Forthcoming events in this series
Nodes in complex networks organize into communities of nodes that share a common property, role or function, such as social communities, functionally related proteins, or topically related webpages. Identifying such communities is crucial to the understanding of the structural and functional roles of networks.
Current work on overlapping community detection (often implicitly) assumes that community overlaps are less densely connected than non-overlapping parts of communities. This is unnatural as it means that the more communities nodes share, the less likely it is they are linked. We validate this assumption on a diverse set of large networks and find an increasing relationship between the number of shared communities of a pair of nodes and the probability of them being connected by an edge, which means that parts of the network where communities overlap tend to be more densely connected than the non-overlapping parts of communities.
Existing community detection methods fail to detect communities with such overlaps. We propose a model-based community detection method that builds on bipartite node-community affiliation networks. Our method successfully detects overlapping, non-overlapping and hierarchically nested communities. We accurately identify relevant communities in networks ranging from biological protein-protein interaction networks to social, collaboration and information networks. Our results show that while networks organize into overlapping communities, globally networks also exhibit a nested core-periphery structure, which arises as a consequence of overlapping parts of communities being more densely connected.
We show how the reduction procedure for generalized Kahler
structures can be used to recover Hitchin's results about the
existence of a generalized Kahler structure on the moduli space of
instantons on bundle over a generalized Kahler manifold. In this setup
the proof follows closely the proof of the same claim for the Kahler
case and clarifies some of the stranger considerations from Hitchin's
proof.
In recent years, surprising connections between type theory and homotopy theory have been discovered. In this talk I will recall the notions of intensional type theories and identity types. I will describe "infinity groupoids", formal algebraic models of topological spaces, and explain how identity types carry the structure of an infinity groupoid. I will finish by discussing categorical semantics of intensional type theories.
The talk will take place in Lecture Theatre B, at the Department of Computer Science.
Algebraic theories, locally presentable categories and their application to type theories. The seminar will take place in Lecture Theatre A of the Department of Computer Science.
The seminar will take place in Lecture Theatre A, Department of Computer Science.
-------------------
Contextuality and non-locality are features of quantum mechanics which stand in sharp contrast to the realistic picture underlying classical physics. We shall describe a unified geometric perspective on these notions in terms of *obstructions to the existence of global sections*. This allows general results and structural notions to be uncovered, with quantum mechanics appearing as a special case. The natural language to use here is that of sheaves and presheaves; and cohomological obstructions can be defined which witness contextuality in a number of salient examples.
This is joint work with Adam Brandenburger
http://iopscience.iop.org/1367-2630/13/11/113036/
http://arxiv.org/abs/1102.0264
and Shane Mansfield and Rui Soares Barbosa
http://arxiv.org/abs/1111.3620
Introductory talk on topological quantum field theories (TQFTs) and the cobordism hypothesis, focusing on the conceptual issues involved.
The lecture will take place this Friday at 11am in Lecture Theatre A of the Department of Computer Science
We will demonstrate the following. Category theory, usually conceived as some very abstract form of metamathematics, is present everywhere around us. Explicitly, we show how it provides a kindergarten version of quantum theory, an how it will help Google to understand sentences rather than words.
Some references are:
-[light] BC (2010) "Quantum picturalism". Contemporary Physics 51, 59-83. arXiv:0908.1787
-[a bit heavier] BC and Ross Duncan (2011) "Interacting quantum observables: categorical algebra and diagrammatics". New Journal of Physics 13, 043016. arXiv:0906.4725
-[light] New Scientist (8 December 2010) "Quantum links let computers understand language". www.cs.ox.ac.uk/people/bob.coecke/NewScientist.pdf
-[a bit heavier] BC, Mehrnoosh Sadrzadeh and Stephen Clark (2011) "Mathematical foundations for a compositional distributional model of meaning". Linguistic Analysis - Lambek Festschrift. arXiv:1003.439
This meeting will mark the 80th birthday of Sir Roger Penrose. Twistor theory is one of his most remarkable discoveries and continues to have applications across pure mathematics and mathematical physics. This meeting will focus on some recent developments with speakers both on geometry and physics.
Speakers:
Registration will start at 1.30pm on the 21st with the first lecture at 2.15pm. The meeting will finish by 4.30pm on the 22nd. See the programme for more details.
There will be a reception at 6.30pm on the 21st July (Wadham College) followed by dinner at 7.15 in Wadham College.
We review the relation between the geometry of Kleinian singularities and Dynkin diagrams of types ADE, recalling in particular the construction of a braid group action of type A, D, or E on the derived category of coherent sheaves on the minimal resolution of a Kleinian singularity. By work of Seidel-Thomas, this action was known to be faithful in type A. We extend this faithfulness result to types ADE, which provides the missing ingredient for completing Bridgeland's description of spaces of stability conditions for certain triangulated categories associated to Kleinian singularities. Our main tool is the Garside normal form for braid group elements. This project is joint work with Hugh Thomas from the University of New Brunswick.