

"A fact is a simple statement that everyone believes. It is innocent unless found guilty.
A hypothesis is a novel suggestion that no one wants to believe. It is guilty until found
effective." 
Edward Teller 

I work in the general area of complex systems research,
bringing and developing tools from mathematics, equilibrium and nonequlibrium
statistical physics, nonlinear dynamics and chaos theory to bear on applications
ranging from fluid flows, processes in solids, to complex networked systems.
Lately I have been increasingly interested
in nontraditional models of learning and computation by physical systems, in
particular brain neuronal systems and agentbased approaches to social behavior.


Solving hard Sudokus with a continuoustime solver:

Mária ErcseyRavasz
has implemented an analog Sudoku solver (+1in9 SAT)
based on the paper ♣ below, and with Erzsébet
Ravasz Regan have generated a
movie about
the "flow of thoughts" in some of the number fields (the right frame of the movie) by the solver,
when solving one of the hardest Sudoku puzzles on record (the puzzle is from Elser et.al.,
PNAS, 104(2) 418423 (2007), Fig 5 of the Supporting Info). The movie can also be
downloaded in wmv format and in mp4
format. Also see: arxiv.org: 1208.0370


Recent papers
• N.T. Markov, M. ErcseyRavasz, D.C. Van Essen,
K. Knoblauch, Z. Toroczkai and H. Kennedy.
"Cortical highdensity counterstream architectures."
Science
342(6158), 1238406 (2013).

• M. ErcseyRavasz, N.T. Markov, C. Lamy,
D.C. Van Essen, K. Knoblauch, Z. Toroczkai and H. Kennedy.
"A predictive network model of cerebral cortical connectivity based on a
distance rule."
Neuron
80(1), 184197 (2013).

• P. L. Erdős, I. Miklós, Z. Toroczkai.
"A decomposition based proof for fast mixing
of a Markov chain over balanced realizations of a joint degree matrix."
SIAM J. Discr. Math., submitted (2013)
 arxiv.org:1307.5295 (math.CO)

• N.T. Markov, M. ErcseyRavasz, C. Lamy, A.R. Ribeiro
Gomes, L. Magrou, P. Misery, P. Giroud, P. Barone, C. Dehay, Z. Toroczkai, K. Knoblauch,
D.C. Van Essen, H. Kennedy.
"The role of distance on the specificity of interareal connectivity in the
macaque cerebral cortex."
Proc. Natl. Acad. Sci. USA
110(13), 51875192 (2013).

• H. Kennedy, K. Knoblauch and Z. Toroczkai.
"Data coherence and completion actually do count for interareal cortical network"
Neuroimage
80, 3745 (2013).

• M. ErcseyRavasz and Z. Toroczkai.
"The Chaos Within Sudoku."
Scientific Reports,
2, 755 (2012).
 doi:10.1038/srep00725
 arxiv.org: 1208.0370

• B. Molnár, M. ErcseyRavasz and Z. Toroczkai.
"Continuoustime Neural Networks Without Local Traps for Solving Boolean Satisfiability."
13th International Workshop on Cellular Nanoscale Networks and their Applications (CNNA).
Aug 2931 (2012) Turin, Italy. Book Editors: F. Corinto and G.E. Pazienza.
(2012). pdf

• M. ErcseyRavasz, R. Lichtenwalter, N.V. Chawla and Z. Toroczkai.
"Rangelimited centrality measures in nonweighted and weighted complex networks."
Phys. Rev. E
85, 066103 (2012).
arxiv.org/1111.5382

• H. Kim, C.I. Del Genio, K.E. Bassler and Z. Toroczkai.
"Constructing and sampling directed graphs with given degree sequences."
New J. Phys.
14, 023012 (2012).
arxiv.org/1109.4590

• N. T. Markov, M. ErcseyRavasz,
A.R. Ribiero Gomes, C. Lamy, J. Vezoli, L. Magrou, P. Misery, A. Falchier, R. Quilodran,
J. Sallet, M.A. Gariel, R. Gamanut, C. Huissoud, S. Clavagnier, P. Giroud, D. SappeyMarinier,
P. Barone, C. Dehay, Z. Toroczkai, K. Knoblauch, D.C. Van Essen, H. Kennedy.
"A weighted and directed interareal connectivity matrix for macaque cerebral cortex"
Cereb. Cortex ,
advance access, Sep. 25 (2012) 
free journal access

• M. ErcseyRavasz, Z. Toroczkai, Z. Lakner and J. Baranyi.
"Complexity of the International AgroFood Trade Network and its
Impact on Food Safety."
PLoS ONE
7(5), e37810 (2012) 
doi:10.1371/journal.pone.0037810

♣ M. ErcseyRavasz and Z. Toroczkai.
"Optimization hardness as transient chaos in an analog approach to constraint satisfaction."
Nature Physics
7, 966970 (2011). Coverpage article.  doi:10.1038/nphys2105
 arxiv.org: 1208.0526v1

• N.T. Markov, P. Misery, A. Falchier, C. Lamy,
J. Vezoli, R. Quilodran, P. Giroud, M.A.
Gariel, M. ErcseyRavasz, L.J. Pilaz, C. Huissoud, P. Barone, C. Dehay, Z. Toroczkai,
D.C. Van Essen, H. Kennedy, K. Knoblauch.
"Weight consistency specifies regularities of cortical networks."
Cereb. Cortex
21 , 12541272 (2011).
free journal access .

• A. Asztalos and Z. Toroczkai.
"Network discovery by generalized random walks."
Europhysics Letters
92 50008 (2010).
arxiv.org/1008.4980 (the arxiv version
contains the proofs as well).

• M. ErcseyRavasz and Z. Toroczkai.
"Centrality scaling in large networks."
Phys. Rev. Lett.
105 , 038701 (2010).
physics.socph/1003.0692v2.pdf

• C.I. Del Genio, H. Kim, Z. Toroczkai and K.E. Bassler.
"Efficient and exact sampling of simple graphs with given arbitrary degree sequence."
PLoS ONE
5(4) , e10012 (2010).
physics.socph/1002.2975v1.pdf

• P. L. Erdős, I. Miklós, Z. Toroczkai.
"A simple HavelHakimi type algorithm to
realize graphical degree sequences of directed graphs."
Electronic J. Combinatorics
17(1) , R66 (2010).
math.CO/0905.4913v2.pdf






Zoltán Toroczkai
Professor, Physics Department,
Concurrent Professor,
Computer Science and Engineering,
University of Notre Dame
Erdős
nr: 2


♣ Twitter: @zoltantoroczkai


iCeNSA
University of Notre Dame
Bldg. 1050, Suite. 384
Contact Ms. Yentl Ceballo, Rm 384E
Phone: +1 (574) 6317095
FAX: +1 (574) 6315952
Email: icensa@nd.edu


 