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\chapter{Biographical Sketches}

\section{Tommaso Toffoli}

 \begin{flushleft}
	Principal Research Scientist\\
	MIT Laboratory for Computer Science\\
	545 Technology Sq.\\
	Cambridge, MA 02139\\
	email: {\tt tt@im.lcs.mit.edu}
 \end{flushleft}

\subsection*{Brief curriculum vitae}

Tommaso Toffoli received a Doctorate in Physics from the University of
Rome, Italy, in 1967, and a Ph.D. in Computer and Communication Sciences
from the University of Michigan, Ann Arbor, in 1976.
In 1977 he joined the MIT Laboratory for Computer Science,
where he is currently leader of the Information Mechanics group.

His main areas of interest, information mechanics, deals with
fundamental connections between physical and computational processes.
One application of this research is the development of
massively-parallel, fine-grained computational schemes that directly
reflect essential aspects of physics, such as uniformity, locality,
and microscopic reversibility, inertia, and other conservation laws.

Dr.\ Toffoli has pioneered the development of cellular automata
machines and their use in physical modeling. He was one of the
originators of fluid modeling by lattice gases. His book (with Norman
Margolus), ``Cellular Automata Machines---A new environment for
modeling,'' now in its first printing and translated in Russian, has
become the standard introduction to fine-grained modeling techniques
using cellular automata. A new cellular automata architecture (\cam-8),
developed by Dr.\ Toffoli's group and currently being produced in
collaboration with SUN Research, literally embodies the concept of
``Programmable Matter,'' and is ideally suited for problems of
theoretical and applied materials science.

Other current research topics include: relativistic aspects of
parallel computation; correspondence rules between microscopic
computing mechanisms and macroscopic phenomenology; modeling of
polymer dynamics and other dynamics that separately conserve molecular
species; and the emergence of variational principles in discrete
dynamical processes.

\subsection*{Main recent publications}

 {\def\bib#1{\item[]}
 \begin{trivlist} 	
 \bib{toffoli-ep}{\sc Toffoli}, Tommaso, ``Cellular
automata,'' {\sl Encyclopedia of Physics}, VCH Publ., NY (1991),
126--127.
 \bib{toffoli-pm}{\sc Toffoli}, Tommaso, and Norman {\sc Margolus},
``Programmable matter,'' {\sl Physica D \bf 47} (1991), 263--272.
 \bib{toffoli-ica}{\sc Toffoli}, Tommaso, and Norman {\sc
Margolus}, ``Invertible Cellular Automata: A Review,'' {\sl Physica
D \bf 45} (1990), 1--3.
 \bib{toffoli-cheap}{\sc Toffoli}, Tommaso, ``How cheap can
mechanics' first principles be?''  {\sl Complexity, Entropy, and the
Physics of Information} (W. H. {\sc Zurek} ed.), Addison-Wesley
(1990), 301--318.  
 \bib{}{\sc Toffoli}, Tommaso, ``Information Transport
Obeying the Continuity Equation,'' {\sl IBM J. Res.\ Develop.\ \bf
32}:1 (January 1988), 29--36.  
 \bib{}{\sc Toffoli}, Tommaso, and Norman {\sc Margolus},
{\sl Cellular Automata Machines---A New Environment for Modeling}, MIT
Press (1987), 259 pp.  
 \bib{}{\sc Margolus}, Norman, Tommaso {\sc Toffoli}, and
G\'erard {\sc Vichniac}, ``Cellular-Automata Supercomputers for
Fluid-Dynamics Processing,'' {\sl Phys.\ Rev.\ Lett.} {\bf 56} (1986),
1694--1696.
 \bib{}{\sc Toffoli}, Tommaso, ``Cellular automata as an
alternative to (rather than an approximation of) differential
equations in modeling physics,'' {\sl Physica} {\bf 10D} (1984),
117--127.
 \bib{}{\sc Toffoli}, Tommaso, ``CAM: A high-performance
cellular-automaton machine,'' {\sl Physica} {\bf 10D} (1984),
195--204.
 \bib{}{\sc Fredkin}, Edward, and Tommaso {\sc Toffoli},
``Conservative Logic,'' {\sl Int.\ J. Theor.\ Phys.} {\bf 21} (1982),
219--253.
 \end{trivlist}
 }

\section{Norman Margolus}

 \begin{flushleft}
	Research Scientist\\
	MIT Laboratory for Computer Science\\
	545 Technology Sq.\\
	Cambridge, MA 02139\\
	email: {\tt nhm@im.lcs.mit.edu}
 \end{flushleft}

Norman Margolus received his Ph.D. in Physics in 1987 from MIT,
investigating computers and computations which closely reflect the
structure of microscopic physics.  He has continued this work as a
researcher at MIT with the Information Mechanics Group.

Dr.\ Margolus has made seminal contributions to the theory of
reversible computation and reversible cellular automata, to the study
of physically ideal computation (and in particular, quantum
computation), and to the application of physical techniques to the
analysis of computations which incorporate realistic physical
constraints.  He was the first to synthesize cellular automata models
of a number of basic physical processes, and with Toffoli pioneered
the use of cellular automata simulations for fluid modeling.

As a research tool and practical offshoot of more theoretical
investigations, he has developed the CAM-8 cellular automata machine
architecture, which is an efficient and scalable mechanism for
fine-grained, spacially organized computations.  He is the author of a
US patent that covers the main original aspects of the \cam-8
architecture.

Dr.\ Margolus has co-authored, with Tommaso Toffoli, a book on
physical modeling with cellular automata and cellular automata
machines.  His next book, on physics-like models of computation, is
slated to come out later this year.


\subsection*{Main recent publications}

 {\def\bib#1{\item[]}
 \begin{trivlist} 	
 \bib{}{\sc Margolus}, Norman, ``Multidimensional Cellular Data Array
Processing System Which Separately Permutes Stored Data Elements and
Applies Transformation Rules to Permuted Elements,'' {\sl United
States Patent 5159690} (Issued October 1992).
 \bib{} {\sc Toffoli}, Tommaso, and Norman {\sc Margolus},
``Programmable matter,''
{\sl Physica D}, 47:263-272, 1990.
 \bib{} {\sc Toffoli}, Tommaso, and Norman {\sc Margolus},
``Invertible Cellular Automata: A Review,''
{\sl Physica D}, 45(1-3), 1990.
 \bib{}{\sc Margolus}, Norman, ``Parallel Quantum
Computation,'' {\sl Complexity, Entropy, and the Physics of Information}
(W. H. {\sc Zurek} ed.), Addison-Wesley (1990), 273--287.
 \bib{}{\sc Margolus}, Norman, and Tommaso {\sc Toffoli},
``Cellular Automata Machines,'' {\sl Lattice Gas Methods for Partial
Differential Equations} (Gary {\sc Doolen} {\sl et al.}\ ed.),
Addison-Wesley (1988), 219--248.
 \bib{}{\sc Toffoli}, Tommaso, and Norman {\sc Margolus},
{\sl Cellular Automata Machines---A New Environment for Modeling}, MIT
Press (1987), 259 pp.  
 \bib{} {\sc Margolus}, Norman, {\sl Physics and
Computation}, MIT Doctoral Thesis (1987).
 \bib{}{\sc Margolus}, Norman, Tommaso {\sc Toffoli}, and
G\'erard {\sc Vichniac}, ``Cellular-Automata Supercomputers for
Fluid-Dynamics Processing,'' {\sl Phys.\ Rev.\ Lett.} {\bf 56} (1986),
1694--1696.
 \bib{} {\sc Margolus}, Norman, ``Quantum
Computation,'' {\sl New Techniques and Ideas in Quantum Measurement
Theory} (Daniel {\sc Greenberger} ed.), New York Academy of Sciences
(1986), 487--497.
 \bib{}{\sc Margolus}, Norman, ``Physics-like models of
computation,'' {\sl Physica} {\bf 10D} (1984), 81--95.
 \end{trivlist}
 }


