Multivariate texture discrimination based on geodesics to class centroids on a generalized Gaussian Manifold

A texture discrimination scheme is proposed wherein probability distributions are deployed on a probabilistic manifold for modeling the wavelet statistics of images. We consider the Rao geodesic distance (GD) to the class centroid for texture discrimination in various classification experiments. We compare the performance of GD to class centroid with the Euclidean distance in a similar context, both in terms of accuracy and computational complexity. Also, we compare our proposed classification scheme with the k-nearest neighbor algorithm. Univariate and multivariate Gaussian and Laplace distributions, as well as generalized Gaussian distributions with variable shape parameter are each evaluated as a statistical model for the wavelet coefficients. The GD to the centroid outperforms the Euclidean distance and yields superior discrimination compared to the k-nearest neighbor approach

Detection of brain functional-connectivity difference in post-stroke patients using group-level covariance modeling

Functional brain connectivity, as revealed through distant correlations in the signals measured by functional Magnetic Resonance Imaging (fMRI), is a promising source of biomarkers of brain pathologies. However, establishing and using diagnostic markers requires probabilistic inter-subject comparisons. Principled comparison of functional-connectivity structures is still a challenging issue. We give a new matrix-variate probabilistic model suitable for inter-subject comparison of functional connectivity matrices on the manifold of Symmetric Positive Definite (SPD) matrices. We show that this model leads to a new algorithm for principled comparison of connectivity coefficients between pairs of regions. We apply this model to comparing separately post-stroke patients to a group of healthy controls. We find neurologically-relevant connection differences and show that our model is more sensitive that the standard procedure. To the best of our knowledge, these results are the first report of functional connectivity differences between a single-patient and a group and thus establish an important step toward using functional connectivity as a diagnostic tool

Cleaving-temperature dependence of layered-oxide surfaces

The surfaces generated by cleaving non-polar, two-dimensional oxides are often considered to be perfect or ideal. However, single particle spectroscopies on Sr2RuO4, an archetypal non-polar two dimensional oxide, show significant cleavage temperature dependence. We demonstrate that this is not a consequence of the intrinsic characteristics of the surface: lattice parameters and symmetries, step heights, atom positions, or density of states. Instead, we find a marked increase in the density of defects at the mesoscopic scale with increased cleave temperature. The potential generality of these defects to oxide surfaces may have broad consequences to interfacial control and the interpretation of surface sensitive measurements

Characterizing Distances of Networks on the Tensor Manifold

At the core of understanding dynamical systems is the ability to maintain and control the systems behavior that includes notions of robustness, heterogeneity, or regime-shift detection. Recently, to explore such functional properties, a convenient representation has been to model such dynamical systems as a weighted graph consisting of a finite, but very large number of interacting agents. This said, there exists very limited relevant statistical theory that is able cope with real-life data, i.e., how does perform analysis and/or statistics over a family of networks as opposed to a specific network or network-to-network variation. Here, we are interested in the analysis of network families whereby each network represents a point on an underlying statistical manifold. To do so, we explore the Riemannian structure of the tensor manifold developed by Pennec previously applied to Diffusion Tensor Imaging (DTI) towards the problem of network analysis. In particular, while this note focuses on Pennec definition of geodesics amongst a family of networks, we show how it lays the foundation for future work for developing measures of network robustness for regime-shift detection. We conclude with experiments highlighting the proposed distance on synthetic networks and an application towards biological (stem-cell) systems.Comment: This paper is accepted at 8th International Conference on Complex Networks 201

Second-order Democratic Aggregation

Aggregated second-order features extracted from deep convolutional networks have been shown to be effective for texture generation, fine-grained recognition, material classification, and scene understanding. In this paper, we study a class of orderless aggregation functions designed to minimize interference or equalize contributions in the context of second-order features and we show that they can be computed just as efficiently as their first-order counterparts and they have favorable properties over aggregation by summation. Another line of work has shown that matrix power normalization after aggregation can significantly improve the generalization of second-order representations. We show that matrix power normalization implicitly equalizes contributions during aggregation thus establishing a connection between matrix normalization techniques and prior work on minimizing interference. Based on the analysis we present {\gamma}-democratic aggregators that interpolate between sum ({\gamma}=1) and democratic pooling ({\gamma}=0) outperforming both on several classification tasks. Moreover, unlike power normalization, the {\gamma}-democratic aggregations can be computed in a low dimensional space by sketching that allows the use of very high-dimensional second-order features. This results in a state-of-the-art performance on several datasets

Magnetic relaxation of exchange biased (Pt/Co) multilayers studied by time-resolved Kerr microscopy

Magnetization relaxation of exchange biased (Pt/Co)5/Pt/IrMn multilayers with perpendicular anisotropy was investigated by time-resolved Kerr microscopy. Magnetization reversal occurs by nucleation and domain wall propagation for both descending and ascending applied fields, but a much larger nucleation density is observed for the descending branch, where the field is applied antiparallel to the exchange bias field direction. These results can be explained by taking into account the presence of local inhomogeneities of the exchange bias field.Comment: To appear in Physical Review B (October 2005

Statistical Computing on Non-Linear Spaces for Computational Anatomy

International audienceComputational anatomy is an emerging discipline that aims at analyzing and modeling the individual anatomy of organs and their biological variability across a population. However, understanding and modeling the shape of organs is made difficult by the absence of physical models for comparing different subjects, the complexity of shapes, and the high number of degrees of freedom implied. Moreover, the geometric nature of the anatomical features usually extracted raises the need for statistics on objects like curves, surfaces and deformations that do not belong to standard Euclidean spaces. We explain in this chapter how the Riemannian structure can provide a powerful framework to build generic statistical computing tools. We show that few computational tools derive for each Riemannian metric can be used in practice as the basic atoms to build more complex generic algorithms such as interpolation, filtering and anisotropic diffusion on fields of geometric features. This computational framework is illustrated with the analysis of the shape of the scoliotic spine and the modeling of the brain variability from sulcal lines where the results suggest new anatomical findings

Stochastic Development Regression on Non-Linear Manifolds

We introduce a regression model for data on non-linear manifolds. The model describes the relation between a set of manifold valued observations, such as shapes of anatomical objects, and Euclidean explanatory variables. The approach is based on stochastic development of Euclidean diffusion processes to the manifold. Defining the data distribution as the transition distribution of the mapped stochastic process, parameters of the model, the non-linear analogue of design matrix and intercept, are found via maximum likelihood. The model is intrinsically related to the geometry encoded in the connection of the manifold. We propose an estimation procedure which applies the Laplace approximation of the likelihood function. A simulation study of the performance of the model is performed and the model is applied to a real dataset of Corpus Callosum shapes

Cracking Piles of Brittle Grains

A model which accounts for cracking avalanches in piles of grains subject to external load is introduced and numerically simulated. The stress is stochastically transferred from higher layers to lower ones. Cracked areas exhibit various morphologies, depending on the degree of randomness in the packing and on the ductility of the grains. The external force necessary to continue the cracking process is constant in wide range of values of the fraction of already cracked grains. If the grains are very brittle, the force fluctuations become periodic in early stages of cracking. Distribution of cracking avalanches obeys a power law with exponent $\tau = 2.4 \pm 0.1$.Comment: RevTeX, 6 pages, 7 postscript figures, submitted to Phys. Rev.

Evidence of triggered star formation in G327.3-0.6. Dust-continuum mapping of an infrared dark cloud with P-ArT\'eMiS

Aims. Expanding HII regions and propagating shocks are common in the environment of young high-mass star-forming complexes. They can compress a pre-existing molecular cloud and trigger the formation of dense cores. We investigate whether these phenomena can explain the formation of high-mass protostars within an infrared dark cloud located at the position of G327.3-0.6 in the Galactic plane, in between two large infrared bubbles and two HII regions. Methods: The region of G327.3-0.6 was imaged at 450 ? m with the CEA P-ArT\'eMiS bolometer array on the Atacama Pathfinder EXperiment telescope in Chile. APEX/LABOCA and APEX-2A, and Spitzer/IRAC and MIPS archives data were used in this study. Results: Ten massive cores were detected in the P-ArT\'eMiS image, embedded within the infrared dark cloud seen in absorption at both 8 and 24 ?m. Their luminosities and masses indicate that they form high-mass stars. The kinematical study of the region suggests that the infrared bubbles expand toward the infrared dark cloud. Conclusions: Under the influence of expanding bubbles, star formation occurs in the infrared dark areas at the border of HII regions and infrared bubbles.Comment: 4 page