Basque Center for Applied Mathematics

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    2063 research outputs found

    Evaluating the risk of mosquito-borne diseases in non-endemic regions: A dynamic modeling approach

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    Mosquito-borne diseases are spreading into temperate zones, raising concerns about local outbreaks driven by imported cases. Using stochastic methods, we developed a vector-host model to estimate the risk of import-driven autochthonous outbreaks in non-endemic regions. The model explores key factors such as imported cases and vector abundance. Our analysis shows that mosquito population abundance significantly affects the probability and timing of outbreaks. Even with moderate mosquito populations, isolated or clustered outbreaks can be triggered, highlighting the importance of monitoring vector abundance for effective public health planning and interventions.This work is supported by the ARBOSKADI project for monitoring vector-borne diseases in the Basque Country, Euskadi. We wish to extend our acknowledgments to Jesús Ángel Ocio Armentia, Oscar Goñi Laguardia and Ana Ramírez de La Peciña Pérez, Dirección de Salud Pública for their fruitful discussions, and to Madalen Oribe Amores, Unidad de Vigilancia Epidemiológica de Bizkaia, for her cooperation in providing the requested epidemiological data that was essential for carrying out this research. M.A. and A.C acknowledges the financial support by the Ministerio de Ciência e Innovacion (MICINN) of the Spanish Government through the Ramon Cajal grant RYC2021-031380-I, RYC2021-033084-I, respectively. This research is also supported by the Basque Government through the “Mathematical Modeling Applied to Health” (BMTF) Project, BERC 2022–2025 program and by the Spanish Ministry of Sciences, Innovation and Universities : BCAM Severo Ochoa accreditation CEX2021-001142-S/MICIN / AEI/10.13039/501100011033

    Self-Composing Policies for Scalable Continual Reinforcement Learning

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    Reliable deployment of machine learning models such as neural networks continues to be challenging due to several limitations. Some of the main shortcomings are the lack of interpretability and the lack of robustness against adversarial examples or out-of-distribution inputs. In this paper, we comprehensively review the possibilities and limits of adversarial attacks for explainable machine learning models. First, we extend the notion of adversarial examples to fit in explainable machine learning scenarios where a human assesses not only the input and the output classification, but also the explanation of the model’s decision. Next, we propose a comprehensive framework to study whether (and how) adversarial examples can be generated for explainable models under human assessment. Based on this framework, we provide a structured review of the diverse attack paradigms existing in this domain, identify current gaps and future research directions, and illustrate the main attack paradigms discussed. Furthermore, our framework considers a wide range of relevant yet often ignored factors such as the type of problem, the user expertise or the objective of the explanations, in order to identify the attack strategies that should be adopted in each scenario to successfully deceive the model (and the human). The intention of these contributions is to serve as a basis for a more rigorous and realistic study of adversarial examples in the field of explainable machinIt1504-22 PID2019-104966GB.I00 PID2022-137442NB-I0

    TDOA-based localization under uniform prior knowledge: Performance bounds and its efficient calculation

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    The emergence of a myriad of location-based services has imposed a key role on wireless localization systems. The accuracy of such systems can be enhanced by using prior information on the target location area, commonly available through a map or wireless system coverage area. In the map-aware localization context, performance limits have been mainly explored for Time-of-Arrival positioning systems. This paper presents performance bounds for Time-Difference-of-Arrival (TDOA) localization using a uniform prior information of the location area. In particular, the paper derives a closed-form approximation of the Ziv-Zakai lower bound (ZZB) and Bayesian Cramer-Rao lower bound (BCRB). The presented bounds are evaluated under different configurations and compared with the maximum a posteriori (MAP) estimator, which incorporates a priori information about the location area, and with the Cramer-Rao lower bound (CRB) and the maximum likelihood (ML) estimator, both without prior information. Numerical results show that the proposed ZZB and BCRB exploit the a priori knowledge to increase the localization accuracy and provide tighter performance lower bounds of a MAP estimator, and are properly matched to the actual limits of practical positioning systems. In addition, the proposed closed-form ZZB approximation allows us to avoid numerical evaluation of integrals needed to compute BCRB and exact ZZB, while maintaining similar accuracy and decreasing the computational complexity

    Poisson transform and unipotent complex geometry

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    Our concern is with Riemannian symmetric spaces Z=G/KZ=G/K of the non-compact type and more precisely with the Poisson transform Pλ\mathcal{P}_\lambda which maps generalized functions on the boundary Z\partial Z to λ\lambda-eigenfunctions on ZZ. Special emphasis is given to a maximal unipotent group N<GN<G which naturally acts on both ZZ and Z\partial Z. The NN-orbits on ZZ are parametrized by a torus A=(R>0)r<GA=(\mathbb{R}_{>0})^r<G (Iwasawa) and letting the level aAa\in A tend to 00 on a ray we retrieve NN via lima0Na\lim_{a\to 0} Na as an open dense orbit in Z\partial Z (Bruhat). For positive parameters λ\lambda the Poisson transform Pλ\mathcal{P}_\lambda is defined an injective for functions fL2(N)f\in L^2(N) and we give a novel characterization of Pλ(L2(N))\mathcal{P}_\lambda(L^2(N)) in terms of complex analysis. For that we view eigenfunctions ϕ=Pλ(f)\phi = \mathcal{P}_\lambda(f) as families (ϕa)aA(\phi_a)_{a\in A} of functions on the NN-orbits, i.e. ϕa(n)=ϕ(na)\phi_a(n)= \phi(na) for nNn\in N. The general theory then tells us that there is a tube domain T=Nexp(iΛ)NC\mathcal{T}=N\exp(i\Lambda)\subset N_\mathbb{C} such that each ϕa\phi_a extends to a holomorphic function on the scaled tube Ta=Nexp(iAd(a)Λ)\mathcal{T}_a=N\exp(i\operatorname{Ad}(a)\Lambda). We define a class of NN-invariant weight functions { wλ{\bf w}_\lambda on the tube T\mathcal{T}}, rescale them for every aAa\in A to a weight wλ,a{\mathbf{w}}_{\lambda, a} on Ta\mathcal{T}_a, and show that each ϕa\phi_a lies in the L2L^2-weighted Bergman space B(Ta,wλ,a):=O(Ta)L2(Ta,wλ,a)\mathcal{B}(\mathcal{T}_a, {\mathbf{w}}_{\lambda, a}):=\mathcal{O}(\mathcal{T}_a)\cap L^2(\mathcal{T}_a, {\mathbf{w}}_{\lambda, a}). The main result of the article then describes Pλ(L2(N))\mathcal{P}_\lambda(L^2(N)) as those eigenfunctions ϕ\phi for which ϕaB(Ta,wλ,a)\phi_a\in \mathcal{B}(\mathcal{T}_a, {\mathbf{w}}_{\lambda, a}) and ϕ:=supaAaReλ2ρϕaBa,λ<\|\phi\|:=\sup_{a\in A} a^{\operatorname{Re}\lambda -2\rho} \|\phi_a\|_{\mathcal{B}_{a,\lambda}}<\infty holds.Ikerbasque RYC2018-025477-I CNS2023-143893 PID2023-146646NB-I0

    Estimates of Solutions for Integro-Differential Equations in Epidemiological Modeling

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    Integro-differential equations (IDE) have been applied in a variety of areas of research, including epidemiology. Recently, IDE systems were applied to study dengue fever transmission dynamics at the population level. In this study, we extend the approach presented in a previous study for describing the epidemiological model of dengue fever. In this paper, we find the exact solutions of the corresponding linearized system model by constructing the Cauchy and Green’s matrices. Furthermore, we extend our investigation towards estimating the solutions of a closely related nonlinear system. Given that the coefficients of the model are only known approximately, we address the problem of the stability of a system with uncertain coefficients. Furthermore, we estimate the influence of errors in the coefficient determination on solution behavior

    A Unified View of Double-Weighting for Marginal Distribution Shift

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    Supervised classification traditionally assumes that training and testing samples are drawn from the same underlying distribution. However, practical scenarios are often affected by distribution shifts, such as covariate and label shifts. Most existing techniques for correcting distribution shifts are based on a reweighted approach that weights training samples, assigning lower relevance to the samples that are unlikely at testing. However, these methods may achieve poor performance when the weights obtained take large values at certain training samples. In addition, in multi-source cases, existing methods do not exploit complementary information among sources, and equally combine sources for all instances. In this paper, we establish a unified learning framework for distribution shift adaptation. We present a double-weighting approach to deal with distribution shifts, considering weight functions associated with both training and testing samples. For the multi-source case, the presented methods assign source-dependent weights for training and testing samples, where weights are obtained jointly using information from all sources. We also present generalization bounds for the proposed methods that show a significant increase in the effective sample size compared with existing approaches. Empirically, the proposed methods achieve enhanced classification performance in both synthetic and empirical experiments.PID2022-137063NBI00, CNS2022-135203, European Union “NextGenerationEU”/PRTR

    Settling dynamics of a non-Brownian suspension of spherical and cubic particles in Stokes flow

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    The present study investigates the gravity-driven settling dynamics of non-Brownian suspensions consisting of spherical and cubic particles within a triply periodic domain. We numerically examine the impact of solid volume fraction on the evolving microstructure of the suspension using the rigid multiblob method under Stokes flow conditions. Our simulations match macroscopic trends observed in experiments, and align well with established semi-empirical correlations across a broad range of volume fractions. At low to moderate solid volume fractions, the settling mechanism is governed primarily by hydrodynamic interactions between the particles and the surrounding fluid. However, frequent collisions between particles in a highly packed space tend to suppress velocity fluctuations at denser regimes. For dilute suspensions, transport properties are shaped predominantly by an anisotropic microstructure, though this anisotropy diminishes as many-body interactions intensify at higher volume fractions. Notably, cubic particles exhibit lower anisotropy in velocity fluctuations compared to spherical particles, owing to more efficient momentum and energy transfer from the gravity-driven direction to transverse directions. Finally, bidisperse suspensions with mixed particle shapes show enhanced velocity fluctuations, driven by shape-induced variations in drag and increased hydrodynamic disturbances. These fluctuations in turn affect the local sedimentation velocity field, leading to the segregation of particles in the mixture

    Mesoscale Transport of Enveloped Viruses

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    Enveloped viruses are characterized by spike proteins that protrude from and decorate the viral membrane. These proteins play a crucial role in host cell interactions and exhibit dynamic behaviors, such as tilting, sliding, and clustering, which vary across different types of enveloped viruses. For instance, SARS-CoV-2 spikes tilt to facilitate receptor binding, Influenza spikes migrate during infection, and HIV spikes migrate and cluster to enhance infectivity. In this study, we investigate how such dynamics influence the virus mobility. We characterize viral mobility through translational and rotational diffusion coefficients using a mesoscopic model that incorporates the dynamics of both the flexible spike proteins and the viral envelope. Using the smoothed dissipative particle dynamics (SDPD) method, we construct three virion models with varying spike flexibility. The first is a fully rigid virus with static spikes, the second is a model with spikes that tilt but remain fixed in position, and the third is a model allowing both tilting and sliding of spikes across the envelope. Our results show that spike flexibility primarily affects rotational diffusion, whereas the envelope dominates translational mobility of the virus. We also explore spike clustering driven purely by hydrodynamic interactions and compare with an experimental model reference using DNA-PAINT super-resolution imaging of HIV-like particles. We identify that hydrodynamic interactions alone can be responsible for dynamic clustering of spike proteins. Where, the characteristic size and lifespan of such clusters indicate predominantly doublets and triplets formations. Our findings highlight the role of spike dynamics in whole virion mobility, and motivate further investigations with time-resolved experimental evidence to fully characterize clustering behavior

    Simulating non-Brownian suspensions with non-homogeneous Navier slip boundary conditions

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    Fluid-structure interactions are commonly modeled using no-slip boundary conditions. However, small deviations from these conditions can significantly alter the dynamics of sus- pensions and particles, especially at the micro and nano scales. This work presents a robust implicit numerical method for simulating non-colloidal suspensions with non-homogeneous Navier slip boundary conditions. Our approach is based on a regularized boundary inte- gral formulation, enabling accurate and efficient computation of hydrodynamic interactions. This makes the method well-suited for large-scale simulations. We validate the method by comparing computed drag forces on homogeneous and Janus particles with analytical results. Additionally, we consider the effective viscosity of suspensions with varying slip lengths, benchmarking against available analytical no-slip and partial-slip theories

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