Frieden / Gatenby Exploratory Data Analysis Using Fisher Information

2007
ISBN: 978-1-84628-777-0
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 363 Seiten, eBook

This book uses a mathematical approach to deriving the laws of science and technology, based upon the concept of Fisher information. The approach that follows from these ideas is called the principle of Extreme Physical Information (EPI). The authors show how to use EPI to determine the theoretical input/output laws of unknown systems. Will benefit readers whose math skill is at the level of an undergraduate science or engineering degree.

Zielgruppe

Research

Autoren/Hrsg.

Frieden, Roy

Gatenby, Robert A.

Inhaltsverzeichnis

to Fisher Information: Its Origin, Uses, and Predictions.- Financial Economics from Fisher Information.- Growth Characteristics of Organisms.- Information and Thermal Physics.- Parallel Information Phenomena of Biology and Astrophysics.- Encryption of Covert Information Through a Fisher Game.- Applications of Fisher Information to the Management of Sustainable Environmental Systems.- Fisher Information in Ecological Systems.- Sociohistory: An Information Theory of Social Changef.

Leseproben

"7 Applications of Fisher Information to the Management of Sustainable Environmental Systems (p. 217-218)

AUDREYL. MAYER, CHRISTOPHER W. PAWLOWSKI, BRIAN D. FATH, ANDHERIBERTOCABEZAS

All organisms alter their surroundings, and humans now have the ability to affect environments at increasingly larger temporal and spatial scales. Indeed , mechanical and engineering advances of the twentieth century greatly enhanced the scale of human activities. Among these are the use and redistribution of natural resources . Unfortunately, these activities can have unexpected and unintended consequences. Environmental systems often respond to these activities with diminished or lost capacity of natural function. Fortunately, environmental management can play an important role in ameliorating these negative effects.

The aim is to promote sustainable development, i.e., enrichment of the lives of the majority of people without seriously degrading the diversity and richness of the environment. However, the management tools themselves often fall prey to the same narrow levels of perspective that generated the negative conditions. The challenge is to develop a system-level index, one that indicates the organizati on and direction of ecological system dynamics. This index could detect when the system is changing its configuration to a new, perhaps less desirable, dynamic regime and may be incorporated into a sustainable management plan for the system. In this chapter, we demonstrate the use of Fisher information (FI) as such an environmental system index.

7.1. Summary

We derive an expression for FI based on sampling of the system trajectory as it evolves in the phase space defined by the state variables of the system. This FI index is derived as a measure ofsystem dynami c order; as defined by its speed and acceleration along periodic steady-state trajectories. We illustrate the concepts on data collected from both computer model simulations and real-world environmental systems. PI is found to provide a valuable tool to identify impending and in-progress shifts in regime, as distinguished from normal cycles, fluctuations , and noise in the systems.

7.2. Introduction

"Sustainability" is often used in a qualitative sense. However, there is at present a great need to quantitatively measure (and monitor) its many qualitative aspects in real systems. Real systems are regarded as sustainable if they can maintain their current, desirable productivity and character without creating unfavorable conditions elsewhere or in the future [1-4]. Sustainability therefore incorporates both concern for the future of the current system (temporal sustainability) and concern about the degree to which some areas and cultures of the planet are improved at the expense of other areas and cultures (spatial sustainability). That is, sustainability is to hold over both space and time."

Über Autor(innen)

Professor Emeritus - B. Roy Frieden:

B.S., M.S., Ph.D., Professor of Optical Sciences, Univ. of Arizona 1966-2002; books "Probability, Statistical Optics and Data Testing" (Springer-Verlag, 3 ed., 2001), "Physics from Fisher Information" (Cambridge Univ. Press, 1998), "Science from Fisher Information" (Cambridge Univ. Press, 2004); inventor of principle of Extreme physical information (EPI)

Dr. Robert A. Gatenby:

BSE, Princeton Univ. MD, University of Pennsylvania.