An Email Attachment is Worth a Thousand Words, or Is It?

There is an extensive body of research on Social Network Analysis (SNA) based on the email archive. The network used in the analysis is generally extracted either by capturing the email communication in From, To, Cc and Bcc email header fields or by the entities contained in the email message. In the latter case, the entities could be, for instance, the bag of words, url's, names, phones, etc. It could also include the textual content of attachments, for instance Microsoft Word documents, excel spreadsheets, or Adobe pdfs. The nodes in this network represent users and entities. The edges represent communication between users and relations to the entities. We suggest taking a different approach to the network extraction and use attachments shared between users as the edges. The motivation for this is two-fold. First, attachments represent the "intimacy" manifestation of the relation's strength. Second, the statistical analysis of private email archives that we collected and Enron email corpus shows that the attachments contribute in average around 80-90% to the archive's disk-space usage, which means that most of the data is presently ignored in the SNA of email archives. Consequently, we hypothesize that this approach might provide more insight into the social structure of the email archive. We extract the communication and shared attachments networks from Enron email corpus. We further analyze degree, betweenness, closeness, and eigenvector centrality measures in both networks and review the differences and what can be learned from them. We use nearest neighbor algorithm to generate similarity groups for five Enron employees. The groups are consistent with Enron's organizational chart, which validates our approach.Comment: 12 pages, 4 figures, 7 tables, IML'17, Liverpool, U

The Elliptic curves in gauge theory, string theory, and cohomology

Elliptic curves play a natural and important role in elliptic cohomology. In earlier work with I. Kriz, thes elliptic curves were interpreted physically in two ways: as corresponding to the intersection of M2 and M5 in the context of (the reduction of M-theory to) type IIA and as the elliptic fiber leading to F-theory for type IIB. In this paper we elaborate on the physical setting for various generalized cohomology theories, including elliptic cohomology, and we note that the above two seemingly unrelated descriptions can be unified using Sen's picture of the orientifold limit of F-theory compactification on K3, which unifies the Seiberg-Witten curve with the F-theory curve, and through which we naturally explain the constancy of the modulus that emerges from elliptic cohomology. This also clarifies the orbifolding performed in the previous work and justifies the appearance of the w_4 condition in the elliptic refinement of the mod 2 part of the partition function. We comment on the cohomology theory needed for the case when the modular parameter varies in the base of the elliptic fibration.Comment: 23 pages, typos corrected, minor clarification

Twisted equivariant K-theory, groupoids and proper actions

In this paper we define twisted equivariant K-theory for actions of Lie groupoids. For a Bredon-compatible Lie groupoid, this defines a periodic cohomology theory on the category of finite CW-complexes with equivariant stable projective bundles. A classification of these bundles is shown. We also obtain a completion theorem and apply these results to proper actions of groups.Comment: 26 page

Lectures on BCOV holomorphic anomaly equations

The present article surveys some mathematical aspects of the BCOV holomorphic anomaly equations introduced by Bershadsky, Cecotti, Ooguri and Vafa. It grew from a series of lectures the authors gave at the Fields Institute in the Thematic Program of Calabi-Yau Varieties in the fall of 2013.Comment: reference added, typos correcte

AQFT from n-functorial QFT

There are essentially two different approaches to the axiomatization of quantum field theory (QFT): algebraic QFT, going back to Haag and Kastler, and functorial QFT, going back to Atiyah and Segal. More recently, based on ideas by Baez and Dolan, the latter is being refined to "extended" functorial QFT by Freed, Hopkins, Lurie and others. The first approach uses local nets of operator algebras which assign to each patch an algebra "of observables", the latter uses n-functors which assign to each patch a "propagator of states". In this note we present an observation about how these two axiom systems are naturally related: we demonstrate under mild assumptions that every 2-dimensional extended Minkowskian QFT 2-functor ("parallel surface transport") naturally yields a local net. This is obtained by postcomposing the propagation 2-functor with an operation that mimics the passage from the Schroedinger picture to the Heisenberg picture in quantum mechanics. The argument has a straightforward generalization to general pseudo-Riemannian structure and higher dimensions.Comment: 39 pages; further examples added: Hopf spin chains and asymptotic inclusion of subfactors; references adde

On Graph-Theoretic Identifications of Adinkras, Supersymmetry Representations and Superfields

In this paper we discuss off-shell representations of N-extended supersymmetry in one dimension, ie, N-extended supersymmetric quantum mechanics, and following earlier work on the subject codify them in terms of certain graphs, called Adinkras. This framework provides a method of generating all Adinkras with the same topology, and so also all the corresponding irreducible supersymmetric multiplets. We develop some graph theoretic techniques to understand these diagrams in terms of a relatively small amount of information, namely, at what heights various vertices of the graph should be "hung". We then show how Adinkras that are the graphs of N-dimensional cubes can be obtained as the Adinkra for superfields satisfying constraints that involve superderivatives. This dramatically widens the range of supermultiplets that can be described using the superspace formalism and organizes them. Other topologies for Adinkras are possible, and we show that it is reasonable that these are also the result of constraining superfields using superderivatives. The family of Adinkras with an N-cubical topology, and so also the sequence of corresponding irreducible supersymmetric multiplets, are arranged in a cyclical sequence called the main sequence. We produce the N=1 and N=2 main sequences in detail, and indicate some aspects of the situation for higher N.Comment: LaTeX, 58 pages, 52 illustrations in color; minor typos correcte

Topological Aspects of Gauge Fixing Yang-Mills Theory on S4

For an $S_4$ space-time manifold global aspects of gauge-fixing are investigated using the relation to Topological Quantum Field Theory on the gauge group. The partition function of this TQFT is shown to compute the regularized Euler character of a suitably defined space of gauge transformations. Topological properties of the space of solutions to a covariant gauge conditon on the orbit of a particular instanton are found using the $SO(5)$ isometry group of the $S_4$ base manifold. We obtain that the Euler character of this space differs from that of an orbit in the topologically trivial sector. This result implies that an orbit with Pontryagin number \k=\pm1 in covariant gauges on $S_4$ contributes to physical correlation functions with a different multiplicity factor due to the Gribov copies, than an orbit in the trivial \k=0 sector. Similar topological arguments show that there is no contribution from the topologically trivial sector to physical correlation functions in gauges defined by a nondegenerate background connection. We discuss possible physical implications of the global gauge dependence of Yang-Mills theory.Comment: 13 pages, uuencoded and compressed LaTeX file, no figure

The curvature of semidirect product groups associated with two-component Hunter-Saxton systems

In this paper, we study two-component versions of the periodic Hunter-Saxton equation and its $\mu$-variant. Considering both equations as a geodesic flow on the semidirect product of the circle diffeomorphism group \Diff(\S) with a space of scalar functions on $\S$ we show that both equations are locally well-posed. The main result of the paper is that the sectional curvature associated with the 2HS is constant and positive and that 2$\mu$HS allows for a large subspace of positive sectional curvature. The issues of this paper are related to some of the results for 2CH and 2DP presented in [J. Escher, M. Kohlmann, and J. Lenells, J. Geom. Phys. 61 (2011), 436-452].Comment: 19 page

Critical Indices as Limits of Control Functions

A variant of self-similar approximation theory is suggested, permitting an easy and accurate summation of divergent series consisting of only a few terms. The method is based on a power-law algebraic transformation, whose powers play the role of control functions governing the fastest convergence of the renormalized series. A striking relation between the theory of critical phenomena and optimal control theory is discovered: The critical indices are found to be directly related to limits of control functions at critical points. The method is applied to calculating the critical indices for several difficult problems. The results are in very good agreement with accurate numerical data.Comment: 1 file, 5 pages, RevTe