arXiv subjects

Roberto González

Publications and source records attributed to Roberto González.

4 recordsLinked to original sources

arXiv2026

Space-time finite element interpolation of nonsmooth functions satisfying boundary conditions

We construct Scott-Zhang-type space-time quasi-interpolation operators on tensor- product meshes for parabolic settings. Specifically, these are linear and uniformly bounded projections from the classical parabolic energy space onto a space-time tensor-product finite element space that preserve discrete Dirichlet boundary conditions on the lateral space-time boundary. We apply our operator in the context of space-time first-order system least-squares finite elements for parabolic equations to establish a quasi-optimal method for inhomogeneous Dirichlet boundary conditions.

math.NA↗

arXiv2023

Well-posedness of first-order acoustic wave equations and space-time finite element approximation

We study a first-order system formulation of the (acoustic) wave equation and prove that the operator of this system is an isomorphsim from an appropriately defined graph space to L^2. The results rely on well-posedness and stability of the weak and ultraweak formulation of the second-order wave equation. As an application we define and analyze a space-time least-squares finite element method for solving the wave equation. Some numerical examples for one- and two- dimensional spatial domains are presented.

math.NA↗

arXiv2019

Answering Visual-Relational Queries in Web-Extracted Knowledge Graphs

A visual-relational knowledge graph (KG) is a multi-relational graph whose entities are associated with images. We explore novel machine learning approaches for answering visual-relational queries in web-extracted knowledge graphs. To this end, we have created ImageGraph, a KG with 1,330 relation types, 14,870 entities, and 829,931 images crawled from the web. With visual-relational KGs such as ImageGraph one can introduce novel probabilistic query types in which images are treated as first-class citizens. Both the prediction of relations between unseen images as well as multi-relational image retrieval can be expressed with specific families of visual-relational queries. We introduce novel combinations of convolutional networks and knowledge graph embedding methods to answer such queries. We also explore a zero-shot learning scenario where an image of an entirely new entity is linked with multiple relations to entities of an existing KG. The resulting multi-relational grounding of unseen entity images into a knowledge graph serves as a semantic entity representation. We conduct experiments to demonstrate that the proposed methods can answer these visual-relational queries efficiently and accurately.

cs.LG↗

arXiv2010

Clustering and descendants of MUSYC galaxies at z<1.5

We measure the evolution of galaxy clustering out to a redshift of z~1.5 using data from two MUSYC fields, the Extended Hubble Deep Field South (EHDF-S) and the Extended Chandra Deep Field South (ECDF-S). We use photometric redshift information to calculate the projected-angular correlation function, omega(sigma), from which we infer the projected correlation function Xi(sigma). We demonstrate that this technique delivers accurate measurements of clustering even when large redshift measurement errors affect the data. To this aim we use two mock MUSYC fields extracted from a LambdaCDM simulation populated with GALFORM semi-analytic galaxies which allow us to assess the degree of accuracy of our estimates of Xi(sigma) and to identify and correct for systematic effects in our measurements. We study the evolution of clustering for volume limited subsamples of galaxies selected using their photometric redshifts and rest-frame r-band absolute magnitudes. We find that the real-space correlation length r_0 of bright galaxies, M_r<-21 (rest-frame) can be accurately recovered out to z~1.5, particularly for ECDF-S given its near-infrared photometric coverage. There is mild evidence for a luminosity dependent clustering in both fields at the low redshift samples (up to =0.57), where the correlation length is higher for brighter galaxies by up to 1Mpc/h between median rest-frame r-band absolute magnitudes of -18 to -21.5. As a result of the photometric redshift measurement, each galaxy is assigned a best-fit template; we restrict to E and E+20%Sbc types to construct subsamples of early type galaxies (ETGs). Our ETG samples show a strong increase in r_0 as the redshift increases, making it unlikely (95% level) that ETGs at median redshift z_med=1.15 are the direct progenitors of ETGs at z_med=0.37 with equivalent passively evolved luminosities. (ABRIDGED)

astro-ph.CO↗