arXiv subjects

David Gonzalez

Publications and source records attributed to David Gonzalez.

At least 37 records · Page 2Linked to original sources

arXiv2024

On the feasibility of foundational models for the simulation of physical phenomena

We explore the feasibility of foundation models for the simulation of physical phenomena, with emphasis on continuum (solid and fluid) mechanics. Although so-called learned simulators have shown some success when applied to specific tasks, it remains to be studied to what extent they are able to undergo severe changes in domain shape, boundary conditions and/or constitutive laws and still provide robust (i.e., hallucination-free) and accurate results. In this paper we perform an exhaustive study of these features, put ourselves in the worst-case scenario and study their resistance to such strong changes in their domain of application.

cs.CE↗

arXiv2024

Scott analysis, linear orders and almost periodic functions

For any limit ordinal $λ$, we construct a linear order $L_λ$ whose Scott complexity is $Σ_{λ+1}$. This completes the classification of the possible Scott sentence complexities of linear orderings. Previously, there was only one known construction of any structure (of any signature) with Scott complexity $Σ_{λ+1}$, and our construction gives new examples, e.g., rigid structures, of this complexity. Moreover, we can construct the linear orders $L_λ$ so that not only does $L_λ$ have Scott complexity $Σ_{λ+1}$, but there are continuum-many structures $M \equiv_λL_λ$ and all such structures also have Scott complexity $Σ_{λ+1}$. In contrast, we demonstrate that there is no structure (of any signature) with Scott complexity $Π_{λ+1}$ that is only $λ$-equivalent to structures with Scott complexity $Π_{λ+1}$. Our construction is based on functions $f \colon \mathbb{Z}\to \mathbb{N}\cup \{\infty\}$ which are almost periodic but not periodic, such as those arising from shifts of the $p$-adic valuations.

math.LO↗

arXiv2024

Hybrid Maximal Filter Spaces

We introduce a new way of encoding general topology in second order arithmetic that we call hybrid maximal filter (hybrid MF) spaces. This notion is a modification of the notion of a proper MF space introduced by Montalbán. We justify the shift by showing that proper MF spaces are not able to code most topological spaces, while hybrid MF spaces can code any second countable MF space. We then answer Montalbán's question about metrization of well-behaved MF spaces to this shifted context. To be specific, we show that in stark contrast to the original MF formalization used by Mummert and Simpson, the metrization theorem can be proven for hybrid MF spaces within $\text{ACA}_0$ instead of needing $Π_2^1-\text{CA}_0$.

math.LO↗

arXiv2024

Generically Computable Linear Orderings

We study notions of generic and coarse computability in the context of computable structure theory. Our notions are stratified by the $Σ_β$ hierarchy. We focus on linear orderings. We show that at the $Σ_1$ level all linear orderings have both generically and coarsely computable copies. This behavior changes abruptly at higher levels; we show that at the $Σ_{α+2}$ level for any $α\inω_1^{ck}$ the set of linear orderings with generically or coarsely computable copies is $\mathbfΣ_1^1$-complete and therefore maximally complicated. This development is new even in the general analysis of generic and coarse computability of countable structures. In the process of proving these results we introduce new tools for understanding generically and coarsely computable structures. We are able to give a purely structural statement that is equivalent to having a generically computable copy and show that every relational structure with only finitely many relations has coarsely and generically computable copies at the lowest level of the hierarchy.

math.LO↗

arXiv2023

Scott sentence complexities of linear orderings

We study possible Scott sentence complexities of linear orderings using two approaches. First, we investigate the effect of the Friedman-Stanley embedding on Scott sentence complexity and show that it only preserves $Π^{\mathrm{in}}_α$ complexities. We then take a more direct approach and exhibit linear orderings of all Scott complexities except $Σ^{\mathrm{in}}_{3}$ and $Σ^{\mathrm{in}}_{λ+1}$ for $λ$ a limit ordinal. We show that the former can not be the Scott sentence complexity of a linear ordering. In the process we develop new techniques which appear to be helpful to calculate the Scott sentence complexities of structures.

math.LO↗

arXiv2022

The $ω$-Vaught's Conjecture

We introduce the $ω$-Vaught's conjecture, a strengthening of the infinitary Vaught's conjecture. We believe that if one were to prove the infinitary Vaught's conjecture in a structural way without using techniques from higher recursion theory, then the proof would probably be a proof of the $ω$-Vaught's conjecture. We show the existence of an equivalent condition to the $ω$-Vaught's conjecture and use this tool to show that all infinitary sentences whose models are linear orders satisfy the $ω$-Vaught's conjecture.

math.LO↗

arXiv2022

A Thermodynamics-informed Active Learning Approach to Perception and Reasoning about Fluids

Learning and reasoning about physical phenomena is still a challenge in robotics development, and computational sciences play a capital role in the search for accurate methods able to provide explanations for past events and rigorous forecasts of future situations. We propose a thermodynamics-informed active learning strategy for fluid perception and reasoning from observations. As a model problem, we take the sloshing phenomena of different fluids contained in a glass. Starting from full-field and high-resolution synthetic data for a particular fluid, we develop a method for the tracking (perception) and analysis (reasoning) of any previously unseen liquid whose free surface is observed with a commodity camera. This approach demonstrates the importance of physics and knowledge not only in data-driven (grey box) modeling but also in the correction for real physics adaptation in low data regimes and partial observations of the dynamics. The method presented is extensible to other domains such as the development of cognitive digital twins, able to learn from observation of phenomena for which they have not been trained explicitly.

cs.CV↗

arXiv2022

Physics perception in sloshing scenes with guaranteed thermodynamic consistency

Physics perception very often faces the problem that only limited data or partial measurements on the scene are available. In this work, we propose a strategy to learn the full state of sloshing liquids from measurements of the free surface. Our approach is based on recurrent neural networks (RNN) that project the limited information available to a reduced-order manifold so as to not only reconstruct the unknown information, but also to be capable of performing fluid reasoning about future scenarios in real time. To obtain physically consistent predictions, we train deep neural networks on the reduced-order manifold that, through the employ of inductive biases, ensure the fulfillment of the principles of thermodynamics. RNNs learn from history the required hidden information to correlate the limited information with the latent space where the simulation occurs. Finally, a decoder returns data back to the high-dimensional manifold, so as to provide the user with insightful information in the form of augmented reality. This algorithm is connected to a computer vision system to test the performance of the proposed methodology with real information, resulting in a system capable of understanding and predicting future states of the observed fluid in real-time.

cs.CV↗

arXiv2021

How to Quantify the Security Level of Embedded Systems? A Taxonomy of Security Metrics

Embedded Systems (ES) development has been historically focused on functionality rather than security, and today it still applies in many sectors and applications. However, there is an increasing number of security threats over ES, and a successful attack could have economical, physical or even human consequences, since many of them are used to control critical applications. A standardized and general accepted security testing framework is needed to provide guidance, common reporting forms, and the possibility to compare the results along the time. This can be achieved by introducing security metrics into the evaluation or assessment process. If carefully designed and chosen, metrics could provide a quantitative, repeatable and reproducible value that would reflect the level of security protection of the ES. This paper analyzes the features that a good security metric should exhibit, introduces a taxonomy for classifying them, and finally, it carries out a literature survey on security metrics for the security evaluation of ES. In this review, more than 500 metrics were collected and analyzed. Then, they were reduced to 169 metrics that have the potential to be applied to ES security evaluation. As expected, the 77.5 % of them is related exclusively to software, and only the 0.6 % of them addresses exclusively hardware security. This work aims to lay the foundations for constructing a security evaluation methodology that uses metrics to quantify the security level of an ES.

cs.CR↗

arXiv2021

MORPH-DSLAM: Model Order Reduction for PHysics-based Deformable SLAM

We propose a new methodology to estimate the 3D displacement field of deformable objects from video sequences using standard monocular cameras. We solve in real time the complete (possibly visco-)hyperelasticity problem to properly describe the strain and stress fields that are consistent with the displacements captured by the images, constrained by real physics. We do not impose any ad-hoc prior or energy minimization in the external surface, since the real and complete mechanics problem is solved. This means that we can also estimate the internal state of the objects, even in occluded areas, just by observing the external surface and the knowledge of material properties and geometry. Solving this problem in real time using a realistic constitutive law, usually non-linear, is out of reach for current systems. To overcome this difficulty, we solve off-line a parametrized problem that considers each source of variability in the problem as a new parameter and, consequently, as a new dimension in the formulation. Model Order Reduction methods allow us to reduce the dimensionality of the problem, and therefore, its computational cost, while preserving the visualization of the solution in the high-dimensionality space. This allows an accurate estimation of the object deformations, improving also the robustness in the 3D points estimation.

cs.CV↗

arXiv2021

Deep learning of thermodynamics-aware reduced-order models from data

We present an algorithm to learn the relevant latent variables of a large-scale discretized physical system and predict its time evolution using thermodynamically-consistent deep neural networks. Our method relies on sparse autoencoders, which reduce the dimensionality of the full order model to a set of sparse latent variables with no prior knowledge of the coded space dimensionality. Then, a second neural network is trained to learn the metriplectic structure of those reduced physical variables and predict its time evolution with a so-called structure-preserving neural network. This data-based integrator is guaranteed to conserve the total energy of the system and the entropy inequality, and can be applied to both conservative and dissipative systems. The integrated paths can then be decoded to the original full-dimensional manifold and be compared to the ground truth solution. This method is tested with two examples applied to fluid and solid mechanics.

cs.CE↗

arXiv2020

Structure-preserving neural networks

We develop a method to learn physical systems from data that employs feedforward neural networks and whose predictions comply with the first and second principles of thermodynamics. The method employs a minimum amount of data by enforcing the metriplectic structure of dissipative Hamiltonian systems in the form of the so-called General Equation for the Non-Equilibrium Reversible-Irreversible Coupling, GENERIC [M. Grmela and H.C Oettinger (1997). Dynamics and thermodynamics of complex fluids. I. Development of a general formalism. Phys. Rev. E. 56 (6): 6620-6632]. The method does not need to enforce any kind of balance equation, and thus no previous knowledge on the nature of the system is needed. Conservation of energy and dissipation of entropy in the prediction of previously unseen situations arise as a natural by-product of the structure of the method. Examples of the performance of the method are shown that include conservative as well as dissipative systems, discrete as well as continuous ones.

cs.LG↗

arXiv2019

An upper bound for the restricted online Ramsey number

The restricted $(m,n;N)$-online Ramsey game is a game played between two players, Builder and Painter. The game starts with $N$ isolated vertices. Each turn Builder picks an edge to build and Painter chooses whether that edge is red or blue, and Builder aims to create a red $K_m$ or blue $K_n$ in as few turns as possible. The restricted online Ramsey number $\tilde{r}(m,n;N)$ is the minimum number of turns that Builder needs to guarantee her win in the restricted $(m,n;N)$-online Ramsey game. We show that if $N=r(n,n)$, \[ \tilde{r}(n,n;N)\le \binom{N}{2} - Ω(N\log N), \] motivated by a question posed by Conlon, Fox, Grinshpun and He. The equivalent game played on infinitely many vertices is called the online Ramsey game. As almost all known Builder strategies in the online Ramsey game end up reducing to the restricted setting, we expect further progress on the restricted online Ramsey game to have applications in the general case.

math.CO↗

arXiv2017

Optical and Infrared Photometry of SN 2005df

We present optical BVRI and near-infrared YJHK_s photometry of the normal Type Ia supernova 2005df, obtained with the CTIO 1.3-m and 0.9-m telescopes. The B- and V-band photometry, S-corrected to the filter prescriptions of Bessell(1990), matches the corresponding photometry from the ANU published by Milne et al. (2010). The R-band photometry from CTIO and ANU matches well without any corrections. A combination of V-band and near-IR photometry shows that SN 2005df is unreddened in its host galaxy. Spectropolarimetry of this supernova was obtained with the VLT, and the distance to the host galaxy is being determined from observations of Cepheids using the Hubble Space Telescope.

astro-ph.SR↗

arXiv2012

Fixing the U-band photometry of Type Ia supernovae

We present previously unpublished photometry of supernovae 2003gs and 2003hv. Using spectroscopically-derived corrections to the U-band photometry, we reconcile U-band light curves made from imagery with the Cerro Tololo 0.9-m, 1.3-m and Las Campanas 1-m telescopes. Previously, such light curves showed a 0.4 mag spread at one month after maximum light. This gives us hope that a set of corrected ultraviolet light curves of nearby objects can contribute to the full utilization of rest frame U-band data of supernovae at redshift ~0.3 to 0.8. As pointed out recently by Kessler et al. in the context of the Sloan Digital Sky Survey supernova search, if we take the published U-band photometry of nearby Type Ia supernovae at face value, there is a 0.12 mag U-band anomaly in the distance moduli of higher redshift objects. This anomaly led the Sloan survey to eliminate from their analyses all photometry obtained in the rest frame U-band. The Supernova Legacy Survey eliminated observer frame U-band photometry, which is to say nearby objects observed in the U-band, but they used photometry of high redshift objects no matter in which band the photons were emitted.

astro-ph.CO↗

arXiv2009

The fast declining Type Ia supernova 2003gs, and evidence for a significant dispersion in near-infrared absolute magnitudes of fast decliners at maximum light

We obtained optical photometry of SN 2003gs on 49 nights, from 2 to 494 days after T(B_max). We also obtained near-IR photometry on 21 nights. SN 2003gs was the first fast declining Type Ia SN that has been well observed since SN 1999by. While it was subluminous in optical bands compared to more slowly declining Type Ia SNe, it was not subluminous at maximum light in the near-IR bands. There appears to be a bimodal distribution in the near-IR absolute magnitudes of Type Ia SNe at maximum light. Those that peak in the near-IR after T(B_max) are subluminous in the all bands. Those that peak in the near-IR prior to T(B_max), such as SN 2003gs, have effectively the same near-IR absolute magnitudes at maximum light regardless of the decline rate Delta m_15(B). Near-IR spectral evidence suggests that opacities in the outer layers of SN 2003gs are reduced much earlier than for normal Type Ia SNe. That may allow gamma rays that power the luminosity to escape more rapidly and accelerate the decline rate. This conclusion is consistent with the photometric behavior of SN 2003gs in the IR, which indicates a faster than normal decline from approximately normal peak brightness.

astro-ph.CO↗

arXiv2008

Do the photometric colors of Type II-P Supernovae allow accurate determination of host galaxy extinction?

We present infrared photometry of SN 1999em, plus optical photometry, infrared photometry, and optical spectroscopy of SN 2003hn. Both objects were Type II-P supernovae. The V-[RIJHK] color curves of these supernovae evolved in a very similar fashion until the end of plateau phase. This allows us to determine how much more extinction the light of SN 2003hn suffered compared to SN 1999em. Since we have an estimate of the total extinction suffered by SN 1999em from model fits of ground-based and space-based spectra as well as photometry of SN 1999em, we can estimate the total extinction and absolute magnitudes of SN 2003hn with reasonable accuracy. Since the host galaxy of SN 2003hn also produced the Type Ia SN 2001el, we can directly compare the absolute magnitudes of these two SNe of different types.

astro-ph↗

arXiv2006

The Type Ia supernova 2004S, a clone of SN 2001el, and the optimal photometric bands for extinction estimation

We present optical (UBVRI) and near-infrared (YJHK) photometry of the normal Type Ia supernova 2004S. We also present eight optical spectra and one near-IR spectrum of SN 2004S. The light curves and spectra are nearly identical to those of SN 2001el. This is the first time we have seen optical and IR light curves of two Type Ia supernovae match so closely. Within the one parameter family of light curves for normal Type Ia supernovae, that two objects should have such similar light curves implies that they had identical intrinsic colors and produced similar amounts of Ni-56. From the similarities of the light curve shapes we obtain a set of extinctions as a function of wavelength which allows a simultaneous solution for the distance modulus difference of the two objects, the difference of the host galaxy extinctions, and R_V. Since SN 2001el had roughly an order of magnitude more host galaxy extinction than SN 2004S, the value of R_V = 2.15 (+0.24 -0.22) pertains primarily to dust in the host galaxy of SN 2001el. We have also shown via Monte Carlo simulations that adding rest frame J-band photometry to the complement of BVRI photometry of Type Ia SNe decreases the uncertainty in the distance modulus by a factor of 2.7. A combination of rest frame optical and near-IR photometry clearly gives more accurate distances than using rest frame optical photometry alone.

astro-ph↗