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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 in network science, neuroscience, biophysics, fluid dynamics, processes in solids, social sciences and foundations of computing.

Recent papers
•  F. Molnár, A.R. Ribeiro Gomes, Sz. Horvát, M. Ercsey-Ravasz, K. Knoblauch, H. Kennedy, Z. Toroczkai. "Predictability of cortico-cortical connections in the mammalian brain." Network Neuroscience, in press (2023). | doi.org/10.1162/netn_a_00345 (open access)
•  P.L. Erdős, G. Harcos, S.R. Kharel, P. Maga, T.R. Mezei, Z. Toroczkai. "The sequence of prime gaps is graphic" Mathematische Annalen (2023), 21 pgs. | doi: 10.1016/j.cpc.2020.107469 (open access) | arXiv: 2205.00580 [math.CO],[math.NT]
•  T.R. Mezei, S.R. Kharel, P.L. Erdős, Z. Toroczkai. "On graphic degree sequences and matching numbers" submitted (2023). | arXiv: 2204.07423 [math.CO]
•  P.L. Erdős, S.R. Kharel, T.R. Mezei, Z. Toroczkai. "Degree-preserving graph dynamics -- a versatile process to construct random networks" Journal of Complex Networks, 11(6), cnad46 (2023) | doi: 10.1093/comnet/cnad046 | arXiv: 2111.11994 [math.CO]
•  S.R. Kharel, T.R. Mezei, S. Chung, P.L. Erdős and Z. Toroczkai. "Degree-preserving network growth" Nature Physics 18(1), 100-106 (2022).
•  Czabarka, L.A. Székely, Z. Toroczkai, S. Walker "An algebraic Monte-Carlo algorithm for the Bipartite Partition Adjacency Matrix realization problem" Algebraic Statistics 12(2), 1150124 (2021). | arXiv:1708.08242 [math.CO]
•  S. Dutta, A. Khanna, H. Paik, D. Schlom, A. Raychowdhury, Z. Toroczkai, S. Datta "Ising Hamiltonian Solver using Stochastic Phase-Transition Nano-Oscillators" Nature Electronics 4 502-512 (2021) . | arXiv:2007.12331 [cond-mat.mes-hall]
•  F. Molnár, S. R. Kharel, X. Hu, Z. Toroczkai "Accelerating a continuous-time analog SAT solver using GPUs" Computer Physics Communications, 256 107469 (2020) | doi: 10.1016/j.cpc.2020.107469
•  S. Dutta, A. Khanna, J. Gomez, K. Ni, Z. Toroczkai, S. Datta. "Experimental Demonstration of Phase Transition Nano-Oscillator Based Ising Machine." 2019 IEEE International Electron Devices Meeting (IEDM19), San Francisco, CA, USA, pp. 37.8.1-37.8.4 (2019) | doi: 10.1109/IEDM19573.2019.8993460
•  H. Yamashita, H. Suzuki, Z. Toroczkai and K. Aihara. "Bounded Continuous-Time Satisfiability Solver" Proceedings of the 2019 International Symposium on Nonlinear Theory and its Applications (NOLTA2019) pp. 436-439 (2019).
•  B. Molnár, F. Molnár, M. Varga, Z. Toroczkai, M. Ercsey-Ravasz. "A continuous-time Max-SAT solver with high analog performance." Nature Comm. 9 4864 (2018) | arXiv:1801.06620 [cs.CC] | doi: 10.1038/s41467-018-07327-2
•  R. Gamanut, H. Kennedy, Z. Toroczkai, M. Ercsey-Ravasz, D.C. Van Essen, K. Knoblauch and A. Burkhalter "The Mouse Cortical Connectome, Characterized by an Ultra-Dense Cortical Graph, Maintains Specificity by Distinct Connectivity Profiles" Neuron 97, 698-715 (2018) | doi: 10.1016/j.neuron.2017.12.037

Selected publications
•  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]
•  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]
•  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
•  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
•  M. Ercsey-Ravasz and Z. Toroczkai. "The Chaos Within Sudoku." Scientific Reports, 2, 725 (2012). | doi:10.1038/srep00725 | arxiv.org: 1208.0370
♣  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
•  S. Eubank, H. Guclu, V.S.A. Kumar, M. Marathe, A. Srinivasan, Z. Toroczkai, N. Wang. "Modelling disease outbreaks in realistic urban social networks." Nature 429(6988), 180 (2004).
• M. Anghel, Z. Toroczkai, K.E. Bassler, G. Korniss "Competition-driven Network Dynamics: Emergence of a Scale-free Leadership Structure and Collective Efficiency." Phys.Rev.Lett. 92 , 058701 (2004).
•  G. Korniss, M.A. Novotny, H. Guclu, Z. Toroczkai, P.A. Rikvold "Suppressing Roughness of Virtual Times in Parallel Discrete-Event Simulations" Science 299 , 677 (2003).
• I.J. Benczik, Z. Toroczkai and T. Tél. "Selective Sensitivity of Open Chaotic Flows on Inertial Tracer Advection: Catching Particles with a Stick" Phys.Rev.Lett. 89, 164501 (2002).
• Z. Toroczkai "Topological classification of the Horton-Strahler index on binary trees" Phys.Rev.E 65, 016130 (2001). | arxiv.org: cond-mat/0108448
• G. Károlyi, Á. Péntek, I. Sheuring, T. Tél, and Z. Toroczkai "Chaotic flow: the physics of species coexistence" Proc.Natl.Acad.Sci.USA 97(25), 13661-13665 (2000).

For Fun: solving hard Sudokus with a continuous-time solver:
Sudoku is an exact cover type of constraint satisfaction problem and can be formulated as a Boolean Satisfiability problem (+1-in-9 SAT) and in turn transformed into conjunctive normal form (CNF). Our analog and deterministic solver published in above can be used to efficiently solve CNF SAT problems, and thus Sudoku as well. Here, Mária Ercsey-Ravasz with Erzsébet 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
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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