Basque Center for Applied Mathematics

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    1312 research outputs found

    Uniform maximal Fourier restriction for convex curves

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    We extend the estimates for maximal Fourier restriction operators proved by M\"{u}ller, Ricci, and Wright in \cite{MR3960255} and Ramos in \cite{MR4055940} to the case of arbitrary convex curves in the plane, with constants uniform in the curve. The improvement over M\"{u}ller, Ricci, and Wright and Ramos is given by the removal of the C2\mathcal{C}^2 regularity condition on the curve. This requires the choice of an appropriate measure for each curve, that is suggested by an affine invariant construction of Oberlin in \cite{MR1960918}. As corollaries, we obtain a uniform Fourier restriction theorem for arbitrary convex curves and a result on the Lebesgue points of the Fourier transform on the curve.CRC 1060 \emph{The Mathematics of Emergent Effects} at the University of Bonn, funded through the Deutsche Forschungsgemeinschaf

    A revisited branch-and-cut algorithm for large-scale orienteering problems

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    The orienteering problem is a route optimization problem which consists of finding a simple cycle that maximizes the total collected profit subject to a maximum distance limitation. In the last few decades, the occurrence of this problem in real-life applications has boosted the development of many heuristic algorithms to solve it. However, during the same period, not much research has been devoted to the field of exact algorithms for the orienteering problem. The aim of this work is to develop an exact method which is able to obtain the optimum in a wider set of instances than with previous methods, or to improve the lower and upper bounds in its disability. We propose a revisited version of the branch-and-cut algorithm for the orienteering problem which includes new contributions in the separation algorithms of inequalities stemming from the cycle problem, in the separation loop, in the variables pricing, and in the calculation of the lower and upper bounds of the problem. Our proposal is compared to three state-of-the-art algorithms on 258 benchmark instances with up to 7397 nodes. The computational experiments show the relevance of the designed components where 18 new optima, 76 new best-known solutions and 85 new upper-bound values were obtained

    Symmetry in a multi-strain epidemiological model with distributed delay as a general cross-protection period and disease enhancement factor

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    Important biological features of viral infectious diseases caused by multiple agents with interacting strain dynamics continue to pose challenges for mathematical modelling development. Motivated by dengue fever epidemiology, we study a system of Integro-Differential Equations (IDE) considering strain structure of pathogens. Knowing that complex dynamics observed in dengue models are driven by the combination of two biological features, the temporary cross-immunity (TCI) and disease enhancement via the antibody-dependent enhancement process (ADE), our IDE system incorporates the TCI with a general time delay term, and the ADE effect by a constant factor to differentiate the susceptibility of individuals experiencing a primary or a secondary infection. Aiming at analysing the effect of the symmetry on dengue serotypes in the IDE framework, a detailed qualitative analysis of the model is performed and the instability of the coexistence steady state is shown using the perturbation theory approach. Numerical simulations identify the bifurcation structures and confirm the stability analysis. Results for the symmetric and asymmetric models are discussed

    Exploiting Kronecker structure in exponential integrators: Fast approximation of the action ofā€‰ phi-functions of matrices via quadrature

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    In this article, we propose an algorithm for approximating the action ofā€‰ Ļ†\varphi-functions of matrices against vectors, which is a key operation in exponential time integrators. In particular, we consider matrices with Kronecker sum structure, which arise from problems admitting a tensor product representation. The method is based on quadrature approximations of the integral form of theā€‰ Ļ†\varphi-functions combined with a scaling and modified squaring method. Owing to the Kronecker sum representation, only actions of 1D matrix exponentials are needed at each quadrature node and assembly of the full matrix can be avoided. Additionally, we derive a priori bounds for the quadrature error, which show that, as expected by classical theory, the rate of convergence of our method is supergeometric. Guided by our analysis, we construct a fast and robust method for estimating the optimal scaling factor and number of quadrature nodes that minimizes the total cost for a prescribed error tolerance. We investigate the performance of our algorithm by solving several linear and semilinear time-dependent problems in 2D and 3D. The results show that our method is accurate and orders of magnitude faster than the current state-of-the-art

    The effects of public health measures on severe dengue cases: An optimal control approach

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    Dengue fever is the most important viral mosquito-borne disease worldwide, with approximately 3.9 billion people at risk of acquiring dengue infection. Measures against mosquito bite combined with vector control programs to reduce mosquito population have been used in endemic countries for several years. Most recently, vaccines have become an important ally to prevent and control disease transmission. Economic costs of dengue control programs vary from region to region and therefore designing an optimal control strategy must be evaluated at different epidemiological contexts. Using a multi-strain vector-host mathematical model, we investigate the impact of different control measures to reduce dengue prevalence. A detailed sensitivity analysis to identify the key parameters influencing disease transmission is followed by an exploratory analysis of the possible solutions for the optimal control problem considering preventive measures to avoid mosquito bites, reduce mosquito population and vaccinate human hosts. The proposed cost functional includes a weighted sum of several efforts (not necessarily quantified as economic costs) for the controls which are evaluated alone and combined. The control system is analyzed using the Pontryagin`s Principle for optimal control where different strategies are compared. Our results have shown that the simultaneous use of intervention measures are highly effective to reduce disease cases, however, the use of a single control measure can be as effective as the use of two or more controls combined. A careful evaluation of the epidemiological scenario is advised before designing strategies for disease prevention and control, allowing an optimal allocation of the public health resources


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    According to the principle of compressed sensing (CS), under-sampled seismic data can be interpolated when the data becomes sparse in a transform domain. To sparsify the data, dictionary learning presents a data-driven approach trained to be optimized for each target dataset. This study presents an interpolation method for seismic data in which dictionary learning is employed to improve the sparsity of data representation using improved Kth Singular Value Decomposition (K-SVD). In this way, the transformation will be highly compatible with the input data, and the data in the converted domain will be sparser. In addition, the sampling matrix is produced with the restricted isometry property (RIP). To reduce the sensitivity of the minimizer term to the outliers, we use the smooth L1 minimizer as a regularization term in the regularized orthogonal matching pursuit (ROMP). We apply the proposed method to both synthetic and real seismic data. The results show that it can successfully reconstruct the missing seismic traces

    Physics-guided deep-learning inversion method for the interpretation of noisy logging-while-drilling resistivity measurements

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    Deep learning (DL) inversion is a promising method for real-Time interpretation of logging-while-drilling (LWD) resistivity measurements for well-navigation applications. In this context, measurement noise may significantly affect inversion results. Existing publications examining the effects of measurement noise on DL inversion results are scarce. We develop a method to generate training data sets and construct DL architectures that enhance the robustness of DL inversion methods in the presence of noisy LWD resistivity measurements. We use two synthetic resistivity models to test the three approaches that explicitly consider the presence of noise: (1) adding noise to the measurements in the training set, (2) augmenting the training set by replicating it and adding varying noise realizations and (3) adding a noise layer in the DL architecture. Numerical results confirm that each of the three approaches enhances the noise-robustness of the trained DL inversion modules, yielding better inversion results-in both the predicted earth model and measurements-compared to the basic DL inversion and also to traditional gradient-based inversion results. A combination of the second and third approaches delivers the best results

    Mapping flagellated swimmers to surface-slip driven swimmers.

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    Flagellated microswimmers are ubiquitous in natural habitats. Understanding the hydrodynamic behavior of these cells is of paramount interest, owing to their applications in bio-medical engineering and disease spreading. Since the last two decades, computational efforts have been continuously improved to accurately capture the complex hydrodynamic behavior of these model systems. However, modeling the dynamics of such swimmers with fine details is computationally expensive due to the large number of unknowns and the small time-steps required to solve the equations. In this work we propose a method to map fully resolved flagellated microswimmers to coarse, active slip driven swimmers which can be simulated at a reduced computational cost. Using the new method, the slip driven swimmers move with the same velocity, to machine precision, as the flagellated swimmers and generate a similar flow field with a controlled accuracy. The method is validated for swimming patterns near a no-slip boundary, interactions between swimmers and scattering with large obstacles

    Importance of methodological choices in data manipulation for validating epileptic seizure detection models

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    Epilepsy is a chronic neurological disorder that affects a significant portion of the human population and imposes serious risks in the daily life. Despite advances in machine learning and IoT, small, non-stigmatizing wearable devices for continuous monitoring and detection in outpatient environments are not yet widely available. Part of the reason is the complexity of epilepsy itself, including highly imbalanced data, multimodal nature, and very subject-specific signatures. However, another problem is the heterogeneity of methodological approaches in research, leading to slower progress, difficulty in comparing results, and low reproducibility. Therefore, this article identifies a wide range of methodological decisions that must be made and reported when training and evaluating the performance of epilepsy detection systems. We characterize the influence of individual choices using a typical ensemble random-forest model and the publicly available CHB-MIT database, providing a broader picture of each decision and giving good-practice recommendations, based on our experience, where possible.RYC2021-032853-

    Supervised Learning in Time-dependent Environments with Performance Guarantees

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    In practical scenarios, it is common to learn from a sequence of related problems (tasks). Such tasks are usually time-dependent in the sense that consecutive tasks are often significantly more similar. Time-dependency is common in multiple applications such as load forecasting, spam main filtering, and face emotion recognition. For instance, in the problem of load forecasting, the consumption patterns in consecutive time periods are significantly more similar since human habits and weather factors change gradually over time. Learning from a sequence tasks holds promise to enable accurate performance even with few samples per task by leveraging information from different tasks. However, harnessing the benefits of learning from a sequence of tasks is challenging since tasks are characterized by different underlying distributions. Most existing techniques are designed for situations where the tasksā€™ similarities do not depend on their order in the sequence. Existing techniques designed for timedependent tasks adapt to changes between consecutive tasks accounting for a scalar rate of change by using a carefully chosen parameter such as a learning rate or a weight factor. However, the tasksā€™ changes are commonly multidimensional, i.e., the timedependency often varies across different statistical characteristics describing the tasks. For instance, in the problem of load forecasting, the statistical characteristics related to weather factors often change differently from those related to generation. In this dissertation, we establish methodologies for supervised learning from a sequence of time-dependent tasks that effectively exploit information from all tasks, provide multidimensional adaptation to tasksā€™ changes, and provide computable tight performance guarantees. We develop methods for supervised learning settings where tasks arrive over time including techniques for supervised classification under concept drift (SCD) and techniques for continual learning (CL). In addition, we present techniques for load forecasting that can adapt to time changes in consumption patterns and assess intrinsic uncertainties in load demand. The numerical results show that the proposed methodologies can significantly improve the performance of existing methods using multiple benchmark datasets. This dissertation makes theoretical contributions leading to efficient algorithms for multiple machine learning scenarios that provide computable performance guarantees and superior performance than state-of-the-art techniques


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