On the 1-loop calculations of softly broken fermion-torsion theory in curved space using the Stuckelberg procedure

The soft breaking of gauge or other symmetries is the typical Quantum Field Theory phenomenon. In many cases one can apply the Stuckelberg procedure, which means introducing some additional field (or fields) and restore the gauge symmetry. The original softly broken theory corresponds to a particular choice of the gauge fixing condition. In this paper we use this scheme for performing quantum calculations for fermion-torsion theory, softly broken by the torsion mass in arbitrary curved spacetime.Comment: Talk given at the 7th Alexander Friedmann International Seminar on Gravitation and Cosmology, Joao Pessoa, Brazil, 29 Jun - 5 Jul 2008. 4 pages and one figur

A note on the heat kernel method applied to fermions

The spectrum of the fermionic operators depending on external fields is an important object in Quantum Field Theory. In this paper we prove, using transition to the alternative basis for the $\gamma$-matrices, that this spectrum does not depend on the sign of the fermion mass, up to a constant factor. This assumption has been extensively used, but usually without proof. As an illustration, we calculated the coincidence limit of the coefficient $a_2(x,x^\prime)$ on the general metric background, vector and axial vector fields.Comment: 5 pages, LaTeX, no figures. Revised versio

A network approach to topic models

One of the main computational and scientific challenges in the modern age is to extract useful information from unstructured texts. Topic models are one popular machine-learning approach which infers the latent topical structure of a collection of documents. Despite their success --- in particular of its most widely used variant called Latent Dirichlet Allocation (LDA) --- and numerous applications in sociology, history, and linguistics, topic models are known to suffer from severe conceptual and practical problems, e.g. a lack of justification for the Bayesian priors, discrepancies with statistical properties of real texts, and the inability to properly choose the number of topics. Here we obtain a fresh view on the problem of identifying topical structures by relating it to the problem of finding communities in complex networks. This is achieved by representing text corpora as bipartite networks of documents and words. By adapting existing community-detection methods -- using a stochastic block model (SBM) with non-parametric priors -- we obtain a more versatile and principled framework for topic modeling (e.g., it automatically detects the number of topics and hierarchically clusters both the words and documents). The analysis of artificial and real corpora demonstrates that our SBM approach leads to better topic models than LDA in terms of statistical model selection. More importantly, our work shows how to formally relate methods from community detection and topic modeling, opening the possibility of cross-fertilization between these two fields.Comment: 22 pages, 10 figures, code available at https://topsbm.github.io

On the Consistency of a Fermion-Torsion Effective Theory

We discuss the possibility to construct an effective quantum field theory for an axial vector coupled to a Dirac spinor field. A massive axial vector describes antisymmetric torsion. The consistency conditions include unitarity and renormalizability in the low-energy region. The investigation of the Ward identities and the one- and two-loop divergences indicate serious problems arising in the theory. The final conclusion is that torsion may exist as a string excitation, but there are very severe restrictions for the existence of a propagating torsion field, subject to the quantization procedure, at low energies.Comment: LaTeX, 26 pages, 4 figure

Sampling motif-constrained ensembles of networks

The statistical significance of network properties is conditioned on null models which satisfy spec- ified properties but that are otherwise random. Exponential random graph models are a principled theoretical framework to generate such constrained ensembles, but which often fail in practice, either due to model inconsistency, or due to the impossibility to sample networks from them. These problems affect the important case of networks with prescribed clustering coefficient or number of small connected subgraphs (motifs). In this paper we use the Wang-Landau method to obtain a multicanonical sampling that overcomes both these problems. We sample, in polynomial time, net- works with arbitrary degree sequences from ensembles with imposed motifs counts. Applying this method to social networks, we investigate the relation between transitivity and homophily, and we quantify the correlation between different types of motifs, finding that single motifs can explain up to 60% of the variation of motif profiles.Comment: Updated version, as published in the journal. 7 pages, 5 figures, one Supplemental Materia