arXiv subjects

Héctor Ramírez

Publications and source records attributed to Héctor Ramírez.

15 recordsLinked to original sources

arXiv2026

A Two-Stage Operating Room Allocation Framework for Reducing Surgical Waiting Lists in Public Hospitals

Operating-room allocation is a major challenge for public hospitals with limited surgical capacity and large elective waiting lists. This work proposes a two-stage operating-room allocation framework for specialty-block scheduling environments. The methodology combines a mixed-integer linear programming model for medical specialty block allocation with a priority-based patient allocation procedure. The framework was evaluated through one-week and multi-week simulation scenarios using parameters estimated from historical surgical and waiting-list data. The proposed methodology was compared against an integrated mixed-integer linear programming baseline adapted from the literature under realistic operational disruptions, including failed patient confirmations and surgery suspensions. Results show that the proposed framework achieves a more balanced distribution between offered and demanded surgical time across specialties while maintaining high operating-room utilization and substantially lower computational times than the integrated baseline. In the 20-week scenario, the proposed methodology achieved lower waiting times and operated a larger number of patients while preserving operational flexibility. These results suggest that decomposition-based operating-room allocation strategies provide a practical and computationally efficient alternative for reducing surgical waiting lists in public hospitals.

math.OC↗

arXiv2026

Forecasting Seasonal Peaks of Pediatric Respiratory Infections Using an Alert-Based Model Combining SIR Dynamics and Historical Trends in Santiago, Chile

Acute respiratory infections (ARI) are a major cause of pediatric hospitalization in Chile, producing marked winter increases in demand that challenge hospital planning. This study presents an alert-based forecasting model to predict the timing and magnitude of ARI hospitalization peaks in Santiago. The approach integrates a seasonal SIR model with a historical mobile predictor, activated by a derivative-based alert system that detects early epidemic growth. Daily hospitalization data from DEIS were smoothed using a 15-day moving average and Savitzky-Golay filtering, and parameters were estimated using a penalized loss function to reduce sensitivity to noise. Retrospective evaluation and real-world implementation in major Santiago pediatric hospitals during 2023 and 2024 show that peak date can be anticipated about one month before the event and predicted with high accuracy two weeks in advance. Peak magnitude becomes informative roughly ten days before the peak and stabilizes one week prior. The model provides a practical and interpretable tool for hospital preparedness.

stat.AP↗

arXiv2025

Improved error bounds for Koopman operator and reconstructed trajectories approximations with kernel-based methods

In this article, we propose a new error bound for Koopman operator approximation using Kernel Extended Dynamic Mode Decomposition. The new estimate is $O(N^{-1/2})$, with a constant related to the probability of success of the bound, given by Hoeffding's inequality, similar to other methodologies, such as Philipp et al. Furthermore, we propose a \textit{lifting back} operator to obtain trajectories generated by embedding the initial state and iterating a linear system in a higher dimension. This naturally yields an $O(N^{-1/2})$ error bound for mean trajectories. Finally, we show numerical results including an example of nonlinear system, exhibiting successful approximation with exponential decay faster than $-1/2$, as suggested by the theoretical results.

math.NA↗

arXiv2025

Koopman Kalman Filter (KKF): An asymptotically optimal nonlinear filtering algorithm with error bounds and its application to parameter estimation

In this article, we propose a new filtering algorithm based in the Koopman operator, showing that a nonlinear filtering problem can be seen as an equivalent problem where the dynamics is infinite dimensional, but linear. Using Extended Dynamic Mode Decomposition (EDMD), we create a finite dimensional approximation of the filtering problem of dimension $N$, in state and error covariance matrix, that accomplishes an error bound of order $O(N^{-1/2})$ in both where $N$ denotes the number of points used in the Koopman approximation. The algorithm is denominated Koopman Kalman Filter (KKF), and has computational complexity $O(T\cdot N^3)$ in time, and $O(T \cdot N^2)$ in space, where $T$ is the number of iterations of the filtering problem. We test the algorithm in linear and nonlinear dynamics cases, showing and effective error bound with respect to the Kalman filter, that corresponds to the optimal solution in the linear case, and equals the error performance of other methods in the state of the art, but with a much lower execution time. Also, we propose a parameter estimation algorithm based in KKF, comparing it with Markov Chain Monte Carlo techniques, showing similar performance with lower execution time.

math.DS↗

arXiv2024

A minimal face constant rank constraint qualification for reducible conic programming

In a previous paper [R. Andreani, G. Haeser, L. M. Mito, H. Ramírez, T. P. Silveira. First- and second-order optimality conditions for second-order cone and semidefinite programming under a constant rank condition. Mathematical Programming, 2023. DOI: 10.1007/s10107-023-01942-8] we introduced a constant rank constraint qualification for nonlinear semidefinite and second-order cone programming by considering all faces of the underlying cone. This condition is independent of Robinson's condition and it implies a strong second-order necessary optimality condition which depends on a single Lagrange multiplier instead of the full set of Lagrange multipliers. In this paper we expand on this result in several directions, namely, we consider the larger class of $\mathcal{C}^2-$cone reducible constraints and we show that it is not necessary to consider all faces of the cone; instead a single specific face should be considered (which turns out to be weaker than Robinson's condition) in order for the first order necessary optimality condition to hold. This gives rise to a notion of facial reduction for nonlinear conic programming, that allows locally redefining the original problem only in terms of this specific face instead of the whole cone, providing a more robust formulation of the problem in which Robinson's condition holds. We were also able to prove the strong second-order necessary optimality condition in this context by considering only the subfaces of this particular face, which is a new result even in nonlinear programming.

math.OC↗

arXiv2022

Weak notions of nondegeneracy in nonlinear semidefinite programming

The constraint nondegeneracy condition is one of the most relevant and useful constraint qualifications in nonlinear semidefinite programming. It can be characterized in terms of any fixed orthonormal basis of the, let us say, $\ell$-dimensional kernel of the constraint matrix, by the linear independence of a set of $\ell(\ell+1)/2$ derivative vectors. We show that this linear independence requirement can be equivalently formulated in a smaller set, of $\ell$ derivative vectors, by considering all orthonormal bases of the kernel instead. This allows us to identify that not all bases are relevant for a constraint qualification to be defined, giving rise to a strictly weaker variant of nondegeneracy related to the global convergence of an external penalty method. We use some of these ideas to revisit an approach of Forsgren [Math. Prog. 88, 105--128, 2000] for exploiting the sparsity structure of a transformation of the constraints to define a constraint qualification, which led us to develop another relaxed notion of nondegeneracy using a simpler transformation. If the zeros of the derivatives of the constraint function at a given point are considered, instead of the zeros of the function itself in a neighborhood of that point, we obtain an even weaker constraint qualification that connects Forsgren's condition and ours.

math.OC↗

arXiv2021

A Lyapunov Approach to Robust Regulation of Distributed Port-Hamiltonian Systems

This paper studies robust output tracking and disturbance rejection for boundary controlled infinite-dimensional port--Hamiltonian systems including second order models such as the Euler--Bernoulli beam. The control design is achieved using the internal model principle and the stability analysis using a Lyapunov approach. Contrary to existing works on the same topic no assumption is made on the external well-posedness of the considered class of PDEs. The results are applied to robust tracking of a piezo actuated tube used in atomic force imaging.

math.OC↗

arXiv2020

The running of featureful primordial power spectra

Current measurements of the temperature and polarization anisotropy power spectra of the Cosmic Microwave Background (CMB) seem to indicate that the naive expectation for the slow-roll hierarchy within the most simple inflationary paradigm may not be respected in nature. We show that a primordial power spectra with localized features could in principle give rise to the observed slow-roll anarchy when fitted to a featureless power spectrum. Future CMB missions have the key to disentangle among the two possible paradigms and firmly establish the slow-roll mechanism as the responsible one for the inflationary period in the early universe. From a model comparison perspective, and assuming that nature has chosen a featureless primordial power spectrum, we find that, while with mock Planck data there is only weak evidence against a model with localized features, upcoming CMB measurements may provide strong evidence against such a non-standard primordial power spectrum.

astro-ph.CO↗

arXiv2020

Refining the partition for multifold conic optimization problems

In this paper we give a unified treatment of two different definitions of complementarity partition of multifold conic programs introduced independently in [J. F. Bonnans and H. Ramírez C., Math. Program. 104 (2005), no. 2-3, Ser. B, 205--227] for conic optimization problems, and in [J. Peña and V. Roshchina, Math. Program. 142 (2013), no 1-2, Ser. A, 579--589] for homogeneous feasibility problems. We show that both can be treated within the same unified geometric framework, and extend the latter notion to optimization problems. We also show that the two partitions do not coincide, and their intersection gives a seven-set index partition. Finally, we demonstrate that the partitions are preserved under the application of nonsingular linear transformations, and in particular that a standard conversion of a second-order cone program into a semidefinite programming problem preserves the partitions.

math.OC↗

arXiv2019

Noncanonical Approaches To Inflation

In this Thesis by publication, we cover both phenomenological and theoretical approaches to the study of inflation: from model-independent parametrizations to modifications of gravity. In a review style, we provide a short introduction to the standard cosmological model and an overview of the dynamics of the canonical single-field inflationary scenario---including the dynamics and evolution of the primordial quantum fluctuations and their signatures on current observations. We then briefly discuss the Mukhanov parametrization, a model-independent approach to study the allowed parameter space of the canonical inflationary scenario. Later, we review the construction of the most general scalar-tensor and scalar-vector-tensor theories of gravity yielding second-order equations of motion, as well as the main models of inflation developed within these frameworks. Finally, we demonstrate new techniques that move beyond the slow-roll approximation---Generalized Slow-roll and Optimized Slow-Roll---to compute the inflationary observables more accurately, in both canonical and noncanonical scenarios. We complement the discussion with detailed appendices on the cosmological perturbation theory and useful expressions for the beyond-GR cosmology. Conclusions are drawn from the results obtained for this Thesis.

gr-qc↗

arXiv2018

Inflation with mixed helicities and its observational imprint on CMB

In the framework of effective field theories with prominent helicity-0 and helicity-1 fields coupled to each other via a dimension-3 operator, we study the dynamics of inflation driven by the helicity-0 mode, with a given potential energy, as well as the evolution of cosmological perturbations, influenced by the presence of a mixing term between both helicities. In this scenario, the temporal component of the helicity-1 mode is an auxiliary field and can be integrated out in terms of the time derivative of the helicity-0 mode, so that the background dynamics effectively reduces to that in single-field inflation modulated by a parameter $β$ associated to the coupling between helicity-0 and helicity-1 modes. We discuss the evolution of a longitudinal scalar perturbation $ψ$ and an inflaton fluctuation $δϕ$, and explicitly show that a particular combination of these two, which corresponds to an isocurvature mode, is subject to exponential suppression by the vector mass comparable to the Hubble expansion rate during inflation. Furthermore, we find that the effective single-field description corrected by $β$ also holds for the power spectrum of curvature perturbations generated during inflation. We compute the standard inflationary observables such as the scalar spectral index $n_s$ and the tensor-to-scalar ratio $r$ and confront several inflaton potentials with the recent observational data provided by Planck 2018. Our results show that the coupling between helicity-0 and helicity-1 modes can lead to a smaller value of the tensor-to-scalar ratio especially for small-field inflationary models, so our scenario exhibits even better compatibility with the current observational data.

gr-qc↗

arXiv2018

Reconciling tensor and scalar observables in G-inflation

The simple $m^2ϕ^2$ potential as an inflationary model is coming under increasing tension with limits on the tensor-to-scalar ratio $r$ and measurements of the scalar spectral index $n_s$. Cubic Galileon interactions in the context of the Horndeski action can potentially reconcile the observables. However, we show that this cannot be achieved with only a constant Galileon mass scale because the interactions turn off too slowly, leading also to gradient instabilities after inflation ends. Allowing for a more rapid transition can reconcile the observables but moderately breaks the slow-roll approximation leading to a relatively large and negative running of the tilt $α_s$ that can be of order $n_s-1$. We show that the observables on CMB and large scale structure scales can be predicted accurately using the optimized slow-roll approach instead of the traditional slow-roll expansion. Upper limits on $|α_s|$ place a lower bound of $r\gtrsim 0.005$ and conversely a given $r$ places a lower bound on $|α_s|$, both of which are potentially observable with next generation CMB and large scale structure surveys.

astro-ph.CO↗

arXiv2016

The present and future of the most favoured inflationary models after $Planck$ 2015

The value of the tensor-to-scalar ratio $r$ in the region allowed by the latest $Planck$ 2015 measurements can be associated to a large variety of inflationary models. We discuss here the potential of future Cosmic Microwave Background cosmological observations in disentangling among the possible theoretical scenarios allowed by our analyses of current $Planck$ temperature and polarization data. Rather than focusing only on $r$, we focus as well on the running of the primordial power spectrum, $α_s$ and the running of thereof, $β_s$. Our Fisher matrix method benefits from a detailed and realistic appraisal of the expected foregrounds. Future cosmological probes, as the COrE mission, may be able to reach an unprecedented accuracy in the extraction of $β_s$ and rule out the most favoured inflationary models.

astro-ph.CO↗

arXiv2015

Does Current Data Prefer a Non-minimally Coupled Inflaton?

We examine the impact of a non-minimal coupling of the inflaton to the Ricci scalar, $\frac12 ξRϕ^2$, on the inflationary predictions. Such a non-minimal coupling is expected to be present in the inflaton Lagrangian on fairly general grounds. As a case study, we focus on the simplest inflationary model governed by the potential $V\propto ϕ^2$, using the latest combined 2015 analysis of Planck and BICEP2/Keck Array. We find that the presence of a coupling $ξ$ is favoured at a significance of $99\%$ CL, assuming that nature has chosen the potential $V\propto ϕ^2$ to generate the primordial perturbations and a number of e-foldings $N=60$. Within the context of the same scenario, we find that the value of $ξ$ is different from zero at the $2σ$ level. When considering the cross-correlation polarization spectra from BICEP2/Keck Array and Planck, a value of $r=0.038_{-0.030}^{+0.039}$ is predicted in this particular non-minimally coupled scenario. Future cosmological observations may therefore test these values of $r$ and verify or falsify the non-minimally coupled model explored here.

astro-ph.CO↗

arXiv2015

Phenomenological approaches of inflation and their equivalence

In this work, we analyze two possible alternative and model-independent approaches to describe the inflationary period. The first one assumes a general equation of state during inflation due to Mukhanov, while the second one is based on the slow-roll hierarchy suggested by Hoffman and Turner. We find that, remarkably, the two approaches are equivalent from the observational viewpoint, as they single out the same areas in the parameter space, and agree with the inflationary attractors where successful inflation occurs. Rephrased in terms of the familiar picture of a slowly rolling, canonically normalized scalar field, the resulting inflaton excursions in these two approaches are almost identical. Furthermore, once the Galactic dust polarization data from Planck are included in the numerical fits, inflaton excursions can safely take sub-Planckian values.

astro-ph.CO↗