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Page 1: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division
Page 2: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

Sorin Solomon short CV

Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem.

Director, Division of Multi-Agent Systems; Institute for Scientific Interchange Torino.

Past Tasks: Head of the Theoretical Physics Section at the Racah Institute of Physics,  Head of the Center for Microphysics and Cosmology, Scientific Head of the Visualization Center at HUJ.

Awards: Levinson Prize,  Bantrel Prize at Caltech,  J.F. Kennedy Prize, Weizmann Fellowship, Keren Kayemet Prize.

Committees Member: Center for Complexity Science, Jerusalem, Complexus journal, Int. J. Mod. Phys. C, Journal of Statistical Mechanics.

Representative Paper (out of about 200):  The importance of being discrete: Life always wins on the surface with Shnerb, Louzoun, Bettelheim,   Proc. Natl. Acad. Sci. USA, Vol. 97, Issue 19, 10322-10324, September 12, 2000

Conference Talks (a few tens) , e.g. Plenary talk at EPS-12; The General Conference of the European Physical Society.

Book: Microscopic Simulation of Financial Markets, with M. Levy and H. Levy, Academic Press, New York, 2000.

Media Coverage: BBC, New York Times, Herald Tribune, Boston Globe, Der Standard, New Scientist, Neue Zurische Zeitung, Le Figaro, Business2.0, The Guardian, Nature, Science, Ha’Aretz, Europhysics News, Globe and Mail (Canada), Reuters

Page 3: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

What is Complexity?

Page 4: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

T-99 0CA water molecule in a container at 990C

Page 5: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

T-99 0C

The molecule moves in a disordered way bumping on the walls from time to time.

A water molecule in a container at 990C

Page 6: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

T-99 0C

What Happens if one heats the walls of the container by 2 degrees?

A water molecule in a container at 990C

The molecule moves in a disordered way bumping on the walls from time to time.

Page 7: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

T-99 0C T-101 0C

Almost nothing: the molecule will bump on the walls in average a little bit faster.

A water molecule in a container at 990C

What Happens if one heats the walls of the container by 2 degrees?

Page 8: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

T-99 0C T-101 0C

What happens if one adds 3 more water molecules (at T= 990C) ?

A water molecule in a container at 990C

Page 9: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

T-99 0C T-101 0C

Almost nothing! They will also occasionally bump among themselves; Their average speed will be equal to the one of the single molecule before.

T-99 0C

What happens if one adds 3 more water molecules (at T= 990C) ?

Page 10: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

T-99 0C T-101 0C

What happens if one increases now the temperature by 20C?

T-99 0C

Page 11: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

T-99 0C T-101 0C

Almost nothing, they will just increase a bit their average speed.

T-99 0C T-101 0C

What happens if one increases now the temperature by 20C?

Page 12: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

T-99 0C T-101 0C

What happens now, if one introduces in the container 1Kg of such molecules and repeats the experiment of heating the walls by 20C?

T-99 0C T-101 0C

Page 13: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

T-99 0C T-101 0C

T-99 0C T-101 0CVery Dramatic Effect:

What happens now, if one introduces in the container 1Kg of such molecules and repeats the experiment of heating the walls by 20C?

Page 14: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

T-99 0C T-101 0C

T-99 0C T-101 0C

Very Dramatic Effect: the spatial and speed distributions become inhomogeneous, and a lot of coordinated motion (bubbles) takes place: The water boils.

Page 15: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

T-99 0C T-101 0C

Does a new fundamental law of Nature become active in between the 4 molecules and the 1 Kg of water?

Page 16: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

T-99 0C T-101 0C

Yes and No: the actual interaction laws between molecules are not changed.

Does a new fundamental law of Nature become active in between the 4 molecules and the 1 Kg of water?

Page 17: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

T-99 0C T-101 0C

Yes and No: the actual interaction laws between molecules are not changed.But the existence of a large number of molecules leads to some new, collective, emergent, complex effects of those laws. This is a law of nature of a new type: More is Different(Anderson 1972)

Page 18: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

T-99 0C T-101 0C

Could it be that similar effects govern the emergence of life from chemistry, of meaning from simple signals, of societies from individuals, of health from simple cells?

(Anderson 1972)

Page 19: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

Could it be that similar effects govern the emergence

of life from chemistry,

of meaning from simple signals,

of societies from individuals,

of health from simple cells

etc?

Page 20: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

Could it be that many complex phenomena unexplained until nowcould be the result of simple interactions among their simple components?

To answer this one needs to transcend the traditional research within a single discipline and use trans-disciplinary methods.

This requires growing a new generation of bi- or multi-lingual scientists.

This requires more than a juxtaposition of expertizes.

Page 21: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

Main research frameworks:

-The micro-macro representation

-The triangle team

The interdisciplinary research requires typically (at least) 2 senior researchers from the relevant fields (the one knowing about “water molecules” and the one knowing about “boiling”) and one student. It is typically in the mind of the student that the connection between the laws of the water molecules and the laws of boiling will become one.

The research structure of the project will then be

Prof. in Field 1 PhD Student Prof in Field 2

The conceptual structure will be:

Microscopic Elements Microscopic Interactions Emergent Macroscopic Complex Phenomena

My coworkers and I implemented this scheme in a wide range of domains as seen on the following page.

In the process the students became professors, I indicate in brackets their present position .

One can click for their home pages.

Page 22: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

Moshe Levy; Assist Prof Finance HUJhttp://bschool.huji.ac.il/levy_shiki.htmlRepresentation of Markets in terms of

Inhomogenous individuals Book Acad Press

Sorin Solomon

Yoram Louzoun; Assist Prof. BIUhttp://www.cs.biu.ac.il/~louzouy/Localization in Groups with Self-

Enhancing trends Bul Math Bio; Artif life

Ester Adi Japha; Faculty BIUElements of children drawings

associated with meaningCognitive Development

Jacob Goldenberg; Assoc Prof HUJhttp://pluto.huji.ac.il/~msgolden/home_page/

Creativity; Novelty Science;NYT

Nava Rubin; Assoc Prof NYU http://www.cns.nyu.edu/~nava/

3D rigid sensation from 2D retina sensors Vision Research

Yehuda Stolov, PhD Dynamics of Stories and

Thought; IJMPC

Lev Muchnikhttp://www.nature.com/nsu/020923/020923-18.html

Collective Phenomena from Individual Behavior

Eran Shir PhD Stud TA;Internet Group Behav;

Europhys News

Avishalom Shalithttp://www.cs.huji.ac.il/~vish/

Self Organization of Open Self-Representation

Uri Hershberg; Postdoc Yalehttp://shum.huji.ac.il/~uriher/Representation of Diseases in terms of many interacting

antigens and antibodies; Phys A

Ifat Levy, Postdoc NYUBrain activity maps

elicited by visual stimuliNature

Page 23: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

The resulting complexity publications grouped by “target research field”

(only papers since 1995 are listed)

Page 24: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

Generic Complexity

The Microscopic Representation of Complex Macroscopic Phenomena, S. Solomon, Annual Reviews of Computational Physics II pp 243-294, editor D. Stauffer, World Scientific 1995.

Collective Degrees of Freedom and Multiscale Dynamics in Spin Glasses N. Persky and S.Solomon, Phys. Rev. E. 54 (1996) 4399; http://xxx.lanl.gov/abs/cond-mat/9603056

Complexity a Science at 30, S. Solomon and E. Shir, Europhysics News Feb-March 2003 p54

Page 25: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

Visual System (reconstructing 3D bodies from 2D moving points)

Restricted Ability to Recover 3D Global Motion from 1 D Motion Signals: Theoretical Observations, N. Rubin, S. Hochstein and S. Solomon, Vision Research 35 (1995) 569-578.

Restricted Ability to Recover 3D Global Motion from 1 D Motion Signals: Psychophysical Observations, N. Rubin, S. Hochstein and S. Solomon, Vision Research 35 (1995) 463-476.

The Microscopic Bases of Vision S. Solomon, in Perspectives on Cognitive Science, vol. 2, ed. B. Kokinov (NBU 1995)

Page 26: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

Multiplicative Random walks, Lotka –Volterra systems, Returns Distributions and Pareto Laws

Dynamical Explanation for the Emergence of Power Law in a Stock Market Model, M. Levy and S. Solomon, International Journal of Modern Physics C, Vol. 7, No. 1 (1996) 65-72

Power Laws are Logarithmic Boltzmann Laws M. Levy and S. Solomon International Journal of Modern Physics C , Vol. 7, No. 4 (1996) 595; http://xxx.lanl.gov/abs/adap-org/9607001

Spontaneous Scaling Emergence in Generic Stochastic Systems S. Solomon and M. Levy International Journal of Modern Physics C , Vol. 7, No. 5 (1996) 745 ; http://xxx.lanl.gov/abs/adap-org/9609002

Power-law distributions and L\'evy-stable intermittent fluctuations in stochastic systems of many autocatalytic elements. O. Malcai O. Biham and S. Solomon, Phys. Rev. E, 60, 1299 (1999). http://xxx.lanl.gov/abs/cond-mat/9907320

Page 27: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

New Evidence for the Power Law Distribution of Wealth M. Levy and S. Solomon Physica A 242 (1997) 90. http://shum.huji.ac.il/~sorin/power-shiki.ps Generic emergence of power law distributions and L\'evy-stable intermittent fluctuations in discrete logistic systems. O. Biham, O. Malcai, M. Levy and S. Solomon, Phys. Rev. E 58, 1352 (1998). http://xxx.lanl.gov/abs/adap-org/9804001 Stochastic Lotka-Volterra Systems of Competing Auto-catalytic Agents lead Generically to Truncated Pareto Power Wealth Distribution, Truncated Levy Distribution of Market Returns, Clustered Volatility, Booms and Crashes. S. Solomon, in Decision Technologies for Computational Finance, edited by A.-P. Refenes, A. N. Burgess, and J. E. Moody (Kluwer Academic Publishers, 1998). http://xxx.lanl.gov/abs/cond-mat/9803367Generalized Lotka Volterra (GLV) Models of Stock Markets S. Solomon, pp 301-322 in "Applications of Simulation to Social Sciences" , Eds: G Ballot and G Weisbuch; Hermes Science Publications 2000 http://xxx.lanl.gov/abs/cond-mat/9901250Power laws in cities population, financial markets and internet sites (scaling in systems with a variable number of components) Aharon Blank and Sorin Solomon, Physica A 287 (1-2) (2000) pp.279-288 http://xxx.lanl.gov/abs/cond-mat/0003240

Page 28: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

Power, Lévy, exponential and Gaussian-like regimes in autocatalytic financial systems, Z.F. Huang and S. Solomon Eur. Phys. J. B 20, (2001) 601-607 http://xxx.lanl.gov/abs/cond-mat/0008026

Finite market size as a source of extreme wealth inequality and market instability Zhi-Feng Huang and Sorin Solomon Physica A , 294 (3-4) (2001) pp. 503-513 http://xxx.lanl.gov/abs/cond-mat/0103170

Long-time fluctuations in a dynamical model of stock market indices Ofer Biham, Zhi-Feng Huang, Ofer Malcai and Sorin Solomon Phys. Rev. E 64, 026101 (2001) http://link.aps.org/abstract/PRE/v64/e026101

Stochastic Multiplicative Processes for Financial Markets Zhi-Feng Huang and Sorin Solomon, Physica A 306 (2002) 412-422

Stability of Pareto-Zipf law in non-stationary economies S. Solomon and P. Richmond in: Economics with heterogeneous interacting agents, ed. by A.Kirman and J.B. Zimmermann, Lecture Notes in Economics and Mathematical Systems, Springer, Berlin- Heidelberg 2001 page 141 http://xxx.lanl.gov/abs/cond-mat/012479

Page 29: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

Power Laws of Wealth, Market Order Volumes and Market Returns Sorin Solomon, Peter Richmond Physica A: Statistical Mechanics and its Applications, Vol. 299 (1-2) (2001) pp. 188-197 http://xxx.lanl.gov/abs/cond-mat/0102423

Power Laws are disguised Boltzmann Laws Peter Richmond, Sorin Solomon, International Journal of Modern Physics C, Vol. 12, No. 3 (2001) 333-343 http://xxx.lanl.gov/abs/cond-mat/0010222

Self-Organization and Non-Self-Averaging Effects in Systems of Discrete Auto-Catalytic Elements S. Solomon, pp 351-360 in Multiscale Computational Methods in Chemistry and Physics eds. A. Brandt, J. Bernholc and K. Binder, IOS Press 2001; NATO Science Series III: computer and Systems Sciences Vol. 177.

Volatility driven markets in a generalized Lotka Voltera formalism Louzoun. Y. Solomon. S. (2001). Physica A 302 220-233 http://xxx.lanl.gov/abs/cond-mat/0109493

Theoretical analysis and simulations of the generalized Lotka-Volterra model. O. Malcai, O. Biham, P. Richmond and S. Solomon, Phys. Rev. E66, 031102 (2002).

Page 30: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

Co-Evolutionist Stochastic Dynamics: Emergence of Power-LawsPower-laws in stochastic Lotka-Volterra-Eigen-Schuster Systems S. Solomon, P. Richmond, O. Biham and O. Malcai, in: "Towards Cognitive Economics", Eds: P. Bourgine and J.-P. Nadal, Springer (2003).

Page 31: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

Artificial Creativity and Novelty Emergence

Creative Sparks Jacob Goldenberg, David Mazursky, and Sorin Solomon Science 285: 1495-1496, 1999; http://shum.huji.ac.il/~sorin/creative-sparks.htm

Toward Identifying the Inventive Templates of New Products: A Channeled Ideation Approach, Goldenberg Jacob, David Mazursky, and Sorin Solomon (1999), Journal of Marketing Research, 36 (May), p. 200-210.

Meme's the Word, Jacob Goldenberg, David Mazursky, and Sorin Solomon Science 1999 November 19; 286: 1477 http://shum.huji.ac.il/~sorin/meme.htm

Templates of original innovation: Projecting original incremental innovations from intrinsic information Goldenberg J. Mazursky D. Solomon S., (1999) Technological Forecasting and Social Change, May, Vol. 61/1 P. 1-12. Creativity Templates: Towards Identifying the Fundamental Schemes of Quality Advertisements; Goldenberg J. Mazursky D. Solomon S. Marketing Science, Volume 18, Number 3, 1999

Scrutinizing Creativity Dennis Hollenberg;, Jacob Goldenberg, David Mazursky, and Sorin Solomon Science 1999 December 17; 286: 2269 http://shum.huji.ac.il/~sorin/creativity.htm

Page 32: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

Agent Based Simulations of Stock Markets

Microscopic Simulation of the Stock Market M. Levy, H. Levy and S. Solomon, Journal de Physique I France 5 (1995) 1087-1103.  A microscopic model of the stock market; Cycles, booms and crashes, M. Levy, H. Levy and S. Solomon, Economics Letters 45 (1994) 103-111.

The Complex Dynamics of a Simple Stock Market Model M. Levy, N. Persky and S. Solomon Int. J. of High Speed Computing 8 (1996) 93 http://shum.huji.ac.il/~sorin/pers.ps

Behaviorally realistic simulations of stock markets; Traders with a soul, Computer Solomon S Physics Communications 121-122 (1999) 161 . http://xxx.lanl.gov/abs/adap-org/9901003

Pioneers on a new continent: on physics and economicsSorin Solomon and Moshe Levy Quantitative Finance (IoP) Volume 3, Number 1, C12 February 2003

Page 33: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

The Interacting Gaps Model: Reconciling Theoretical andNumerical Approaches to Limit-Order Models. L. Muchnik, F. Slanina, and S. Solomon. Physica A 330 (2003) 232.

Statistical Mechanics of Conventional Traders May Lead to Non-Conventional Market Behavior, Lev Muchnik and Sorin Solomon Physica Scripta. Vol. T106, 41–47, 2003

An updated Review of the LLS Stock Market Model: Complex Market Ecology, Power Laws in Wealth Distribution and Market Returns, Sorin Siolomon and Moshe Levy, p69, in New Directions in Statistical Physics, ed. Luc Wille, Springer-Verlag 2004

Page 34: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

  Other Mental Processes

The Dynamics of Childrens's Drawings. E. Adi, I. Levin and S. Solomon, in Perspectives on Cognitive Science, vol. 2, ed. B. Kokinov (NBU 1995)

Emergence of Representation in Drawing: The Relation Between Kinematic and Referential Aspects Ester Adi-Japha, Iris Levin and S. Solomon Cognitive Development 13, 25-51 (1998)

What Are Stories Made Of? Quantitative Categorical Deconstruction of Creation Y. Stolov, M. Idel, S. Solomon, International Journal of Modern Physics C, Vol. 11, No. 4 (2000) 827-835 http://xxx.lanl.gov/abs/cond-mat/0008192

Structures of the Mind and Universal Music Jacob Goldenberg, David Mazursky, and Sorin Solomon Science 2001 June 29; 292: 2433 http://shum.huji.ac.il/~sorin/structures.htm

Page 35: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

Global Propagation by local rules

Marketing percolation J. Goldenberg, B. Libai, S. Solomon, N. Jan and D. Stauffer Physica A, 284 (1-4) (2000) pp. 335-347 , http://xxx.lanl.gov/abs/cond-mat/0005426

Social percolation models Sorin Solomon, Gerard Weisbuch, Lucilla de Arcangelis, Naeem Jan, Dietrich Stauffer Physica A: 277 (1-2) (2000) pp. 239-247 http://shum.huji.ac.il/~sorin/soc-per.ps

Self-organized percolation and critical sales fluctuations Weisbuch G, Solomon S Int. J. Mod. Phys. C 11: (6) 1263-1272 SEP 2000 http://shum.huji.ac.il/~sorin/ws.ps

Social Percolators and Self Organized Criticality. in Handbook of Graphs and Networks: From the Genome to the Internet, pp.113-132 eds. S. Bornholdt and H. G. Schuster, Wiley-VCH, Berlin, 2002.

Solving Traffic Jams: Human Intervention or Self-Organization? E. Mar Or, E. Shir and S. Solomon, International Journal of Modern Physics, Vol. 14, No. 8 p 1007

Page 36: Sorin Solomon short CV Full Professor Full Professor at the Racah Institute of Physics of the Hebrew University of Jerusalem. DirectorDirector, Division

Emergence and Patterns in Stochastic Autocatalytic Systems

The importance of being discrete: Life always wins on the surface Nadav M. Shnerb, Yoram Louzoun, Eldad Bettelheim, and Sorin Solomon Proc. Natl. Acad. Sci. USA, Vol. 97, Issue 19, 10322-10324, September 12, 2000 http://xxx.lanl.gov/abs/adap-org/9912005

Adaptation of Autocatalytic Fluctuations to Diffusive Noise N. M. Shnerb, E. Bettelheim, Y. Louzoun, O. Agam, S. Solomon Phys Rev E Vol 63, No 2, 2001; http://xxx.lanl.gov/abs/cond-mat/0007097

HIV time hierarchy: winning the war while, loosing all the battles Uri Hershberg, Yoram Louzoun, Henri Atlan and Sorin Solomon Physica A: 289 (1-2) (2001) pp.178-190 ; http://xxx.lanl.gov/abs/nlin.AO/0006023

The Emergence of Spatial Complexity in the immune System. Louzoun, Y, Solomon. S., Atlan. H., Cohen.I.R. (2001) Physica A, 297 (1-2) pp. 242-252.

http://xxx.lanl.gov/html/cond-mat/0008133 The risk of being unfair, the unstable fate of globalization. Louzoun. Y. Mazurski. D.,

Goldberg. J. Solomon. S. (2003) Artificial Life 4(9) 357 - 370 Innovations Refuse to Die:-The Unforeseen Longevity of Society Fundamental

Ideas. Mazurski. D., Goldberg. J. Barak.L. Louzoun. Y. Solomon. S. (2003) Technological forecasting and Social Change In press

Proliferation and competition in discrete biological systems. Louzoun, Y., Atlan, H., Solomon. S., Cohen, I.R (2003) Bulletin of mathematical biology 65(3) 375-396

Reactive Glass and vegetation patterns, N.M. Shnerb, P. Sarah, H. Lavee and S. Solomon, Phys. Rev. Lett. 90 0381011 (2003)  [pdf file]