Abstract: We describe an equivalence of categories between the category of mixed Hodge structures and a category of equivariant vector bundles on a toric model of the complex projective plane which verify some semistability condition. We then apply this correspondence to define an invariant which generalizes the notion of R-split mixed Hodge structure and give calculations for the first group of cohomology of possibly non smooth or non-complete curves of genus 0 and 1. Finally, we describe some extension groups of mixed Hodge structures in terms of equivariant extensions of coherent sheaves. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Abstract: The exploitation of cellular network data for studying human mobility has been a popular research topic in the last decade. Indeed, mobile terminals could be considered ubiquitous sensors that allow the observation of human movements on large scale without the need of relying on non-scalable techniques, such as surveys, or dedicated and expensive monitoring infrastructures. In particular, Call Detail Records (CDRs), collected by operators for billing purposes,
have been extensively employed due to their rather large availability, compared to other types of cellular data (e.g., signaling). Despite the interest aroused around this topic, the research community has generally agreed about the scarcity of information provided by CDRs: the position of mobile terminals is logged when some kind of activity (calls, SMS, data connections) occurs, which translates in a picture of mobility somehow biased by the activity degree of users.
By studying two datasets collected by a Nation-wide operator in 2014 and 2016, we show that the situation has drastically changed in terms of data volume and quality. The increase of flat data plans and the higher penetration of “
always connected” terminals have driven up the number of recorded CDRs, providing higher temporal accuracy for users’ locations.

Abstract: This manuscript evaluates the usage of fused cross-spectral images in a monocular visual odometry approach. Fused images are obtained through a Discrete Wavelet Transform (DWT) scheme, where the best setup is empirically obtained by means of a mutual information based evaluation metric. The objective is to have a flexible scheme where fusion parameters are adapted according to the characteristics of the given images. Visual odometry is computed from the fused monocular images using an off the shelf approach. Experimental results using data sets obtained with two different platforms are presented. Additionally, comparison with a previous approach as well as with monocular-visible/infrared spectra are also provided showing the advantages of the proposed scheme.

Abstract: This paper presents a novel algorithm for mobile-object segmentation from static background scenes, which is both robust and accurate under most of the common problems found in motionsegmentation. In our first contribution, a case analysis of motionsegmentation errors is presented taking into account the inaccuracies associated with different cues, namely colour, edge and intensity. Our second contribution is an hybrid architecture which copes with the main issues observed in the case analysis by fusing the knowledge from the aforementioned three cues and a temporal difference algorithm. On one hand, we enhance the colour and edge models to solve not only global and local illumination changes (i.e. shadows and highlights) but also the camouflage in intensity. In addition, local information is also exploited to solve the camouflage in chroma. On the other hand, the intensity cue is applied when colour and edge cues are not available because their values are beyond the dynamic range. Additionally, temporal difference scheme is included to segment motion where those three cues cannot be reliably computed, for example in those background regions not visible during the training period. Lastly, our approach is extended for handling ghost detection. The proposed method obtains very accurate and robust motionsegmentation results in multiple indoor and outdoor scenarios, while outperforming the most-referred state-of-art approaches.

Abstract: The automatic segmentation of multiple subcortical structures in brain Magnetic Resonance Images (MRI) still remains a challenging task. In this paper, we address this problem using sparse representation and discriminative dictionary learning, which have shown promising results in compression, image denoising and recently in MRI segmentation. Particularly, we use multiclass dictionaries learned from a set of brain atlases to simultaneously segment multiple subcortical structures.
We also impose dictionary atoms to be specialized in one given class using label consistent K-SVD, which can alleviate the bias produced by unbalanced libraries, present when dealing with small structures. The proposed method is compared with other state of the art approaches for the segmentation of the Basal Ganglia of 35 subjects of a public dataset.
The promising results of the segmentation method show the eciency of the multiclass discriminative dictionary learning algorithms in MRI segmentation problems.

Abstract: In real-life logistics and distribution activities it is usual to face situations in which the distribution of goods has to be made from multiple warehouses or depots to the nal customers. This problem is known as the Multi-Depot Vehicle Routing Problem (MDVRP), and it typically includes two sequential and correlated stages: (a) the assignment map of customers to depots, and (b) the corresponding design of the distribution routes. Most of the existing work in the literature has focused on minimizing distance-based distribution costs while satisfying a number of capacity constraints. However, no attention has been given so far to potential variations in demands due to the tness of the customerdepot mapping in the case of heterogeneous depots. In this paper, we consider this realistic version of the problem in which the depots are heterogeneous in terms of their commercial oer and customers show dierent willingness to consume depending on how well the assigned depot ts their preferences. Thus, we assume that dierent customer-depot assignment maps will lead to dierent customer-expenditure levels. As a consequence, market-segmentation strategiesneed to be considered in order to increase sales and total income while accounting for the distribution costs. To solve this extension of the MDVRP, we propose a hybrid approach that combines statistical learning techniques with a metaheuristic framework. First, a set of predictive models is generated from historical data. These statistical models allow estimating the demand of any customer depending on the assigned depot. Then, the estimated expenditure of each customer is included as part of an enriched objective function as a way to better guide the stochastic local search inside the metaheuristic framework. A set of computational experiments contribute to illustrate our approach and how the extended MDVRP considered here diers in terms of the proposed solutions from the traditional one.

Abstract: Multiple Instance Learning (MIL) has become an important topic in the pattern recognition community, and many solutions to this problemhave been proposed until now. Despite this fact, there is a lack of comparative studies that shed light into the characteristics and behavior of the different methods. In this work we provide such an analysis focused on the classification task (i.e.,leaving out other learning tasks such as regression). In order to perform our study, we implemented
fourteen methods grouped into three different families. We analyze the performance of the approaches across a variety of well-known databases, and we also study their behavior in synthetic scenarios in order to highlight their characteristics. As a result of this analysis, we conclude that methods that extract global bag-level information show a clearly superior performance in general. In this sense, the analysis permits us to understand why some types of methods are more successful than others, and it permits us to establish guidelines in the design of new MIL
methods.

Abstract: World Health Organization estimates that 80% of the world population is affected by back-related disorders during his life. Current practices to analyze musculo-skeletal disorders (MSDs) are expensive, subjective, and invasive. In this work, we propose a tool for static body posture analysis and dynamic range of movement estimation of the skeleton joints based on 3D anthropometric information from multi-modal data. Given a set of keypoints, RGB and depth data are aligned, depth surface is reconstructed, keypoints are matched, and accurate measurements about posture and spinal curvature are computed. Given a set of joints, range of movement measurements is also obtained. Moreover, gesture recognition based on joint movements is performed to look for the correctness in the development of physical exercises. The system shows high precision and reliable measurements, being useful for posture reeducation purposes to prevent MSDs, as well as tracking the posture evolution of patients in rehabilitation treatments.