2063 research outputs found
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Understanding non-convex optimization problems and stochastic optimization algorithms
Get PDFThis thesis presents significant contributions in the field of iterative stochastic heuristics. Various aspects related to the comparison and improvement of optimisation algorithms are addressed. Firstly, a methodology is proposed to fairly compare the performance of algorithms run on different machines, ensuring an equitable allocation of computational resources. Additionally, a methodology based on stochastic dominance is introduced to compare the performance of optimisation algorithms as random variables. Furthermore, the relationship between Hamming distance and the quadratic assignment problem is analysed. A general early stopping method for learning policies in episodic problems, which does not require specific problem information, is developed. In summary, this thesis contributes to the understanding and improvement of iterative stochastic heuristics in the field of optimisation
Optimal vaccine allocation for the control of sexually transmitted infections
Get PDFThe burden of sexually transmitted infections (STIs) poses a challenge due to its
large negative impact on sexual and reproductive health worldwide. Besides simple
prevention measures and available treatment efforts, prophylactic vaccination is a
powerful tool for controlling some viral STIs and their associated diseases. Here, we
investigate how prophylactic vaccines are best distributed to prevent and control STIs.
We consider sex-specific differences in susceptibility to infection, as well as disease
severity outcomes. Different vaccination strategies are compared assuming distinct
budget constraints that mimic a scarce vaccine stockpile. Vaccination strategies are
obtained as solutions to an optimal control problem subject to a two-sex Kermack–
McKendrick-type model, where the control variables are the daily vaccination rates
for females and males. One important aspect of our approach relies on conceptualizing
a limited but specific vaccine stockpile via an isoperimetric constraint. We solve the
optimal control problem via Pontryagin’sMaximum Principle and obtain a numerical
approximation for the solution using a modified version of the forward–backward
sweep method that handles the isoperimetric budget constraint in our formulation. The
results suggest that for a limited vaccine supply (20%–30%vaccination coverage), onesex
vaccination, prioritizing females, appears to be more beneficial than the inclusion
of both sexes into the vaccination program.Whereas, if the vaccine supply is relatively
large (enough to reach at least 40% coverage), vaccinating both sexes, with a slightly
higher rate for females, is optimal and provides an effective and faster approach to
reducing the prevalence of the infection
Nonequilibrium thermodynamics of the asymmetric Sherrington-Kirkpatrick model
Get PDFMost natural systems operate far from equilibrium, displaying time-asymmetric, irreversible dynamics characterized by a positive entropy production while exchanging energy and matter with the environment. Although stochastic thermodynamics underpins the irreversible dynamics of small systems, the nonequilibrium thermodynamics of larger, more complex systems remains unexplored. Here, we investigate the asymmetric Sherrington-Kirkpatrick model with synchronous and asynchronous updates as a prototypical example of large-scale nonequilibrium processes. Using a path integral method, we calculate a generating functional over trajectories, obtaining exact solutions of the order parameters, path entropy, and steady-state entropy production of infinitely large networks. Entropy production peaks at critical order-disorder phase transitions, but is significantly larger for quasi-deterministic disordered dynamics. Consequently, entropy production can increase under distinct scenarios, requiring multiple thermodynamic quantities to describe the system accurately. These results contribute to developing an exact analytical theory of the nonequilibrium thermodynamics of large-scale physical and biological systems and their phase transitions.Junior Leader fellowship from “la Caixa” Foundation (ID 100010434, code LCF/BQ/PI23/11970024
Fast K-Medoids With the l_1-Norm
Get PDFK-medoids clustering is one of the most popular techniques in exploratory data analysis. The most commonly used algorithms to deal with this problem are quadratic on the number of instances, n, and usually the quality of the obtained solutions strongly depends upon their initialization phase. In this work, we propose an algorithm for the K -medoids problem on the l_1-norm/Manhattan distance with a computational complexity of O(n⋅max{log n,K}⋅d) , along with theoretical guarantees in terms of the accuracy of the obtained approximation. In addition, we propose a cheap split-merge mechanism that can be used to re-start the proposed algorithm after its convergence to a fixed point. Under some mild assumptions, we prove that such a re-start procedure reduces the error of the given fixed point. The work also includes an extensive experimentation, in which we compare our method to the most popular approaches for the K -medoids problem: PAM, CLARA and Park's K -medoids. The obtained empirical results show the proposed algorithm to consistently converge to the solutions with the lowest errors, up to two orders of magnitude of relative error lower than the previously mentioned methods, while also requiring the lowest computational running times among them: up to three orders of magnitude lower
Tribological variable-friction coefficient models for the simulation of dense suspensions of rough polydisperse particles
Get PDFThe rheology of concentrated suspensions of particles is complex and typically exhibits a shear-thickening behavior in the case of repulsive interactions. Despite the recent interest arisen, the causes of the shear-thickening remain unclear. Frictional contacts have been able to explain the discontinuous shear thickening in simulations. However, the interparticle friction coefficient is considered to be constant in most simulations and theoretical works reported to date despite the fact that tribological experiments demonstrate that the friction coefficient can not only be constant (boundary regime) but also decrease (mixed regime) or even increase (full-film lubrication regime), depending on the normal force and the relative velocity between the particles and the interstitial liquid between them. Interestingly, the transition between the boundary regime and the full-lubrication regime is governed by the particle average roughness. Particle-level simulations of suspensions of hard spheres were carried out using short-range lubrication and roughness-dependent frictional forces describing the full Stribeck curve. Suspensions with different particle's roughness were simulated to show that the particle roughness is a key factor in the shear-thickening behavior; for sufficiently rough particles, the suspension exhibits a remarkable shear-thickening, while for sufficiently smooth particles, the discontinuous shear-thickening disappears
Event-based sampled ECG morphology reconstruction through self-similarity
Get PDFBackground and Objective: Event-based analog-to-digital converters allow for sparse bio-signal acquisition, enabling local sub-Nyquist sampling frequency. However, aggressive event selection can cause the loss of important bio-markers, not recoverable with standard interpolation techniques. In this work, we leverage the self-similarity of the electrocardiogram (ECG) signal to recover missing features in event-based sampled ECG signals, dynamically selecting patient-representative templates together with a novel dynamic time warping algorithm to infer the morphology of event-based sampled heartbeats. Methods: We acquire a set of uniformly sampled heartbeats and use a graph-based clustering algorithm to define representative templates for the patient. Then, for each event-based sampled heartbeat, we select the morphologically nearest template, and we then reconstruct the heartbeat with piece-wise linear deformations of the selected template, according to a novel dynamic time warping algorithm that matches events to template segments. Results: Synthetic tests on a standard normal sinus rhythm dataset, composed of approximately 1.8 million normal heartbeats, show a big leap in performance with respect to standard resampling techniques. In particular (when compared to classic linear resampling), we show an improvement in P-wave detection of up to 10 times, an improvement in T-wave detection of up to three times, and a 30% improvement in the dynamic time warping morphological distance. Conclusion: In this work, we have developed an event-based processing pipeline that leverages signal self-similarity to reconstruct event-based sampled ECG signals. Synthetic tests show clear advantages over classical resampling techniques.RYC2021-032853-
Fast rotating non-homogeneous fluids in thin domains and the Ekman pumping effect
Get PDFIn this paper, we perform the fast rotation limit ε → 0+ of the density-dependent incompressible Navier-Stokes- Coriolis system in a thin strip Ωε := R2×] − lε,lε[, where ε ∈]0,1] is the size of the Rossby number and lε > 0 for any ε > 0. By letting lε −→ 0+ for ε → 0+ and considering Navier-slip boundary conditions at the boundary of Ωε, we give a rigorous justification of the phenomenon of the Ekman pumping in the context of non-homogeneous fluids. With respect to previous studies (performed for flows of contant density and for compressible fluids), our approach has the advantage of circumventing the complicated analysis of boundary layers. To the best of our knowledge, this is the first study dealing with the asymptotic analysis of fast rotating incompressible fluids with variable density in a 3-D setting. In this respect, we remark that the case lε > l > 0 for all ε > 0 remains largely open at present
BayFlux: A Bayesian Method to Quantify Metabolic Fluxes and their Uncertainty at the Genome Scale.
Get PDFMetabolic fluxes, the number of metabolites traversing each biochemical reaction in a cell per unit time, are crucial for assessing and understanding cell function. 13C Metabolic Flux Analysis (13C MFA) is considered to be the gold standard for measuring metabolic fluxes. 13C MFA typically works by leveraging extracellular exchange fluxes as well as data from 13C labeling experiments to calculate the flux profile which best fit the data for a small, central carbon, metabolic model. However, the nonlinear nature of the 13C MFA fitting procedure means that several flux profiles fit the experimental data within the experimental error, and traditional optimization methods offer only a partial or skewed picture, especially in “non-gaussian” situations where multiple very distinct flux regions fit the data equally well. Here, we present a method for flux space sampling through Bayesian inference (BayFlux), that identifies the full distribution of fluxes compatible with experimental data for a comprehensive genome-scale model. This Bayesian approach allows us to accurately quantify uncertainty in calculated fluxes. We also find that, surprisingly, the genome-scale model of metabolism produces narrower flux distributions (reduced uncertainty) than the small core metabolic models traditionally used in 13C MFA. The different results for some reactions when using genome-scale models vs core metabolic models advise caution in assuming strong inferences from 13C MFA since the results may depend significantly on the completeness of the model used. Based on BayFlux, we developed and evaluated novel methods (P-13C MOMA and P-13C ROOM) to predict the biological results of a gene knockout, that improve on the traditional MOMA and ROOM methods by quantifying prediction uncertainty
Minimax Forward and Backward Learning of Evolving Tasks with Performance Guarantees
Get PDFFor a sequence of classification tasks that arrive over time, it is common that tasks
are evolving in the sense that consecutive tasks often have a higher similarity. The
incremental learning of a growing sequence of tasks holds promise to enable accurate
classification even with few samples per task by leveraging information from
all the tasks in the sequence (forward and backward learning). However, existing
techniques developed for continual learning and concept drift adaptation are either
designed for tasks with time-independent similarities or only aim to learn the
last task in the sequence. This paper presents incremental minimax risk classifiers
(IMRCs) that effectively exploit forward and backward learning and account for
evolving tasks. In addition, we analytically characterize the performance improvement
provided by forward and backward learning in terms of the tasks’ expected
quadratic change and the number of tasks. The experimental evaluation shows
that IMRCs can result in a significant performance improvement, especially for
reduced sample sizes.Funding in direct support of this work has been provided by projects PID2022-137063NBI00,
PID2022-137442NB-I00, CNS2022-135203, and CEX2021-001142-S funded by
MCIN/AEI/10.13039/501100011033 and the European Union “NextGenerationEU”/PRTR,
BCAM Severo Ochoa accreditation CEX2021-001142-S / MICIN / AEI/ 10.13039/501100011033
funded by the Ministry of Science and Innovation, and programes ELKARTEK, IT1504-22, and
BERC-2022-2025 funded by the Basque Government
On an adaptive stabilized mixed finite element method for the Oseen problem with mixed boundary conditions
Get PDFWe consider the Oseen problem with nonhomogeneous Dirichlet boundary conditions on a part of the boundary and a Neumann type boundary condition on the remaining part. Suitable least squares terms that arise from the constitutive law, the momentum equation and the Dirichlet boundary condition are added to a dual-mixed formulation based on the pseudostress- velocity variables. We prove that the new augmented variational formulation and the corresponding Galerkin scheme are well-posed, and a Céa estimate holds for any finite element subspaces. We also provide the rate of convergence when each row of the pseudostress is approximated by Raviart–Thomas elements and the velocity is approximated by continuous piecewise polynomials. We develop an a posteriori error analysis based on a Helmholtz-type decomposition, and derive a posteriori error indicators that consist of two residual terms per element except on those elements with a side on the Dirichlet boundary, where they both have two additional terms. We prove that these a posteriori error indicators are reliable and locally efficient. Finally, we provide several numerical experiments that support the theoretical results.
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