Gravitational slopes, geomorphology, and material strengths of the nucleus of comet 67P/Churyumov-Gerasimenko from OSIRIS observations

Aims. We study the link between gravitational slopes and the surface morphology on the nucleus of comet 67P/Churyumov-Gerasimenko and provide constraints on the mechanical properties of the cometary material (tensile, shear, and compressive strengths). Methods. We computed the gravitational slopes for five regions on the nucleus that are representative of the different morphologies observed on the surface (Imhotep, Ash, Seth, Hathor, and Agilkia), using two shape models computed from OSIRIS images by the stereo-photoclinometry (SPC) and stereo-photogrammetry (SPG) techniques. We estimated the tensile, shear, and compressive strengths using different surface morphologies (overhangs, collapsed structures, boulders, cliffs, and Philae's footprint) and mechanical considerations. Results. The different regions show a similar general pattern in terms of the relation between gravitational slopes and terrain morphology: i) low-slope terrains (0-20 degrees) are covered by a fine material and contain a few large (>10 m) and isolated boulders; ii) intermediate-slope terrains (20-45 degrees) are mainly fallen consolidated materials and debris fields, with numerous intermediate-size boulders from <1m to 10m for the majority of them; and iii) high-slope terrains (45-90 degrees) are cliffs that expose a consolidated material and do not show boulders or fine materials. The best range for the tensile strength of overhangs is 3-15 Pa (upper limit of 150 Pa), 4-30 Pa for the shear strength of fine surface materials and boulders, and 30-150 Pa for the compressive strength of overhangs (upper limit of 1500 Pa). The strength-to-gravity ratio is similar for 67P and weak rocks on Earth. As a result of the low compressive strength, the interior of the nucleus may have been compressed sufficiently to initiate diagenesis, which could have contributed to the formation of layers. Our value for the tensile strength is comparable to that of dust aggregates formed by gravitational instability and tends to favor a formation of comets by the accrection of pebbles at low velocities.

Massively parallelizable list-mode reconstruction using a Monte Carlo-based elliptical Gaussian model

Purpose: A fully three-dimensional (3D) massively parallelizable list-mode ordered-subsets expectation-maximization (LM-OSEM) reconstruction algorithm has been developed for high-resolution PET cameras. System response probabilities are calculated online from a set of parameters derived from Monte Carlo simulations. The shape of a system response for a given line of response (LOR) has been shown to be asymmetrical around the LOR. This work has been focused on the development of efficient region-search techniques to sample the system response probabilities, which are suitable for asymmetric kernel models, including elliptical Gaussian models that allow for high accuracy and high parallelization efficiency. The novel region-search scheme using variable kernel models is applied in the proposed PET reconstruction algorithm. Methods: A novel region-search technique has been used to sample the probability density function in correspondence with a small dynamic subset of the field of view that constitutes the region of response (ROR). The ROR is identified around the LOR by searching for any voxel within a dynamically calculated contour. The contour condition is currently defined as a fixed threshold over the posterior probability, and arbitrary kernel models can be applied using a numerical approach. The processing of the LORs is distributed in batches among the available computing devices, then, individual LORs are processed within different processing units. In this way, both multicore and multiple many-core processing units can be efficiently exploited. Tests have been conducted with probability models that take into account the noncolinearity, positron range, and crystal penetration effects, that produced tubes of response with varying elliptical sections whose axes were a function of the crystal's thickness and angle of incidence of the given LOR. The algorithm treats the probability model as a 3D scalar field defined within a reference system aligned with the ideal LOR. Results: This new technique provides superior image quality in terms of signal-to-noise ratio as compared with the histogram-mode method based on precomputed system matrices available for a commercial small animal scanner. Reconstruction times can be kept low with the use of multicore, many-core architectures, including multiple graphic processing units. Conclusions: A highly parallelizable LM reconstruction method has been proposed based on Monte Carlo simulations and new parallelization techniques aimed at improving the reconstruction speed and the image signal-to-noise of a given OSEM algorithm. The method has been validated using simulated and real phantoms. A special advantage of the new method is the possibility of defining dynamically the cut-off threshold over the calculated probabilities thus allowing for a direct control on the trade-off between speed and quality during the reconstruction.

Genetic algorithms and Gaussian Bayesian networks to uncover the predictive core set of bibliometric indices

The diversity of bibliometric indices today poses the challenge of exploiting the relationships among them. Our research uncovers the best core set of relevant indices for predicting other bibliometric indices. An added difficulty is to select the role of each variable, that is, which bibliometric indices are predictive variables and which are response variables. This results in a novel multioutput regression problem where the role of each variable (predictor or response) is unknown beforehand. We use Gaussian Bayesian networks to solve the this problem and discover multivariate relationships among bibliometric indices. These networks are learnt by a genetic algorithm that looks for the optimal models that best predict bibliometric data. Results show that the optimal induced Gaussian Bayesian networks corroborate previous relationships between several indices, but also suggest new, previously unreported interactions. An extended analysis of the best model illustrates that a set of 12 bibliometric indices can be accurately predicted using only a smaller predictive core subset composed of citations, g-index, q2-index, and hr-index. This research is performed using bibliometric data on Spanish full professors associated with the computer science area.

Regulation and localization of tyrosine216 phosphorylation of glycogen synthase kinase-3β in cellular and animal models of neuronal degeneration

Inactivation of glycogen synthase kinase-3β (GSK3β) by S9 phosphorylation is implicated in mechanisms of neuronal survival. Phosphorylation of a distinct site, Y216, on GSK3β is necessary for its activity; however, whether this site can be regulated in cells is unknown. Therefore we examined the regulation of Y216 phosphorylation on GSK3β in models of neurodegeneration. Nerve growth factor withdrawal from differentiated PC12 cells and staurosporine treatment of SH-SY5Y cells led to increased phosphorylation at Y216, GSK3β activity, and cell death. Lithium and insulin, agents that lead to inhibition of GSK3β and adenoviral-mediated transduction of dominant negative GSK3β constructs, prevented cell death by the proapoptotic stimuli. Inhibitors induced S9 phosphorylation and inactivation of GSK3β but did not affect Y216 phosphorylation, suggesting that S9 phosphorylation is sufficient to override GSK3β activation by Y216 phosphorylation. Under the conditions examined, increased Y216 phosphorylation on GSK3β was not an autophosphorylation response. In resting cells, Y216 phosphorylation was restricted to GSK3β present at focal adhesion sites. However, after staurosporine, a dramatic alteration in the immunolocalization pattern was observed, and Y216-phosphorylated GSK3β selectively increased within the nucleus. In rats, Y216 phosphorylation was increased in degenerating cortical neurons induced by ischemia. Taken together, these results suggest that Y216 phosphorylation of GSK3β represents an important mechanism by which cellular insults can lead to neuronal death.

The asymptotic distribution of canonical correlations and vectors in higher-order cointegrated models

The study of the large-sample distribution of the canonical correlations and variates in cointegrated models is extended from the first-order autoregression model to autoregression of any (finite) order. The cointegrated process considered here is nonstationary in some dimensions and stationary in some other directions, but the first difference (the “error-correction form”) is stationary. The asymptotic distribution of the canonical correlations between the first differences and the predictor variables as well as the corresponding canonical variables is obtained under the assumption that the process is Gaussian. The method of analysis is similar to that used for the first-order process.

On ANOVA Decompositions of Kernels and Gaussian Random Field Paths

The FANOVA (or “Sobol’-Hoeffding”) decomposition of multivariate functions has been used for high-dimensional model representation and global sensitivity analysis. When the objective function f has no simple analytic form and is costly to evaluate, computing FANOVA terms may be unaffordable due to numerical integration costs. Several approximate approaches relying on Gaussian random field (GRF) models have been proposed to alleviate these costs, where f is substituted by a (kriging) predictor or by conditional simulations. Here we focus on FANOVA decompositions of GRF sample paths, and we notably introduce an associated kernel decomposition into 4 d 4d terms called KANOVA. An interpretation in terms of tensor product projections is obtained, and it is shown that projected kernels control both the sparsity of GRF sample paths and the dependence structure between FANOVA effects. Applications on simulated data show the relevance of the approach for designing new classes of covariance kernels dedicated to high-dimensional kriging.

Reappraising contemporary theories of subcortical participation in language: Proposing an interhemispheric regulatory function for the subthalamic nucleus (STN) in the mediation of high-level linguistic processes

Apropos the basal ganglia, the dominant striatum and globus pallidus internus (GPi) have been hypothesised to represent integral components of subcortical language circuitry. Working subcortical language theories, however, have failed thus far to consider a role for the STN in the mediation of linguistic processes, a structure recently defined as the driving force of basal ganglia output. The aim of this research was to investigate the impact of surgically induced functional inhibition of the STN upon linguistic abilities, within the context of established models of basal ganglia participation in language. Two males with surgically induced 'lesions' of the dominant and non-dominant dorsolateral STN, aimed at relieving Parkinsonian motor symptoms, served as experimental subjects. General and high-level language profiles were compiled for each subject up to 1 month prior to and 3 months following neurosurgery, within the drug-on state (i.e., when optimally medicated). Comparable post-operative alterations in linguistic performance were observed subsequent to surgically induced functional inhibition of the left and right STN. More specifically, higher proportions of reliable decline as opposed to improvement in post-operative performance were demonstrated by both subjects on complex language tasks, hypothesised to entail the interplay of cognitive-linguistic processes. The outcomes of the current research challenge unilateralised models of functional basal ganglia organisation with the proposal of a potential interhemispheric regulatory function for the STN in the mediation of high-level linguistic processes.

A comparison of different choices for the regularization parameter in inverse electrocardiography models

Calculating the potentials on the heart’s epicardial surface from the body surface potentials constitutes one form of inverse problems in electrocardiography (ECG). Since these problems are ill-posed, one approach is to use zero-order Tikhonov regularization, where the squared norms of both the residual and the solution are minimized, with a relative weight determined by the regularization parameter. In this paper, we used three different methods to choose the regularization parameter in the inverse solutions of ECG. The three methods include the L-curve, the generalized cross validation (GCV) and the discrepancy principle (DP). Among them, the GCV method has received less attention in solutions to ECG inverse problems than the other methods. Since the DP approach needs knowledge of norm of noises, we used a model function to estimate the noise. The performance of various methods was compared using a concentric sphere model and a real geometry heart-torso model with a distribution of current dipoles placed inside the heart model as the source. Gaussian measurement noises were added to the body surface potentials. The results show that the three methods all produce good inverse solutions with little noise; but, as the noise increases, the DP approach produces better results than the L-curve and GCV methods, particularly in the real geometry model. Both the GCV and L-curve methods perform well in low to medium noise situations.

Using generative models for handwritten digit recognition

We describe a method of recognizing handwritten digits by fitting generative models that are built from deformable B-splines with Gaussian ``ink generators'' spaced along the length of the spline. The splines are adjusted using a novel elastic matching procedure based on the Expectation Maximization (EM) algorithm that maximizes the likelihood of the model generating the data. This approach has many advantages. (1) After identifying the model most likely to have generated the data, the system not only produces a classification of the digit but also a rich description of the instantiation parameters which can yield information such as the writing style. (2) During the process of explaining the image, generative models can perform recognition driven segmentation. (3) The method involves a relatively small number of parameters and hence training is relatively easy and fast. (4) Unlike many other recognition schemes it does not rely on some form of pre-normalization of input images, but can handle arbitrary scalings, translations and a limited degree of image rotation. We have demonstrated our method of fitting models to images does not get trapped in poor local minima. The main disadvantage of the method is it requires much more computation than more standard OCR techniques.

Prediction with Gaussian processes: from linear regression to linear prediction and beyond

The main aim of this paper is to provide a tutorial on regression with Gaussian processes. We start from Bayesian linear regression, and show how by a change of viewpoint one can see this method as a Gaussian process predictor based on priors over functions, rather than on priors over parameters. This leads in to a more general discussion of Gaussian processes in section 4. Section 5 deals with further issues, including hierarchical modelling and the setting of the parameters that control the Gaussian process, the covariance functions for neural network models and the use of Gaussian processes in classification problems.

Sparse on-line Gaussian processes

We develop an approach for sparse representations of Gaussian Process (GP) models (which are Bayesian types of kernel machines) in order to overcome their limitations for large data sets. The method is based on a combination of a Bayesian online algorithm together with a sequential construction of a relevant subsample of the data which fully specifies the prediction of the GP model. By using an appealing parametrisation and projection techniques that use the RKHS norm, recursions for the effective parameters and a sparse Gaussian approximation of the posterior process are obtained. This allows both for a propagation of predictions as well as of Bayesian error measures. The significance and robustness of our approach is demonstrated on a variety of experiments.

Gaussian processes:iterative sparse approximations

In recent years there has been an increased interest in applying non-parametric methods to real-world problems. Significant research has been devoted to Gaussian processes (GPs) due to their increased flexibility when compared with parametric models. These methods use Bayesian learning, which generally leads to analytically intractable posteriors. This thesis proposes a two-step solution to construct a probabilistic approximation to the posterior. In the first step we adapt the Bayesian online learning to GPs: the final approximation to the posterior is the result of propagating the first and second moments of intermediate posteriors obtained by combining a new example with the previous approximation. The propagation of em functional forms is solved by showing the existence of a parametrisation to posterior moments that uses combinations of the kernel function at the training points, transforming the Bayesian online learning of functions into a parametric formulation. The drawback is the prohibitive quadratic scaling of the number of parameters with the size of the data, making the method inapplicable to large datasets. The second step solves the problem of the exploding parameter size and makes GPs applicable to arbitrarily large datasets. The approximation is based on a measure of distance between two GPs, the KL-divergence between GPs. This second approximation is with a constrained GP in which only a small subset of the whole training dataset is used to represent the GP. This subset is called the em Basis Vector, or BV set and the resulting GP is a sparse approximation to the true posterior. As this sparsity is based on the KL-minimisation, it is probabilistic and independent of the way the posterior approximation from the first step is obtained. We combine the sparse approximation with an extension to the Bayesian online algorithm that allows multiple iterations for each input and thus approximating a batch solution. The resulting sparse learning algorithm is a generic one: for different problems we only change the likelihood. The algorithm is applied to a variety of problems and we examine its performance both on more classical regression and classification tasks and to the data-assimilation and a simple density estimation problems.

Improved robust control of nonlinear stochastic systems using uncertain models

We introduce a technique for quantifying and then exploiting uncertainty in nonlinear stochastic control systems. The approach is suboptimal though robust and relies upon the approximation of the forward and inverse plant models by neural networks, which also estimate the intrinsic uncertainty. Sampling from the resulting Gaussian distributions of the inversion based neurocontroller allows us to introduce a control law which is demonstrably more robust than traditional adaptive controllers.

Sparse on-line Gaussian processes

We develop an approach for sparse representations of Gaussian Process (GP) models (which are Bayesian types of kernel machines) in order to overcome their limitations for large data sets. The method is based on a combination of a Bayesian online algorithm together with a sequential construction of a relevant subsample of the data which fully specifies the prediction of the GP model. By using an appealing parametrisation and projection techniques that use the RKHS norm, recursions for the effective parameters and a sparse Gaussian approximation of the posterior process are obtained. This allows both for a propagation of predictions as well as of Bayesian error measures. The significance and robustness of our approach is demonstrated on a variety of experiments.

Subthalamic nucleus neurones in slices from 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine-lesioned mice show irregular, dopamine-reversible firing pattern changes, but without synchronous activity

The loss of dopamine in idiopathic or animal models of Parkinson's disease induces synchronized low-frequency oscillatory burst-firing in subthalamic nucleus neurones. We sought to establish whether these firing patterns observed in vivo were preserved in slices taken from dopamine-depleted animals, thus establishing a role for the isolated subthalamic-globus pallidus complex in generating the pathological activity. Mice treated with 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP) showed significant reductions of over 90% in levels of dopamine as measured in striatum by high pressure liquid chromatography. Likewise, significant reductions in tyrosine hydroxylase immunostaining within the striatum (>90%) and tyrosine hydroxylase positive cell numbers (65%) in substantia nigra were observed. Compared with slices from intact mice, neurones in slices from MPTP-lesioned mice fired significantly more slowly (mean rate of 4.2 Hz, cf. 7.2 Hz in control) and more irregularly (mean coefficient of variation of inter-spike interval of 94.4%, cf. 37.9% in control). Application of ionotropic glutamate receptor antagonists 6-cyano-7-nitroquinoxaline-2,3-dione (CNQX) and 2-amino-5-phosphonopentanoic acid (AP5) and the GABAA receptor antagonist picrotoxin caused no change in firing pattern. Bath application of dopamine significantly increased cell firing rate and regularized the pattern of activity in cells from slices from both MPTP-treated and control animals. Although the absolute change was more modest in control slices, the maximum dopamine effect in the two groups was comparable. Indeed, when taking into account the basal firing rate, no differences in the sensitivity to dopamine were observed between these two cohorts. Furthermore, pairs of subthalamic nucleus cells showed no correlated activity in slices from either control (21 pairs) or MPTP-treated animals (20 pairs). These results indicate that the isolated but interconnected subthalamic-globus pallidus network is not itself sufficient to generate the aberrant firing patterns in dopamine-depleted animals. More likely, inputs from other regions, such as the cortex, are needed to generate pathological oscillatory activity. © 2006 IBRO.