Gilles Pagès - Böcker

Angiogenesis is a multi-stage process that drives the generation of new blood and lymphatic vessels from pre-existing ones. It is highly active during embryogenesis, largely inactive during adulthood but reactivated during wound healing and under a number of pathological conditions including cancer and ocular diseases. In addition to endothelial cells, which line the walls of the vessels, several other cell types (pericytes, macrophages, progenitor cells…) also contribute to angiogenesis. A number of signaling pathways are activated and very finely tune the delicate morphogenetic events that ultimately lead to the formation of stable blood proof neovessels.This book reviews recent advances in our understanding of the molecular and cellular mechanisms of angiogenesis, with a focus on how to integrate these observations into the context of developmental, post-natal and pathological neovascularization.The book was published under the auspices of the French Angiogenesis Society. Most contributors are prominent members of this Society or international researchers who have actively contributed to the Annual Meetings of the Society.

Angiogenesis is a multi-stage process that drives the generation of new blood and lymphatic vessels from pre-existing ones. It is highly active during embryogenesis, largely inactive during adulthood but reactivated during wound healing and under a number of pathological conditions including cancer and ocular diseases. In addition to endothelial cells, which line the walls of the vessels, several other cell types (pericytes, macrophages, progenitor cells…) also contribute to angiogenesis. A number of signaling pathways are activated and very finely tune the delicate morphogenetic events that ultimately lead to the formation of stable blood proof neovessels.This book reviews recent advances in our understanding of the molecular and cellular mechanisms of angiogenesis, with a focus on how to integrate these observations into the context of developmental, post-natal and pathological neovascularization.The book was published under the auspices of the French Angiogenesis Society. Most contributors are prominent members of this Society or international researchers who have actively contributed to the Annual Meetings of the Society.

Vector Quantization, a pioneering discretization method based on nearest neighbor search, emerged in the 1950s primarily in signal processing, electrical engineering, and information theory. Later in the 1960s, it evolved into an automatic classification technique for generating prototypes of extensive datasets. In modern terms, it can be recognized as a seminal contribution to unsupervised learning through the k-means clustering algorithm in data science.In contrast, Functional Quantization, a more recent area of study dating back to the early 2000s, focuses on the quantization of continuous-time stochastic processes viewed as random vectors in Banach function spaces. This book distinguishes itself by delving into the quantization of random vectors with values in a Banach space—a unique feature of its content. Its main objectives are twofold: first, to offer a comprehensive and cohesive overview of the latest developments as well as several new results in optimal quantization theory, spanning both finite and infinite dimensions, building upon the advancements detailed in Graf and Luschgy's Lecture Notes volume. Secondly, it serves to demonstrate how optimal quantization can be employed as a space discretization method within probability theory and numerical probability, particularly in fields like quantitative finance. The main applications to numerical probability are the controlled approximation of regular and conditional expectations by quantization-based cubature formulas, with applications to time-space discretization of Markov processes, typically Brownian diffusions, by quantization trees.While primarily catering to mathematicians specializing in probability theory and numerical probability, this monograph also holds relevance for data scientists, electrical engineers involved in data transmission, and professionals in economics and logistics who are intrigued by optimal allocation problems.

Vector Quantization, a pioneering discretization method based on nearest neighbor search, emerged in the 1950s primarily in signal processing, electrical engineering, and information theory. Later in the 1960s, it evolved into an automatic classification technique for generating prototypes of extensive datasets. In modern terms, it can be recognized as a seminal contribution to unsupervised learning through the k-means clustering algorithm in data science.In contrast, Functional Quantization, a more recent area of study dating back to the early 2000s, focuses on the quantization of continuous-time stochastic processes viewed as random vectors in Banach function spaces. This book distinguishes itself by delving into the quantization of random vectors with values in a Banach space—a unique feature of its content. Its main objectives are twofold: first, to offer a comprehensive and cohesive overview of the latest developments as well as several new results in optimal quantization theory, spanning both finite and infinite dimensions, building upon the advancements detailed in Graf and Luschgy's Lecture Notes volume. Secondly, it serves to demonstrate how optimal quantization can be employed as a space discretization method within probability theory and numerical probability, particularly in fields like quantitative finance. The main applications to numerical probability are the controlled approximation of regular and conditional expectations by quantization-based cubature formulas, with applications to time-space discretization of Markov processes, typically Brownian diffusions, by quantization trees.While primarily catering to mathematicians specializing in probability theory and numerical probability, this monograph also holds relevance for data scientists, electrical engineers involved in data transmission, and professionals in economics and logistics who are intrigued by optimal allocation problems.

Now in a thoroughly revised and expanded second edition, this textbook offers a comprehensive and self-contained introduction to numerical methods in probability, with particular emphasis on stochastic optimization and its applications in financial mathematics.The volume covers a broad range of topics, including Monte Carlo simulation techniques—such as the simulation of random variables, variance reduction strategies, quasi-Monte Carlo methods—and recent advancements like the multilevel Monte Carlo paradigm. It further discusses discretization schemes for stochastic differential equations and optimal quantization methods. A rigorous treatment of stochastic optimization is provided, encompassing stochastic gradient descent, including Langevin-based gradient descent algorithms, new to this edition. Detailed applications are presented in the context of numerical methods for pricing and hedging financial derivatives, the computation of risk measures (including value-at-risk and conditional value-at-risk), parameter implicitation, and model calibration.Intended for graduate students and advanced undergraduates, the textbook includes numerous illustrative examples and over 200 exercises, rendering it well-suited for both classroom use and independent study.