2063 research outputs found
Sort by
Taylor-Fourier integration
Get PDFIn this paper we introduce an algorithm which provides approximate solutions to semi-linear ordinary differential equations with highly oscillatory solutions that after an appropriate change of variables can be written as a non-autonomous system with -periodic dependence on . The proposed approximate solutions are written in closed form as functions where is, (i) a truncated Fourier series in for fixed , and (ii) a truncated Taylor series in for fixed
(that is the reason for the name of the proposed integrators). Such approximations are intended to be uniformly accurate in (in the sense that their accuracy is not deteriorated as ). This feature implies that Taylor-Fourier approximations become more efficient than the application of standard numerical integrators for sufficiently high basic frequency . The main goal of the paper is to propose a procedure to efficiently compute such approximations by combining power series arithmetic techniques and the FFT algorithm. We present numerical experiments that demonstrate the effectiveness of our approximation method through its application to well-known problems of interest.PID2022-136585NB-C22
MATHMODE (ITI456-22
On shape design and optimization of gerotor pumps
Get PDFA gerotor pump is a two-piece mechanism where two rotational components, interior and exterior, engage each other via a rotational motion to transfer a fluid in a direction parallel to their rotational axes. A natural question arises on what shape of the gerotor is the optimal one in the sense of maximum fluid being pumped for a unit of time, given the constraint of a fixed material needed to manufacture the pump. As there is no closed-formula to answer this question, we propose a new algorithm to design and optimize the shape of gerotor pumps to be as efficient as possible. The proposed algorithm is based on a fast construction of the envelope of the interior component and subsequent optimization. We demonstrate our algorithm on a benchmark gerotor and show that the optimized solution increases the estimated flowrate by 16%. We also use our algorithm to study the effect of the number of teeth on the cavity area of a gerotor.RYC-2017-22649 funded by MICIU/AEI/10.13039/501100011033 and EI ESF "ESF Investing in your future
Tackling the development of hormone therapy resistance in breast cancer through mathematical modelling
Get PDFPatients suffering from estrogen-driven breast cancer frequently develop hardly predictable resistance to hormone therapy, which significantly complicates treatment. Current approaches for tackling this problem include cell models and clinical studies, both supported by sequencing technologies like RNA-seq, and offering different strengths and limitations. This dissertation addresses the challenge of predicting resistance to hormone therapy in breast cancer by merging advances in bioinformatics and Bayesian statistics, and applying them to two types of data – RNA-seq data and clinical data. First, we explore the statistical analysis of clinical data through Bayesian inference combined with enhanced Markov Chain Monte Carlo techniques, and introduce a novel algorithm for adaptive integration in prospective Modified Hamiltonian Monte Carlo (MHMC) methods. We demonstrate its positive effect on performance of MHMC in biomedical applications using clinical data of breast cancer patients. Next, we propose and implement an RNA-seq pipeline within our interactive web-app for the analysis of resistant breast cancer cell lines sequenced at CIC bioGUNE. Finally, we propose an original approach based on a Bayesian logistics regression model coupled with a simulated annealing-like algorithm for a combined analysis of RNA-seq and clinical data, and apply it to ad hoc data to obtain and validate in-silico and in-vitro a novel 6-gene signature for stratifying patient response to hormone therapy
Ensemble Deep Learning for Enhanced Seismic Data Reconstruction
Get PDFSeismic data often contain gaps due to various obstacles in the investigated area and recording instrument failures. Deep-learning techniques offer promising solutions for reconstructing missing data parts by utilizing existing data. Nonetheless, self-supervised methods frequently struggle with capturing under-represented features such as weaker events, crossing dips, and higher frequencies. To address these challenges, we propose a novel ensemble deep model (EDM) along with a tailored self-supervised training approach for reconstructing seismic data with consecutive missing traces. Our model comprises two branches of U-nets, each fed from distinct data transformation modules aimed at amplifying under-represented features and promoting diversity among learners. Our loss function minimizes relative errors at the outputs of individual branches and the entire model, ensuring accurate reconstruction of various features while maintaining overall data integrity. Additionally, we employ masking while training to enhance sample diversity and memory efficiency. Applications on two benchmark synthetic datasets and two real datasets demonstrate improved accuracy compared to a conventional U-net, successfully reconstructing weak events, diffractions, higher frequencies, and reflections covered by groundroll. Despite these advancements, our method does incur three times the training cost compared to a simple U-net
Learning quantities of interest from parametric PDEs: An efficient neural-weighted Minimal Residual approach
Get PDFThe efficient approximation of parametric PDEs is of tremendous importance in science and
engineering. In this paper, we show how one can train Galerkin discretizations to efficiently
learn quantities of interest of solutions to a parametric PDE. The central component in
our approach is an efficient neural-network-weighted Minimal-Residual formulation, which,
after training, provides Galerkin-based approximations in standard discrete spaces that have
accurate quantities of interest, regardless of the coarseness of the discrete space.PDC2021-121093-I0
Effective generic freeness and applications to local cohomology
No full textLet (Formula presented.) be a Noetherian domain and (Formula presented.) be a finitely generated (Formula presented.) -algebra. We study several features regarding the generic freeness over (Formula presented.) of an (Formula presented.) -module. For an ideal (Formula presented.), we show that the local cohomology modules (Formula presented.) are generically free over (Formula presented.) under certain settings where (Formula presented.) is a smooth (Formula presented.) -algebra. By utilizing the theory of Gröbner bases over arbitrary Noetherian rings, we provide an effective method to b make explicit the generic freeness over (Formula presented.) of a finitely generated (Formula presented.) -module.Ramon y Cajal RYC2020-028976-
GLOBAL EXISTENCE OF WEAK SOLUTIONS FOR A MODEL OF NEMATIC LIQUID CRYSTAL-COLLOIDAL INTERACTIONS
No full textIn this paper we study a mathematical model describing the movement of a colloidal particle in a
fixed, bounded three dimensional container filled with a nematic liquid crystal fluid. The motion of the fluid is
governed by the Beris–Edwards model for nematohydrodynamics equations, which couples the incompressible
Navier-Stokes equations with a parabolic system. The dynamics of colloidal particle within the nematic liquid
crystal is described by the conservation laws of linear and angular momentum. We prove the existence of
global weak solutions for the coupled system
Mixed-precision finite element kernels and assembly: Rounding error analysis and hardware acceleration
Get PDFIn this paper we develop the first fine-grained rounding error analysis of finite element (FE) cell kernels and assembly. The theory includes mixed-precision implementations and accounts for hardware-acceleration via matrix multiplication units, thus providing theoretical guidance for designing reduced- and mixed-precision FE algorithms on CPUs and GPUs. Guided by this analysis, we introduce hardware-accelerated mixed-precision implementation strategies which are provably robust to low-precision computations. Indeed, these algorithms are accurate to the lower-precision unit roundoff with an error constant that is independent from: the conditioning of FE basis function evaluations, the ill-posedness of the cell, the polynomial degree, and the number of quadrature nodes. Consequently, we present the first AMX-accelerated FE kernel implementations on Intel Sapphire Rapids CPUs. Numerical experiments demonstrate that the proposed mixed- (single/half-) precision algorithms are up to 60 times faster than their double precision equivalent while being orders of magnitude more accurate than their fully half-precision counterparts
Efficient set-theoretic algorithms for computing high-order Forman-Ricci curvature on abstract simplicial complexes
Get PDFForman-Ricci curvature (FRC) is a potent and powerful tool for analysing empirical networks, as the distribution of the curvature values can identify structural information that is not readily detected by other geometrical methods. Crucially, FRC captures higher-order structural information of clique complexes of a graph or Vietoris-Rips complexes, which is not readily accessible to alternative methods. However, existing FRC platforms are prohibitively computationally expensive. Therefore, herein we develop an efficient set-theoretic formulation for computing such high-order FRC in simplicial complexes. Significantly, our set theory representation reveals previous computational bottlenecks and also accelerates the computation of FRC. Finally, We provide a pseudo-code, a software implementation coined FastForman, as well as a benchmark comparison with alternative implementations. We envisage that FastForman will be used in Topological and Geometrical Data analysis for high-dimensional complex data sets. Moreover, our development paves the way for future generalisations towards efficient computations of FRC on cell complexes
Estimation of logistic regression parameters for complex survey datasimulation study based on real survey data
Get PDFIn complex survey data, each sampled observation has assigned a sampling weight, indicating the number of units that it represents in the population. Whether sampling weights should or not be considered in the estimation process of model parameters is a question that still continues to generate much discussion among researchers in different fields. We aim to contribute to this debate by means of a real data based simulation study in the framework of logistic regression models. In order to study their performance, three methods have been considered for estimating the coefficients of the logistic regression model: a) the unweighted model, b) the weighted model, and c) the unweighted mixed model. The results suggest the use of the weighted logistic regression model is superior, showing the importance of using sampling weights in the estimation of the model parameters