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40
Parametric ReducedOrder Models for Probabilistic Analysis of Unsteady Aerodynamic Applications
"... Methodology is presented to derive reducedorder models for largescale parametric applications in unsteady aerodynamics. The specific case considered in this paper is a computational fluid dynamic (CFD) model with parametric dependence that arises from geometric shape variations. The first key cont ..."
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Methodology is presented to derive reducedorder models for largescale parametric applications in unsteady aerodynamics. The specific case considered in this paper is a computational fluid dynamic (CFD) model with parametric dependence that arises from geometric shape variations. The first key contribution of the methodology is the derivation of a linearized model that permits the effects of geometry variations to be represented with an explicit affine function. The second key contribution is an adaptive sampling method that utilizes an optimization formulation to derive a reduced basis that spans the space of geometric input parameters. The method is applied to derive efficient reducedorder models for probabilistic analysis of the effects of blade geometry variation for a twodimensional model problem governed by the Euler equations. Reducedorder models that achieve three orders of magnitude reduction in the number of states are shown to accurately reproduce CFD Monte Carlo simulation results at a fraction of the computational cost. I.
Parameter estimation using sparse reconstruction with dynamic dictionaries
 in Proc. IEEE Int. Conf. on Acoustics, Speech, and Signal Processing (ICASSP 11), May 22–27 2011
"... We consider the problem of parameter estimation for signals characterized by sums of parameterized functions. We present a dynamic dictionary subset selection approach to parameter estimation where we iteratively select a small number of dictionary elements and then alter the parameters of these dic ..."
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Cited by 1 (1 self)
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We consider the problem of parameter estimation for signals characterized by sums of parameterized functions. We present a dynamic dictionary subset selection approach to parameter estimation where we iteratively select a small number of dictionary elements and then alter the parameters of these dictionary elements to achieve better signal model fit. The proposed approach avoids the use of highly oversampled (and highly correlated) dictionary elements, which are needed in fixed dictionary approaches to reduce parameter bias associated with dictionary quantization. We demonstrate estimation performance on a sinusoidal signal estimation example. Index Terms — Sparse reconstruction, Parameter estimation,
Distefano J.: A Mathematical Model of BCRABL Autophosphorylation, Signaling through
 the CRKL Pathway, and Gleevec Dynamics in Chronic Myeloid Leukemia, Discrete and Continuous Dynamical Systems  Series B
"... Abstract. A mathematical model is presented that describes several signaling events that occur in cells from patients with chronic myeloid leukemia, i.e. autophosphorylation of the BcrAbl oncoprotein and subsequent signaling through the Crkl pathway. Dynamical effects of the drug STI571 (Gleevec) ..."
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Abstract. A mathematical model is presented that describes several signaling events that occur in cells from patients with chronic myeloid leukemia, i.e. autophosphorylation of the BcrAbl oncoprotein and subsequent signaling through the Crkl pathway. Dynamical effects of the drug STI571 (Gleevec) on these events are examined, and a minimal concentration for drug effectiveness is predicted by simulation. Most importantly, the model suggests that, for cells in blast crisis, cellular drug clearance mechanisms such as drug efflux pumps dramatically reduce the effectiveness of Gleevec. This is a new prediction regarding the efficacy of Gleevec. In addition, it is speculated that these resistance mechanisms might be present from the onset of disease.
A POLYNOMIALTIME INTERIORPOINT METHOD FOR CONIC OPTIMIZATION, WITH INEXACT BARRIER EVALUATIONS ∗
"... Abstract. We consider a primaldual shortstep interiorpoint method for conic convex optimization problems for which exact evaluation of the gradient and Hessian of the primal and dual barrier functions is either impossible or prohibitively expensive. As our main contribution, we show that if appro ..."
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Abstract. We consider a primaldual shortstep interiorpoint method for conic convex optimization problems for which exact evaluation of the gradient and Hessian of the primal and dual barrier functions is either impossible or prohibitively expensive. As our main contribution, we show that if approximate gradients and Hessians of the primal barrier function can be computed, and the relative errors in such quantities are not too large, then the method has polynomial worstcase iteration complexity. (In particular, polynomial iteration complexity ensues when the gradient and Hessian are evaluated exactly.) In addition, the algorithm requires no evaluation—or even approximate evaluation—of quantities related to the barrier function for the dual cone, even for problems in which the underlying cone is not selfdual.
on Aluminum Alloys
"... We present a coupled simulation–optimization procedure for the improvement of the laser welding process. This is achieved by introducing a functional to measure the quality of a weld and later performing a mathematical optimization of it. The welding process to be included in the functional is simul ..."
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We present a coupled simulation–optimization procedure for the improvement of the laser welding process. This is achieved by introducing a functional to measure the quality of a weld and later performing a mathematical optimization of it. The welding process to be included in the functional is simulated using an adaptive finite element method for the thermal and mechanical subproblems. The functional is optimized using a constrained mathematical optimization method and the optimized parameters giving some desired properties of the welds are found. In this paper, the results obtained for two different optimization goals are presented, namely a general test problem in which all good properties of the welds are assumed to have the same importance, and another in which a higher importance is given to the residual stress and the full penetration of the weld. Key words: welding, laser welding PACS: 44.05.+e, 46.35.+z, 81.20.Vj 1.
NOVEL MODELS FOR HOURLY SOLAR RADIATION USING A 2D APPROACH
, 2008
"... Abstract. In this work one year hourly solar radiation data are analyzed and modeled using a novel visualization method. Using a 2D(Dimensional) surface fitting approach, the general behavior of the solar radiation in a year is modeled. By the help of the newly adopted visualization approach, a tot ..."
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Abstract. In this work one year hourly solar radiation data are analyzed and modeled using a novel visualization method. Using a 2D(Dimensional) surface fitting approach, the general behavior of the solar radiation in a year is modeled. By the help of the newly adopted visualization approach, a total of 9 analytical surface models are obtained and compared. The Gaussian surface model with proper model parameters is found to be the most accurate model among the tested analytical models for data characterization purposes. The accuracy of this surface model is tested and compared with a dynamic surface model obtained from a feedforward Neural Network (NN). Analytical surface models and NN surface model are compared in the sense of Root Mean Square Error (RMSE). It is obtained that the NN surface model gives better results with smaller RMSE values. However, unlike the specificity of the NN surface model, the analytical surface model provides a simple, intuitive and more generalized form that can be suitable for several geographical locations on earth.
A Basic Foundation for Unravelling Quantity Discounts: Gaining more Insight into Supplier Cost Mechanisms Summary
"... Selling organizations often offer quantity discounts schedules, but do not provide the underlying Quantity Discount Price Functions (QDPF). In literature an analysis on how QDPF could be derived from discount schedules is lacking. This is remarkable as QDPF contain useful information for buying orga ..."
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Selling organizations often offer quantity discounts schedules, but do not provide the underlying Quantity Discount Price Functions (QDPF). In literature an analysis on how QDPF could be derived from discount schedules is lacking. This is remarkable as QDPF contain useful information for buying organizations. QDPF give more insight into the fixed and variable costs of selling organizations and can be a useful tool for buying organizations in selecting and negotiating processes. Furthermore, QDPF can be used for calculating and allocating price savings in group purchasing and multiple sourcing decisions. In this paper we develop one general QDPF and two related measures for negotiating spaces. We prove that our QDPF gives a highly reliable approximation of 66 quantity discount schedules of different selling organizations. Finally, we compare the QDPF parameters of the 66 schedules and discuss their basic properties. Educator and practitioner summary In this paper we develop a general quantity discount price function and two indicators for negotiating spaces. These instruments provide more insight into the fixed and variable costs of selling organizations and can be used (1) as a tool in selecting and negotiating processes, and (2) to calculate and allocate price savings in multiple sourcing decisions and group purchasing.
Recent Advances in Diffusion MRI Modeling: Angular and Radial Reconstruction
, 2011
"... Recent advances in diffusion magnetic resonance image (dMRI) modeling have led to the development of several state of the art methods for reconstructing the diffusion signal. These methods allow for distinct features to be computed, which in turn reflect properties of fibrous tissue in the brain and ..."
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Recent advances in diffusion magnetic resonance image (dMRI) modeling have led to the development of several state of the art methods for reconstructing the diffusion signal. These methods allow for distinct features to be computed, which in turn reflect properties of fibrous tissue in the brain and in other organs. A practical consideration is that to choose among these approaches requires very specialized knowledge. In order to bridge the gap between theory and practice in dMRI reconstruction and analysis we present a detailed review of the dMRI modeling literature. We place an emphasis on the mathematical and algorithmic underpinnings of the subject, categorizing existing methods according to how they treat the angular and radial sampling of the diffusion signal. We describe the features that can be computed with each method and discuss its advantages and limitations. We also provide a detailed bibliography to guide the reader.
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"... We present a general arc search algorithm for linearly constrained optimization. The method constructs and searches along smooth arcs that satisfy a small and practical set of properties. An activeset strategy is used to manage linear inequality constraints. When second derivatives are used, the me ..."
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We present a general arc search algorithm for linearly constrained optimization. The method constructs and searches along smooth arcs that satisfy a small and practical set of properties. An activeset strategy is used to manage linear inequality constraints. When second derivatives are used, the method is shown to converge to a secondorder critical point and have a quadratic rate of convergence under standard conditions. The theory is applied to the methods of line search, curvilinear search, and modified gradient flow that have previously been proposed for unconstrained problems. A key issue when generalizing unconstrained methods to linearly constrained problems using an activeset strategy is the complexity of how the arc intersects hyperplanes. We introduce a new arc that is derived from the regularized Newton equation. Computing the intersection between this arc and a linear constraint reduces to finding the roots of a quadratic polynomial. The new arc scales to large problems, does not require modification to the Hessian, and is rarely dependent on the scaling of directions of negative curvature. Numerical experiments show the effectiveness of this arc search method on problems from the CUTEr test set and on a specific class of problems for which identifying negative curvature is critical. A second set of experiments demonstrates that when using SR1 quasiNewton updates, this arc search method is competitive with a line search method using