Issues in the assimilation of the sources of a trace gas by inverse modelling

The problem of reconstructing the (otherwise unknown) source and sink field of a tracer in a fluid is studied by developing and testing a simple tracer transport model of a single-level global atmosphere and a dynamic data assimilation system. The source/sink field (taken to be constant over a 10-day assimilation window) and initial tracer field are analysed together by assimilating imperfect tracer observations over the window. Experiments show that useful information about the source/sink field may be determined from relatively few observations when the initial tracer field is known very accurately a-priori, even when a-priori source/sink information is biased (the source/sink a-priori is set to zero). In this case each observation provides information about the source/sink field at positions upstream and the assimilation of many observations together can reasonably determine the location and strength of a test source.

Uniqueness results for direct and inverse scattering by infinite surfaces in a lossy medium

We consider the Dirichlet boundary-value problem for the Helmholtz equation, Au + x2u = 0, with Imx > 0. in an hrbitrary bounded or unbounded open set C c W. Assuming continuity of the solution up to the boundary and a bound on growth a infinity, that lu(x)l < Cexp (Slxl), for some C > 0 and S~< Imx, we prove that the homogeneous problem has only the trivial salution. With this resnlt we prove uniqueness results for direct and inverse problems of scattering by a bounded or infinite obstacle.

Complex-valued b-spline neural networks for modelling and inverse of wiener systems

Communication signal processing applications often involve complex-valued (CV) functional representations for signals and systems. CV artificial neural networks have been studied theoretically and applied widely in nonlinear signal and data processing [1–11]. Note that most artificial neural networks cannot be automatically extended from the real-valued (RV) domain to the CV domain because the resulting model would in general violate Cauchy-Riemann conditions, and this means that the training algorithms become unusable. A number of analytic functions were introduced for the fully CV multilayer perceptrons (MLP) [4]. A fully CV radial basis function (RBF) nework was introduced in [8] for regression and classification applications. Alternatively, the problem can be avoided by using two RV artificial neural networks, one processing the real part and the other processing the imaginary part of the CV signal/system. A even more challenging problem is the inverse of a CV

Improving an inverse model of sheet metal forming by neural network based regression

An inverse model for a sheet meta l forming process aims to determine the initial parameter levels required to form the final formed shape. This is a difficult problem that is usually approached by traditional methods such as finite element analysis. Formulating the problem as a classification problem makes it possible to use well established classification algorithms, such as decision trees. Classification is, however, generally based on a winner-takes-all approach when associating the output value with the corresponding class. On the other hand, when formulating the problem as a regression task, all the output values are combined to produce the corresponding class value. For a multi-class problem, this may result in very different associations compared with classification between the output of the model and the corresponding class. Such formulation makes it possible to use well known regression algorithms, such as neural networks. In this paper, we develop a neural network based inverse model of a sheet forming process, and compare its performance with that of a linear model. Both models are used in two modes, classification mode and a function estimation mode, to investigate the advantage of re-formulating the problem as a function estimation. This results in large improvements in the recognition rate of set-up parameters of a sheet metal forming process for both models, with a neural network model achieving much more accurate parameter recognition than a linear model.

Vesselness features and the inverse compositional AAM for robust face recognition using thermal IR

Over the course of the last decade, infrared (IR) and particularly thermal IR imaging based face recognition has emerged as a promising complement to conventional, visible spectrum based approaches which continue to struggle when applied in the real world. While inherently insensitive to visible spectrum illumination changes, IR images introduce specific challenges of their own, most notably sensitivity to factors which affect facial heat emission patterns, e.g. emotional state, ambient temperature, and alcohol intake. In addition, facial expression and pose changes are more difficult to correct in IR images because they are less rich in high frequency detail which is an important cue for fitting any deformable model. In this paper we describe a novel method which addresses these major challenges. Specifically, to normalize for pose and facial expression changes we generate a synthetic frontal image of a face in a canonical, neutral facial expression from an image of the face in an arbitrary pose and facial expression. This is achieved by piecewise affine warping which follows active appearance model (AAM) fitting. This is the first publication which explores the use of an AAM on thermal IR images; we propose a pre-processing step which enhances detail in thermal images, making AAM convergence faster and more accurate. To overcome the problem of thermal IR image sensitivity to the exact pattern of facial temperature emissions we describe a representation based on reliable anatomical features. In contrast to previous approaches, our representation is not binary; rather, our method accounts for the reliability of the extracted features. This makes the proposed representation much more robust both to pose and scale changes. The effectiveness of the proposed approach is demonstrated on the largest public database of thermal IR images of faces on which it achieved 100% identification rate, significantly outperforming previously described methods

Mechanisms of action in the relationship between mindfulness and problem gambling behaviour

Previous studies have found an inverse relationship between mindfulness and problem gambling severity. This paper presents the findings from two studies of treatment seeking problem gamblers designed to explore the role of mindfulness in problem gambling. Treatment-seeking problem gamblers displayed significantly lower mindfulness scores than adult community members and university students. Mindfulness was significantly related to most indices of gambling, and psychological distress was an important mechanism in these relationships. Rumination, emotion dysregulation and thought suppression were also implicated as mediators in the inverse relationship between mindfulness and psychological distress. Taken together, the findings provide theoretical support for existing models of mindfulness which suggest that mindfulness operates by reducing psychological distress through these cognitive mechanisms. They also suggest that mindfulness training may be a new and innovative avenue for therapy to improve treatment effectiveness for problem

Inverse scattering approach for massive Thirring models with integrable type-II defects

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Optimal trajectory and solution of the inverse kinematics of a robotic manipulator by genetic algorithms

This paper presents the generation of optimal trajectories by genetic algorithms (GA) for a planar robotic manipulator. The implemented GA considers a multi-objective function that minimizes the end-effector positioning error together with the joints angular displacement and it solves the inverse kinematics problem for the trajectory. Computer simulations results are presented to illustrate this implementation and show the efficiency of the used methodology producing soft trajectories with low computing cost. © 2011 Springer-Verlag Berlin Heidelberg.

A generalization of the Moore-Penrose inverse related to matrix subspaces of C(nxm)

[EN]A natural generalization of the classical Moore-Penrose inverse is presented. The so-called S-Moore-Penrose inverse of a m x n complex matrix A, denoted by As, is defined for any linear subspace S of the matrix vector space Cnxm. The S-Moore-Penrose inverse As is characterized using either the singular value decomposition or (for the nonsingular square case) the orthogonal complements with respect to the Frobenius inner product. These results are applied to the preconditioning of linear systems based on Frobenius norm minimization and to the linearly constrained linear least squares problem.

Inverse Static Analysis of Massive Parallel Arrays of Three-State Actuators via Artificial Intelligence

Massive parallel robots (MPRs) driven by discrete actuators are force regulated robots that undergo continuous motions despite being commanded through a finite number of states only. Designing a real-time control of such systems requires fast and efficient methods for solving their inverse static analysis (ISA), which is a challenging problem and the subject of this thesis. In particular, five Artificial intelligence methods are proposed to investigate the on-line computation and the generalization error of ISA problem of a class of MPRs featuring three-state force actuators and one degree of revolute motion.

Regularization methods for the solution of a nonlinear least-squares problem in tomography

In this work we study a polyenergetic and multimaterial model for the breast image reconstruction in Digital Tomosynthesis, taking into consideration the variety of the materials forming the object and the polyenergetic nature of the X-rays beam. The modelling of the problem leads to the resolution of a high-dimensional nonlinear least-squares problem that, due to its nature of inverse ill-posed problem, needs some kind of regularization. We test two main classes of methods: the Levenberg-Marquardt method (together with the Conjugate Gradient method for the computation of the descent direction) and two limited-memory BFGS-like methods (L-BFGS). We perform some experiments for different values of the regularization parameter (constant or varying at each iteration), tolerances and stop conditions. Finally, we analyse the performance of the several methods comparing relative errors, iterations number, times and the qualities of the reconstructed images.

Numerical solutions of elliptic inverse problems via the equation error method

To estimate a parameter in an elliptic boundary value problem, the method of equation error chooses the value that minimizes the error in the PDE and boundary condition (the solution of the BVP having been replaced by a measurement). The estimated parameter converges to the exact value as the measured data converge to the exact value, provided Tikhonov regularization is used to control the instability inherent in the problem. The error in the estimated solution can be bounded in an appropriate quotient norm; estimates can be derived for both the underlying (infinite-dimensional) problem and a finite-element discretization that can be implemented in a practical algorithm. Numerical experiments demonstrate the efficacy and limitations of the method.

SPATIAL UNDERSTANDING OF MATRIX INVERSION FOR INVERSE FORCE ESTIMATION

A basic approach to study a NVH problem is to break down the system in three basic elements – source, path and receiver. While the receiver (response) and the transfer path can be measured, it is difficult to measure the source (forces) acting on the system. It becomes necessary to predict these forces to know how they influence the responses. This requires inverting the transfer path. Singular Value Decomposition (SVD) method is used to decompose the transfer path matrix into its principle components which is required for the inversion. The usual approach to force prediction requires rejecting the small singular values obtained during SVD by setting a threshold, as these small values dominate the inverse matrix. This assumption of the threshold may be subjected to rejecting important singular values severely affecting force prediction. The new approach discussed in this report looks at the column space of the transfer path matrix which is the basis for the predicted response. The response participation is an indication of how the small singular values influence the force participation. The ability to accurately reconstruct the response vector is important to establish a confidence in force vector prediction. The goal of this report is to suggest a solution that is mathematically feasible, physically meaningful, and numerically more efficient through examples. This understanding adds new insight to the effects of current code and how to apply algorithms and understanding to new codes.

Inverse kinematics of a 6 DoF human upper limb using ANFIS and ANN for anticipatory actuation in ADL-based physical Neurorehabilitation

Objective: This research is focused in the creation and validation of a solution to the inverse kinematics problem for a 6 degrees of freedom human upper limb. This system is intended to work within a realtime dysfunctional motion prediction system that allows anticipatory actuation in physical Neurorehabilitation under the assisted-as-needed paradigm. For this purpose, a multilayer perceptron-based and an ANFIS-based solution to the inverse kinematics problem are evaluated. Materials and methods: Both the multilayer perceptron-based and the ANFIS-based inverse kinematics methods have been trained with three-dimensional Cartesian positions corresponding to the end-effector of healthy human upper limbs that execute two different activities of the daily life: "serving water from a jar" and "picking up a bottle". Validation of the proposed methodologies has been performed by a 10 fold cross-validation procedure. Results: Once trained, the systems are able to map 3D positions of the end-effector to the corresponding healthy biomechanical configurations. A high mean correlation coefficient and a low root mean squared error have been found for both the multilayer perceptron and ANFIS-based methods. Conclusions: The obtained results indicate that both systems effectively solve the inverse kinematics problem, but, due to its low computational load, crucial in real-time applications, along with its high performance, a multilayer perceptron-based solution, consisting in 3 input neurons, 1 hidden layer with 3 neurons and 6 output neurons has been considered the most appropriated for the target application.

Novel fast random search clustering approach for mixing matrix identification in MIMO linear blind inverse problems with sparse inputs

In this paper we propose a novel fast random search clustering (RSC) algorithm for mixing matrix identification in multiple input multiple output (MIMO) linear blind inverse problems with sparse inputs. The proposed approach is based on the clustering of the observations around the directions given by the columns of the mixing matrix that occurs typically for sparse inputs. Exploiting this fact, the RSC algorithm proceeds by parameterizing the mixing matrix using hyperspherical coordinates, randomly selecting candidate basis vectors (i.e. clustering directions) from the observations, and accepting or rejecting them according to a binary hypothesis test based on the Neyman–Pearson criterion. The RSC algorithm is not tailored to any specific distribution for the sources, can deal with an arbitrary number of inputs and outputs (thus solving the difficult under-determined problem), and is applicable to both instantaneous and convolutive mixtures. Extensive simulations for synthetic and real data with different number of inputs and outputs, data size, sparsity factors of the inputs and signal to noise ratios confirm the good performance of the proposed approach under moderate/high signal to noise ratios. RESUMEN. Método de separación ciega de fuentes para señales dispersas basado en la identificación de la matriz de mezcla mediante técnicas de "clustering" aleatorio.