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49487 results in Computer Science

Page 104 of 2475

An Introduction to String Diagrams for Computer Scientists

An Introduction to String Diagrams for Computer Scientists
  • Robin Piedeleu, Fabio Zanasi
  • Published online:
    01 May 2025
    Print publication:
    29 May 2025
    • Element
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  • String diagrams are a powerful graphical language used to represent computational phenomena across diverse scientific fields, including computer science, physics, linguistics, amongst others. The appeal of string diagrams lies in their multi-faceted nature: they offer a simple, visual representation of complex scientific ideas, while also allowing rigorous mathematical treatment. Originating in category theory, string diagrams have since evolved into a versatile formalism, extending well beyond their abstract algebraic roots, and offering alternative entry points to their study. This text provides an accessible introduction to string diagrams from the perspective of computer science. Rather than starting from categorical concepts, the authors draw on intuitions from formal language theory, treating string diagrams as a syntax with its own semantics. They survey the basic theory, outline fundamental principles, and highlight modern applications of string diagrams in different fields. This title is also available as open access on Cambridge Core.

  • 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.

  • 6 - Multivariate Probabilities

  • 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 79-98

  • Summary

    Centered on multivariate probabilities, this chapter unravels the intricacies of joint probabilities, covariance matrices, and multivariate normal distributions. The discussion on conditional probability and Bayes’ theorem provides a robust foundation for modeling complex relationships between several variables.

  • 9 - Stochastic Processes and Scaling Laws

  • 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 141-166

  • Summary

    Diving into stochastic processes, this chapter explores stationarity, scaling laws, and fractal dimensions. It delves into diverse processes, from random walks to more general self-affine processes, unraveling their implications in modeling complex phenomena. In line with the rest of the book, it discusses the modeling of stochastic processes as an instance of multivariate sets of random variables.

  • 10 - Causation

  • 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 167-182

  • Summary

    This chapter probes the intricate relationship between cause and effect. It navigates through Wiener–Granger causality and introduces transfer entropy, providing the tools to dissect causal relationships in data-driven models.

  • 5 - Univariate Probabilities

  • 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 49-78

  • Summary

    Within this chapter, the focus is on delving into univariate probability distributions. It dissects the anatomy of the normal distribution, explores characteristic functions, and analyzes stable distributions. This chapter establishes a comprehensive understanding of various probability distributions, setting the stage for more advanced discussions.

Page 104 of 2475