Escuela Superior de Enseñanzas Técnicas

In recent days there are many possibilities in develop solutions for industrial manufacturing process thanks to the emerging technology based in Industry 4.0, where one can measure and manage data from an industrial process in real time been able to know more information than ever before from the process. But still having challenges in complex process where monitoring data and give a solution is less intuitive, mostly due to a complex physical definition of the process and manufacturing car body parts in automotive is a clear example. In deep drawing process is common to have variations in the process parameters and they can carry out bad manufactured parts. The cycle time, the robust process and the complex physics in the process are the main problems to obtain feasible information from the process. In the following it is proposed a new methodology to have full knowledge of the process applying the so-called method Hybrid Twin.

Post-processing meshing algorithms are widely used to achieve the desired quality in quadrilateral meshes. Assuming that the mesh quality depends on the distortion and the size error of each of its convex quadrilaterals, deficiencies arise by considering solutions based in minimizing either the distortion or the size error. To solve this undesirable situation, in this paper we propose a new smoothing post-processing meshing algorithm. This procedure provides a good compromise between the distortion and the size of each element in the mesh. It is formulated by using an elasticity-based argument and allows to be implemented either in sequential or parallel form. Moreover, it provides a good quality output compared with some of the usual smoothing post-processing meshing algorithms.

Solutions of partial differential equations can exhibit multiple time scales. Standard discretization techniques are constrained to capture the finest scale to accurately predict the response of the system. In this paper, we provide an alternative route to circumvent prohibitive meshes arising from the necessity of capturing fine-scale behaviors. The proposed methodology is based on a time-separated representation within the standard Proper Generalized Decomposition, where the time coordinate is transformed into a multi-dimensional time through new separated coordinates, each representing one scale, while continuity is ensured in the scale coupling. For instance, when considering two different time scales, the governing Partial Differential Equation is commuted into a nonlinear system that iterates between the so-called microtime and macrotime, so that the time coordinate can be viewed as a 2D time. The macroscale effects are taken into account by means of a finite element-based macro-discretization, whereas the microscale effects are handled with unidimensional parent spaces that are replicated throughout the time domain. The resulting separated representation allows us a very fine time discretization without impacting the computational efficiency. The proposed formulation is explored and numerically verified on thermal and elastodynamic problems.

The present paper aims at analyzing the topological content of the complex trajectories that weeder-autonomous robots follow in operation. We will prove that the topological descriptors of these trajectories are affected by the robot environment as well as by the robot state, with respect to maintenance operations. Most of existing methodologies enabling efficient diagnosis are based on the data analysis, and in particular on some statistical quantities derived from the data. The present work explores the use of an original approach that instead of analyzing quantities derived from the data, analyzes the “shape” of the data, that is, the time series topology based on the homology persistence. We will prove that this procedure is able to extract valuable patterns able to discriminate the trajectories that the robot follows depending on the particular patch in which it operates, as well as to differentiate the robot behavior before and after undergoing a maintenance operation. Even if it is a preliminary work, and it does not pretend to compare its performances with respect to other existing technologies, this work opens new perspectives in considering quite natural and simple descriptors based on the intrinsic information that data contains, with the aim of performing efficient diagnosis and prognosis.

In this paper, we propose a new splitting algorithm for dynamical low-rank approximation motivated by the fibre bundle structure of the set of fixed rank matrices. We first introduce a geometric description of the set of fixed rank matrices which relies on a natural parametrization of matrices. More precisely, it is endowed with the structure of analytic principal bundle, with an explicit description of local charts. For matrix differential equations, we introduce a first order numerical integrator working in local coordinates. The resulting algorithm can be interpreted as a particular splitting of the projection operator onto the tangent space of the low-rank matrix manifold. It is proven to be exact in some particular case. Numerical experiments confirm this result and illustrate the robustness of the proposed algorithm.

Since its emergence in March 2020, the SARS-CoV-2 global pandemic has produced more than 116 million cases and 2.5 million deaths worldwide. Despite the enormous efforts carried out by the scientific community, no effective treatments have been developed to date. We applied a novel computational pipeline aimed to accelerate the process of identifying drug repurposing candidates which allows us to compare three-dimensional protein structures. Its use in conjunction with two in silico validation strategies (molecular docking and transcriptomic analyses) allowed us to identify a set of potential drug repurposing candidates targeting three viral proteins (3CL viral protease, NSP15 endoribonuclease, and NSP12 RNA-dependent RNA polymerase), which included rutin, dexamethasone, and vemurafenib. This is the first time that a topological data analysis (TDA)-based strategy has been used to compare a massive number of protein structures with the final objective of performing drug repurposing to treat SARS-CoV-2 infection.

This paper presents a real-time global path planning method for mobile robots using harmonic functions, such as the Poisson equation, based on the Proper Generalized Decomposition (PGD) of these functions. The main property of the proposed technique is that the computational cost is negligible in real-time, even if the robot is disturbed or the goal is changed. The main idea of the method is the off-line generation, for a given environment, of the whole set of paths from any start and goal configurations of a mobile robot, namely the computational vademecum, derived from a harmonic potential field in order to use it on-line for decision-making purposes. Up until now, the resolution of the Laplace or Poisson equations has been based on traditional numerical techniques unfeasible for real-time calculation. This drawback has prevented the extensive use of harmonic functions in autonomous navigation, despite their powerful properties. The numerical technique that reverses this situation is the Proper Generalized Decomposition. To demonstrate and validate the properties of the PGD-vademecum in a potential-guided path planning framework, both real and simulated implementations have been developed. Simulated scenarios, such as an L-Shaped corridor and a benchmark bug trap, are used, and a real navigation of a LEGO®MINDSTORMS robot running in static environments with variable start and goal configurations is shown. This device has been selected due to its computational and memory-restricted capabilities, and it is a good example of how its properties could help the development of social robots.

In this paper, we introduce a new geometric description of the manifolds of matrices of fixed rank. The starting point is a geometric description of the Grassmann manifold Gr(Rk) of linear subspaces of dimension r < k in Rk, which avoids the use of equivalence classes. The set Gr(Rk) is equipped with an atlas, which provides it with the structure of an analytic manifold modeled on R(k􀀀r) r. Then, we define an atlas for the set Mr(Rk r) of full rank matrices and prove that the resulting manifold is an analytic principal bundle with base Gr(Rk) and typical fibre GLr, the general linear group of invertible matrices in Rk k. Finally, we define an atlas for the setMr(Rn m) of non-full rank matrices and prove that the resulting manifold is an analytic principal bundle with base Gr(Rn) Gr(Rm) and typical fibre GLr. The atlas ofMr(Rn m) is indexed on the manifold itself, which allows a natural definition of a neighbourhood for a given matrix, this neighbourhood being proved to possess the structure of a Lie group. Moreover, the setMr(Rn m) equipped with the topology induced by the atlas is proven to be an embedded submanifold of the matrix space Rn m equipped with the subspace topology. The proposed geometric description then results in a description of the matrix space Rn m, seen as the union of manifoldsMr(Rn m), as an analytic manifold equipped with a topology for which the matrix rank is a continuous map.

Polymorphisms in the PER3 gene have been associated with several human disease phenotypes, including sleep disorders and cancer. In particular, the long allele of a variable number of tandem repeat (VNTR) polymorphism has been previously linked to an increased risk of breast cancer. Here we carried out a combined germline and somatic genetic analysis of the role of the PER3VNRT polymorphism in breast cancer. The combined data from 8284 individuals showed a non-significant trend towards increased breast cancer risk in the 5-repeat allele homozygous carriers (OR = 1.17, 95% CI: 0.97–1.42). We observed allelic imbalance at the PER3 locus in matched blood and tumor DNA samples, showing a significant retention of the long variant (risk) allele in tumor samples, and a preferential loss of the short repetition allele (p = 0.0005). Gene co-expression analysis in healthy and tumoral breast tissue samples uncovered significant associations between PER3 expression levels with those from genes which belong to several cancerassociated pathways. Finally, relapse-free survival (RFS) analysis showed that low expression levels of PER3 were linked to a significant lower RSF in luminal A (p = 3 × 10−12) but not in the rest of breast cancer subtypes.

Alzheimer’s (AD) and Parkinson’s diseases (PD) are the two most prevalent neurodegenerative disorders in human populations. Epidemiological studies have shown that patients suffering from either condition present a reduced overall risk of cancer than controls (i.e., inverse comorbidity), suggesting that neurodegeneration provides a protective effect against cancer. Reduced risks of several site-specific tumors, including colorectal, lung, and prostate cancers, have also been observed in AD and PD. By contrast, an increased risk of melanoma has been described in PD patients (i.e., direct comorbidity). Therefore, a fundamental question to address is whether these associations are due to shared genetic and molecular factors or are explained by other phenomena, such as flaws in epidemiological studies, exposure to shared risk factors, or the effect of medications. To this end, we first evaluated the transcriptomes of AD and PD post-mortem brain tissues derived from the hippocampus and the substantia nigra and analyzed their similarities to those of a large panel of 22 site-specific cancers, which were obtained through differential gene expression meta-analyses of array-based studies available in public repositories. Genes and pathways that were deregulated in both disorders in each analyzed pair were examined. Second, we assessed potential genetic links between AD, PD, and the selected cancers by establishing interactome-based overlaps of genes previously linked to each disorder. Then, their genetic correlations were computed using cross-trait LD score regression and GWAS summary statistics data. Finally, the potential role of medications in the reported comorbidities was assessed by comparing disease-specific differential gene expression profiles to an extensive collection of differential gene expression signatures generated by exposing cell lines to drugs indicated for AD, PD, and cancer treatment (LINCS L1000). We identified significant inverse associations of transcriptomic deregulation between AD hippocampal tissues and breast, lung, liver, and prostate cancers, and between PD substantia nigra tissues and breast, lung, and prostate cancers. Moreover, significant direct (same direction) associations of deregulation were observed between AD and PD and brain and thyroid cancers, as well as between PD and kidney cancer. Several biological processes, including the immune system, oxidative phosphorylation, PI3K/AKT/mTOR signaling, and the cell cycle, were found to be deregulated in both cancer and neurodegenerative disorders. Significant genetic correlations were found between PD and melanoma and prostate cancers. Several drugs indicated for the treatment of neurodegenerative disorders and cancer, such as galantamine, selegiline, exemestane, and estradiol, were identified as potential modulators of the comorbidities observed between neurodegeneration and cancer.