This paper presents a new method of missing point estimation (MPE) to derive efficient reduced-order models for large-scale parameter-varying systems. Such systems often result from the discretization of nonlinear partial differential equations. A projection-based model reduction framework is used where projection spaces are inferred from proper orthogonal decompositions of data-dependent correlation operators. The key contribution of the MPE method is to perform online computations efficiently by computing Galerkin projections over a restricted subset of the spatial domain. Quantitative criteria for optimally selecting such a spatial subset are proposed and the resulting optimization problem is solved using an efficient heuristic method. The effectiveness of the MPE method is demonstrated by applying it to a nonlinear computational fluid dynamic model of an industrial glass furnace. For this example, the Galerkin projection can be computed using only 25% of the spatial grid points without compromising the accuracy of the reduced model.

/pdf/missing-point-estimation-in-models-described-by-proper-4iz3qmks82.pdf

Missing point estimation in models described by proper orthogonal decomposition

This article addresses the question of the effects of cost setting on the kind of temporal patterns optimal matching (OM) can uncover when applied to social science data It is argued that the balance between indel (insertion and deletion) and substitution costs determines what kind of socio-temporal pattern can be brought to light Insertion and deletion operations favor identically coded states irrespective of their locations whereas substitutions focus on contemporaneous similarities The lower the ratio of substitution to indel costs, the closer OM is to the Hamming distance where only substitutions are used The higher this ratio, the closer OM is to the Levenshtein II distance, which amounts to finding the longest common subsequence When the timing of sequences is crucial, substitutions should be favored over indels and their costs should be carefully fixed Ideally, substitution costs should vary with time to better take into account the timing of the sequences studied As indels warp time, hence 

/pdf/setting-cost-in-optimal-matching-to-uncover-contemporaneous-4iwsa905h0.pdf

Setting cost in Optimal Matching to uncover contemporaneous socio-temporal patterns

Low-resolution (LR) of face images significantly decreases the performance of face recognition. To address this problem, we present a super-resolution method that uses nonlinear mappings to infer coherent features that favor higher recognition of the nearest neighbor (NN) classifiers for recognition of single LR face image. Canonical correlation analysis is applied to establish the coherent subspaces between the principal component analysis (PCA) based features of high-resolution (HR) and LR face images. Then, a nonlinear mapping between HR/LR features can be built by radial basis functions (RBFs) with lower regression errors in the coherent feature space than in the PCA feature space. Thus, we can compute super-resolved coherent features corresponding to an input LR image according to the trained RBF model efficiently and accurately. And, face identity can be obtained by feeding these super-resolved features to a simple NN classifier. Extensive experiments on the Facial Recognition Technology, University of Manchester Institute of Science and Technology, and Olivetti Research Laboratory databases show that the proposed method outperforms the state-of-the-art face recognition algorithms for single LR image in terms of both recognition rate and robustness to facial variations of pose and expression.

Super-Resolution Method for Face Recognition Using Nonlinear Mappings on Coherent Features

Background 
During planning and execution of reaching movements, the activity of cortical motor neurons is modulated by a diversity of motor, sensory, and cognitive signals. Brain-machine interfaces (BMIs) extract part of these modulations to directly control artificial actuators. However, cortical modulations that emerge in the novel context of operating the BMI are poorly understood.


Methodology/Principal Findings 
Here we analyzed the changes in neuronal modulations that occurred in different cortical motor areas as monkeys learned to use a BMI to control reaching movements. Using spike-train analysis methods we demonstrate that the modulations of the firing-rates of cortical neurons increased abruptly after the monkeys started operating the BMI. Regression analysis revealed that these enhanced modulations were not correlated with the kinematics of the movement. The initial enhancement in firing rate modulations declined gradually with subsequent training in parallel with the improvement in behavioral performance.


Conclusions/Significance 
We conclude that the enhanced modulations are related to computational tasks that are significant especially in novel motor contexts. Although the function and neuronal mechanism of the enhanced cortical modulations are open for further inquiries, we discuss their potential role in processing execution errors and representing corrective or explorative activity. These representations are expected to contribute to the formation of internal models of the external actuator and their decoding may facilitate BMI improvement.

/pdf/cortical-modulations-increase-in-early-sessions-with-brain-4ca2q6k6eo.pdf

Cortical modulations increase in early sessions with brain-machine interface.

We consider the problem of reconstructing a surface from scattered points sampled on a physical shape. The sampled shape is approximated as the zero level set of a function. This function is defined as a linear combination of compactly supported radial basis functions. We depart from previous work by using as centers of basis functions a set of points located on an estimate of the medial axis, instead of the input data points. Those centers are selected among the vertices of the Voronoi diagram of the sample data points. Being a Voronoi vertex, each center is associated with a maximal empty ball. We use the radius of this ball to adapt the support of each radial basis function. Our method can fit a user-defined budget of centers: The selected subset of Voronoi vertices is filtered using the notion of lambda medial axis, then clustered to fit the allocated budget.

https://hal.inria.fr/inria-00116651/document

Reconstruction with Voronoi centered radial basis functions

On Thursday, 5 October, and on Friday, 6 October, we had two sessions on &dquo;Geometric Data Analysis&dquo;. The title of the sessions is the English translation of the French &dquo;L’Analyse des Donnees&dquo; which includes different techniques of visualization of data, from principal components analysis to multiple-correspondence analysis. The main idea formulated by the &dquo;father&dquo; of the &dquo;L’Analyse des Donnees&dquo;, Jean-Paul Benzecri, is that the model has to follow the data and not vice versa. Whereas the session from Michael Greenacre on &dquo;Multiple-Correspondence Analysis and its Interpretation&dquo; (Wednesday, 4 October) was mainly focussed on the technique itself, the idea of these two sessions was to give substantive examples using this method. Since correspondence analysis largely found its way into the social sciences via the publications by Pierre Bourdieu, and since many of the below listed contributors are closely connected with him and his work, many of the papers dealt with applications of his theory. In this way, the two sessions can be treated as a continuation of another conference which was hosted in October 1998 also at the Zentralarchiv fuer Empirische Sozialforschung, organized by Henry Rouanet and Joerg Blasius (for

Joerg Blasius

Papers

Geometric Data Analysis