Research

Curriculum Vitæ
Research
Teaching

Research Interests and Papers

My research interests include areas in both pure and applied mathematics. Recently, I have focused almost exclusively on applied topics, studying applications of network theory and modeling to problems in economics, neuroscience, sociology, political science, and psychology. My work in pure mathematics focuses on the study of the solutions of geometric partial differential equations in sub-Riemannian (or Carnot-Caratheodory) geometries.

Applied Mathematics

Journal Articles

Leibon, G., Pauls, S. D., Rockmore, D., and Savell, R. Topological Structures in the Equities Market Network. PNAS, 105:52 (2008), 20589-20594.
Pauls, S. D. Cortical Feature maps via Geometric models, J. Physiology (Paris), 103 (2009), 46-51.
Hlady, R. and Pauls, S. D. Minimal surfaces in the Roto-translation group with applications to a neuro-biological image completion model. J. Math. Imaging and Vision. 36:1 (2010), 1-34.
Braun, R., Leibon, G., Pauls, S. D., and Rockmore, D. Partition Decoupling for Multi-gene Analysis of Gene Expression Profiling Data. BMC Bioinformatics. 12:497 (2011).^a
Remondini, D. and Pauls, S. D. A notion of centrality based on the spectrum of the Laplacian. Phys. Rev. E., 85:066127 (2012).
Foti, N., Pauls, S. D., and Rockmore, D. Stability of the world trade network over time: an extinction analysis. J. Economic Dynamics and Control, 37:9 (2013), 1889-1910.
Pauls, S.D., Foley, N., Foley, D., Laautier, J., Hastings, M., Maywood, E., Silver, R. Differential contributions of intra- and inter-cellular mechanisms to spatial and temporal architecture of the suprachiasmatic nucleus circadian circuitry in wild-type, CRY- and VPAC2 –null mutant mice. Eur. J. Neuroscience. 40:3 (2014), 2528-2540.^b (Code and Data)
Davis, M., Anthony, D., and Pauls, S. D., Seeking and receiving social support on Facebook for surgery, Social Science & Medicine, 131 (2015) 40-47.
Pauls, S. D., Leibon, G., and Rockmore, D., The Social Identity Voting model: ideology and community structures, Research and Politics, April-June 2015, 1-11.
Pauls, S. D., 2015, Replication Data for: The Social Identity Voting model: ideology and community structures, Harvard Dataverse.
Brocklebank, S., Pauls, S. D., Rockmore, D., and Bates, T. C., A Spectral Clustering Approach to the Structure of Personality: Contrasting the FFM and HEXACO Models,” Journal of Research in Personality 57 (2015), 100-109. (doi:10.1016/j.jrp.2015.05.003)
Pauls, S. D., Honma, K-I., Honma, S., Silver, R., Deconstructing circadian rhythmicity with models and manipulations, Trends in Neuroscience, 49:6 (2016). 405-419.^b
Khoo, T., Fu, F., Pauls, S. D., Coevolution of Cooperation and Partner Rewiring Range in Spatial Social Networks, Nature Communications, 6 (2016). 36293.
DeFord, D. R. and Pauls, S. D.,A new framework for dynamics on multiplex networks, accepted, J. Complex Networks.
Pauls, S. D. and Cranmer, S., Affinity Communities in United Nations Voting: Implications for Conflict, Cooperation, and Democracy, Physica A, 484 (2017) 428-439.
Myung, J. and Pauls, S. D., Encoding seasonal information in a two-oscillator model of the multi-oscillator circadian clock, Eur. J. Neuroscience. (2017)
Leib-Lappan, R., Kumar, D., Obbard, R., and Pauls, S. D. A network model for characterizing brine channels in sea ice, under review, The Cryosphere.
DeFord, D. R. and Pauls, S. D., Spectral clustering methods for multiplex networks, under review.
Khoo, T., Fu, F., Pauls, S. D., Double-edged effect of spillover on cooperation in multiplex games, under review

^{a. Designated "Highly Accessed" for BMC Bioinformatics.↩}
^{b. The editorial board of EJN designated this the featured article for this issue of the journal.↩} ^{b. The editor designated this article a featured review for this issue of TINS.↩}

Books and Monographs

Leibon, G., Pauls, S. D., Rockmore, D., and Savell, R. Statistical Learning for Complex Systems. Under contract with Princeton University Press

Pure Mathematics

Journal Articles

Pauls, S. D. The large scale geometry of nilpotent Lie groups, Comm. Anal. Geom., 9 (2001), no. 5, 951-982.
Pauls, S. D. A notion of rectifiability modeled on Carnot groups, Indiana Univ. Math. J. 53 (2004), 49-82.
Pauls, S. D. Minimal surfaces in the Heisenberg group, Geom. Ded. 104 (2004), 201-231.
Cole, D. and Pauls, S. D. C¹ hypersurfaces of the Heisenberg group are N-rectifiable. Houston J. Math. 32:3 (2006), 713-724.
Pauls, S. D. H-minimal graphs of low regularity in H, Comm. Math. Helv. 81 (2006), 337-384.
Hladky, R. and Pauls, S. D. Constant mean curvature surfaces in sub-Riemannian geometry. J. Diff. Geom. 79:1 (2008), 111-139.
Danielli, D., Garofalo, N., Nhieu, D. M., and Pauls, S. D. Instability of graphical strips and a positive answer to the Bernstein problem in the Heisenberg group. J. Diff. Geom., 81:2 (2009), 251-296.
Capogna, L., Pauls, S. D. , and Tyson, J. Convexity in Carnot groups and the horizontal second fundamental form. Trans. Amer. Math. Soc. 362 (2010), 4045-4062.
Danielli, D., Garofalo, N., Nhieu, D. M., and Pauls, S. D. The Bernstein Problem for Embedded Surfaces in the Heisenberg Group H¹. Indiana University Journal of Mathematics, 59 (2010), 563-594.
Hladky, R. and Pauls, S. D. Area Variations in sub-Riemannian geometry. Int. Elec. J. Geom. 6:1 (2013), 8-40.

Books and Monographs

Capogna, L., Pauls, S. D. , and Tyson, J. An Introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem. Progress in Mathematics, volume 259. Birkhauser, 2007.

Other Publications

Cogswell, C., Pauls, S. D., Gauthier, A., DeSilva, E., Schroer, K., Agile and Active: Sustaining Pedagogical Change in a Large-Enrollment Calculus Course, accepted refereed paper for the 2017 ASHE Conference.

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Last modified on January 09, 2018