R 2 N | u ( x ) − u ( y ) | N ∕ s | x − y | 2 N d x d y + ∫ R N V ( x ) | u | N ∕ s d x s ∕ N , where M : [ 0 , ∞ ] → [ 0 , ∞ ) is a continuous function, s ∈ ( 0 , 1 ) , N ≥ 2 , λ > 0 is a parameter, 1 p ∞ , ( − Δ ) N ∕ s s is the fractional N ∕ s -Laplacian, V : R N → ( 0 , ∞ ) is a continuous function, f : R N × R → R is a continuous function, and h : R N → [ 0 , ∞ ) is a measurable function. First, using the mountain pass theorem, a nonnegative solution is obtained when f satisfies exponential growth conditions and λ is large enough, and we prove that the solution converges to zero in W V s , N ∕ s ( R N ) as λ → ∞ . Then, using the Ekeland variational principle, a nonnegative nontrivial solution is obtained when λ is small enough, and we show that the solution converges to zero in W V s , N ∕ s ( R N ) as λ → 0 . Furthermore, using the genus theory, infinitely many solutions are obtained when M is a special function and λ is small enough. We note that our paper covers a novel feature of Kirchhoff problems, that is, the Kirchhoff function M ( 0 ) = 0 .

This paper is concerned with the observer design for one-dimensional linear parabolic partial differential equations whose output is a weighted spatial average of the state over the entire spatial domain. We focus on the backstepping approach, which provides a systematic procedure to design an observer gain for systems with boundary measurement. If the output is not a boundary value of the state, the backstepping approach is not directly applicable to obtaining an observer gain that stabilizes the error dynamics. Therefore, we attempt to convert the error system into another system to which backstepping is applicable. The conversion is successfully achieved for a class of weighting functions, and the resultant observer realizes exponential convergence of the estimation error with an arbitrary decay rate in terms of the L 2 norm. In addition, an explicit expression of the observer gain is available in a special case. The effectiveness of the proposed observer is also confirmed by numerical simulations.

© 2017 The Author(s) Generating economical, high-resolution and high-quality computational grids for Large Eddy Simulation (LES) of wind flow and convective heat transfer (CHT) around surface-mounted obstacles is not straightforward. When the grid size is used as filter, LES grids should ideally consist of cubic cells, while CHT requires a very high near-wall resolution to resolve the thin viscous sublayer and buffer layer that represent the largest resistance to CHT. To avoid very high cell numbers and the need for excessive computational resources, non-conformal grids can be considered. This paper provides a detailed evaluation of the performance of non-conformal grids with cubic cells, for wind flow and CHT around a wall-mounted cubic obstacle. LES results on non-conformal versus conformal grids are compared with each other and with wind-tunnel measurements of wind speed and surface temperature. Moreover, sensitivity analysis is performed concerning the impact of overall grid resolution, subdomain size and grid refinement ratio. Average absolute deviations between LES on non-conformal versus conformal grids are about 0.9% (0.5 °C) for surface temperature on all cube surfaces. Comparison with experiments shows for the non-conformal grid an average and maximum absolute deviation for surface temperature of 2.0% (1.1 °C) and 7.6% (3.6 °C), respectively. The sensitivity analysis shows minor impact of subdomain size on convective heat transfer coefficients (CHTC) where, on average, absolute deviations of less than 2.2% are observed. This study shows that non-conformal grids can strongly reduce the total cell count (here by a factor up to 30.2) without significantly compromising the accuracy of results. ispartof: Building and Environment vol:119 pages:44-61 status: published

We solve the 3D controlled-source electromagnetic (CSEM) problem using the edge-based finite element method. The modeling domain is discretized using unstructured tetrahedral mesh. We adopt the total field formulation for the quasi-static variant of Maxwell's equation and the computation cost to calculate the primary field can be saved. We adopt a new boundary condition which approximate the total field on the boundary by the primary field corresponding to the layered earth approximation of the complicated conductivity model. The primary field on the modeling boundary is calculated using fast Hankel transform. By using this new type of boundary condition, the computation cost can be reduced significantly and the modeling accuracy can be improved. We consider that the conductivity can be anisotropic. We solve the finite element system of equations using a parallelized multifrontal solver which works efficiently for multiple source and large scale electromagnetic modeling. HighlightsThis paper develops an edge-based finite element method for 3D CSEM modeling.The algorithm is capable of dealing with anisotropic conductivity.We adopt a total field formulation and propose a new advanced boundary condition.We use a parallelized multifrontal method to solve the system of equations.The developed method is effective in modeling complex geometry such as bathymetry.

© 2017 Solving a multi-objective optimization problem yields an infinite set of points in which no objective can be improved without worsening at least another objective. This set is called the Pareto front. A Pareto front with adaptive resolution is a representation where the number of points at any segment of the Pareto front is directly proportional to the curvature of this segment. Such representations are attractive since steep segments, i.e., knees, are more significant to the decision maker as they have high trade-off level compared to the more flat segments of the solution curve. A simple way to obtain such representation is the a posteriori analysis of a dense Pareto front by a smart filter to keep only the points with significant trade-offs among them. However, this method suffers from the production of a large overhead of insignificant points as well as the absence of a clear criterion for determining the required density of the initial dense representation of the Pareto front. This paper's contribution is a novel algorithm for obtaining a Pareto front with adaptive resolution. The algorithm overcomes the pitfalls of the smart filter strategy by obtaining the Pareto points recursively while calculating the trade-off level between the obtained points before moving to a deeper recursive call. By using this approach, once a segment of trade-offs insignificant to the decision maker's needs is identified, the algorithm stops exploring it further. The improved speed of the proposed algorithm along with its intuitively simple solution process make it a more attractive route to solve multi-objective optimization problems in a way that better suits the decision maker's needs. ispartof: Computers & Chemical Engineering vol:106 pages:544-558 status: published

Combining lightweight characteristics with favourable noise and vibration behaviour, locally resonant metamaterials with vibro-acoustic stopband behaviour are gaining increasingly more attention. In view of applicability of metamaterials, this paper investigates the effects of curvature on stopband behaviour. Through derivation of curved unit cell models, dispersion curves for cylindrically curved infinite periodic structures are derived. The effect of curvature on metamaterials is investigated through both an academic example of an infinite cylindrically curved panel with added spring-mass systems and a realizable curved panel with resonant structures. It is shown that, whenever pure flexural motion exists in the host structure, the stopband mechanism can be applied to achieve flexural stopbands. ispartof: International Journal of Mechanical Sciences vol:127 pages:73-90 ispartof: location:SLOVENIA, Ljubljana status: published

© 2016 In contrast to classical experiment design methods, often based on alphabetic criteria, economic optimal experiment design assumes that our ultimate goal is to solve an optimization or optimal control problem. As the system parameters of physical models are in practice always estimated from measurements, they cannot be assumed to be exact. Thus, if we solve the model based optimization problem using the estimated, non-exact parameters, an inevitable loss of optimality is faced. The aim of economic optimal experiment design is precisely to plan an experiment in such a way that the expected loss of optimality in the optimization is minimized. This paper analyzes the question how to design economic experiments under the assumption that we have more than one candidate objective function. Here, we want to take measurements and estimate the parameters before we actually decide which objective we want to minimize. publisher: Elsevier articletitle: Multi-purpose economic optimal experiment design applied to model based optimal control journaltitle: Computers & Chemical Engineering articlelink: http://dx.doi.org/10.1016/j.compchemeng.2016.07.004 content_type: article copyright: © 2016 Published by Elsevier Ltd. ispartof: Computers & Chemical Engineering vol:94 pages:212-220 status: published

© 2015 Elsevier Ltd. All rights reserved. Many efficient exact branch and bound maximum clique solvers use approximate coloring to compute an upper bound on the clique number for every subproblem. This technique reasonably promises tight bounds on average, but never tighter than the chromatic number of the graph. Li and Quan, 2010, AAAI Conference, p. 128-133 describe a way to compute even tighter bounds by reducing each colored subproblem to maximum satisfiability problem (MaxSAT). Moreover they show empirically that the new bounds obtained may be lower than the chromatic number. Based on this idea this paper shows an efficient way to compute related >infra-chromatic> upper bounds without an explicit MaxSAT encoding. The reported results show some of the best times for a stand-alone computer over a number of instances from standard benchmarks., Pablo San Segundo is funded by the Spanish Ministry of Economy and Competitiveness (ARABOT: DPI 2010-21247-C02-01) and supervised by CACSA. Alexey Nikolaev and Mikhail Batsyn are supported by Russian Federation Grant 14-41-00039. The authors would like to thank Chu-Min Li and Zhe Quan for the source code of their MaxCLQ algorithm.

© 2015 Elsevier Ltd. All rights reserved. This paper revisits a recently developed methodology based on the matrix Lambert W function for the stability analysis of linear time invariant, time delay systems. By studying a particular, yet common, second order system, we show that in general there is no one to one correspondence between the branches of the matrix Lambert W function and the characteristic roots of the system. Furthermore, it is shown that under mild conditions only two branches suffice to find the complete spectrum of the system, and that the principal branch can be used to find several roots, and not the dominant root only, as stated in previous works. The results are first presented analytically, and then verified by numerical experiments. publisher: Elsevier articletitle: Some special cases in the stability analysis of multi-dimensional time-delay systems using the matrix Lambert W function journaltitle: Automatica articlelink: http://dx.doi.org/10.1016/j.automatica.2015.01.016 content_type: article copyright: Copyright © 2015 Elsevier Ltd. All rights reserved. ispartof: Automatica vol:53 pages:339-345 status: published

Recently, a very general and novel class of implicit bodies has been developed to describe the elastic response of solids. It contains as a special subclass the classical Cauchy and Green elastic bodies. Within the class of such bodies, one can obtain through a rigorous approximation, constitutive relations for the linearized strain as a nonlinear function of the stress. Such an approximation is not possible within classical theories of Cauchy and Green elasticity, where the process of linearization will only lead to the classical linearized elastic body. In this paper, we study numerically the states of stress and strain in a finite rectangular plate with an elliptic hole and a stepped flat tension bar with shoulder fillets, within the context of the new class of models for elastic bodies that guarantees that the linearized strain would stay bounded and limited below a value that can be fixed a priori, thereby guaranteeing the validity of the use of the model. This is in contrast to the classical linearized elastic model, wherein the strains can become large enough in the body leading to an obvious inconsistency.

This contribution proposes a strategy for estimating first excursion probabilities for linear dynamical systems involving uncertain structural parameters subject to Gaussian excitation. The proposed approach is based on Importance Sampling. The novel contribution of this paper is the introduction of an Importance Sampling density function related to the uncertain structural parameters. Such sampling density allows estimating probabilities accurately and efficiently. Numerical examples illustrate the advantages of the proposed approach.

This paper studies batch-end quality prediction using Partial Least Squares (PLS). The applicability of the zeroth-order approximation of Faber and Kowalski (1997) for estimation of the PLS prediction variance is critically assessed. The estimator was originally developed for spectroscopy calibration and its derivation involves a local linearization under specific assumptions, followed by a further approximation. Although the assumptions do not hold for batch process monitoring in general, they are not violated for the selected case study. Based on extensive Monte Carlo simulations, the influence of noise variance, number of components and number of training batches on the bias and variability of the variance estimation is investigated. The results indicate that the zeroth-order approximation is too restrictive for batch process data. The development of a variance estimator based on a full local linearization is required to obtain more reliable variance estimations for the development of prediction intervals. © 2013. ispartof: Computers & Chemical Engineering vol:52 pages:230-239 status: published

This paper investigates the application of first order Taylor series expansion considering intervening variables for estimating second order statistics for problems of stochastic finite element analysis. In particular, two types of intervening variables are considered. The focus is on studying the response of linear elastic static structures whose properties are characterized by means of log-normal random fields. Results obtained indicate that the use of intervening variables can lead to improved estimation of second order statistics when compared with traditional approaches based on Taylor series while numerical efforts remain similar.

This paper proposes a block Arnoldi method for parameterized model order reduction. This method works when design parameters have only low-rank impacts on the system matrix. The method preserves all design parameters in the reduced model and is easy to implement. Numerical results show that the block Arnoldi process outperforms some existing methods up to a factor of ten. ispartof: Applied Mathematics Letters vol:26 issue:6 pages:643-648 status: published

In this paper the feasibility of using a particular feasible direction interior point algorithm for solving reliability-based optimization problems of high dimensional stochastic dynamical systems is investigated. The optimal design problem is formulated in terms of an inequality constrained non-linear optimization problem. A class of interior point algorithms based on the solution of the first-order optimality conditions is considered here. For this purpose, a quasi-Newton iteration is used to solve the corresponding nonlinear system of equations. Several numerical examples are presented to illustrate the feasibility of the proposed methodology.

In this paper, we establish the existence of ground state solutions and bound state solutions for fractional field equations (0.1) ( − Δ + i d ) 1 2 u = f ( u ) in R n , u ∈ H 1 2 ( R n ) . Such solutions decay exponentially at infinity.

This paper deals with the simulation of a stationary vector Gaussian random field whose spatial correlation structure is given by a linear model of coregionalization. Traditionally, simulation is performed by decomposing the vector random field into a set of independent vector random fields with coregionalization models that contain a single nested structure, and a factorization of these fields into principal components. A variation of this approach is proposed, by considering the minimum/maximum autocorrelation factors associated with groups of two nested structures. This variation reduces the total number of independent factors by one-half, thus considerably decreases memory requirements and CPU time for simulation, without any loss of accuracy for reproducing the linear model of coregionalization, regardless of how many nested structures are contained in this model. The proposed approach is implemented in a set of computer programs and illustrated through a synthetic example and a case study in mineral resources evaluation.

This paper proposes an initialization approach for parameter estimation problems (PEPs) involving parameter-affine dynamic models. By using the state measurements, the nonconvex PEP is modified such that a convex approximation to the original PEP is obtained. The modified problem is solved by convex optimization methods yielding an approximate solution to the original PEP. The approximate solution can be further refined by linearizing the original problem around the obtained minimum. An assessment of the distance between the real solution and the one provided by the linearization of the problem around the convex approximation is presented. The optimum obtained by the convex approximation is used to subsequently initialize a simultaneous Gauss-Newton (SGN) approach on the original nonconvex PEP. Comparative results for the SGN with arbitrary initialization and with the proposed approach are presented using three benchmark examples in the chemical and biological fields. © 2009 Elsevier Ltd. All rights reserved. [**] ispartof: Computers & Chemical Engineering vol:34 issue:6 pages:953-964 status: published

Olive (Olea europaea L.) is the main perennial Spanish crop. Soil management in olive orchards is mainly based on intensive and tillage operations, which have a great relevancy in terms of negative environmental impacts. Due to this reason, the European Union (EU) only subsidizes cropping systems which require the implementation of conservation agro-environmental techniques such as cover crops between the rows. Remotely sensed data could offer the possibility of a precise follow-up of presence of cover crops to control these agrarian policy actions, but firstly, it is crucial to explore the potential for classifying variations in spectral signatures of olive trees, bare soil and cover crops using field spectroscopy. In this paper, we used hyperspectral signatures of bare soil, olive trees, and sown and dead cover crops taken in spring and summer in two locations to evaluate the potential of two methods (MultiLogistic regression with Initial and Radial Basis Function covariates, MLIRBF; and SimpleLogistic regression with Initial and Radial Basis Function covariates, SLIRBF) for classifying them in the 400-900 nm spectrum. These methods are based on a MultiLogistic regression model formed by a combination of linear and radial basis function neural network models. The estimation of the coefficients of the model is carried out basically in two phases. First, the number of radial basis functions and the radii and centres' vector are determined by means of an evolutionary neural network algorithm. A maximum likelihood optimization method determines the rest of the coefficients of a MultiLogistic regression with a set of covariates that include the initial variables and the radial basis functions previously estimated. Finally, we apply forward stepwise techniques of structural simplification. We compare the performance of these methods with robust classification methods: Logistic Regression without covariate selection, MLogistic; Logistic Regression with covariate selection, SLogistic; Logistic Model Trees algorithm (LMT); the C4.5 induction tree; Naïve Bayesian tree algorithm (NBTree); and boosted C4.5 trees using AdaBoost.M1 with 10 and 100 boosting iterations. MLIRBF and SLIRBF models were the best discriminant functions in classifying sown or dead cover crops from olive trees and bare soil in both locations and seasons by using a seven-dimensional vector with green (575 nm), red (600, 625, 650 and 675 nm), and near-infrared (700 and 725 nm) wavelengths as input variables. These models showed a correct classification rate between 95.56% and 100% in both locations and seasons. These results suggest that mapping covers crops in olive trees could be feasible by the analysis of high resolution airborne imagery acquired in spring or summer for monitoring the presence or absence of cover crops by the EU or local administrations in order to make the decision on conceding or not the subsidy. © 2010 Elsevier Ltd. All rights reserved., This work has been partially financed by the TIN 2008-06681-C06-03 project (Spanish Inter-Ministerial Commission of Science and Technology), FEDER funds, and the P08-TIC-3745 project (Junta de Andalucia, Spain).

The problem of adaptive stabilization of a class of continuous-time and time-varying nonlinear plants is treated in this paper. The control scheme guarantees that the state of the plant, with bounded time-varying parameters, asymptotically converges to zero. For the nonlinear case with n2+n unknown parameters (n time-varying and n2 constant), when the control matrix B is unknown the controller has to adjust n2+1 parameters providing only local stability results. On the contrary, when the control matrix B is known only one parameter has to be adjusted and the proposed scheme provides global stability results. The general methodology is particularized for the linear case with 2n2 unknown parameters (n2 time-varying and n2 constant), adjusting n2+1 parameters when the control matrix B is unknown and guarantees only local stability results, whereas in the case when the control matrix B is known only one parameter has to be adjusted and the proposed scheme provides global stability results.

In this paper, we consider a method for the localization and recognition of objects, as archaeological ones, hidden in the subsoil. We consider the physical problem and construct a mathematical model. To this end, from the collected measurements, we obtain a set of numerical data. This set allows the use of the method based on the continuous wavelet transform and a statistical test. © 2003 Elsevier Science Ltd. All rights reserved.