Basque Center for Applied Mathematics

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    2063 research outputs found

    Global sensitivity analysis of fuel-type-dependent input variables of a simplified physical fire spread model

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    A new global sensitivity analysis has been conducted of fuel-type-dependent input variables of the simplified physical fire spread model (PhyFire) to understand how the use of spatial averages, that is, fuel models, influences the results of PhyFire with a view to enhancing its understanding and improving its design. The model’s simplicity, the numerical techniques used, and a recent code optimisation, allow undertaking the analysis with very competitive computational times. The fuel data used correspond to grasslands, shrublands and forest in the Spanish region of Galicia. The analysis results validate the flame length sub-model proposed in the paper, which significantly improves the model’s efficiency

    On the motion of a small rigid body in a viscous compressible fluid

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    We consider the motion of a small rigid object immersed in a viscous compressible fluid in the 3-dimensional Euclidean space. Assuming the object is a ball of a small radius ε we show that the behavior of the fluid is not influenced by the object in the asymptotic limit ε→0. The result holds for the isentropic pressure law p(ϱ) = aϱγ for any γ > 3 2 under mild assumptions concerning the rigid body density. In particular, the latter may be bounded as soon as γ > 3. The proof uses a new method of construction of the test functions in the weak formulation of the problem, and, in particular, a new form of the so-called Bogovskii operator

    The Role of Soil Surface in a Sustainable Semiarid Ecosystem

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    Patterns in a semiarid ecosystem are important because they directly and indirectly affect ecological processes, biodiversity, and ecosystem resilience. Understanding the causes and effects of these patterns is critical for long-term land surface management and conservation efforts in semiarid regions, which are especially sensitive to climate change and human-caused disturbances. It is known that there is a regular connection between the vegetation and the living species in a habitat since some animals evolved to live in a semiarid ecosystem and rely on plants for food. In this work, we have constructed a coupled mathematical model to connect the water resource, vegetation and living organisms and have investigated how the soil surface affects the resulting patterns for the long term. This study contributes to a better understanding of ecological patterns and processes in semiarid environments by shedding light on the complex interaction mechanisms that depend on the structure of semiarid ecosystems. The findings provide further critical insight into the influence of efforts for improving ecosystem resilience and adjusting to the challenges posed by climate change and human activities

    Generalized Lagrangian heterogeneous multiscale modelling of complex fluids

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    We introduce a fully Lagrangian heterogeneous multiscale method (LHMM) to model complex fluids with microscopic features that can extend over large spatio/temporal scales, such as polymeric solutions and multiphasic systems. The proposed approach discretizes the fluctuating Navier-Stokes equations in a particle-based setting using smoothed dissipative particle dynamics (SDPD). This multiscale method uses microscopic information derived on-the-fly to provide the stress tensor of the momentum balance in a macroscale problem, therefore bypassing the need for approximate constitutive relations for the stress. We exploit the intrinsic multiscale features of SDPD to account for thermal fluctuations as the characteristic size of the discretizing particles decreases. We validate the LHMM using different flow configurations (reverse Poiseuille flow, flow passing a cylinder array and flow around a square cavity) and fluid (Newtonian and non-Newtonian). We show the framework's flexibility to model complex fluids at the microscale using multiphase and polymeric systems. We also show that stresses are adequately captured and passed from micro to macro scales, leading to richer fluid response at the continuum. In general, the proposed methodology provides a natural link between variations at a macroscale, whereas accounting for memory effects of microscales

    Walter Rudin Meets Elias M. Stein

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    Age or lifestyle-induced accumulation of genotoxicity is associated with a length-dependent decrease in gene expression

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    DNA damage has long been advocated as a molecular driver of aging. DNA dam- age occurs in a stochastic manner, and is therefore more likely to accumulate in longer genes. The length-dependent accumulation of transcription-blocking damage, unlike that of somatic mutations, should be reflected in gene expression datasets of aging. We analyzed gene expression as a function of gene length in several single-cell RNA sequencing datasets of mouse and human aging. We found a pervasive age-associated length-dependent underexpression of genes across species, tissues, and cell types. Furthermore, we observed length-dependent underexpression associated with UV-radiation and smoke exposure, and in progeroid diseases, Cockayne syndrome, and trichothiodystrophy. Finally, we studied published gene sets showing global age-related changes. Genes underexpressed with aging were significantly longer than overexpressed genes. These data highlight a previously undetected hallmark of aging and show that accumulation of genotoxicity in long genes could lead to reduced RNA polymerase II processivity.This work was supported by grants from Instituto de Salud Carlos III (PI22/01247 and PI19/01621), co-funded by the European Union, and Diputación Foral de Gipuzkoa. OI-S received the support of a fellowship from “Programa Investigo” of Lanbide-Servicio Vasco de Empleo, co-funded by the European Union (NextGenerationEU), la Caixa Foundation (ID 100010434; code LCF/BQ/IN18/11660065), and from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No. 713673. The work of IB was financially supported in part by grants from the Departamento de Educación, Política Lingüística y Cultura del Gobierno Vasco [IT1456-22] and by the Ministry of Science and Innovation through BCAM Severo Ochoa accreditation [CEX2021-001142-S/MICIN/AEI/10.13039/501100011033] and through project [PID2020-115882RB-I00/AEI/10.13039/501100011033] funded by Agencia Estatal de Investigación and acronym “S3M1P4R” and also by the Basque Government through the BERC 2022–2025 program

    Constant probe orientation for fast contact-based inspection of 3D free-form surfaces using (3+2)-axis inspection machines

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    A new probe optimization method for contact based (3+2)-axis inspection machines is proposed. Given an inspection path of a stylus on a free-form surface, an optimal orientation of the stylus is computed such that (i) the inclination angle of the stylus is within a given angular range with respect to the surface normal, (ii) the motion of the stylus is globally collision free, and (iii) the stylus remains constant in the coordinate system of the measuring machine. The last condition guarantees that the inspection motion requires only the involvement of the three translational axes of the measuring machine. The numerical simulations were validated through physical experiments on a testcase of a tooth of a bevel gear due to the surface complexity and probe accessibility. This optimized method was compared to 3-axis and 5-axis inspection strategies, showing that the fixed (3+2)-axis stylus returns more accurate inspection results compared to the traditional 3-axis approach and similar to 5-axis approach.RYC-2017-2264

    On inverse construction of isoptics and isochordal-viewed curves

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    Given a regular closed curve α in the plane, a ϕ\phi-isoptic of α\alpha is a locus of points from which pairs of tangent lines to α\alpha span a fixed angle ϕ\phi. If, in addition, the chord that connects the two points delimiting the visibility angle is of constant length \ell, then α\alpha is said to be (ϕ,)(\phi,\ell)-isochordal viewed. Some properties of these curves have been studied, yet their full classification is not known. We approach the problem in an inverse manner, namely that we consider a ϕ\phi-isoptic curve cc as an input and construct a curve whose ϕ\phi-isoptic is cc. We provide thus a sufficient condition that constitutes a partial solution to the inverse isoptic problem. In the process, we also study a relation of isoptics to multihedgehogs. Moreover, we formulate conditions on the behavior of the visibility lines so as their envelope is a (ϕ,)(\phi,\ell)-isochordal-viewed curve with a prescribed ϕ\phi-isoptic cc. Our results are constructive and offer a tool to easily generate this type of curves. In particular, we show examples of (ϕ,)(\phi,\ell)-isochordal-viewed curves whose ϕ\phi-isoptic is not circular. Finally, we prove that these curves allow the motion of a regular polygon whose vertices lie along the (ϕ,)(\phi,\ell)-isochordal-viewed curve

    Competing risk models in early warning systems for in-hospital deterioration: the role of missing data imputation

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    Early Warning Systems (EWS) are useful and very important tools for evaluating the health deteriorating of hospitalised patients, using vital signs (such as heart rate, temperature, etc.) as the main input, based on electronic health records (EHR) which most of the time result in sparse data sets with high rates of missing data. In this work, we aim to study the effect of different imputation techniques on time-to-event (survival) models. For each case we have patient's sex and age, as well as longitudinal data along the hospitalisation for 7 vital signs (temperature, systolic and diastolic pressure, heart and respiratory rates, oxygen saturation and neurological state). We summarise these longitudinal data with the following central tendency, order and dispersion statistics: maximum, minimum, first observation, last observation, mean, standard deviation, average variance percentage and average derivative, transforming the original variables into a cross-sectional higher dimensional space, that still having missing data problems. Each hospitalisation has two possible final states: clinical deterioration or favourable discharge. Here, we model the time-to-event with competitive risk models taking into account the covariates. In the Galdakao-Usansolo University Hospital (Basque Country, Spain), a total of 19.602 hospitalisations (lengths of stay at least 24 hours) were collected during the year 2019, of which 852 (4.35\%) resulted in deterioration. These data correspond to 55.8\% of males and 44.2\% of females. We are using a set of imputation methods, such as central tendency statistics (mean and mode), Multiple Imputation by Chained Equations (MICE), Non-Linear Principal Components Analysis (NLPCA) and Random Forest. We evaluate the performances of the imputation methods described before, via root mean square error and conclude the pros and cons of using each one in medical practice. Then, we use Fine and Gray's competitive risk models and the cause-specific Cox proportional hazard regression to model the time-to-event as a function of imputed summarised data. Finally, we evaluate these models employing the traditional and time-dependent area under the ROC curve, for horizon times of 24, 48, 72, 96 and 120 hospitalisation hours

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