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.

Comment on "From geodesics of the multipole solutions to the perturbed Kepler problem"

In this Comment we explain the discrepancies mentioned by the authors between their results and ours about the in?uence of the gravitational quadrupole moment in the perturbative calculation of corrections to the precession of the periastron of quasielliptical Keplerian equatorial orbits around a point mass. The discrepancy appears to be a consequence of two different calculations of the angular momentum of the orbits.

Asymptotic solution for the two-body problem with constant tangencial acceleration

An analytical solution of the two body problem perturbed by a constant tangential acceleration is derived with the aid of perturbation theory. The solution, which is valid for circular and elliptic orbits with generic eccentricity, describes the instantaneous time variation of all orbital elements. A comparison with high-accuracy numerical results shows that the analytical method can be effectively applied to multiple-revolution low-thrust orbit transfer around planets and in interplanetary space with negligible error.

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.

Adaptive control system based on lineal control theory for the path-following problem of a car-like mobile robot

The objective of this paper is to design a path following control system for a car-like mobile robot using classical linear control techniques, so that it adapts on-line to varying conditions during the trajectory following task. The main advantages of the proposed control structure is that well known linear control theory can be applied in calculating the PID controllers to full control requirements, while at the same time it is exible to be applied in non-linear changing conditions of the path following task. For this purpose the Frenet frame kinematic model of the robot is linearised at a varying working point that is calculated as a function of the actual velocity, the path curvature and kinematic parameters of the robot, yielding a transfer function that varies during the trajectory. The proposed controller is formed by a combination of an adaptive PID and a feed-forward controller, which varies accordingly with the working conditions and compensates the non-linearity of the system. The good features and exibility of the proposed control structure have been demonstrated through realistic simulations that include both kinematics and dynamics of the car-like robot.

Dynamics of brain networks in aesthetic appreciation

Neuroimage experiments have been essential for identifying active brain networks. During cognitive tasks as in, e.g., aesthetic appreciation, such networks include regions that belong to the default mode network (DMN). Theoretically, DMN activity should be interrupted during cognitive tasks demanding attention, as is the case for aesthetic appreciation. Analyzing the functional connectivity dynamics along three temporal windows and two conditions, beautiful and not beautiful stimuli, here we report experimental support for the hypothesis that aesthetic appreciation relies on the activation of two different networks, an initial aesthetic network and a delayed aesthetic network, engaged within distinct time frames. Activation of the DMN might correspond mainly to the delayed aesthetic network. We discuss adaptive and evolutionary explanations for the relationships existing between the DMN and aesthetic networks and offer unique inputs to debates on the mind/brain interaction.

On the approximate parametrization problem of algebraic curves.

The problem of parameterizing approximately algebraic curves and surfaces is an active research field, with many implications in practical applications. The problem can be treated locally or globally. We formally state the problem, in its global version for the case of algebraic curves (planar or spatial), and we report on some algorithms approaching it, as well as on the associated error distance analysis.

El lugar de la mente. Sobre la capilla Sogn Benedetg de Peter Zumthor en Sumvitg/ The place of the mind. On Peter Zumthor’s Sogn Benedetg Chapel in Sumvitg

La Capilla de Sogn Benedetg en Sumvitg, parte de la obra temprana de Peter Zumthor, condensa aspectos de sus ideas, de su forma de proyectar y construir, que aún hoy siguen vigentes en él. Los recuerdos de infancia cimientan su enfoque de la arquitectura, en el que trata de reunir trazas de la vida cotidiana, sensible al lugar y utilizando materiales tratados de un modo preciso que bajo la luz adquieren su presencia. Con un lenguaje táctil y tectónico, desde una aproximación fenomenológica, persigue compartir una experiencia multisensorial, englobando percepciones complementarias que trascienden la geometría visual. Como Kahn, se apoya en el pensamiento de Heidegger, y se inspira en la pequeña cabaña que el filósofo habitaba en la Selva Negra, así como en la arquitectura religiosa de Rudolf Schwarz, cuya huella puede apreciarse tanto en el edificio como en los objetos que se encuentran en él. La tensión que genera entre interior y exterior mantiene despiertos los sentidos del visitante, a la vez que las características de la capilla enlazan con un regionalismo integrador que no se aparta de las formas abstractas contemporáneas. : Sogn Benedetg Chapel in Sumvitg, part of the early work of Peter Zumthor, condenses aspects of his ideas and his way of designing and building, which still remain valid today. Remembrances of childhood lay the foundation for his focus to architecture, which involves the collection of daily life traces, sensitive to the place and using materials treated in a precise manner, acquiring their presence under the light. With a tactile and tectonic language, from a phenomenological approach, he seeks to share a multi-sensory experience, encompassing complementary perceptions that transcend the visual geometry. As Kahn does, he relies on Heidegger?s thinking and is inspired by the little hut that the philosopher inhabited in the Black Forest, as well as by Rudolf Schwarz?s religious architecture, whose imprint can be appreciated in both the building and the objects encountered within it. The tension generated between interior and exterior keeps awake the senses of the visitor, while the characteristics of the chapel connect with an integrative regionalism that does not exclude contemporary abstract forms.

The elliptic rendezvous problem in DROMO formulation

The extension of DROMO formulation to relative motion is evaluated. The orbit of the follower spacecraft can be constructed through differences on the elements defining the orbit of the leader spacecraft. Assuming that the differences are small, the problemis linearized. Typical linearized solutions to relativemotion determine the relative state of the follower spacecraft at a certain time step. Because of the form of DROMO formulation, the performance of a frozen-anomaly transformation is explored. In this case, the relative state is computed for a certain value of the anomaly, equal for leader and follower. Since the time for leader and follower do not coincide, the implicit time delay needs to be corrected to recover the physical sense of the solution. When determining the relative orbit, numerical testing shows significant error reductions compared to previous linearized solutions.

Asymptotic Solution for the Two Body Problem with Radial Perturbing Acceleration

In this article, an approximate analytical solution for the two body problem perturbed by a radial, low acceleration is obtained, using a regularized formulation of the orbital motion and the method of multiple scales. The results reveal that the physics of the problem evolve in two fundamental scales of the true anomaly. The first one drives the oscillations of the orbital parameters along each orbit. The second one is responsible of the long-term variations in the amplitude and mean values of these oscillations. A good agreement is found with high precision numerical solutions.

The evolution of the brain, the human nature of cortical circuits and intellectual creativity

The tremendous expansion and the differentiation of the neocortex constitute two major events in the evolution of the mammalian brain. The increase in size and complexity of our brains opened the way to a spectacular development of cognitive and mental skills. This expansion during evolution facilitated the addition of microcircuits with a similar basic structure, which increased the complexity of the human brain and contributed to its uniqueness. However, fundamental differences even exist between distinct mammalian species. Here, we shall discuss the issue of our humanity from a neurobiological and historical perspective.

Measuring the influence of Cooperative Learning and Project Based Learning on problem solvin skill.

The aim of this study is to evaluate the effects obtained after applying two active learning methodologies (cooperative learning and project based learning) to the achievement of the competence problem solving. This study was carried out at the Technical University of Madrid, where these methodologies were applied to two Operating Systems courses. The first hypothesis tested was whether the implementation of active learning methodologies favours the achievement of ?problem solving?. The second hypothesis was focused on testing if students with higher rates in problem solving competence obtain better results in their academic performance. The results indicated that active learning methodologies do not produce any significant change in the generic competence ?problem solving? during the period analysed. Concerning this, we consider that students should work with these methodologies for a longer period, besides having a specific training. Nevertheless, a close correlation between problem solving self appraisal and academic performance has been detected.

Phase transitions in number theory: from the birthday problem to Sidon sets

In this work, we show how number theoretical problems can be fruitfully approached with the tools of statistical physics. We focus on g-Sidon sets, which describe sequences of integers whose pairwise sums are different, and propose a random decision problem which addresses the probability of a random set of k integers to be g-Sidon. First, we provide numerical evidence showing that there is a crossover between satisfiable and unsatisfiable phases which converts to an abrupt phase transition in a properly defined thermodynamic limit. Initially assuming independence, we then develop a mean-field theory for the g-Sidon decision problem. We further improve the mean-field theory, which is only qualitatively correct, by incorporating deviations from independence, yielding results in good quantitative agreement with the numerics for both finite systems and in the thermodynamic limit. Connections between the generalized birthday problem in probability theory, the number theory of Sidon sets and the properties of q-Potts models in condensed matter physics are briefly discussed

Exact solution for the conjugate fluid-fluid problem in the thermal entrance region of laminar counterflow heat exchangers

A generalized Lévêque solution is presented for the conjugate fluid–fluid problem that arises in the thermal entrance region of laminar counterflow heat exchangers. The analysis, carried out for constant property fluids, assumes that the Prandtl and Peclet numbers are both large compared to unity, and neglects axial conduction both in the fluids and in the plate, assumed to be thermally thin. Under these conditions, the thermal entrance region admits an asymptotic self-similar description where the temperature varies as a power ϳ of the axial distance, with the particularity that the self-similarity exponent must be determined as an eigenvalue by solving a transcendental equation arising from the requirement of continuity of heat fluxes at the heat conducting wall. Specifically, the analysis reveals that j depends only on the lumped parameter ƙ = (A2/A1)1/3 (α1/α2)1/3(k2/k1), defined in terms of the ratios of the wall velocity gradients, A, thermal diffusivities, α i, and thermal conductivities,k i, of the fluids entering, 1, and exiting, 2, the heat exchanger. Moreover, it is shown that for large (small) values of K solution reduces to the classical first (second) Lévêque solution. Closed-form analytical expressions for the asymptotic temperature distributions and local heat-transfer rate in the thermal entrance region are given and compared with numerical results in the counterflow parallel-plate configuration, showing very good agreement in all cases.

A new set of integrals of motion to propagate the perturbed two-body problem

A formulation of the perturbed two-body problem that relies on a new set of orbital elements is presented. The proposed method represents a generalization of the special perturbation method published by Peláez et al. (Celest Mech Dyn Astron 97(2):131?150,2007) for the case of a perturbing force that is partially or totally derivable from a potential. We accomplish this result by employing a generalized Sundman time transformation in the framework of the projective decomposition, which is a known approach for transforming the two-body problem into a set of linear and regular differential equations of motion. Numerical tests, carried out with examples extensively used in the literature, show the remarkable improvement of the performance of the new method for different kinds of perturbations and eccentricities. In particular, one notable result is that the quadratic dependence of the position error on the time-like argument exhibited by Peláez?s method for near-circular motion under the J2 perturbation is transformed into linear.Moreover, themethod reveals to be competitive with two very popular elementmethods derived from theKustaanheimo-Stiefel and Sperling-Burdet regularizations.