I studied Chemistry at the University of Siena and Philosophy at the University of Florence. I got my PhD from Bristol University, in the then newly created Quantum Computation and Information Group. My advisor was Richard Jozsa (whose advisor was Roger Penrose). I was a post-doctoral research fellow in the Institute for Quantum Computing and the Department of Combinatorics & Optimization at the University of Waterloo, where I was mentored by Michele Mosca. I worked at the University of York in the Department of Computer Science and the Department of Mathematics. I did hold a Newton International Fellowship at UCL. I was a visiting student at UC Berkeley, and a long term visitor (with various titles) in a number of places, including CRI, CWI, MIT, Nankai, NUS and RISC-Linz.

My interests are in Discrete Mathematics and its applications., and I like Quantum theory and Complex Systems (in a broad sense). In particular, I like the connections between graphs and formal or physical states and their dynamics, information theoretic quantities, and pattern analysis. According to MathSciNet (see also ZBMATH Database) I work in Combinatorics, Matrix theory, Quantum theory, Relativity and gravitational theory, Statistical mechanics, structure of matter. My papers can be accessed via arXiv, INSPIRE (High Energy Physics (HEP) information system), CiteSeerX, MPRA (Research Papers in Economics (RePEc)), and PubMed (Medical Literature Analysis and Retrieval System Online). Institutional Research Information System (IRIS) is the research portal for UCL.

At UCL, I am affiliated with the following groups Atomic, Molecular, Optical and Positron Physics Group (AMOPP) (UCL Quantum Information Initiative), CoMPLEX, and UCL Institute of Origins. Here is the page of our Complex Networks Interest Group. LCN is the London Centre for Nanotechnology. LINQS is the London Interdisciplinary Network for Quantum Science.

Written works

2012
• L.-C. Kwek, S. Severini, H.-B. Su (guest Eds.), Int. J. Mod. Phys. B: vol. ?? (2012).
• Z.-H. Chen, O. Guehne, Z.-H. Ma, S. Severini, Lower bounds to the concurrence for multi-partite states of arbitrary dimension, May 2012.
• S. Janson, S. Severini, An example of graph limits of growing sequences of random graphs, May 2012.
• T. H. Hall, S. Severini, Locality for quantum systems on graphs depends on the number field, April 2012. arXiv:1204.3681v1 [quant-ph]
• Z.-H. Chen, Z.-H. Ma, J.-L. Chen, S. Severini, Improved lower bounds on GME-concurrence, accepted for publication in Phys. Rev. A. arXiv:1205.3057v1 [quant-ph]
• H. Buhrman, P. T. S. van der Gulik, S. Severini, D. Speijer, Batch selection: gene scrambling counters gene-loss, February 2012.
• C. Godsil, S. Kirkland, S. Severini, J. Smith, Number-theoretic nature of communication in quantum spin chains, January 2012. arXiv:1201.4822v1 [quant-ph]

-2011
• J. West, L. Lacasa, S. Severini, A. E. Teschendorff, Approximate entropy of network parameters, Phys. Rev. E 85, 046111 (2012). arXiv:1201.0045v1 [cond-mat.dis-nn]
• J. West, G. Bianconi, S. Severini, A. E. Teschendorff, On dynamical network entropy in cancer, October 2011. arXiv:1202.3015v1 [q-bio.MN]
• K. Zhao, A. Halu, S. Severini, G. Bianconi, Entropy rate of non-equilibrium growing networks, Phys. Rev. E 84, 066113 (2011). arXiv:1109.0940v1 [cond-mat.dis-nn]
• D. Burgarth, D. D'Alessandro, L. Hogben, S. Severini, M. Young, Zero forcing, linear and quantum controllability for systems evolving on networks, July 2011. arXiv:1111.1475v1 [quant-ph]
• D. Burgarth, V. Giovannetti, L. Hogben, S. Severini, M. Young, Logic circuits from zero forcing, June 2011. arXiv:1106.4403v1 [cs.DM]
• G. Scarpa, S. Severini, On Kochen-Specker sets and the rank-1 quantum chromatic number, IEEE Trans. Inf. Theory, vol. 99 (2012). arXiv:1106.0712v1 [quant-ph]
• R. Duan, S. Severini, A. Winter, Zero-error communication via quantum channels and a quantum Lovasz theta function, to appear in IEEE Trans. Inf. Theory. This is the extended journal version of the following conference paper: Zero-error communication via quantum channels and a quantum Lovasz theta function, 2011 IEEE International Symposium on Information Theory (IEEE ISIT 2011). Available at IEEEXplore
• V. Giovannetti, S. Severini, The Kirchhoff's Matrix-Tree Theorem revisited: counting spanning trees with the quantum relative entropy, to appear in Advances in Network Complexity, A. Mowshowitz and M. Dehmer (Eds.), Wiley-VCH. arXiv:1102.2398v1 [quant-ph]
• W. van Dam, V. M. Kendon, S Severini (Eds.), Theory of Quantum Computation, Communication, and Cryptography, 5th Conference, TQC 2010, Leeds, UK, April 2010, Revised Selected Papers, Lecture Notes in Computer Science 6519, Springer.
• K. Anand, G. Bianconi, S. Severini, The Shannon and the Von Neumann entropy of random networks with heterogeneous expected degrees, Phys. Rev. E 83, 036109 (2011). arXiv:1011.1565v2 [cond-mat.dis-nn]
• A. Cabello, S. Severini, A. Winter, (Non)Contextuality of Physical Theories as an Axiom, October 2010. arXiv:1010.2163v1 [quant-ph]
• G. Gutin, M. Mansour, S. Severini, A characterization of horizontal visibility graphs and combinatorics on words, Physica A: Statistical Mechanics and its Applications, Volume 390, Issue 12, 15 June 2011, Pages 2421-2428. arXiv:1010.1850v1 [physics.data-an]
• S. Kirkland, S. Severini, Spin systems dynamics and faults detection in threshold networks, Phys. Rev. A 83, 012310 (2011). arXiv:1009.3394v1 [quant-ph]
• S. P. Jordan, T. Mansour, S. Severini, On the degeneracy of SU(3)_k topological phases, Russ. J. Math. Phys, Volume 19, Number 1, (2012) 21-26. arXiv:1009.0114v1 [math.CO]
• W. Du, X. Li, Y. Li, S. Severini, A note on the von Neumann entropy of random graphs, Linear Algebra Appl., 443: 11-12 (2010), 1722-1725.
• A. E. Teschendorff, S. Severini, Increased entropy of signal transduction in the cancer metastasis phenotype, BMC Systems Biology 2010, 4:104. arXiv:1007.0876v1 [q-bio.MN] Qualified as 'Highly accessed'; Featured.
• R. Duan, S. Severini, A. Winter, Zero-error communication via quantum channels, non-commutative graphs and a quantum Lovasz theta function, February 2010. arXiv:1002.2514v1 [quant-ph]
• S. Severini, The 3-dimensional cube is the only periodic, connected cubic graph with perfect state transfer, 2010 J. Phys.: Conf. Ser. 254 012012 (invited paper in “Quantum Groups, Quantum Foundations, and Quantum Information: a Festschrift for Tony Sudbery”). arXiv:1001.0674v1 [quant-ph]
• A. Casaccino, S. Mancini, S. Severini, Entanglement manipulation via dynamics in multiple quantum spin systems, Quantum. Inf. Process. June 07, 2010. arXiv:0912.5499v1 [quant-ph]
• A. Hamma, F. Markopoulou, F. Caravelli, S. Lloyd, S. Severini, K. Markstrom, A quantum Bose-Hubbard model with evolving graph as toy model for emergent spacetime, Phys. Rev. D 81, 104032 (2010). arXiv:0911.5075v2 [gr-qc]
• C. Godsil, S. Severini, Control by quantum dynamics on graphs, Phys. Rev. A 81, 052316 (2010). arXiv:0910.5397v1 [quant-ph]
• A. Cosentino, S. Severini, Weight of quadratic forms and graph states, Phys. Rev. A 80, 052309 (2009). arXiv:0906.2488v1 [quant-ph]
• F. Markopoulou, S. Severini, A note on observables for counting trails and paths in graphs, JMMA, Vol. 8, No. 3, 2009. arXiv:0906.0043v1 [math.CO]
• A. Casaccino, S. Lloyd, S. Mancini, S. Severini, Quantum state transfer through a qubit network with energy shifts and fluctuations, Int. J. Quantum Info 7:8, 1417-1427 (2009). arXiv:0904.4510v1 [quant-ph]
• T.-C. Wei, S. Severini, Matrix permanent and entanglement of permutation symmetric states, J. Math. Phys. 51, 092203 (2010). arXiv:0905.0012v1 [quant-ph]
• S. Vazquez, S. Severini, Perturbation theory in a pure exchange non-equilibrium economy, Phys. Rev. E 81, 036102 (2010). arXiv:0904.1402v1 [q-fin.TR]
• A. Hamma, D. Lidar, S. Severini, Entanglement and area law with a fractal boundary in a topologically ordered phase, Phys. Rev. A 81, 010102(R) (2010). arXiv:0903.4444v1 [quant-ph] [featured in PRB Kaleidoscope Images]
• D. Djokovic, S. Severini, F. Szöllösi, Rational Orthogonal versus Real Orthogonal, ELA, Vol. 18, pp. 649-673, October 2009. arXiv:0903.2853v1 [math.CO]
• S. Bose, A. Casaccino, S. Mancini, S. Severini, Communication in XYZ All-to-All Quantum Networks with a Missing Link, Int. J. Quantum Info., 2009, v.7, no. 3. arXiv:0808.0748v2 [quant-ph]
• A. Hamma, T. Mansour, S. Severini, Diffusion on an Ising Chain with Kinks, Phys. Lett. A., Volume 373, Issue 31 (2009), Pages 2622-2628. arXiv:0806.4812v1 [math.CO]
• S. Klavzar, S. Severini, Tensor 2-sums and entanglement, J. Phys. A: Math. Theor. 43 212001 Fast Track Comm. arXiv:0909.1039v2 [math.CO]
• S. Flammia, S. Severini, Weighing matrices and optical quantum computing, J. Phys A: Math. Theor. 42 065302 (2009). arXiv:0808.2057v1 [quant-ph]
• A. Hamma, F. Markopoulou, I. Premont-Schwarz, S. Severini, Lieb-Robinson bounds and the speed of light from topological order, Phys. Rev. Lett. 102, 017204 (2009). arxiv:0808.2495v1 [quant-ph]
• F. Passerini, S. Severini, The von Neumann entropy of networks, December 2008. arXiv:0812.2597v1 [cond-mat.dis-nn]. See also Quantifying complexity in networks: the von Neumann entropy, in John Symons and Jorge Louçã (Eds.): Social structures in communication networks, Int. J. Agent Tech. Sys., Vol. 1, Issue 4. A version with title “Quantifying Disorder in Networks: The von Neumann Entropy” has been published in the book “Developments in Intelligent Agent Technologies and Multi-Agent Systems: Concepts and Applications” (G. Trajkovski Ed.), IGI Global, 2011.
• D. Cheung , D. Maslov, S. Severini, Translation Techniques Between Quantum Circuit Architectures, unpublished (7 citations, 2011)
• A. Bernasconi, C. Godsil, S. Severini, Quantum Networks on Cubelike Graphs, Phys. Rev. A 78,052320 (2008). arXiv:0808.0510v1 [quant-ph]
• T. Mansour, S. Severini, Counting paths in Bratteli diagrams for SU(2)_k, EPL 86 33001. arXiv:0806.4809v1 [math.CO]
• M. Arzano, A. Hamma, S. Severini, Hidden entanglement at the Planck scale: loss of unitarity and the information paradox, Mod. Phys. Lett. A25:437-445, 2010. arXiv:0806.2145v1 [hep-th]. See also "A black hole's secret files: hiding information at the Planck scale", Essay for “The Gravity Research Foundation”, 2008.
• A. Casaccino, E. Galvao, S. Severini, Extrema of discrete Wigner functions and applications, Phys. Rev. A 78, 022310 (2008). arXiv:0805.3466v1 [quant-ph]
• S. Severini, Nondiscriminatory Propagation on Trees, J. Phys A: Math. Theor. 41 482002 (2008), Fast Track Comm. arXiv:0805.0181v1 [math.CO]
• T. Konopka, F. Markopoulou, S. Severini, Quantum Graphity: a model of emergent locality, Phys. Rev. D. 77, 104029 (2008). arXiv:0801.0861v1 [hep-th]. See also the Cover Story of New Scientist magazine, 3 May, 2008. Marshall, Michael (4 March 2010), "Knowing the mind of God: Seven theories of everything", New Scientist.
• M. Batty, A. Casaccino, A. Duncan, S. Rees, S. Severini, An application of the Deutsch-Jozsa algorithm to formal languages and the word problem for groups, LNCS 5106, Springer, 2008. arXiv:0801.2801v1 [quant-ph]
• D. Emms, S. Severini, R. Wilson, E. Hancock, Overcoming cospectrality of graphs and trees via coined quantum walks, Pattern Recognition, Vol 42, Issue 9 (2008), 1988-2002.
• R. Hildebrand, S. Mancini, S. Severini, Combinatorial laplacians and positivity under partial transpose, Math. Struct. in Comp. Science (2008), vol. 18, pp. 205–219. arXiv:cs.CC/0607036
• M. Schork, T. Mansour, S. Severini, Noncrossing normal ordering for functions of boson operators, Internat. J. Theoret. Phys., Vol. 47, No 3 (2008), 832-849. arXiv:quant-ph/0607074
• Q.-H. Hou, T. Mansour, S. Severini, Partial transpose of permutation matrices, Integers, The Electronic Journal of Combinatorial Number Theory, Vol. 8:1, (2008). arXiv:0709.3547v1 [math.CO]
• S. Severini, F. Szöllösi, A further look into combinatorial orthogonality, ELA, Vol. 17 (2008) pp. 376-388. arXiv:0709.3651v1 [math.CO]
• M. Schork, T. Mansour, S. Severini, A generalization of the boson normal ordering, Phys. Letters A, 364 (2007). arXiv:quant-ph/0608081v2
• S. Braunstein, S. Ghosh, S. Severini, Estimation of pure qubits on circles, J. Phys. A: Math. Theor. 40 (2007) 1809-1834. arXiv:quant-ph/0412101v1 [IOP Select - Best papers of 2006]
• L. Clarisse, S. Ghosh, A. Sudbery, S. Severini, The disentangling power of unitaries, Physics Letters A, 365 (2007). arXiv:quant-ph/0611075v2
• S. Mancini, S. Severini, The Quantum Separability Problem for Gaussian States, Electron. Notes Theor. Comput. Sci., 169, Elsevier Sci. B. V., Amsterdam, 2007. arXiv:cs/0603047v2 [cs.CC]
• G. Gutin, A. Rafiey, S. Severini, A. Yeo, Hamilton Cycles in Digraphs of Unitary Matrices, Discrete Appl. Math. 173 (2006), no. 1-3, 67-78. arXiv:math/0409228v2 [math.CO]
• S. Severini, Universal quantum computation with unlabeled qubits, J. Phys. A: Math. Theor. 39 (2006) 8507-8515. arXiv:quant-ph/0601078v3
• D. Emms, S. Severini, R. Wilson, E. Hancock, A matrix representation of graphs and its spectrum as a graph invariant, The Electronic Journal of Combinatorics, R34, Volume 13(1), 2006. arXiv:quant-ph/0505026v2
• S. Severini, On the structure of the adjacency matrix of the line digraph of a regular digraph, Discrete Appl. Math. 154 (2006), no 12, 1663-1665. arXiv:quant-ph/0210055v3
• S. Braunstein, S. Ghosh, S. Severini, The laplacian of a graph as a density matrix: a basic combinatorial approach to separability of mixed states, Ann. Comb., 10:3 (2006), 291-317. arXiv:quant-ph/0406165v2
• T. Mansour, S. Severini, Grid polygons from permutations and their enumeration by the kernel method, Proceedings of The 19th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC2007), July 2-6, 2007. Nankai University, Tianjin, China. arXiv:math/0603225v1 [math.CO]
• S. Severini, Two-colorable graph states with maximal Schmidt measure, Physics Letters A, 356 (2006). arXiv:quant-ph/0511147v1
• T. J. Osborne, S. Severini, Quantum Algorithms and Covering Spaces, Quantum Computers and Computing, 6:1 (2006), 1-22. arXiv:quant-ph/0403127v3
• S. Braunstein, S. Ghosh, T. Mansour, S. Severini, R. Wilson, Some families of density matrices for which separability is easily tested, Phys. Rev. A, 73:1, 012320 (2006). arXiv:quant-ph/0508020v3
• D. Emms, S. Severini, R. Wilson, E. Hancock, Coined quantum walks lift the cospectrality of graphs and trees, Pattern Recognition, 42:9 (2009), 1988-2002. ACM Digital Library
• C. Bebeacua, T. Mansour, A. Postnikov, S. Severini, On the X-rays of permutations, ENDM, Vol. 20, 2005. arXiv:math/0506334v1 [math.CO] [Featured in Jeux et Mathématiques]
• N. Grayson , T. Keef, S. Severini, R. Twarock, Self-Assembly of Viral Capsids via a Hamiltonian Paths Approach: The Case of Bacteriophage MS2, Foundations of Nanoscience (FNANO) 2007. poster
• L. Clarisse, S. Ghosh, S. Severini, A. Sudbery, Entangling power of permutations, Phys. Rev. A 72, 012314 (2005). arXiv:quant-ph/0502040v2
• K. B. Reid, R. Lundgren, S. Severini, D. Stewart, Quadrangularity and Strong Quadrangularity in Tournaments, Australas. J. Combin. 34 (2006), 247-260. arXiv:math/0409474v1 [math.CO]
• G. Gutin, N. Jones, A. Rafiey, S. Severini, A. Yeo, Mediated Digraphs and Quantum Nonlocality, Discrete Appl. Math. 150 (2005), no. 1-3, 41-50. arXiv:math/0411653v2 [math.CO]
• S. Severini, Graphs of unitary matrices, Ars Comb., XC, January 2009. arXiv:math/0303084v3 [math.CO]
• S. Severini, On the digraph of a unitary matrix, SIAM J. Matrix Anal. Appl. (SIMAX), 25:1 (2003), 295-300. arXiv:math/0205187v2 [math.CO]
• T. Mansour, S. Severini, Enumeration of (k,2)-noncrossing partitions, Discrete Math. 308:20 (2008) 4570-4577. arXiv:0808.1157v1 [math.CO]
• N. Saxena, S. Severini, I. Shparlinski, Parameters of circulant integral graphs and periodic quantum dynamics, Int. J. Quantum Info 5, 417-430 (2007). arXiv:quant-ph/0703236v1
• M. Schork, T. Mansour, S. Severini, Wick’s theorem for q-deformed boson operators, J. Phys. A: Math. Theor. 40 (2007) 8393-8401. arXiv:quant-ph/0703086v1
• P. J. Cameron, A. Montanaro, M. Newman, S. Severini, A. Winter, On the quantum chromatic number of a graph, The Electronic Journal of Combinatorics, R81 of Volume 14(1), 2007. arXiv:quant-ph/0608016v3

Selected meetings

• The 8^th Conference on Theory of Quantum Computation, Communication and Cryptography, TQC2013, Guelph, Canada, 2013. (Programme Committee Chair)
• Quantum Africa 2, September 3-7, 2012, KwaZulu-Natal, South Africa. (Invited speaker)
• Quantum Physics of Information, Summer School & Workshop, Shanghai Jiao-Tong University, 22-28 August 2012. (Program committee)
• 2012 SIAM Conference on Applied Linear Algebra, June 18th-22nd, Valencia, Spain. (Invited speaker)
• The 2012 South African School and Workshop on Theoretical Aspects of Quantum Information and Quantum Computing, African Institute for Mathematical Sciences, AIMS, Cape Town, South Africa. (Lecturer)
• First Cambridge Networks Day, The Sainsbury Laboratory, Cambridge, 18 May. (Invited Speaker)
• Royal Society Kavli Centre - Complex Networks Meeting, 28-29 May 2012. (Invited participant/speaker)
• Quantum Technologies Programme 2012, Cumberland Lodge, Windsor, UK, 2-4 April, 2012. (Speaker)
• BAMC 2012, British Applied Mathematics Colloquium 2012, 27-29 March 2012. Minisymposium “Quantum Information”. (Invited speaker)
• Operator structures in quantum information theory, Banff International Research Station for Mathematical Innovation and Discovery, Banff, Alberta, Canada, 26 February -2 March, 2012. (Invited participant)
• Interdisciplinary Symposium on Complex Systems, September 19-25, 2012, Kos Island, Greece. (Programme committee) Alan Turing Year
• Joint Mathematics Meetings, AMS Special Session on Matrices and Graphs, and AMS Special Session on Mathematical Theory of Control of Quantum Systems, John B. Hynes Veterans Memorial Convention Center, Boston Marriott Hotel, and Boston Sheraton Hotel, Boston, MA, January 4-7, 2012. (Invited speaker)

• Newton International Fellowship Day, The Royal Society, 25 October 2011. (Invited speaker / Q&A panelist)
• UCL Town Meeting – Quantum Information and Quantum Technology, Wednesday, November 9, 2011. (Programme comittee)
• 2011 Workshop on Algebraic Combinatorics, 15-18 September 2011, Shanghai Jiao-Tong University. (Invited speaker)
• Quantum Information Workshop, Benasque, Centro de Ciencias de Benasque Pedro Pascual, July 2011. (Participant)
• Quantum Information: Codes, Geometry and Random Structures, Centre de recherches mathematiques (CRM), Montreal, 24-26/10, 2011. (Invited speaker)
• 14^th Workshop in Quantum Information Processing, QIP2011, 10-14 January, 2011, Singapore. Presentation Pdf (Contributed talk)
• Algebraic Graph Theory Workshop, Banff International Research Station for Mathematical Innovation and Discovery, Banff, Alberta, Canada, 24-29 April, 2011. (Invited Speaker)
• Annual International Academic Conference on Quantum and Molecular Computing, QMC 2011, Singapore, 15-16 August 2011. (Technical Committee)
• EuroComb'11, Budapest, August 29-September 2, 2011, Rényi Institute. (Referee)
• 7th Slovenian International Conference on Graph Theory, Bled, Slovenia, June 19-24, 2011. Mini-symposium: Information Theory of Graphs (Invited speaker)
• 5th Asian-Pacific Conference on Quantum Information Science, in conjunction with the Festschriff in honour of Vladimir Korepin, Singapore, 25-28 May 2011. (Programme Committee)
• 3rd biennial Canadian Discrete and Algorithmic Mathematics Conference (CanaDAM) May 31-June 3, 2011, University of Victoria, BC, Canada. (Invited speaker)
• Interdisciplinary Symposium on Complex Systems, 9th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM), Halkidiki, Greece, September 19-25, 2011. (Programme Committee)
• The 6th Conference on Theory of Quantum Computation, Communication and Cryptography, TQC2011, Madrid, 24-26 May 2011. (Programme Committee)
• The 5th Conference on Theory of Quantum Computation, Communication and Cryptography, TQC2010, University of Leeds, 13-15 April, 2010. (Co-chair of the Programme Committee together with Wim van Dam)
• The 3th Conference on Theory of Quantum Computation, Communication and Cryptography, TQC2008, The University of Tokyo, January 30-1 February, 2008. (Contributed talk)
• International Program on Quantum Information (IPQI), Institute of Physics, Bhubaneswar, Orissa, India, Jan 4th-30th, 2010. (Invited lecturer)
• Collaborative Research Group for Mathematics of Quantum Information, Pacific Institute for Mathematics Sciences (PIMS), Vancouver, BC, 2010-2012. (Affiliate)
• The 19th International Linear Algebra Society Conference, ILAS 2010, Pisa, 21-25 June, 2010. Mini-symposium: Linear Algebra and Quantum Information Processing. (Programme Committee)
• DocSpot: Monsters From The Id, The Barbican, London, 26 May 2010. (Q&A panelist)
• AMS 2010 Fall Southeastern Section Meeting, Richmond, VA, November 6-7, 2010. Special Session on Minimum Rank Problems. (Invited Speaker)
• VideoClocks Workshop, NABA, The New Academy of Fine Arts, Milan (24 hours workshop), December 2009. (Lecturer with Giuseppe Ragazzini)
• CombPhys II: "Quantum and Combinatorics" (Zakopane, Poland, 2009). (Invited speaker)
• Italian Quantum Information Science Conference, 2009, 5-8 November 2009, Scuola Normale Superiore, Pisa, Italy. (Contributed talk)
• Italian Quantum Information Science Conference, 2008, 24-29 October 2008, Palazzo Ducale, Camerino, Italy. (Contributed talk)
• CMS/CSHPM Summer Meeting 2009. Memorial University of Newfoundland, St. John's, Newfoundland, June 6 - 8, 2009. (Invited speaker: Scientific Session on Algebraic Combinatorics)
• Quantum Information and Graph Theory: emerging connections, Perimeter Institute for Theoretical Physics, April 28 - May 2, 2008. (Organizing Committee)
• Joint International Meeting of the AMS and Shanghai Math Society, December 17-21, 2008, Shanghai, Peoples Republic of China. (Invited speaker: Special Session on Combinatorics and Discrete Dynamical Systems)
• Emergent Gravity, August 25-29, 2008, Massachusetts Institute of Technology / Center for Theoretical Physics.
• 2007 International Conference on Combinatorial Physics, 24-27 November, Krakow, Poland. (Invited speaker)
• The 19th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC2007), July 2-6, 2007, Nankai University, Tianjin, China. (Contributed talk)
• QCQC-2007, Centre for Theoretical Studies, IIT Kharagpur, India, December 11-13, 2007. (Invited speaker)
• ERATO conference on Quantum Information Science 2005, August 26-30, 2005 - National Museum of Emerging Science and Innovation "Nihon Kagaku Miraikan", JST, Tokyo, Japan. (Contributed talk)
• KIAS-KAIST Workshop on Quantum Information Science, Seoul, 22-24 August 2005. (Invited speaker)
• 20th British Combinatorial Conference University of Durham, 11-15 July 2005. (Contributed talk)
• Rutgers Experimental Mathematics Seminar, 16 June, 2005, Rutgers University, Department of Mathematics and the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS). (Invited speaker; host: Doron Zeilberger)
• 1st Asia-Pacific Conference on Quantum Information Science, Tainan, Taiwan, December 10-13, 2004. (Invited speaker)
• Fifth Haifa Workshop on Interdisciplinary Applications of Graph theory, Combinatorics, and Algorithms (Honoring Michael O. Rabin), May 16-19, 2005, CRI, Haifa. (Invited speaker)
• The Third Haifa Workshop on Interdisciplinary Applications of Graph, Combinatorics, and Algorithms (Honoring Peter Hammer), May 27-29, 2003, 2003, CRI, Haifa. (Contributed talk)
• Workshop on Permutation Patterns, May 29–June 3, 2005, University of Haifa, Israel. (Invited speaker)
• Eurocomb'03, Prague, Czech Republic, 8-12 September, 2003. (Contributed talk)

Collaborators

Current

• Name Surname (Postdoctoral Research Associate in Adiabatic Quantum Computation, EPSRC; London Centre for Nanotechnology (Paul Warburton) and CS). Apply here!
• Name Surname (PhD, EngD, EPRSC/Arup; Project team: Licia Capra (CS), Muki Haklay (Civil, Environmental and Geomatic Engineering), Duncan Wilson (Arup Foresight)), Sept 25 2012 – Sept 24 2016). Apply here!
• James West (PhD., CoMPLEX; Network Physics and Cancer Systems Biology; LSS: AET), 2010-2013

Former

• Bobby Bentham (MRes Project CP3; CoMPLEX; Perturbations of Networks and the Transition to Cancer. Life Science supervisor (LSS): Andrew Teschendorff (AET)), 2012
• Thomas Wyatt (MRes Project CP3; CoMPLEX; Closed Walks in Biological Networks. LSS: AET), 2012
• Tim Lucas (MRes Project CP2; CoMPLEX; LSS: AET; Subgraphs in Cancer Research)
• Christopher Banerji (MRes Project; CoMPLEX; CP2, LSS: AET; Information Theoretic Models for Oncogenically Perturbed Biological Networks. CP3, LSS: Sophia Tsoka (King's College London); The Underlying Geometry of Complex Weighted Networks and Applications to the Analysis of Complex Disease)
• Opponent at the Disputas (Ph.d.-grad) of Ramji Rahaman (Study of nonlocal correlations and entanglement in the context of quantum information Processing), The Faculty of Mathematics and Natural Sciences, University of Bergen.
• Sophie Atkinson (MRes Project; CoMPLEX; LSS: AET; Applying networks and graphs theory to breast cancer genomics; now: PhD student with Jürg Bähler; Elia Stupka and Robin Ketteler, Roles of non-coding RNAs in cellular lifespan of fission yeast)
• Alessandro Cosentino (MSci in Computer Science, Pisa; On some combinatorial properties of graph states, co-supervised with Anna Bernasconi; now: PhD student with John Watrous, IQC)
• Tommaso Gagliardoni (MSci in Mathematics, Perugia, Classical simulation of quantum circuits, co-supervised with Marco Baioletti; now: PhD student at the Centre for Advanced Security Research Darmstadt)
• Andrea Casaccino (PhD in Information Engineering, Siena/MIT; Quantum computation and communication with qubit systems, co-supervised with Enrico Martinelli; now at General Electric Energy)
• Si Bing (MSci in Computer Science, Bristol; Genetic algorithms for weighing and Hadamard matrices, co-supervised with Tim Kovacs)

Academic visitors

• Zhihao Ma (Department of Mathematics, Shanghai Jiao Tong University), Oct 2011- Sept 2012

Coauthors

Adan Cabello, Alessandro Cosentino, Alexander Postnikov, Alioscia Hamma, Anders Yeo, Andrea Casaccino, Andreas Winter, Andrew Duncan, Andrew Teschendorff, Anna Bernasconi, Anthony Sudbery, Arash Rafiey, Arda Halu, Ashley Montanaro, Cecilia Bebeacua, Chris Godsil, Daniel Burgarth, Daniel Lidar, David Emms, David Speijer, Domenico D'Alessandro, Dragomir Djokovic, Dustin Stewart, Edwin Hancock, Ernesto Galvao, Ferenc Szöllosi, Filippo Passerini, Fotini Markopoulou, Francesco Caravelli, Giannicola Scarpa, Ginestra Bianconi, Gregor Tanner, Gregory Gutin, Harry Burhman, H. Tracy Hall, Igor Shparlinski, Isabeau Premont-Schwarz, J.-L. Chen, J. Lundgren, James West, Jamie Smith, K. B. Reid, Kartik Anand, Klas Markstrom, Kun Zhao, Leslie Hogben, Lieven Clarisse, Lucas Lacasa, Matthias Schork, Michael Young, Michele Arzano, Mike Batty, Mike Newman, Nick Grayson, Nick Jones, Nitin Saxena, Otfried Guehne, Peter J. Cameron, Peter van der Gulik, Q.-H. Hou, Reidun Twarock, Richard Wilson, Roland Hildebrand, Runyao Duan, Samuel Vazquez, Samuel Braunstein, Sandi Klavzar, Sarah Rees, Seth Lloyd, Sibasish Ghosh, Sougato Bose, Stefano Mancini, Stephen Jordan, Stephen Kirkland, Svante Janson, Tobias Osborne, Tom Keef, Tomasz Konopka, Toufik Mansour, Tzu-Chieh Wei, Vittorio Giovannetti, Vivien Kendon, W. Du, Wim van Dam, X. Li, Y. Li. Zhihua Chen, Zhihao Ma. (88)

My Erdős number is 2 (P. J. Cameron → Erdős; C. Godsil → Erdős).

Teaching/slides

Teaching

“Not only God knows, I know, and by the end of the semester, you will know.” (Sidney Coleman)

• May 2012: Network Theory and Applications to Genomics (CoMPLEX module). The module is subdivided into two parts: (1) Maths part; (2) Bio part. Below are PDF slides to guide the study of the Maths part:

1. Structural graph theory: General references, Graphs, Subgraphs, Induced subgraphs, Spanning subgraphs, Isomorphisms, Degrees, Degree distributions, Regular, Complete graphs, Cliques, Paths and cycles, Connectedness, Domination, Independence, Hamiltonicity, Walks and tours, Eulerian graphs, Diameter, Clustering coefficient, Minors, Trees, Spanning trees, Chromatic number, Girth, Bipartite graphs, Complete bipartite graphs, Star graphs, Perfect graphs, Matchings, Edge cuts, Vertex/edge connectivity, Genus, Euler's formula, Four colour theorem, Thickness, Bridges, Graph products, Line graphs, Betweeness centrality, Assortativity, Regularity Lemma, Ramsey numbers, Max-Flow Min-Cut, Visibility graphs, Intersection graphs, Graph widths.
2. Algebraic graph theory: General references, Automorphism group, Frucht's Theorem, Adjacency matrix, Adjacency spectrum, Spectral indices, Strongly regular graphs, Expansion, Laplacian matrix, Laplacian spectrum, Algebraic connectivity, Random walks, Mixing/hitting, Kemeny constant, Cayley graphs, Circulant graphs, Ihara zeta function, Grover matrix, Zero-error information, Shannon capacity and Lovász number, PageRank, Colin de Verdière parameter, Control theory on graphs, Spectral bisection algorithm, Spectral graph drawing, Quantum walks, Clustering, Geometric graphs, Community structure eigenvectors, Cheeger's inequality, Optimizing random walks, Spielman-Teng sparsifiers, Chew's spanners. […]
3. Real-world graphs: work in progress.

Slides

• Networks Through a Quantum Lens, Cambridge Networks Network Day 2012.
• Networks 101, Computer Science Reading Group, UCL, Sept 2011. [A very basic intro to the networks' landscape.]
• 14^th Workshop in Quantum Information Processing, QIP2011, 10-14 January, 2011, Singapore. (Non-)Contextuality of Physical Theories as an Axiom (Contributed talk).

Refereeing

I served as a referee for the following journals:

IEEE Transactions in Information Theory, Information Processing Letters, Physical Review Letters, Physical Review A, Physical Review E, Physical review D, Quantum Information and Computation, Journal of Physics A: Mathematical and Theoretical, New Journal of Physics, Physics Letters A, Physics Letter B, Physica A, Physica D, Journal of Mathematical Physics, Europhysics Letters, Chinese Physics Letters, Acta Mathematica Sinica, International Journal of Quantum Information, International Journal of Theoretical Physics, Journal of Difference Equations and Applications, PLoS ONE, Discrete Mathematics, Computers & Mathematics with Applications, Discrete and Applied Mathematics, Electronic Journal of Combinatorics, European Journal of Combinatorics, The Australasian Journal of Combinatorics, Applicable Analysis and Discrete Mathematics, Automatica, Applied Mathematics Letters, Journal of Statistical Mechanics, Journal of Machine Learning Research, Central European Journal of Mathematics, Linear Algebra and its Applications, Pure Mathematics and Applications.

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Quantum information and graphs

In 2008, at Perimeter Institute for Theoretical Physics, we organized a conference titled Quantum Information and Graph Theory: emerging connections. Below is an incomplete list of references on this topic (Oct 2011):

Graph states:

• R. Raussendorf, D.E. Browne, H.J. Briegel, Measurement-based quantum computation with cluster states, Phys. Rev. A 68, 022312 (2003). arXiv:quant-ph/0301052v2
• M. Hein, W. Dür, J. Eisert, R. Raussendorf, M. Van den Nest, H.-J. Briegel, Entanglement in Graph States and its Applications, Proceedings of the International School of Physics "Enrico Fermi" on "Quantum Computers, Algorithms and Chaos", Varenna, Italy, July, 2005. arXiv:quant-ph/0602096v1

State transfer on spin systems:

• M. Christandl, N. Datta, T. C. Dorlas, A. Ekert, A. Kay, A. J. Landahl, Perfect Transfer of Arbitrary States in Quantum Spin Networks, Phys. Rev. A 71, 032312 (2005). arXiv:quant-ph/0411020v2
• C. Godsil, State Transfer on Graphs, 2011. arXiv:1102.4898v2 [math.CO]

Quantum expanders:

• A. Ben-Aroya, A. Ta-Shma, Quantum expanders and the quantum entropy difference problem, 2007. arXiv:quant-ph/0702129v3
• A. W. Harrow, R. A. Low, Efficient Quantum Tensor Product Expanders and k-designs, Proceedings of RANDOM 2009, LNCS, 5687:548-561, 2009. arXiv:0811.2597v3 [quant-ph]

Quantum walks:

• D. Aharonov, A. Ambainis, J. Kempe, U. Vazirani, Quantum walks on graphs, Proceedings of ACM Symposium on Theory of Computation (STOC'01), July 2001, p. 50-59.
• A. Ambainis, Quantum walks and their algorithmic applications, International Journal of Quantum Information, 1:507-518, 2003. arXiv:quant-ph/0403120v3.
• M. Mohseni, P. Rebentrost, S. Lloyd, A. Aspuru-Guzik. Environment-assisted quantum walks in photosynthetic energy transfer, Journal of Chemical Physics 129, 174106 (2008). arXiv:0805.2741v2 [quant-ph]
• A. M. Childs, Universal computation by quantum walk, Phys. Rev. Lett. 102, 180501 (2009). arXiv:0806.1972v1 [quant-ph]

Quantum graphs:

• T. Kottos and U. Smilansky, Quantum Chaos on Graphs, Phys. Rev. Lett. 79, 4794-797, (1997).
• U. Smilansky, Quantum chaos on discrete graphs, 2007. arXiv:0704.3525v1 [math-ph]

Graphs of unitary matrices:

• L. Deaett, The minimum semidefinite rank of a triangle-free graph, Linear Algebra and its Applications 434 (2011), 1945-1955.
• T. J. Osborne, Approximate Locality for Quantum Systems on Graphs, Phys. Rev. Lett. 101, 140503 (2008). arXiv:quant-ph/0611231v2

Complexity metrics:

• R. Jozsa, On the simulation of quantum circuits, 2006. arXiv:quant-ph/0603163v1
• I. L. Markov, Y. Shi, Simulating quantum computation by contracting tensor networks, SIAM Journal on Computing, 38(3):963-981, 2008. arXiv:quant-ph/0511069v7
• D. Aharonov, Z. Landau, J. Makowsky, The quantum FFT can be classically simulated, 2006, arXiv:quant-ph/0611156v2

Isomorphism (via encoding):

• K. Audenaert, C. D. Godsil, G. F. Royle, T. Rudolph, Symmetric squares of graphs, J. Comb. Theory, Ser. B 97(1): 74-90 (2007). arXiv:math/0507251v1 [math.CO]
• J. K. Gamble, M. Friesen, D. Zhou, R. Joynt, S. N. Coppersmith, Two-particle quantum walks applied to the graph isomorphism problem. Phys. Rev. A, 81(5):052313, 2010. arXiv:1002.3003v1 [quant-ph]

Network coding:

• M. Hayashi, K. Iwama, H. Nishimura, R. Raymond, and S. Yamashita. Quantum network coding. In STACS 2007, volume 4393 of Lecture Notes in Computer Science, pages 610–621, 2007. arXiv:quant-ph/0601088v2
• D. Leung, J. Oppenheim, and A.Winter. Quantum network communication — the butterfly and beyond. IEEE Transactions on Information Theory, 56(7):3478–3490, 2010. arXiv:quant-ph/0608223v5

Complex networks:

• S. Perseguers, M. Lewenstein, A. Acín, J. I. Cirac, Quantum complex networks, Nature Physics 6, 539 - 543 (2010). arXiv:0907.3283v1 [quant-ph]

Graphs as channels:

• T. S. Cubitt, D. Leung, W. Matthews, A. Winter, Improving zero-error classical communication with entanglement, Phys. Rev. Lett., 104(23):230503, 2010. arXiv:0911.5300v2 [quant-ph]
• D. Leung, L. Mancinska, W. Matthews, M. Ozols, A. Roy, Entanglement can increase asymptotic rates of zero-error classical communication over classical channels, 2010. arXiv:1009.1195v2 [quant-ph]

Quantum colouring:

• C. Godsil, M. W. Newman, Coloring an Orthogonality Graph, SIAM J. Discrete Math. 22(2): 683-692 (2008). arXiv:math/0509151v1 [math.CO]
• J. Fukawa, Hi. Imai, F. Le Gall, Quantum Coloring Games via Symmetric SAT Games. Presented as a long talk at the 11th Asian Quantum Information Science Conference (AQIS 2011).

Background independent models of quantum gravity:

• A. Hamma, F. Markopoulou, Background independent condensed matter models for quantum gravity, New J. Phys. 13:095006, 2011. arXiv:1011.5754v1 [gr-qc]
• F. Caravelli, F. Markopoulou, Properties of quantum graphity at low temperature, Phys. Rev. D 84 024002, 2011. arXiv:1008.1340v3 [gr-qc]

Zero-error quantum information

I like zero-error quantum information. Here is a list of references:

• Jianxin Chen, Toby S. Cubitt, Aram W. Harrow, Graeme Smith, Entanglement can completely defeat quantum noise, Phys. Rev. Lett. 107, 250504 (2011). arXiv:1109.0540v1 [quant-ph]
• Giannicola Scarpa, Simone Severini, Kochen-Specker Sets and the Rank-1 Quantum Chromatic Number, IEEE Trans. Inf. Theory, 99 (2011). arXiv:1106.0712v1 [quant-ph]
• G. Kuperberg, N. Weaver, A von Neumann Algebra Approach to Quantum Metrics/Quantum Relations, Memoirs of the AMS 215 (2012).
• Debbie Leung, Laura Mancinska, William Matthews, Maris Ozols, Aidan Roy, Entanglement can increase asymptotic rates of zero-error classical communication over classical channels. arXiv:1009.1195v2 [quant-ph]
• Toby S. Cubitt, Debbie Leung, William Matthews, Andreas Winter, Zero-error channel capacity and simulation assisted by non-local correlations, IEEE Trans. Info. Theory, Volume 57, Issue 8, pages 5509 - 5523 (Aug 2011). arXiv:1003.3195v2 [quant-ph]
• Runyao Duan, Simone Severini, Andreas Winter, Zero-error communication via quantum channels, non-commutative graphs and a quantum Lovasz theta function. arXiv:1002.2514v2 [quant-ph] (see also above)
• Salman Beigi, Entanglement-assisted zero-error capacity is upper bounded by the Lovasz theta function, Phys. Rev. A 82, 010303(R) (2010). arXiv:1002.2488v2 [quant-ph]
• Toby S. Cubitt, Graeme Smith, An Extreme form of Superactivation for Quantum Zero-Error Capacities. arXiv:0912.2737v2 [quant-ph]
• Toby S. Cubitt, Debbie Leung, William Matthews, Andreas Winter, Improving zero-error classical communication with entanglement, Phys. Rev. Lett. 104, 230503 (2010). arXiv:0911.5300v2 [quant-ph]
• Runyao Duan, Super-Activation of Zero-Error Capacity of Noisy Quantum Channels. arXiv:0906.2527v1 [quant-ph]
• Salman Beigi, Peter W. Shor, On the Complexity of Computing Zero-Error and Holevo Capacity of Quantum Channels. arXiv:0709.2090v3 [quant-ph]
• Rex A. C. Medeiros, Francisco M. De Assis, Quantum Zero-error Capacity, Telecommunications and Networking - ICT 2004, Lecture Notes in Computer Science, 2004, Volume 3124/2004, arXiv:quant-ph/0611089

Learning theory and quantum information (miscellanea)

• Esma Aïmeur, Gilles Brassard and Sébastien Gambs, Machine Learning in a Quantum World, Lecture Notes in Computer Science, 2006, Volume 4013/2006, 431-442.
• A. Hentschel and B. C. Sanders, Machine Learning for Precise Quantum Measurement, Phys. Rev. Lett. 104, 063603 (2010). arXiv:0910.0762v2 [quant-ph]
• R. A. Servedio and S. J. Gortler, Equivalences and separations between quantum and classical learnability, SIAM J. Comput., 33:1067, 2004.
• D. Gavinsky, Quantum Predictive Learning and Communication Complexity with Single Input, arXiv:0812.3429v2 [quant-ph]
• Kristen L. Pudenz, Daniel A. Lidar, Quantum adiabatic machine learning, arXiv:1109.0325v1 [quant-ph]
• G. Sentís, J. Calsamiglia, R. Munoz-Tapia, E. Bagan, Quantum learning without quantum memory, arXiv:1106.2742v1 [quant-ph]
• A. Bisio, G. Chiribella, G. M. D'Ariano, S. Facchini, P. Perinotti, Optimal quantum learning of a unitary transformation, Phys. Rev. A 81, 032324 (2010). arXiv:0903.0543v2 [quant-ph]
• A. Blum, K. Yang, On Statistical Query Sampling and NMR Quantum Computing, 18th Aunnual IEEE Conference of Computational Complexity (CCC 2003). arXiv:quant-ph/0307071v1
• Scott Aaronson, The Learnability of Quantum States, arXiv:quant-ph/0608142v3
• Manfred K Warmuth, Dima Kuzmin, Bayesian Generalized Probability Calculus for Density Matrices, arXiv:0901.1273v1 [quant-ph] Talk (see also below)
• Hartmut Neven, Vasil S. Denchev, Geordie Rose, William G. Macready, Training a Binary Classifier with the Quantum Adiabatic Algorithm, arXiv:0811.0416v1 [quant-ph]

Memoranda

2012
• R. Penrose, On the nature of quantum geometry, in Magic Without Magic, ed. J. Klauder, Freeman, San Francisco, 1972, pp. 333-354.
• N. Linial, Z. Luria, An upper bound on the number of high dimensional permutations, arXiv:1106.0649v1 [math.CO]
• A. Ashikhmin, A. Robert Calderbank, W. Kewlin, Multidimensional Second Order Reed-Muller Codes as Grassmannian Packings, ISIT 2006, Seattle, USA, July 9 14, 2006.
• P. Diaconis and J. Salzman, Projection pursuit for discrete data. IMS Collections Probability and Statistics: Essays in Honor of David A. Freedman, Vol. 2 (2008) 265–288. arXiv:0805.3043v1 [math.ST]
• B. J. Frey and D. Dueck, Clustering by Passing Messages Between Data Points, Science 315, 972–976, February 2007. citeseerx. Software.
• D. Jakobson, S. D.Miller, I. Rivin, Z. Rudnick, Eigenvalue spacings for regular graphs, IMA vol. 109 (Emerging applications of number theory, Minneapolis, MN 1996). arXiv:hep-th/0310002v1
• S. M. Pincus, Approximate entropy as a measure of system complexity, PNAS March 15, 1991 vol. 88 no. 6 2297-2301. (See our work arXiv:1201.0045v1 [cond-mat.dis-nn].)
• H. R. Kleinberg, and A. Lehman, On the capacity of information networks, IEEE Transactions on Information Theory, 52(6):2345–2364, 2006.
• N. Goldenfeld, L. P. Kadanoff, Simple lessons from complexity, Science 2 April 1999: Vol. 284 no. 5411 pp. 87-89.
• G. Tkacik and A M. Walczak, Information transmission in gene regulatory networks: a review, J. Phys.: Condens. Matter 23 (2011) 153102 (31pp). arXiv:1101.4240v1 [physics.bio-ph]
• E. Carlstein. Non-parametric change point estimation, The Annals of Statistics, Vol. 16, No. 1. (1988), pp. 188-197.
• S. Janson, D. E. Knuth, T. Łuczak, B. Pittel, The birth of the giant component, Random Structures Algorithms 4 (1993), no. 3, 231-358. arXiv:math/9310236v1 [math.PR]
• D. Deutsch, Physics, Philosophy and Quantum Technology (talk PDF), The Sixth International Conference on Quantum Communication, Measurement and Computing, in Proceedings of the Sixth International Conference on Quantum Communication, Measurement and Computing, Shapiro, J.H. and Hirota, O., Eds. (Rinton Press, Princeton, NJ. 2003).
• E. A. Rietman, R. L. Karp, and J. A Tuszynski, Review and application of group theory to molecular systems biology, Theoretical Biology and Medical Modelling 2011, 8:21.
• L. A. Zager, G. C. Verghese, Graph similarity scoring and matching, Applied Mathematics Letters, 21:1(2008), 86-94.
• M. M. Wilde, From Classical to Quantum Shannon Theory, 2011. arXiv:1106.1445v2 [quant-ph]
• N. Alon, C. Avin, M. Koucky, G. Kozma, Z. Lotker, M. R. Tuttle, Many Random Walks Are Faster Than One, Combinatorics, Probability and Computing (2011), 20 : pp 481-502. arXiv:0705.0467v2 [math.PR]
• P. Expert, T. Evans, V. D. Blondel, R. Lambiotte, Beyond Space For Spatial Networks, PNAS 2011 108 (19) 7663-7668.
• Planar Separator Theorem: D. A. Spielman, S.-H. Teng (1996), Disk packings and planar separators, Proc. 12th ACM Symposium on Computational Geometry (SCG '96), pp. 349–358; D. A. Spielman, S.-H. Teng (2007), Spectral partitioning works: Planar graphs and finite element meshes, Linear Algebra and its Applications 421 (2–3): 284–305,
• J. H. Conway, A. J. Jones, Trigonometric Diophantine equations (On vanishing sums of roots of unity), Acta Arith. 30 (1976), no. 3, 229--240.
• B. Poonen, M. Rubinstein, The Number of Intersection Points Made by the Diagonals of a Regular Polygon, SIAM Journal on Discrete Mathematics 11 (1998), no. 1, 135-156. arXiv:math/9508209v3 [math.MG]
• P. Bourgade, J. P. Keating, Quantum chaos, random matrix theory, and the Riemann zeta-function, Seminaire Poincare, XIV (2010) 115-153.
• C. W. J. Granger, Investigating causal relations by econometric models and cross-spectral methods, Econometrica 37:3 (1969), 424–438.
• Y.-A. Kim, S. Wuchty, T. M. Przytycka, Identifying causal genes and dysregulated pathways in complex disease, PLoS Comput Biol 7(3): e1001095.
• T. Ideker, N. J. Krogan, Differential network biology, Molecular Systems Biology 8:565.
• T. Manke, L. Demetrius, and M. Vingron, An entropic characterization of protein interaction networks and cellular robustness, J. R. Soc. Interface. 2006 December 22; 3(11): 843–850.
• A. E. Motter, Cascade control and defense in complex networks, Phys. Rev. Lett. 93, 098701 (2004).
• T. Schreiber, Meauring information transfer, Phys. Rev. Lett. 85, 461 (2000).
• H. G. Tanner, On the controllability of nearest neighbor interconnections, Decision and Control, 2004. CDC. 43rd IEEE Conference on.
• D. Ruelle, Is our mathematics natural: The case of equilibrium statistical mechanics, Bull. Amer. Math. Soc. (N.S.) Volume 19, Number 1 (1988).
• J. Paris, J. and L. Harrington, A Mathematical Incompleteness in Peano Arithmetic. In Handbook for Mathematical Logic (Ed. J. Barwise). Amsterdam, Netherlands: North-Holland, 1977.
• M. Warmuth, A Bayes Rule for Density Matrices, In Y. Weiss, B. Schölkopf, and J. Platt, editors, Advances in Neural Information Processing Systems 18, pages 1457–1464. MIT Press, Cambridge, MA, 2005.
• M. K. Warmuth, D. Kuzmin, Bayesian Generalized Probability Calculus for Density Matrices, In Proceedings of the 22^nd Annual Conference on Uncertainty in Artificial Intelligence, 2006.
• S. Boyd, P. Diaconis, and L. Xiao, Fastest Mixing Markov Chain on a Graph, SIAM Review, 46(4):667-689, 2004.
• K. P. Murphy, An introduction to graphical models, 2001.
• J. Gunawardena, Six Lectures on System Biology (Cambridge 2011).
• Hedetniemi conjecture.
• J. Cooper, Graph Theory Study Guide.
• Rotor Router Model by Jim Propp. The model involves a bug moving along a directed graph.
• Igraph is a free software package for creating and manipulating undirected and directed graphs. Cytoscape is an open source software platform for visualizing complex networks. CFinder is a free software for finding and visualizing overlapping dense groups of nodes in networks, based on the Clique Percolation Method (CPM) of Palla et. al., Nature 435, 814-818 (2005).
• Mathoverflow: Rewiring graphs (by me).
• KONECT is the Koblenz Network Collection. KONECT is a project to collect large network datasets of all types in order to perform research in the area of network mining, collected by the Institute of Web Science and Technologies of the University of Koblenz–Landau. (7/2/12)
• Mark Newman Network Data.
• E. D. Kolaczyk, (2009), Statistical Analysis of Network Data: Methods and Models. Springer, New York.
• Kappalanguage: A rule-based language for modeling protein interaction networks.
• Two interesting topics in Markov chains analysis: P. Doyle, Kemeny constant: C. D. Meyer, Stochastic Complementation.
• Smart Cities: World Economic Forum, Urban Sustainability. Companies in Smart Cities.
• Subhash A. Khot, Nisheeth K. Vishnoi, The Unique Games Conjecture, Integrality Gap for Cut Problems and Embeddability of Negative Type Metrics into l_1, 2005.
• A. Kavruk, V. I. Paulsen, I. G. Todorov, M. Tomforde, Tensor products of operator systems. J. Funct. Anal. 261 (2011), no. 2, 267–299.
• M.V. Berry and J.P. Keating The Riemann zeros and eigenvalue asymptotics, SIAM Review, 41, No. 2 (1999), 236-266.
• A. Ferrante, M. Pavon, Matrix completion à la Dempster by the principle of parsimony, IEEE Trans. Inform. Theory 57 (2011), no. 6, 3925-3931.
• Information System on Graph Classes and their Inclusions.
• Yvo Desmedt, Yongge Wang, Perfectly Secure Message Transmission Revisited, IEEE Trans. Inform. Theory 54 (2008), 25820-2595. arXiv:cs/0208041v1 [cs.CR]
• Asu Ozdaglar: Learning and dynamics on networks, Acemoglu, Daron, Munther Dahleh, Ilan Lobel, and Asuman Ozdaglar (2008), Bayesian learning in social networks, LIDS Working Paper 2780, Massachusetts nstitute of Technology.
• M. Agrawal, Axiomatic / Postulatory Quantum Mechanics, in Fundamental Physics in Nano-Structured Materials and Devices (Stanford University, 2008).
• R. Diestel, Graph Theory, Electronic Edition 2010.
• Measuring Worth, historical data on important economic aggregates, with particular emphasis on nominal measures.
• Hà Quang Minh, Reproducing Kernel Hilbert Spaces and Learning Problems on the Hypercube , preprint, 2012.
• Network Workbench: A Large-Scale Network Analysis, Modeling and Visualization Toolkit for Biomedical, Social Science and Physics Research.
• Gephi The Open Graph Viz Platform.
• Measuring complexity (by S. Lloyd): 1. How hard is it to describe? Entropy; Algorithmic Complexity or Algorithmic Information Content; Minimum Description Length; Fisher Information; Renyi Entropy; Code Length (prefix-free, Huffman, Shannon-Fano, error-correcting, Hamming); Chernoff Information; Dimension; Fractal Dimension; Lempel-Ziv Complexity. 2. How hard is it to create? Time Computational Complexity; Space Computational Complexity; Information--Based Complexity; Logical Depth; Thermodynamic Depth; Cost; Crypticity. 3. What is its degree of organization? Metric Entropy; Fractal Dimension; Excess Entropy; Stochastic Complexity; Sophistication; Effective Measure Complexity; True Measure Complexity; Topological epsilon-machine size; Conditional Information; Conditional Algorithmic Information Content; Schema length; Ideal Complexity; Hierarchical Complexity; Tree subgraph diversity; Homogeneous Complexity; Grammatical Complexity. Algorithmic Mutual Information; Channel Capacity; Correlation; Stored Information; Organization.
• S. Bhamidi, R. Rajagopal, S. Roch, Network Delay Inference from Additive Metrics. arXiv:math/0604367v2 [math.PR]
• R. Castro, M. Coates, G. Liang, R. Nowak and B. Yu, Network Tomography: Recent Developments, Statistical Science, Vol. 19, No. 3, 499–517, 2004.
• GraphCrunch2 is a software tool for network analysis, modelling and alignment.
• L. Lovász, Very large graphs, Current Developments in Mathematics 2008 (eds. D. Jerison, B. Mazur, T. Mrowka, W. Schmid, R. Stanley, and S. T. Yau), International Press, Somerville, MA (2009), 67-128.
• A. Clauset, C. R. Shalizi, M. E. J. Newman, Power law distribution of empirical data, SIAM Review 51, 661-703 (2009).
• Blonstein, D. Fahmy, H., and Grbavec, A, (1996), Issues in the practical use of graph rewriting.
• Bioconductor provides tools for the analysis and comprehension of high-throughput genomic data.
• NetworkX is a Python language software package for the creation, manipulation, and study of the structure, dynamics, and functions of complex networks.
• Pajek, program for large networks analysis.
• Guess, the graph exploration system.

• Pegasus, open-source, graph-mining system with massive scalability.

• NetLogo is a multi-agent programmable modeling environment.
• Massey Tutorial on Zero-error Information Theory, Information Theory Winter School, La Colle Sur Loup, March 2007.
• D. Zelazo and M. Mesbahi, Graph-theoretic methods for networked dynamic systems: Heterogeneity and H₂ Performance, in Efficient Modeling and Control of Large-Scale Systems (J. Mohammadpour and K.M. Grigoriadis, eds.), New York, New York: Springer, pp. 219-249.
• B. Chazelle, The Convergence of Bird Flocking, arXiv:0905.4241v1 [cs.CG]
• Arora, S., Rao, S., and Vazirani, U. 2009., Expander flows, geometric embeddings and graph partitioning, J. ACM 56, 2, Article 5 (April 2009).
• T. Bu, N. Duffield, F. Lo Presti, D. Towsley, Network Tomography on General Topology, Proc. of ACM SIGMETRICS 2002.

Blogosphere, etc.

• Information Processing, Sthetl-Optimized, My biased coin, Michael Nielsen, The n-Cathegory Cafe', Timothy Gowers, Computational Complexity, Backreaction, Terence Tao, In Theory, Cosmic Variance, Andrew Jaffe: Leaves on the Line, Gödel’s lost letter and P=NP, Math overflow, Peter Cameron's blog, Not Even Wrong, Combinatorics and more