Les Houches School, October 11-15, 1999

This book introduces biological examples of Branching Processes from molecular and cellular biology as well as from the fields of human evolution and medicine and discusses them in the context of the relevant mathematics. It provides a useful introduction to how the modeling can be done and for what types of problems branching processes can be used.

While the natural world is often described as organic, it is in fact structured to the very molecule, replete with patterned order that can be decoded with basic mathematical algorithms and principles. In a nautilus shell one can see logarithmic spirals, and the Golden Ratio can be seen in the seed head of the sunflower plant. These patterns and shapes have inspired artists, writers, designers, and musicians for thousands of years. "Patterns in Nature: Why the Natural World Looks the Way It Does" illuminates the amazing diversity of pattern in the natural world and takes readers on a visual tour of some of the world s most incredible natural wonders. Featuring awe-inspiring galleries of nature s most ingenious designs, "Patterns in Nature" is a synergy of art and science that will fascinate artists, nature lovers, and mathematicians alike."

From the New York Times-bestselling author of The Secret World of Weather and The Lost Art of Reading Nature’s Signs, learn to tap into nature and notice the hidden clues all around you Before GPS, before the compass, and even before cartography, humankind was navigating. Now this singular guide helps us rediscover what our ancestors long understood—that a windswept tree, the depth of a puddle, or a trill of birdsong can help us find our way, if we know what to look and listen for. Adventurer and navigation expert Tristan Gooley unlocks the directional clues hidden in the sun, moon, stars, clouds, weather patterns, lengthening shadows, changing tides, plant growth, and the habits of wildlife. Rich with navigational anecdotes collected across ages, continents, and cultures, The Natural Navigator will help keep you on course and open your eyes to the wonders, large and small, of the natural world.

The purpose of this book is to give a unified treatment of the limit theory of branching processes. Since the publication of the important book of T E. Harris (Theory of Branching Processes, Springer, 1963) the subject has developed and matured significantly. Many of the classical limit laws are now known in their sharpest form, and there are new proofs that give insight into the results. Our work deals primarily with this decade, and thus has very little overlap with that of Harris. Only enough material is repeated to make the treatment essentially self-contained. For example, certain foundational questions on the construction of processes, to which we have nothing new to add, are not developed. There is a natural classification of branching processes according to their criticality condition, their time parameter, the single or multi-type particle cases, the Markovian or non-Markovian character of the pro cess, etc. We have tried to avoid the rather uneconomical and un enlightening approach of treating these categories independently, and by a series of similar but increasingly complicated techniques. The basic Galton-Watson process is developed in great detail in Chapters I and II.

Written in a style that is accessible to a wide audience, The Fractal Geometry of Nature inspired popular interest in this emerging field. Mandelbrot's unique style, and rich illustrations will inspire readers of all backgrounds.

Nature's design magic is found in its perfect ratios. This illustrated drawing book focuses on four natural designs--Star, Branch, Spiral, and Fan--and why they work.

Sunday Times Bestseller‘A paradigm-smashing chronicle of joyous entanglement’ Charles Foster Waterstones Non-Fiction Book of the Month (September) Are trees social beings? How do trees live? Do they feel pain or have awareness of their surroundings?

Branching processes form one of the classical fields of applied probability and are still an active area of research. The field has by now grown so large and diverse that a complete and unified treat ment is hardly possible anymore, let alone in one volume. So, our aim here has been to single out some of the more recent developments and to present them with sufficient background material to obtain a largely self-contained treatment intended to supplement previous mo nographs rather than to overlap them. The body of the text is divided into four parts, each of its own flavor. Part A is a short introduction, stressing examples and applications. In Part B we give a self-contained and up-to-date pre sentation of the classical limit theory of simple branching processes, viz. the Gal ton-Watson ( Bienayme-G-W) process and i ts continuous time analogue. Part C deals with the limit theory of Il!arkov branching processes with a general set of types under conditions tailored to (multigroup) branching diffusions on bounded domains, a setting which also covers the ordinary multitype case. Whereas the point of view in Parts A and B is quite pedagogical, the aim of Part C is to treat a large subfield to the highest degree of generality and completeness possi"ble. Thus the exposition there is at times quite technical.