# Faculty Profile

## Kevin E. Bassler

Moores Professor of Physics and Mathematics

Department Chair

**Department of Physics**

**Office:** SR1-619C

**Contact:** bassler@uh.edu - (713) 743-3568

**Education:** Ph.D., Carnegie Mellon University

### Complexity Theory and Non-Equilibrium Statistical Mechanics

The focus of my research is to understand and identify the fundamental principles that govern the dynamics of complex systems. I am interested in processes of growth, adaptation, self-organization, self-assembly, and evolution. Often, my approach is to construct simple models that capture the essence of experimental behavior of a class of systems, and use them to explore the common features that underlie their dynamics. My work usually involves a combination of analytic calculations and computer simulations.

Much of my current interest is in the dynamics of systems organized as complex networks. The applications include physical, biological, social, and engineered systems. I am currently working on projects to determine how to optimally route congested transport on networks, to optimally detect structure in network dynamics, to understand adaptive or evolutionary behavior of complex networks, and to understand the role of symmetry in complex network dynamics. I also interested in random matrix theory (RMT), and in applying RMT to understand the dynamics of networks.

Other current projects of mine involve the dynamics of financial markets and the behavior of materials systems, including the self-assembly of nano-structured arrays in semiconductor multilayers and the critical behavior of solids with extended defects.

### Refereed Journal Articles

- K.E. Bassler, K. Sasaki, and R.B. Griffiths, “Interface Interactions in Modulated Phases, and Upsilon Points,” J. Stat. Phys.
**62**, 45-88 (1991).

DOI: 10.1007/BF01020859 - K.E. Bassler and M. Olvera de la Cruz, “Monte Carlo Study of Diblock Copolymers in Dilute Solution,” J. de Physique I
**3**, 2387-2395 (1993).

DOI: 10.1051/jp1:1993251 - K.E. Bassler, B. Schmittmann, and R.K.P. Zia, “Spatial Structures with Nonzero Winding Number in Biased Diffusion of Two Species,” Europhys. Lett.
**24**, 115-120 (1993).

DOI: 10.1209/0295-5075/24/2/007 - K.E. Bassler and R.B. Griffiths, “Numerical Study of the Ground States of a New Type of Nonconvex Frenkel-Kontorova Model,” Phys. Rev. B
**49**, 904-915 (1994).

DOI: 10.1103/PhysRevB.49.904 - B. Schmittmann, K.E. Bassler, K. Hwang, and R.K.P. Zia, “Biased Diffusion of Two Species,” Physica A
**205**, 284-291 (1994).

DOI: 10.1016/0378-4371(94)90505-3 - K.E. Bassler and B. Schmittmann, “Renormalization Group Study of a Hybrid Driven Diffusive System,” Phys. Rev. E
**49**, 3614-3620 (1994).

DOI: 10.1103/PhysRevE.49.3614 - K.E. Bassler and R.K.P. Zia, “Phase Transitions in a Nonequilibrium Potts Model: A Monte Carlo Study of Critical Behavior,” Phys. Rev. E
**49**, 5871-5874 (1994).

DOI: 10.1103/PhysRevE.49.5871 - K.E. Bassler and Z. Racz, “Bicritical Point and Crossover in a Two Temperature, Diffusive Kinetic Ising Model,” Phys. Rev. Lett.
**73**, 1320-1323 (1994).

DOI: 10.1103/PhysRevLett.73.1320 - K.E. Bassler and B. Schmittmann, “Critical Dynamics of Nonconserved Ising-Like Systems,” Phys. Rev. Lett.
**73**, 3343-3346 (1994).

DOI: 10.1103/PhysRevLett.73.3343 - K.E. Bassler and Z. Racz, “Existence of Long-Range Order in the Steady State of a Two Dimensional, Two-Temperature XY Model,” Phys. Rev. E
**52**, R9-R12 (1995).

DOI: 10.1103/PhysRevE.52.R9 - K.E. Bassler and R.K.P. Zia, “Phase Transitions in a Driven Lattice Gas at Two Temperatures,” J. Stat. Phys.
**80**, 499-515 (1995).

DOI: 10.1007/BF02178545 - B. Schmittmann and K.E. Bassler, “Frozen Disorder in a Driven System,” Phys. Rev. Lett.
**77**, 3581-3584 (1996).

DOI: 10.1103/PhysRevLett.77.3581 - K.E. Bassler and D.A. Browne, “Nonequilibrium Critical Dynamics of a Three Species Monomer-Monomer Model,” Phys. Rev. Lett.
**77**, 4094-4097 (1996).

DOI: 10.1103/PhysRevLett.77.4094 - K.E. Bassler and D.A. Browne, “The Three-Species Monomer-Monomer Model: A Mean-field Analysis and Monte Carlo Study,” Phys. Rev. E
**55**, 5225-5233 (1997).

DOI: 10.1103/PhysRevE.55.5225 - K.S. Brown, K.E. Bassler and D.A. Browne, “Mean-field Analysis and Monte Carlo Study of an Interacting Two-Species Monomer-Monomer Model,” Phys. Rev. E
**56**, 3953-3958 (1997).

DOI: 10.1103/PhysRevE.56.3953 - K.E. Bassler and D.A. Browne, “The Three Species Monomer-Monomer Model in the Reaction-Controlled Limit,” J. Phys. A: Math Gen.
**31**, 6309-6318 (1998).

DOI: 10.1088/0305-4470/31/30/001 - J. Trenkler, P.C. Chow, P. Wochner, H. Abe, K.E. Bassler, R. Paniago, H. Reichert, D. Scarfe, T.H. Metzger, J. Peisl, J. Bai, and S.C. Moss, “Two Length Scales and Crossover Behavior in the Critical Diffuse Scattering from V
_{2}H,” Phys. Rev. Lett.**81**, 2276-2279 (1998).

DOI: 10.1103/PhysRevLett.81.2276 - K.E. Bassler and M. Paczuski, “A Simple Model of Superconducting Vortex Avalanches,” Phys. Rev. Lett.
**81**, 3761-3764 (1998).

DOI: 10.1103/PhysRevLett.81.3761 - K.E. Bassler, M. Paczuski, and G.F. Reiter, “Braided Rivers and Superconducting Vortex Avalanches,” Phys. Rev. Lett.
**83**, 3956-3959 (1999).

DOI: 10.1103/PhysRevLett.83.3956 - M. Paczuski, K.E. Bassler, and A. Corral, “Self-Organized Networks of Competing Boolean Agents,” Phys. Rev. Lett.
**84**, 3185-3189 (2000).

DOI: 10.1103/PhysRevLett.84.3185 - M. Paczuski, and K.E. Bassler, “Theoretical Results for Sandpile Models of Self-Organized Criticality with Multiple Topplings,” Phys. Rev. E
**62**, 5347-5352 (2000).

DOI: 10.1103/PhysRevE.62.5347 - J.R. Claycomb, K.E. Bassler, J.H. Miller, Jr., M. Nersesyan, and D. Luss, “Avalanche Behavior in the Dynamics of Chemical Reactions,” Phys. Rev. Lett.
**87**, 178303 (2001).

DOI: 10.1103/PhysRevLett.87.178303 - K.E. Bassler, M. Paczuski, and E. Altshuler, “A Simple Model for the Plastic Dynamics of a Disordered Flux Line Lattice,” Phys. Rev. B
**64**, 224517 (2001).

DOI: 10.1103/PhysRevB.64.224517 - G.H. Gunarante, C.S. Rajapaksa, K.E. Bassler, K.K. Mohanty, and S.J. Wimalawansa, “A Model for Bone Strength and Osteoporotic Fracture,” Phys. Rev. Lett.
**88**, 068101 (2002).

DOI: 10.1103/PhysRevLett.88.068101 - E. Altshuler, O. Ramos, A.J. Batista-Leyva, A. Rivera, and K.E. Bassler, “Sandpile Formation by Revolving Rivers,” Phys. Rev. Lett.
**91**, 014501 (2003).

DOI: 10.1103/PhysRevLett.91.014501 - M. Anghel, Z. Toroczkai, K.E. Bassler, and G. Korniss “Competition-Driven Network Dynamics: Emergence of a Scale-free Leadership Structure and Collective Efficiency,” Phys. Rev. Lett.
**92**, 058701 (2004).

DOI: 10.1103/PhysRevLett.92.058701 - Z. Toroczkai and K.E. Bassler, “Jamming is Limited in Scale-Free Networks,” Nature
**428**, 716 (2004).

DOI: 10.1038/428716a - K.E. Bassler, C. Lee, and Y. Lee, “Evolution of Developmental Canalization in Networks of Competing Boolean Nodes,” Phys. Rev. Lett.
**93**, 038101 (2004).

DOI: 10.1103/PhysRevLett.93.038101 - E. Altshuler, T.H. Johansen, Y. Paltiel, P. Jin, K.E. Bassler, O. Ramos, G.F. Reiter, E. Zeldov, and C.W. Chu, “Experiments in Superconducting Vortex Avalanches,” Physica C
**408**, 501-504 (2004).

DOI: 10.1016/j.physc.2004.03.191 - E. Altshuler, T.H. Johansen, Y. Paltiel, P. Jin, K.E. Bassler, Q. Chen, O. Ramos, G.F. Reiter, E. Zeldov, and C.W. Chu, “Vortex Avalanches and Self Organized Criticality in Superconducting Niobium,” Phys. Rev. B
**70**, Rapid Communications, 140505 (2004).

DOI: 10.1103/PhysRevB.70.140505 - J.H. Li, D.W. Stokes, O. Caha, S.L. Ammu, J. Bai, K.E. Bassler, and S.C. Moss, “Morphological Instability in InAs/GaSb Superlattices Due to Interfacial Bonds,” Phys. Rev. Lett.
**95**, 096104 (2005).

DOI: 10.1103/PhysRevLett.95.096104 - G. Korniss, M.B. Hastings, K.E. Bassler, M.J. Berryman, B. Kozma, and D. Abbott, “Scaling in Small-World Resistor Networks,” Phys. Letts. A
**350**, 324-330 (2006).

DOI: 10.1016/j.physleta.2005.09.081 - A. Alejandro-Quinones, K.E. Bassler, M. Field, J.L. McCauley, M. Nicol, I. Timofeyev, A. Torok, and G. Gunaratne, “A Theory of Fluctuations in Stock Prices,” Physica A
**363**, 383-392 (2006).

DOI: 10.1016/j.physa.2005.08.037 - O. Caha, V. Holy, and K.E. Bassler, “Nonlinear Evolution of Surface Morphology in InAs/AlAs Superlattices via Surface Diffusion,” Phys. Rev. Letts.
**96**, 136102 (2006).

DOI: 10.1103/PhysRevLett.96.136102 - K.E. Bassler, G.H. Gunaratne, and J.L. McCauley, “Markov Processes, Hurst Exponents, and Nonlinear Diffusion Equations,” Physica A
**369**, 343-353 (2006).

DOI: 10.1016/j.physa.2006.01.081 - B. Danila, Y. Yu, S. Earl, J.A. Marsh, Z. Toroczkai, and K.E. Bassler, “Congestion-Gradient Driven Transport on Complex Networks,” Phys. Rev. E
**74**, 046114 (2006).

DOI: 10.1103/PhysRevE.74.046114 - M. Liu and K.E. Bassler, “Emergent Criticality from Coevolution in Random Boolean Networks,” Phys. Rev. E
**74**, 041910 (2006).

DOI: 10.1103/PhysRevE.74.041910 - B. Danila, Y. Yu, J.A. Marsh and K.E. Bassler, “Optimal Transport on Complex Networks,” Phys. Rev. E
**74**, 046106 (2006).

DOI: 10.1103/PhysRevE.74.046106 - J.L. McCauley, G.H. Gunaratne, and K.E. Bassler, “Hurst Exponents, Markov Processes, and Fractal Brownian Motion,” Physica A
**379**, 1-9 (2007).

DOI: 10.1016/j.physa.2006.12.028 - C.J. Olsen Reichhardt, and K.E. Bassler, “Canalization and Symmetry in Boolean Models for Genetic Regulatory Networks,” J. Phys. A: Math. Theor.
**40**, 4339 (2007).

DOI: 10.1088/1751-8113/40/16/006 - J.L. McCauley, G.H. Gunaratne, and K.E. Bassler, “Martingale Option Pricing,” Physica A
**380**, 351-356 (2007).

DOI: 10.1016/j.physa.2007.02.038 - B. Danila, Y. Yu, J.A. Marsh and K.E. Bassler, “Transport Optimization on Complex Networks,” Chaos
**17**, 026102 (2007).

DOI: 10.1063/1.2731718 - Y. Yu, B. Danila, J.A. Marsh and K.E. Bassler, “Transport Optimization on Wireless Networks,” Europhys. Lett.
**79**, 48004 (2007).

DOI: 10.1209/0295-5075/79/48004 - K.E. Bassler, J.L. McCauley, and G.H. Gunaratne, “Nonstationary Increments, Scaling Distributions, and Variable Diffusion Processes in Financial Markets,” Proc. Nat. Acad. Sci. USA
**104**, 17287-17290 (2007).

DOI: 10.1073/pnas.0708664104 - J.L. McCauley, K.E. Bassler, and G.H. Gunaratne, “Martingales, Detrending Data, and the Efficient Market Hypothesis,” Physica A
**387**, 202-216 (2008).

DOI: 10.1016/j.physa.2007.08.019 - K.E. Bassler, G.H. Gunaratne, and J.L. McCauley, “Dynamics of Real Financial Markets: A Response to Frank’s Comment,” Physica A
**387**, 3239-3241 (2008).

DOI: 10.1016/j.physa.2008.02.009 - J.L. McCauley, K.E. Bassler, and G.H. Gunaratne, “Martingales, Nonstationary Increments, and the Efficient Market Hypothesis,” Physica A
**387**, 3916-3920 (2008).

DOI: 10.1016/j.physa.2008.01.049 - Z. Toroczkai, B. Kozma, K.E. Bassler, N.W. Hengartner, and G. Korniss, “Gradient Networks,” J. Phys. A: Math. Theor.
**41**, 155103 (2008).

DOI: 10.1088/1751-8113/41/15/155103 - K.E. Bassler, G.H. Gunaratne, and J.L. McCauley, “Empirically Based Modeling in Finance and Beyond and Spurious Stylized Facts,” Int. Rev. Fin. Anal.
**17**, 767-783 (2008).

DOI: 10.1016/j.irfa.2008.02.002 - K.E. Bassler, P.J. Forrester, and N.E. Frankel, “Eigenvalue Separation in Some Random Matrix Models,” J. Math. Phys.
**50**, 033302 (2009).

DOI: 10.1063/1.3081391 - J.L. McCauley, G.H. Gunaratne, and K.E. Bassler, “Is Integration I(d) applicable to observed economics and financial time series,” Int. Rev. Fin. Anal.
**18**, 101-108 (2009).

DOI: 10.1016/j.irfa.2009.03.004 - Y. Sun, B. Danila, K. Josic, and K.E. Bassler, “Improved community structure detection using a modified fine tuning strategy,” EPL
**86**, 28004 (2009).

DOI: 10.1209/0295-5075/86/28004 - C.I. Del Genio, J. Trenkler, K.E. Bassler, P. Wochner, D.R. Haeffner, G.F. Reiter, J. Bai, and S.C. Moss, “Depth-dependent critical behavior in V
_{2}H,” Phys. Rev. B**79**, 184113 (2009).

DOI: 10.1103/PhysRevB.79.184113 - B. Danila, Y. Sun, and K.E. Bassler, “Collectively optimal routing for link capacity limited congested traffic,” Phys. Rev. E
**80**, 066116 (2009).

DOI: 10.1103/PhysRevE.80.066116 - C.I. Del Genio, K.E. Bassler, A.L. Korzhenevskii, R.I. Barabash, J. Trenkler, G.F. Reiter, and S.C. Moss, “Depth-dependent ordering, two length-scale phenomena, and crossover behavior in a crystal featuring a skin-layer with defects,” Phys. Rev. B
**81**, 144111 (2010).

DOI: 10.1103/PhysRevB.81.144111 - C.I. Del Genio, H. Kim, Z. Toroczkai, and K.E. Bassler, “Efficient and Exact Sampling of Simple Graphs with Arbitrary Given Degree Sequence,” PLoS ONE
**5**, e10012 (2010).

DOI: 10.1371/journal.pone.0010012 - J.H. Li, D.W. Stokes, J.C. Wickett, O. Caha, K.E. Bassler, and S.C. Moss, “Effect of Strain on the Growth of InAs/GaSb Superlattices: An X-Ray Study,” J. Appl. Phys.
**107**, 123504 (2010).

DOI: 10.1063/1.3429100 - C.I. Del Genio and K.E. Bassler, “Anomalous ordering in inhomogeneously strained materials,” Phys. Rev. E
**82**, 031115 (2010).

DOI: 10.1103/PhysRevE.82.031115 - M.D. Reichl, C.I. Del Genio and K.E. Bassler, “Phase diagram for a two-dimensional, twotemperature, diffusive XY model,” Phys. Rev. E
**82**, 040102 (2010), Rapid Communication.

DOI: 10.1103/PhysRevE.82.040102 - K.E. Bassler, P.J. Forrester, and N.E. Frankel, “Edge effects in some perturbations of the Gaussian unitary ensemble,” J. Math. Phys.
**51**, 123305 (2010).

DOI: 10.1063/1.3521288 - M. Liu and K.E. Bassler, “Finite Size Effects and Symmetry Breaking in the Evolution of Networks of Competing Boolean Nodes,” J. Phys. A: Math. Theor.
**44**, 045101 (2011).

DOI: 10.1088/1751-8113/44/4/045101 - C.I. Del Genio, T. Gross, and K.E. Bassler, “All scale-free networks are sparse,” Phys. Rev. Lett.
**107**, 178701 (2011).

DOI: 10.1103/PhysRevLett.107.178701 - M.D. Reichl and K.E. Bassler, “Canalization in the critical states of highly connected networks of competing Boolean nodes,” Phys. Rev. E.
**84**, 056103 (2011).

DOI: 10.1103/PhysRevE.84.056103 - H. Kim, C.I. Del Genio, K.E. Bassler, and Z. Toroczkai, “Constructing and sampling directed graphs with given degree sequence,” New J. Phys.
**14**, 023012 (2012).

DOI:10.1088/1367-2630/14/2/023012 - S. Trevino III, Y. Sun, T.F. Cooper, and K.E. Bassler, “Robust detection of hierarchical communities from Escherichia coli gene expression data,” PLoS Comput. Biol.
**8**, e1002391 (2012).

DOI: 10.1371/journal.pcbi.1002391 - S.K. Bhavnani, G. Bellala, S. Victor, K.E. Bassler, and S. Visweswaran, “The role of complementary bipartite visual analytical representation in the analysis of SNPs: A case study in ancestral informative markers,” J. Am. Med. Infom. Assoc.
**19**, e5 (2012).

DOI: 10.1136/amiajnl-2011-000745 - 67. B. Li, J. Li, K.E. Bassler, and C.S. Ting, “Magnetic and superconducting structures near twin boundaries in low doped Fe-pnictides,” New J. Phys.
**15**, 103018 (2013).

DOI: 10.1088/1367-2630/15/10/103018 - S. Hossein, M.D. Reichl, and K.E. Bassler, “Symmetry in Critical Random Boolean Network Dynamics,” Phys. Rev. E
**89**, 042808 (2014).

DOI: 10.1103/PhysRevE.89.042808 - S. Trevino, A. Nyberg, C.I. Del Genio, and K.E. Bassler, “Fast and accurate determination of modularity and its effect size,” J. Stat. Mech.: Theo. and Exper. P02003 (2015).

DOI: 10.1088/1742-5468/2015/02/P02003 - A. Nyberg, T. Gross, and K.E. Bassler, “Mesoscale structures and the Laplacian spectra of random geometic graphs,” J. Complex Networks
**3**, 543-551 (2015).

DOI: 10.1093/comnet/cnv004 - K.E. Bassler, W. Liu, B. Schmittmann, and R.K.P. Zia, “Extreme Thouless effect in a minimal model of dynamic social networks,” Phys. Rev. E
**91**, 042102 (2015).

DOI: 10.1103/PhysRevE.91.042102 - B. Li, L.H. Pan, Y.Y. Tai, M.J. Graf, J.X. Zhu, K.E. Bassler, and C.S. Ting, “Unified description of superconducting pairing symmetry in electron-doped Fe-based-122 compounds,” Phys. Rev. B
**91**, 220509 (2015).

DOI: 10.1103/PhysRevB.91.220509 - K.E. Bassler, D. Dhar, and R.K.P. Zia, “Networks with preferred degree: a mini-review and some new results,” J. Stat. Mech.: Theo. and Exper. P07013 (2015).

DOI: 10.1088/1742-5468/2015/07/P07013 - K.E. Bassler, C.I. Del Genio, P.L. Erdos, I. Miklos, and Z. Toroczkai, “Exact sampling of graphs with prescribed degree correlations,” New J. Phys.
**17**, 083052 (2015).

DOI: 10.1088/1367-2630/17/8/083052 - C. Orsini, M.M. Dankulov, P. Colomer-de-Simon, A. Jamakovic, P. Mahadevan, A. Vahdat, K.E. Bassler, Z. Toroczkai, M. Boguna, G. Caldarelli, S. Fortunato, and D. Krioukov, “Quantifying randomness in real networks,” Nature Comm.
**6**, 8627 (2015).

DOI: 10.1038/ncomms9627 - R. Chauhan, J. Ravi, P. Datta, T. Chen, D. Schnappinger, K.E. Bassler, G. Balazsi, and M.L. Gennaro, “Reconstruction and topological characterization of the sigma factor regulatory network of Mycobacterium tuberculosis,” Nature Comm.
**7**, 11062 (2016).

DOI: 10.1038/ncomms11062 - Y.Y. Zhou, B. Li, W. Li, H.Y. Chen, K.E. Bassler, and C.S. Ting, “Effects of single- and multisubstituted Zn ions in doped 122-type iron-based superconductors,” Phys. Rev. B
**93**, 144510 (2016).

DOI: 10.1103/PhysRevB.93.144510 - L. Chen, K.E. Bassler, J.L. McCauley, and G.H. Gunaratne, “Anomalous scaling of stochastic processes and the Moses effect,” Phys. Rev. E
**95**, 042141 (2017).

DOI: 10.1103/PhysRevE.95.042141 - K.E. Bassler and R.K.P. Zia, “Emergence of a spectral gap in a class of random matrices associated with split graphs,” J. Phys. A
**51**, 014002 (2018).

DOI: 10.1088/1751-8121/aa94a9 - T. Chen, P. Singh and K.E. Bassler, “Network community detection using modularity density measures,” J. Stat. Mech.: Theo. and Exper. 053406 (2018).

DOI: 10.1088/1742-5468/aabfc8 - S. Stolarczyk, M. Bhardwaj, K.E. Bassler, W.J. Ma and K. Josic, “Loss of information in feedforward social networks,” J. Complex Networks
**6**, 448-469 (2018).

DOI: 10.1093/comnet/cnx032 - S.K. Bhavnani, B. Dang, S. Visweswaran, K.E. Bassler, T. Chen, M. Raji, R. Divekar, A. Karmarkar, A. Tan, Y.-F. Kuo, and K. Ottenbacher, “How high-risk comorbidites co-occur in readmitted hip fracture patients: Implications for precision medicine and predictive modeling,” preprint.
- T. Paixao, K.E. Bassler, and R. Azevedo, “Emergent speciation by multiple Dobzhansky-Muller incompatibilities,” preprint, bioRxiv:008268.
- P. Meyer, V. Adlakha, H. Kantz, and K.E. Bassler, “Anomalous diffusion and the Moses effect in a model of aging,” preprint, arXiv:1808.08139.
- K.E. Bassler, E. Frey and R.K.P. Zia, “Co-evolution of nodes and links: diversity driven co-existence in cyclic competition of three species,” preprint, arXiv:1808.05875.
- R.K.P. Zia, W. Zhang, M. Ezzatabadipour, and K.E. Bassler, “Exact results for the extreme Thouless effect in a model of network dynamics,” preprint.

### Book Chapters and Conference Proceedings

- K.E. Bassler, “Critical Properties of Nonequilibrium Ising Systems,” in
*Computer Simulation Studies in Condensed Matter Physics VII*, eds. D.P. Landau, K.K. Mon, and H.-B. Schuttler, (Springer-Verlag, 1994). - K.E. Bassler and M. Paczuski, “Cellular Model of Superconducting Vortex Dynamics,” in
*Complexity from Microscopic to Macroscopic Scales: Coherence and Large Deviations*, A. Skjeltorp, ed. (Kluwer Academic Publishers, Dordrecht, 2001). - M. Anghel, Z. Toroczkai, G. Korniss, and K.E. Bassler, “Effect of Inter-Agent Communication on the Collective,” in
*Collectives and the Design of Complex Systems*, K. Turner and D.H. Wolpert, eds., (Springer, 2003). - T.J. Vadakkan and K.E. Bassler, “Phase Diagram and Clustering in an Anisotropic 3D Sandpile Model of Vortex Motion,” Proc. SPIE 5845, 72 (2005).

DOI: 10.1117/12.609506 - K.E. Bassler and M. Liu, “Effects of Stochastic Noise on the Evolution of Canalization,” Invited paper, Proc. SPIE 5845, 104 (2005).

DOI: 10.1117/12.609453 - A.L. Alejandro-Quinones, K.E. Bassler, J.L. McCauley, and G. Gunaratne, “A Theory of Fluctuations in Stock Prices: Effects of Discreteness,” Proc. SPIE 5848, 27 (2005).

DOI: 10.1117/12.609574 - J.L. McCauley, G.H. Gunaratne, and K.E. Bassler, “What Economists Should Learn from Econophysics,” in
*Dynamics of Complex Interconnected Systems, Networks and Bioprocesses*, A. Skjeltorp and A. Belyushkin, eds., (Springer, 2005). - K.E. Bassler and O. Caha, “Nonlinear Evolution of Surface Morphology in Short-Period Superlattices,” in
*Diffuse Scattering in the 21**st**Century: Emerging Insights into Materials Structure and Behavior*, (Momentum Press, 2009). - D. Dhar, K.E. Bassler, and R.K.P. Zia, “The many-agent limit of the Extreme Introvert-Extrovert model,” in Econophysics and Sociophysics: Recent Progress and Future Directions, F. Abergel, H. Aoyama, B.K. Chakrabarti, A. Chakraborti, N. Deo, D. Raina, and I. Vodenska, eds. (Springer, 2017).

### Reduced Network Extremal Ensemble Learning (RenEEL)

RenEEL is an algorithmic scheme for finding the network partition with maximum modularity, which is a challenging, NP-hard computational problem. It uses a Machine Learning method we call Extremal Ensemble Learning (EEL). The underlying idea of RenEEL is to first find an ensemble of partitions, then use information within the ensemble to efficiently find a new partition that is used to update the ensemble using extremal criteria. The updating continues until a consensus about what the best partition is is reached. Tests on benchmark networks have shown that RenEEL outperforms all other known methods for maximizing modularity.

RenEEL is a powerful and versatile scheme. It uses a conventional algorithm to find network partitions to create and update the ensemble. The C code in the GitHub respository linked to below uses a fast greedy agglomeration algorithm for this purpose, but any conventional algorithm could be used. RenEEL is presented in *Scientific Reports* **9**, 14234 (2019). Please cite that paper if you use the code, or some version of it.