Foreword by Stephen L Adler (Institute for Advanced Study, USA) Illustrations by Peggy Adler The term Phyllotaxis refers to the patterns on plants formed by the arrangement of repeated biological units. In nearly all cases, the Fibonacci Numbers and the Golden Ratio occur in these arrangements. This topic has long fascinated scientists. Over a period of more than two decades, Irving Adler wrote a number of papers that construct a rigorously derived mathematical model for Phyllotaxis, which are major and enduring contributions to the field. These papers are collected in this reprint volume to enable their access to a wider readership.

This book presents a new formulation of quantum mechanics using quaternionic, rather than complex, numbers. The author is a highly respected theoretical physicist who has been working on quaternionic quantum mechanics for the last fourteen years. The author clearly explicates the relations between quaternionic, complex and real quantum mechanics, and the book is certain to be a major contribution to theoretical physics. Accessible to readers with a first-year graduate level quantum mechanics course.

PAMIR (Parameterized Adaptive Multidimensional Integration Routines) is a suite of Fortran programs for multidimensional numerical integration over hypercubes, simplexes, and hyper-rectangles in general dimension p, intended for use by physicists, applied mathematicians, computer scientists, and engineers. The programs, which are available on the internet at www.pamir-integrate.com and are free for non-profit research use, are capable of following localized peaks and valleys of the integrand. Each program comes with a Message-Passing Interface (MPI) parallel version for cluster use as well as serial versions.The first chapter presents introductory material, similar to that on the PAMIR website, and the next is a "manual" giving much more detail on the use of the programs than is on the website. They are followed by many examples of performance benchmarks and comparisons with other programs, and a discussion of the computational integration aspects of PAMIR, in comparison with other methods in the literature. The final chapter provides details of the construction of the algorithms, while the Appendices give technical details and certain mathematical derivations.

PAMIR (Parameterized Adaptive Multidimensional Integration Routines) is a suite of Fortran programs for multidimensional numerical integration over hypercubes, simplexes, and hyper-rectangles in general dimension p, intended for use by physicists, applied mathematicians, computer scientists, and engineers. The programs, which are available on the internet at www.pamir-integrate.com and are free for non-profit research use, are capable of following localized peaks and valleys of the integrand. Each program comes with a Message-Passing Interface (MPI) parallel version for cluster use as well as serial versions.The first chapter presents introductory material, similar to that on the PAMIR website, and the next is a "manual" giving much more detail on the use of the programs than is on the website. They are followed by many examples of performance benchmarks and comparisons with other programs, and a discussion of the computational integration aspects of PAMIR, in comparison with other methods in the literature. The final chapter provides details of the construction of the algorithms, while the Appendices give technical details and certain mathematical derivations.

Quantum mechanics is our most successful physical theory. However, it raises conceptual issues that have perplexed physicists and philosophers of science for decades. This book develops a new approach, based on the proposal that quantum theory is not a complete, final theory, but is in fact an emergent phenomenon arising from a deeper level of dynamics. The dynamics at this deeper level are taken to be an extension of classical dynamics to non-commuting matrix variables, with cyclic permutation inside a trace used as the basic calculational tool. With plausible assumptions, quantum theory is shown to emerge as the statistical thermodynamics of this underlying theory, with the canonical commutation/anticommutation relations derived from a generalized equipartition theorem. Brownian motion corrections to this thermodynamics are argued to lead to state vector reduction and to the probabilistic interpretation of quantum theory, making contact with recent phenomenological proposals for stochastic modifications to Schrodinger dynamics.

Quantum mechanics is our most successful physical theory. However, it raises conceptual issues that have perplexed physicists and philosophers of science for decades. This 2004 book develops an approach, based on the proposal that quantum theory is not a complete, final theory, but is in fact an emergent phenomenon arising from a deeper level of dynamics. The dynamics at this deeper level are taken to be an extension of classical dynamics to non-commuting matrix variables, with cyclic permutation inside a trace used as the basic calculational tool. With plausible assumptions, quantum theory is shown to emerge as the statistical thermodynamics of this underlying theory, with the canonical commutation/anticommutation relations derived from a generalized equipartition theorem. Brownian motion corrections to this thermodynamics are argued to lead to state vector reduction and to the probabilistic interpretation of quantum theory, making contact with phenomenological proposals for stochastic modifications to Schroedinger dynamics.