Convolutional Fractional Stochastic Fields And Their Deep Learning
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Convolutional Fractional Stochastic Fields and their Deep Learning
In a stochastic environment where reality is described through samples or examples, artificial intelligence learns by penalizing weighted differential and/or integral viewpoints. The convolutional neural framework is relevant to encompass the mathematical operations performed by such an artificial intelligence. Conversely, mathematical compositions alternating convolutions and non linear operators are powerful tools for generating complex artificial realities. This book proposes a stochastic integral perspective of deep machine learning in artificial intelligence. The organization of the book is as follows. Chapter 1 introduces the basics of stochastic reasoning and the most useful properties of stochastic processes. Chapters 2 and 3 derive stochastic convoluted models for the construction, analysis and simulation of fractionally integrated fields. Chapter 4 highlights how some deep artificial neurons can disentangle the very long-range stochastic dependencies, when these neurons are parameterized to integrate spectral responses.
Poincaré Lemma on Differential Forms and Connections with Čech-De Rham-Dolbeault Cohomologies
Poincaré Lemma on Differential Forms and Connections with Čech-De Rham-Dolbeault Cohomologies deals with the connections between Čech-De Rham-Dolbeault cohomologies and the Dolbeault- Grothendieck lemma. It begins by discussing one-parameter groups of diffeomorphisms or flow, Lie derivative and interior products, as well as Cartan’s formula and the Poincaré lemma on differential forms. Throughout the book, we study sheaves, Čech cohomology and De Rham cohomology, and present some of their most basic properties. We also explore the Mayer-Vietoris sequence by demonstrating its use when calculating the cohomology group of the sphere. We introduce the Künneth formula (and as an application) and compute the cohomology of the torus. The final sections of the book study the delta bar-Poincaré lemma – as well as the Dolbeault-Grothendieck lemma and its consequences – while also proving the delta bar-Poincaré lemma in one variable, the Grothendieck Poincaré lemma, and the Dolbeault’s theorem when establishing the isomorphism between Dolbeault and Čech cohomology. Some results related to the connections, curvature and first Chern class of line bundles are also given. The text is enriched by concrete examples, along with exercises and their solutions.
Artificial Intelligence and Machine Learning Techniques in Image Processing and Computer Vision
This new volume provides in-depth and detailed knowledge about the latest research in image processing and computer vision techniques. Explaining the machine learning algorithms and models involved, the authors differentiate between the various algorithms available and how to choose which to use for the most precise results for a specific task involving certain constraints. The volume provides real-world examples to illustrate the concepts and methods. The authors discuss machine learning in healthcare systems for detection, diagnosis, classification, and segmentation. They also explore the diverse applications of image and video processing, including image colorization and restoration using deep learning, using machine learning to record the climate changes in over time with remote sensing, and more.