What underlying forces are responsible for the observed patterns of variability, given a collection of DNA sequences?" In approaching this question a number of probability models are introduced and anyalyzed.Throughout the book, the theory is developed in close connection with data from more than 60 experimental studies that illustrate the use of these results.
This clear and lively introduction to probability theory concentrates on the results that are the most useful for applications, including combinatorial probability and Markov chains. Concise and focused, it is designed for a one-semester introductory course in probability for students who have some familiarity with basic calculus. Reflecting the author's philosophy that the best way to learn probability is to see it in action, there are more than 350 problems and 200 examples. The examples contain all the old standards such as the birthday problem and Monty Hall, but also include a number of applications not found in other books, from areas as broad ranging as genetics, sports, finance, and inventory management.
What do legendary leaders from Disney, GE, GM, Johnson & Johnson, Boeing, eBay, Microsoft, Time Warner, LensCrafters, Chiquita, Walmart, Pepsi, and Saatchi+Saatchi have in common? They all learned the critical importance of values as managers at Procter & Gamble. And, since departing for leadership roles elsewhere, many have remained members of the P & G Alumni Network. Now you can share the powerful lessons learned at P & G. The P & G Alumni Network's When Core Values Are Strategic offers no-nonsense insights into why values really are so important, and practical ways to propagate, strengthen, and act on them. Bringing together contributions from influential P & G alumni worldwide, it offers a legacy to future leaders across organizations of every type and size. Discover why core values are timely, universal, and the secret to long term success on both financial and other metrics ... how top executives were shaped at P & G to make historic change in energy, aviation, technology, government, transportation, entertainment, healthcare, consumer packaged goods, and other industries ... how to build a learning culture that increases shareholder value ... why values and marketing initiatives are inseparable, and much more. This book will be an inspiration and practical resource to emerging leaders in organizations of every size and type, in every field or industry. Procter & Gamble and P & G are trade names of The Procter & Gamble Company and are used pursuant to an agreement with The Procter & Gamble Company. P & G Alumni Network is an independent organization apart from The Procter & Gamble Company.
The theory of random graphs began in the late 1950s in several papers by Erdos and Renyi. In the late twentieth century, the notion of six degrees of separation, meaning that any two people on the planet can be connected by a short chain of people who know each other, inspired Strogatz and Watts to define the small world random graph in which each site is connected to k close neighbors, but also has long-range connections. At a similar time, it was observed in human social and sexual networks and on the Internet that the number of neighbors of an individual or computer has a power law distribution. This inspired Barabasi and Albert to define the preferential attachment model, which has these properties. These two papers have led to an explosion of research. The purpose of this book is to use a wide variety of mathematical argument to obtain insights into the properties of these graphs. A unique feature is the interest in the dynamics of process taking place on the graph in addition to their geometric properties, such as connectedness and diameter.
In (1994) Durrett and Levin proposed that the equilibrium behavior of stochastic spatial models could be determined from properties of the solution of the mean field ordinary differential equation (ODE) that is obtained by pretending that all sites are always independent. Here we prove a general result in support of that picture. We give a condition on an ordinary differential equation which implies that densities stay bounded away from 0 in the associated reaction-diffusion equation, and that coexistence occurs in the stochastic spatial model with fast stirring. Then using biologists' notion of invadability as a guide, we show how this condition can be checked in a wide variety of examples that involve two or three species: epidemics, diploid genetics models, predator-prey systems, and various competition models.
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