A guided heuristic approach to the MEG inverse problem.

There is general agreement within the scientific community in considering Biology as the science with more potential to develop in the XXI century. This is due to several reasons, but probably the most important one is the state of development of the rest of experimental and technological sciences. In this context, there are a very rich variety of mathematical tools, physical techniques and computer resources that permit to do biological experiments that were unbelievable only a few years ago. Biology is nowadays taking advantage of all these newly developed technologies, which are been applied to life sciences opening new research fields and helping to give new insights in many biological problems. Consequently, biologists have improved a lot their knowledge in many key areas as human function and human diseases. However there is one human organ that is still barely understood compared with the rest: The human brain. The understanding of the human brain is one of the main challenges of the XXI century. In this regard, it is considered a strategic research field for the European Union and the USA. Thus, there is a big interest in applying new experimental techniques for the study of brain function. Magnetoencephalography (MEG) is one of these novel techniques that are currently applied for mapping the brain activity1. This technique has important advantages compared to the metabolic-based brain imagining techniques like Functional Magneto Resonance Imaging2 (fMRI). The main advantage is that MEG has a higher time resolution than fMRI. Another benefit of MEG is that it is a patient friendly clinical technique. The measure is performed with a wireless set up and the patient is not exposed to any radiation. Although MEG is widely applied in clinical studies, there are still open issues regarding data analysis. The present work deals with the solution of the inverse problem in MEG, which is the most controversial and uncertain part of the analysis process3. This question is addressed using several variations of a new solving algorithm based in a heuristic method. The performance of those methods is analyzed by applying them to several test cases with known solutions and comparing those solutions with the ones provided by our methods.

Don't blame the economists. It is an inverse problem!

The seriousness of the current crisis urgently demands new economic thinking that breaks the austerity vs. deficit spending circle in economic policy. The core tenet of the paper is that the most important problems that natural and social science are facing today are inverse problems, and that a new approach that goes beyond optimization is necessary. The approach presented here is radical in the sense that it identifies the roots in key assumptions in economic theory such as optimal behavior and stability to provide an inverse thinking perspective to economic modeling, of use in economic and financial stability policy. The inverse problem provides a truly multidisciplinary platform where related problems from different disciplines can be studied under a common approach with comparable results.

An evolutionary algorithm for the surface structure problem

Many macroscopic properties: hardness, corrosion, catalytic activity, etc. are directly related to the surface structure, that is, to the position and chemical identity of the outermost atoms of the material. Current experimental techniques for its determination produce a “signature” from which the structure must be inferred by solving an inverse problem: a solution is proposed, its corresponding signature computed and then compared to the experiment. This is a challenging optimization problem where the search space and the number of local minima grows exponentially with the number of atoms, hence its solution cannot be achieved for arbitrarily large structures. Nowadays, it is solved by using a mixture of human knowledge and local search techniques: an expert proposes a solution that is refined using a local minimizer. If the outcome does not fit the experiment, a new solution must be proposed again. Solving a small surface can take from days to weeks of this trial and error method. Here we describe our ongoing work in its solution. We use an hybrid algorithm that mixes evolutionary techniques with trusted region methods and reuses knowledge gained during the execution to avoid repeated search of structures. Its parallelization produces good results even when not requiring the gathering of the full population, hence it can be used in loosely coupled environments such as grids. With this algorithm, the solution of test cases that previously took weeks of expert time can be automatically solved in a day or two of uniprocessor time.

An inverse optimization strategy to determine single crystal mechanical behavior from polycrystal tests: Application to AZ31 Mg alloy

An inverse optimization strategy was developed to determine the single crystal properties from experimental results of the mechanical behavior of polycrystals. The polycrystal behavior was obtained by means of the finite element simulation of a representative volume element of the microstructure in which the dominant slip and twinning systems were included in the constitutive equation of each grain. The inverse problem was solved by means of the Levenberg-Marquardt method, which provided an excellent fit to the experimental results. The iterative optimization process followed a hierarchical scheme in which simple representative volume elements were initially used, followed by more realistic ones to reach the final optimum solution, leading to important reductions in computer time. The new strategy was applied to identify the initial and saturation critical resolved shear stresses and the hardening modulus of the active slip systems and extension twinning in a textured AZ31 Mg alloy. The results were in general agreement with the data in the literature but also showed some differences. They were partially explained because of the higher accuracy of the new optimization strategy but it was also shown that the number of independent experimental stress-strain curves used as input is critical to reach an accurate solution to the inverse optimization problem. It was concluded that at least three independent stress-strain curves are necessary to determine the single crystal behavior from polycrystal tests in the case of highly textured Mg alloys.

Determination of the mechanical properties of amorphous materials through instrumented nanoindentation

A novel methodology based on instrumented indentation is developed to determine the mechanical properties of amorphous materials which present cohesive-frictional behaviour. The approach is based on the concept of a universal hardness equation, which results from the assumption of a characteristic indentation pressure proportional to the hardness. The actual universal hardness equation is obtained from a detailed finite element analysis of the process of sharp indentation for a very wide range of material properties, and the inverse problem (i.e. how to extract the elastic modulus, the compressive yield strength and the friction angle) from instrumented indentation is solved. The applicability and limitations of the novel approach are highlighted. Finally, the model is validated against experimental data in metallic and ceramic glasses as well as polymers, covering a wide range of amorphous materials in terms of elastic modulus, yield strength and friction angle.

Reliability of tunnel liners

The possibility of application of structural reliability theory to the computation of the safety margins of excavated tunnels is presented. After a brief description of the existing procedures the limitations of the safety coefficients such as they usually defined, the proposed limit states are precised as well as the random variables and the applied methodology. Also presented are simple examples, some of them based in actual cases, and to end, some conclusions are established the most important one being the probability of using the method to solve the inverse problem of identification.

Level II reliability methods for tunnels

In tunnel construction, as in every engineering work, it is usual the decision making, with incomplete data. Nevertheless, consciously or not, the builder weighs the risks (even if this is done subjectively) so that he can offer a cost. The objective of this paper is to recall the existence of a methodology to treat the uncertainties in the data so that it is possible to see their effect on the output of the computational model used and then to estimate the failure probability or the safety margin of a structure. In this scheme it is possible to include the subjective knowledge on the statistical properties of the random variables and, using a numerical model consistent with the degree of complexity appropiate to the problem at hand, to make rationally based decisions. As will be shown with the method it is possible to quantify the relative importance of the random variables and, in addition, it can be used, under certain conditions, to solve the inverse problem. It is then a method very well suited both to the project and to the control phases of tunnel construction.

Reliability of tunnel liners

The possibility of application of structural reliability theory to the computation of the safety margins of excavated tunnels is presented. After a brief description of the existing procedures and the limitations of the safety coefficients such as they are usually defined, the proposed limit states are precised as well as the random variables and the applied methodology. Also presented are simple examples, some of them based in actual cases, and to end, some conclusions are established the most important one being the probability of using the method to solve the inverse problem of identification.

On the free-boundary for an elliptic inverse nonlocal problem arising in the nuclear fusion. A numerical approach

We consider a mathematical model related to the stationary regime of a plasma magnetically confined in a Stellarator device in the nuclear fusion. The mathematical problem may be reduced to an nonlinear elliptic inverse nonlocal two dimensional free{boundary problem. The nonlinear terms involving the unknown functions of the problem and its rearrangement. Our main goal is to determinate the existence and the estimate on the location and size of region where the solution is nonnegative almost everywhere (corresponding to the plasma region in the physical model)

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.

Inverse kinematics of a humanoid robot with non-spherical hip: a hybrid algorithm approach

This paper describes an approach to solve the inverse kinematics problem of humanoid robots whose construction shows a small but non negligible offset at the hip which prevents any purely analytical solution to be developed. Knowing that a purely numerical solution is not feasible due to variable efficiency problems, the proposed one first neglects the offset presence in order to obtain an approximate “solution” by means of an analytical algorithm based on screw theory, and then uses it as the initial condition of a numerical refining procedure based on the Levenberg‐Marquardt algorithm. In this way, few iterations are needed for any specified attitude, making it possible to implement the algorithm for real‐time applications. As a way to show the algorithm’s implementation, one case of study is considered throughout the paper, represented by the SILO2 humanoid robot.