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"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 non-equilibrium statistical physics, nonlinear dynamics and chaos theory to bear on problems from network science, neuroscience, biophysics, fluid dynamics, processes in solids, social sciences and foundations of computing.

Solving hard Sudokus with a continuous-time solver:
Mária Ercsey-Ravasz has implemented an analog Sudoku solver (+1-in-9 SAT) based on our joint 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) 418-423 (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
•  Sz. Horváth, R. Gămănuț, M. Ercsey-Ravasz, L. Magrou, B. Gămănuț, D.C. Van Essen, A. Burkhalter, K. Knoblauch, Z. Toroczkai, H. Kennedy. "Spatial Embedding and Wiring Cost Constrain the Functional Layout of the Cortical Network of Rodents and Primates" PLOS Biology, 14(7), e1002512 (2016).
•  P.L. Erdős, I. Miklós, Z. Toroczkai "New classes of degree sequences with fast mixing swap Markov chain sampling." Combinatorics Probability and Computing, in press (2017). | arXiv:1601.08224 [cs.DM, math.CO]
•  M. Varga, R. Sumi, Z. Toroczkai, M. Ercsey-Ravasz. "Order-to-chaos transition in the hardness of random Boolean satisfiability problems." Phys. Rev. E, 93 052211 (2016). | arXiv:1602.05152 [cs.CC, cond-mat.stat-mech]
•  C. Orsini et al. "Quantifying randomness in real networks" Nature Comm., 6, 8627 (2015) | arXiv:1505.07503 [physics.soc-ph]
•  K.E. Bassler, C.I. Del Genio, P.L. Erdős, I. Miklós, Z. Toroczkai "Exact sampling of graphs with prescribed degree correlations." New. J. Phys., 17 083052 (2015). | arXiv:1503.06725 [cs.DM, cond-mat.stat-mech, cs.DS, math.CO, physics.soc-ph]
•  Sz. Horvát, É. Czabarka and Z. Toroczkai. "Reducing Degeneracy in Maximum Entropy Models of Networks." Phys. Rev. Lett., 114 158701 (2015) | doi:10.1103/PhysRevLett.114.158701 | arXiv:1407.0991 [cond-mat.stat-mech]
•  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. 29, 481-499 (2015). | arxiv.org:1307.5295 [math.CO]
•  Y. Ren, M. Ercsey-Ravasz, P. Wang, M. C. González and Z. Toroczkai. "Predicting commuter flows in spatial networks using a radiation model based on temporal ranges." Nature Comm. 5, 5347 (2014) | doi: 10.1038/ncomms6347 | arXiv:1410.4849 [physics.soc-ph]
•  K. Knoblauch, M. Ercsey-Ravasz, H. Kennedy and Z. Toroczkai. "The Brain in Space". Chapter in The 22nd Colloque Médecine et Recherche of the Fondation Ipsen in the Neurosciences series: "Micro-, meso- and macro-connectomics of the brain" Fondation IPSEN, Paris, France. Eds: H. Kennedy, D. Van Essen, Y. Christen. Springer, Heidelberg, in press, (2014). pdf
•  N.T. Markov, M. Ercsey-Ravasz, D.C. Van Essen, K. Knoblauch, Z. Toroczkai and H. Kennedy. "Cortical high-density counter-stream architectures." Science 342(6158), 1238406 (2013). | Link to journal | | doi: 10.1126/science.1238406
•  M. Ercsey-Ravasz, 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), 184-197 (2013). | doi: 10.1016/j.neuron.2013.07.036
•  N.T. Markov, M. Ercsey-Ravasz, 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 speci ficity of inter-areal connectivity in the macaque cerebral cortex." Proc. Natl. Acad. Sci. USA 110(13), 5187-5192 (2013). | Link to journal | doi: 10.1073/pnas.1218972110
•  H. Kennedy, K. Knoblauch and Z. Toroczkai. "Data coherence and completion actually do count for interareal cortical network." Neuroimage 80, 37-45 (2013).
•  M. Ercsey-Ravasz and Z. Toroczkai. "The Chaos Within Sudoku." Scientific Reports, 2, 725 (2012). | doi:10.1038/srep00725 | arxiv.org: 1208.0370
•  B. Molnár, M. Ercsey-Ravasz and Z. Toroczkai. "Continuous-time Neural Networks Without Local Traps for Solving Boolean Satisfiability." 13th International Workshop on Cellular Nanoscale Networks and their Applications (CNNA). Aug 29-31 (2012) Turin, Italy. Book Editors: F. Corinto and G.E. Pazienza. (2012). pdf
•  M. Ercsey-Ravasz, R. Lichtenwalter, N.V. Chawla and Z. Toroczkai. "Range-limited centrality measures in non-weighted 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. Ercsey-Ravasz, 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. Sappey-Marinier, 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. Ercsey-Ravasz, Z. Toroczkai, Z. Lakner and J. Baranyi. "Complexity of the International Agro-Food Trade Network and its Impact on Food Safety." PLoS ONE 7(5), e37810 (2012) | doi:10.1371/journal.pone.0037810
♣  M. Ercsey-Ravasz and Z. Toroczkai. "Optimization hardness as transient chaos in an analog approach to constraint satisfaction." Nature Physics 7, 966-970 (2011). Cover-page 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. Ercsey-Ravasz, 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 , 1254-1272 (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. Ercsey-Ravasz and Z. Toroczkai. "Centrality scaling in large networks." Phys. Rev. Lett. 105 , 038701 (2010). physics.soc-ph/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.soc-ph/1002.2975v1.pdf
•  P. L. Erdős, I. Miklós, Z. Toroczkai. "A simple Havel-Hakimi type algorithm to realize graphical degree sequences of directed graphs." Electronic J. Combinatorics 17(1) , R66 (2010). math.CO/0905.4913v2.pdf
Zoltán Toroczkai
Physics Department,

Concurrent Professor,
Computer Science and Engineering,
University of Notre Dame

Erdős nr: 2

♣  Twitter: @zoltantoroczkai

Contact Info
Snail Mail:
225 Nieuwland Science Hall (NSH),
Department of Physics,
University of Notre Dame,
Notre Dame, IN 46556-5670, U.S.A.
Phone: +1-574-631-2618 (Office)

Office: 384D, NSH (iCeNSA)

University of Notre Dame
Bldg. 1050, Suite. 384
Contact Ms. Yentl Ceballo, Rm 384E
Phone: +1 (574) 631-7095
FAX: +1 (574) 631-5952
E-mail: icensa@nd.edu

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