All Years Seminars
[INMA] 2019-03-19 (14:00) : Investigating the theoretical and neural framework of predictive mechanisms in eye-hand coordination
At Euler building (room A.002)
Speaker :
Mathew, James
Abstract :
The ability to coordinate efficiently eye and hand actions is central for humans in everyday activities. Furthermore it is argued that the ability to predict the sensory consequences of self-initiated movements is crucial for skilled motor behavior. Here by means of a task in which participants were asked to track with the eyes a visual target that was moved by their hand, we investigated the predictive mechanisms underlying eye-hand coordination. In a first study, using a protocol in which participants had to adapt to rotated hand visual feedback, we show that these predictive mechanisms can be updated independently of the ability to perform accurate hand movements. In a follow up study we tested the effect of hand dominance, and showed that, despite obvious differences in the accuracy of hand movement control, the ability to predict visual consequences of right and left hand actions was similar. Finally, by means of transcranial magnetic stimulation, we tested the hypothesis that those predictive mechanisms rely on hand efferent signals from the primary motor cortex (M1). However our results failed to support this view, and instead suggest that if such a contribution exists, it must be upstream of M1. Overall, we propose that eye-hand coordination relies on similar predictive mechanisms for both hands, possibly located upstream of M1, which can be updated independently of hand movement control.
[INMA] 2019-03-12 (14:00) : One-Bit Sensing of Low-Rank and Bisparse Matrices
At Euler building (room A.002)
Speaker :
Jacques, Laurent
Abstract :
In this talk, we will consider the worst-case recovery error of
low-rank and bisparse matrices as a function of the number of one-bit
measurements used to acquire them, i.e., when these matrices are
randomly projected into a low-dimensional domain and only the signs of
the resulting coordinates are recorded.
Such matrices are of practical interest for instance in the problems of
sparse phase retrieval, sparse PCA, or in optical applications involving
far-field observations of sparse scenes. First, by way of the concept of
consistency width, we will review precise estimates on how fast the
recovery error can in theory decay. Next, we will analyze an idealized
recovery method reaching the fourth-root of the optimal decay rate for
Gaussian sensing schemes. This idealized method being impractical, an
implementable recovery algorithm will be finally proposed in the context
of factorized Gaussian sensing schemes. In this case, the recovery error
provably decays as the sixth-root of the optimal rate.
Joint work with Simon Foucart (Texas A&M University, USA)
[INMA] 2019-03-05 (14:00) : Diffusion in complex systems: random walks, fast ions and fake news
At Euler building (room A.002)
Speaker :
Bovet, Alexandre
Abstract :
After a quick overview of my past work on the anomalous diffusion of fast ions in turbulent plasmas I will present
my recent work on the investigation of diffusion of news in Twitter.
To understand the role of fake news in Twitter during the 2016 US election, we combined machine learning,
network science, statistical physics and causality analysis to not only measure the importance of fake news
compared to traditional news in Twitter but also understand their influence and the mechanisms of their diffusion.
Using a dataset of more than 170 million tweets covering the five months preceding election day and concerning
the two main candidates of the 2016 US presidential election, we find that 25% of the tweets linking to a news spread
either fake or extremely biased news. We analyzed the networks of information flow and found the most important
news spreaders by using the theory of optimal percolation and used a multivariate causal network reconstruction to
uncover how fake news influenced the presidential election.
I will end with the presentation of my current work and my future research plan about random walks to investigate
spatio-temporal structures in temporal networks.
[INMA] 2019-02-26 (14:00) : Geometric Tools for Human Behavior Understanding
At Euler building (room A.002)
Speaker :
Anis Kacem (IMT Lille Douai)
Abstract :
Developing intelligent systems dedicated to human behavior understanding has been a very hot research topic in the few recent decades. Indeed, it is crucial to understand human behavior in order to make machines able to interact with, assist, and help humans in their daily life. Recent breakthroughs in computer vision and machine learning have made this possible. For instance, human-related computer vision problems can be approached by first detecting and tracking 2D or 3D landmark points from visual data. Two relevant examples of this are given by the facial landmarks detected on the human face and the skeletons tracked along videos of human bodies. These techniques generate temporal sequences of landmark configurations, which exhibit several distortions in their analysis, especially in uncontrolled environments, due to view variations, inaccurate detection and tracking, missing data, etc. In this thesis, we propose two novel space-time representations of human landmark sequences along with suitable computational tools for human behavior understanding. Firstly, we propose a representation based on the trajectories of Gram matrices of human landmarks. Gram matrices are positive semi-definite matrices of fixed rank and lie on a nonlinear manifold where standard computational and machine learning techniques could not be applied in a straightforward way. To overcome this issue, we make use of some notions of the Riemannian geometry and derive suitable computational tools for analyzing Gram trajectories. We evaluate the proposed approach in several human-related applications involving 2D and 3D landmarks of human faces and bodies such us emotion recognition from facial expression and body movements and also action recognition from skeletons. Secondly, we propose another representation based on the barycentric coordinates of 2D facial landmarks. While being related to the Gram trajectory representation and robust to view variations, the barycentric representation allows to directly work with standard computational tools. The evaluation of this second approach is conducted on two face analysis tasks namely, facial expression recognition and depression severity level assessment. The obtained results with the two proposed approaches on real benchmarks are competitive with respect to recent state-of-the-art methods.
[INMA] 2019-02-19 (14:00) : Minkowski Set Operations and Morphological Openings of Ellipsoids - Application for Processing Positive Definite Matrix-Valued Images
At Euler building (room A.002)
Speaker :
Jesús Angulo (CMM-Centre de Morphologie Mathématique, MINES ParisTech, PSL-Research University, France)
Abstract :
Morphological dilation and erosion for sets are based on (geometric) Minkowski sum and difference of two sets. In this talk we deal with the particular case of ellipsoids. Indeed ellipsoidal sets appear nowadays in different image and data representations, e.g., in diffusion tensor imaging each voxel is valued with a 3D ellipsoid; the dispersion of a scatter set of points can be described by a multivariate Gaussian distribution where the covariance matrix may be seen as ellipsoidal shape centered at the mean position.
The Minkowski sum and difference of two ellipsoidal sets are in general not ellipsoidal. However, in many applications, we are interested in computing the ellipsoidal set which approximates in a certain sense the Minkowski operations.
A closed-form characterization of Minkowski operations of two ellipsoids has been recently introduced (Yan and Chirikjian, 2015), which provide implicit surface expression and parametric formulas for the boundary of the Minkowski sum and difference of two arbitrary oriented ellipsoids. We adopt in this study a different approach based on the so-called ellipsoidal calculus (Kurzhanski and Valyi, 1996). Ellipsoidal calculus is a method for solving problems in control and estimation theory having unknown but bounded errors in terms of sets of approximating ellipsoidal-value functions.
Using the theory and algorithms from ellipsoidal calculus, we consider parameterized families of external and internal ellipsoids that tightly approximate the Minkowski sum and difference of ellipsoids. Approximations are tight along a direction l in the sense that the support functions on l of the ellipsoids are equal to the support function on l of the sum and difference. External (resp. internal) support function-based approximation can be then selected according to minimal (resp. maximal) measures of volume or trace of the corresponding ellipsoid. We focus in particular on the ellipsoidal approximations to the morphological opening between two ellipsoids and its interest in practical examples.
We discuss also the connection between the approximations to the Minkowski sum and difference of two positive definite matrices and their mean using their Euclidean or Riemannian geometries, which is also related to their Bures-Wasserstein mean (Bhatia et al., 2018).
References
Bhatia R., Jain T., Lim Y. (2018) On the Bures-Wasserstein Distance Between Positive Definite Matrices. Expositiones Mathematicae, to appear.
Kurzhanski A.B, Valyi I (1996). Ellipsoidal Calculus for Estimation and Control. Birkhäuser, Boston, MA, 1996.
Mazure M.-L (1991) Equations de convolution et formes quadratiques. Annali di Maematica pura et applicata (IV), Vol. CLVIII, 75-97.
Yan Y, Chirikjian G.S (2015) Closed characterization of the Minkowski sum and difference of two ellipsoids. Geom. Dedicata 177:103-128.
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