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2540 results in Computational Science

Page 4 of 127

  • 3 - Non-Local Inpainting Methods

  • Simone Parisotto, Fitzwilliam Museum, Cambridge, Patricia Vitoria, Universitat Pompeu Fabra, Barcelona, Coloma Ballester, Universitat Pompeu Fabra, Barcelona, Aurélie Bugeau, Université de Bordeaux, Suzanne Reynolds, Fitzwilliam Museum, Cambridge, Carola-Bibiane Schönlieb, University of Cambridge
  • Book:
    The Art of Inpainting
    Published online:
    22 May 2025
    Print publication:
    22 May 2025, pp 52-114

  • Summary

    Chapter 3 provides a historical view of non-local inpainting methods, also called examplar-based or patch-based methods. These approaches rely on the self-similarity principle, i.e. on the idea that the missing information in the inpainting domain can be copied from somewhere else within the intact part of the image. Over the years. many improvements and algorithms have been proposed, enabling us to offer visually plausible solutions to the inpainting problem, especially for large damages and areas with texture.

Probabilistic Data-Driven Modeling
  • Tomaso Aste
  • Published online:
    17 May 2025
    Print publication:
    01 May 2025
  • This book introduces relevant and established data-driven modeling tools currently in use or in development, which will help readers master the art and science of constructing models from data and dive into different application areas. It presents statistical tools useful to individuate regularities, discover patterns and laws in complex datasets, and demonstrates how to apply them to devise models that help to understand these systems and predict their behaviors. By focusing on the estimation of multivariate probabilities, the book shows that the entire domain, from linear regressions to deep learning neural networks, can be formulated in probabilistic terms. This book provides the right balance between accessibility and mathematical rigor for applied data science or operations research students, graduate students in CSE, and machine learning and uncertainty quantification researchers who use statistics in their field. Background in probability theory and undergraduate mathematics is assumed.

High-Accuracy Finite Difference Methods
  • Bengt Fornberg
  • Published online:
    16 May 2025
    Print publication:
    05 June 2025
  • Scientific computing plays a critically important role in almost all areas of engineering, modeling, and forecasting. The method of finite differences (FD) is a classical tool that is still rapidly evolving, with several key developments barely yet in the literature. Other key aspects of the method, in particular those to do with computations that require high accuracy, often 'fall through the cracks' in many treatises. Bengt Fornberg addresses that failing in this book, which adopts a practical perspective right across the field and is aimed at graduate students, scientists, and educators seeking a follow-up to more typical curriculum-oriented textbooks. The coverage extends from generating FD formulas and applying them to solving ordinary and partial differential equations, to numerical integration, evaluation of infinite sums, approximation of fractional derivatives, and computations in the complex plane.

  • 7 - Entropies

  • from Part II - Foundations of Probabilistic Modeling
  • Tomaso Aste, University College London
  • Book:
    Probabilistic Data-Driven Modeling
    Published online:
    17 May 2025
    Print publication:
    01 May 2025, pp 99-112

  • Summary

    This chapter introduces the concept of entropy and its significance in modeling. The focus extends to joint entropy, Kullback–Leibler divergence, and conditional entropy. Readers are equipped with tools to quantify information and uncertainty, pivotal in probabilistic modeling. The chapter focuses on Shannon entropy but also introduces to other entropy formulations.

Page 4 of 127