Falcó Montesinos, Antonio

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.

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.

In this paper, we establish sufficient conditions for the existence of optimal nonlinear approximations to a linear subspace generated by a given weakly-closed (non-convex) cone of a Hilbert space. Most non-linear problems have difficulties to implement good projection-based algorithms due to the fact that the subsets, where we would like to project the functions, do not have the necessary geometric properties to use the classical existence results (such as convexity, for instance). The theoretical results given here overcome some of these difficulties. To see this we apply them to a fractional model for image deconvolution. In particular, we reformulate and prove the convergence of a computational algorithm proposed in a previous paper by some of the authors. Finally, some examples are given.

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.

A fundamental robotics task is to plan collision-free motions for complex bodies from a start to a goal position among a set of static and dynamic obstacles. This problem is well known in the literature as motion planning (or the piano mover's problem). The complexity of the problem has motivated many works in the field of robot path planning. One of the most popular algorithms is the Artificial Potential Field technique (APF). This method defines an artificial potential field in the configuration space (C-space) that produces a robot path from a start to a goal position. This technique is very fast for RT applications. However, the robot could be trapped in a deadlock (local minima of the potential function). The solution of this problem lies in the use of harmonic functions in the generation of the potential field, which satisfy the Laplace equation. Unfortunately, this technique requires a numerical simulation in a discrete mesh, making useless for RT applications. In our previous work, it was presented for the first time, the Proper Generalized Decomposition method to solve the motion planning problem. In that work, the PGD was designed just for static obstacles and computed as a vademecum for all Start and Goal combinations. This work demonstrates that the PGD could be a solution for the motion planning problem. However, in a realistic scenario, it is necessary to take into account more parameters like for instance, dynamic obstacles. The goal of the present paper is to introduce a diffusion term into the Laplace equation in order to take into account dynamic obstacles as an extra parameter. Both cases, isotropic and non-isotropic cases are into account in order to generalize the solution.

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.

Background: Due to antibiotic resistance and the lack of investment in antimicrobial R&D, QSAR methods appear as an ideal approach for the discovery of new antibiotics. Result/Methodology: Molecular topology and LDA were used to construct a model to predict activity against Escherichia coli. This model establishes new SARs, of which, molecular size and complexity (Nclass), stand out for their discriminant power. This model was used for the virtual screening of the Index Merck database, with results showing a high success rate as well as a moderate restriction. Conclusions: The model efficiently finds new active compounds. The topological index Nclass can act as a filter in other QSAR models predicting activity against E. coli.

We are interested in evaluating the state of drivers to determine whether they are attentive to the road or not by using motion sensor data collected from car driving experiments. That is, our goal is to design a predictive model that can estimate the state of drivers given the data collected from motion sensors. For that purpose, we leverage recent developments in topological data analysis (TDA) to analyze and transform the data coming from sensor time series and build a machine learning model based on the topological features extracted with the TDA. We provide some experiments showing that our model proves to be accurate in the identification of the state of the user, predicting whether they are relaxed or tense.

In this study, molecular topology was used to develop several discriminant equations capable of classifying compounds according to their antibacterial activity. Topological indices were used as structural descriptors and their relation to antibacterial activity was determined by applying linear discriminant analysis (LDA) on a group of quinolones and quinolone-like compounds. Four equations were constructed, named DF1, DF2, DF3, and DF4, all with good statistical parameters such as Fisher–Snedecor’s F (over 25 in all cases), Wilk’s lambda (below 0.36 in all cases) and percentage of correct classification (over 80% in all cases), which allows a reliable extrapolation prediction of antibacterial activity in any organic compound. From the four discriminant functions, it can be extracted that the presence of sp3 carbons, ramifications, and secondary amine groups in a molecule enhance antibacterial activity, whereas the presence of 5-member rings, sp2 carbons, and sp2 oxygens hinder it. The results obtained clearly reveal the high e ciency of combining molecular topology with LDA for the prediction of antibacterial activity.

Experimentation in mammals is a long and expensive process in which ethical aspects must beconsidered, which has led the scientific community to develop alternative models such as that ofGalleria mellonella. This model is a cost and time effective option to act as a filter in the drugdiscovery process. The main limitation of this model is the lack of variety in the solvents used toadminister compounds, which limits the compounds that can be studied using this model. Fiveaqueous (DMSO, MeOH, acetic acid, HCl and NaOH) and four non-aqueous (olive oil, isopropylmyristate, benzyl benzoate and ethyl oleate) solvents was assessed to be used as vehicles fortoxicity and antimicrobial activityin vivoassays. All the tested solvents were innocuous at thetested concentrations except for NaOH, which can be used at a maximum concentration of 0.5 M.The toxicity of two additional compounds, 5-aminosalicylic acid and DDT, was also assessed. Theresults obtained allow for the testing of a broader range of compounds using wax moth larvae.This model appears as an alternative to mammal models, by acting as a filter in the drugdevelopment process and reducing costs and time invested in new drugs.