arXiv subjects

Juan Cortés

Publications and source records attributed to Juan Cortés.

4 recordsLinked to original sources

arXiv2025

Post-clustering Inference under Dependence

Recent work by Gao et al. (JASA 2022) has laid the foundations for post-clustering inference, establishing a theoretical framework allowing to test for differences between means of estimated clusters. Additionally, they studied the estimation of unknown parameters while controlling the selective type I error. However, their theory was developed for independent observations identically distributed as $p$-dimensional Gaussian variables, where the parameter estimation could only be performed for spherical covariance matrices. Here, we aim at extending this framework to a more convenient scenario for practical applications, where arbitrary dependence structures between observations and features are allowed. We establish sufficient conditions for extending the setting presented by Gao et al. to the general dependence framework. Moreover, we assess theoretical conditions allowing the compatible estimation of a covariance matrix. The theory is developed for hierarchical agglomerative clustering algorithms with several types of linkages, and for the $k$-means algorithm. We illustrate our method with synthetic data and real data of protein structures.

stat.ME↗

arXiv2023

Two-sample goodness-of-fit tests on the flat torus based on Wasserstein distance and their relevance to structural biology

This work is motivated by the study of local protein structure, which is defined by two variable dihedral angles that take values from probability distributions on the flat torus. Our goal is to provide the space $\mathcal{P}(\mathbb{R}^2/\mathbb{Z}^2)$ with a metric that quantifies local structural modifications due to changes in the protein sequence, and to define associated two-sample goodness-of-fit testing approaches. Due to its adaptability to the space geometry, we focus on the Wasserstein distance as a metric between distributions. We extend existing results of the theory of Optimal Transport to the $d$-dimensional flat torus $\mathbb{T}^d=\mathbb{R}^d/\mathbb{Z}^d$, in particular a Central Limit Theorem. Moreover, we propose different approaches for two-sample goodness-of-fit testing for the one and two-dimensional case, based on the Wasserstein distance. We prove their validity and consistency. We provide an implementation of these tests in \textsf{R}. Their performance is assessed by numerical experiments on synthetic data and illustrated by an application to protein structure data.

stat.ME↗

arXiv2023

Coordinated Multi-Robot Trajectory Tracking Control over Sampled Communication

In this paper, we propose an inverse-kinematics controller for a class of multi-robot systems in the scenario of sampled communication. The goal is to make a group of robots perform trajectory tracking in a coordinated way when the sampling time of communications is much larger than the sampling time of low-level controllers, disrupting theoretical convergence guarantees of standard control design in continuous time. Given a desired trajectory in configuration space which is precomputed offline, the proposed controller receives configuration measurements, possibly via wireless, to re-compute velocity references for the robots, which are tracked by a low-level controller. We propose joint design of a sampled proportional feedback plus a novel continuous-time feedforward that linearizes the dynamics around the reference trajectory: this method is amenable to distributed communication implementation where only one broadcast transmission is needed per sample. Also, we provide closed-form expressions for instability and stability regions and convergence rate in terms of proportional gain $k$ and sampling period $T$. We test the proposed control strategy via numerical simulations in the scenario of cooperative aerial manipulation of a cable-suspended load using a realistic simulator (Fly-Crane). Finally, we compare our proposed controller with centralized approaches that adapt the feedback gain online through smart heuristics, and show that it achieves comparable performance.

cs.RO↗

arXiv2016

Small-angle scattering studies of intrinsically disordered proteins and their complexes

Intrinsically Disordered Proteins (IDPs) perform a broad range of biological functions. Their relevance has motivated intense research activity seeking to characterize their sequence/structure/function relationships. However, the conformational plasticity of these molecules hampers the application of traditional structural approaches, and new tools and concepts are being developed to address the challenges they pose. Small-Angle Scattering (SAS) is a structural biology technique that probes the size and shape of disordered proteins and their complexes with other biomolecules. The low-resolution nature of SAS can be compensated with specially designed computational tools and its combined interpretation with complementary structural information. In this review, we describe recent advances in the application of SAS to disordered proteins and highly flexible complexes and discuss current challenges.

physics.bio-ph↗