Power Euclidean metrics for covariance matrices with application to diffusion tensor imaging

Various metrics for comparing diffusion tensors have been recently proposed in the literature. We consider a broad family of metrics which is indexed by a single power parameter. A likelihood-based procedure is developed for choosing the most appropriate metric from the family for a given dataset at hand. The approach is analogous to using the Box-Cox transformation that is frequently investigated in regression analysis. The methodology is illustrated with a simulation study and an application to a real dataset of diffusion tensor images of canine hearts

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

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

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

Interplay between magnetic anisotropy and interlayer coupling in nanosecond magnetization reversal of spin-valve trilayers

The influence of magnetic anisotropy on nanosecond magnetization reversal in coupled FeNi/Cu/Co trilayers was studied using a photoelectron emission microscope combined with x-ray magnetic circular dicroism. In quasi-isotropic samples the reversal of the soft FeNi layer is determined by domain wall pinning that leads to the formation of small and irregular domains. In samples with uniaxial magnetic anisotropy, the domains are larger and the influence of local interlayer coupling dominates the domain structure and the reversal of the FeNi layer

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

Bonobo Conservation as a means for Local Development: an Innovative Local Initiative of Community-based Conservation in the DemocraticRepublic of the Congo

International audienceThe Democratic Republic of the Congo (DRC) ranks fifth in the world in terms of biodiversity (fauna and flora) and first for mammal diversity in Africa. There are numerous endemic species including bolobos (Pan paniscus). Bolobos are endangered, threatened mainly by deforestation, poaching and diseases, and the current population is estimated from 15,000 to 50,000 individuals. Nowadays, one national park (Salonga National Park) and six reserves exist for wild bolobo conservation, representing about 73,000 km2 of protected areas over an estimated distribution area of 565,000 km2. In the Bolobo Territory, an original local project of bolobo conservation was initiated in 2001 by the Congolese NGO Mbou-Mon-Tour (MMT). From 2008 to 2013, we studied bolobo-habitat-human interactions in this forest-savanna mosaic habitat, totalizing 12 months of survey over six periods. Besides eco-ethological studies, an ethnoecological approach was developed in order to better understand how the MMT project emerged and how it has evolved. We performed semi-structured interviews, participant observation, and informal discussions with local people. We also used grey literature associated to the region. MMT use the bolobo conservation as a means to reach local development goals, which is the opposite of what is frequent in the “community-based conservation” project managed by environmental NGOs. The location of the community forests and the rules established for regulating activities in these forests were decided by the villagers under the organization of traditional chiefs according to their knowledge on bolobo ecology and range, and the disturbance they perceived of the traditional activities in the forest. Such a process is a novel and promising approach for wildlife conservation that maintains the place of local people and traditional authorities in the decision-making process and the governance

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

Shock waves in two-dimensional granular flow: effects of rough walls and polydispersity

We have studied the two-dimensional flow of balls in a small angle funnel, when either the side walls are rough or the balls are polydisperse. As in earlier work on monodisperse flows in smooth funnels, we observe the formation of kinematic shock waves/density waves. We find that for rough walls the flows are more disordered than for smooth walls and that shock waves generally propagate more slowly. For rough wall funnel flow, we show that the shock velocity and frequency obey simple scaling laws. These scaling laws are consistent with those found for smooth wall flow, but here they are cleaner since there are fewer packing-site effects and we study a wider range of parameters. For pipe flow (parallel side walls), rough walls support many shock waves, while smooth walls exhibit fewer or no shock waves. For funnel flows of balls with varying sizes, we find that flows with weak polydispersity behave qualitatively similar to monodisperse flows. For strong polydispersity, scaling breaks down and the shock waves consist of extended areas where the funnel is blocked completely.Comment: 11 pages, 15 figures; accepted for PR