Bifundamental Fuzzy 2-Sphere and Fuzzy Killing Spinors

We review our construction of a bifundamental version of the fuzzy 2-sphere and its relation to fuzzy Killing spinors, first obtained in the context of the ABJM membrane model. This is shown to be completely equivalent to the usual (adjoint) fuzzy sphere. We discuss the mathematical details of the bifundamental fuzzy sphere and its field theory expansion in a model-independent way. We also examine how this new formulation affects the twisting of the fields, when comparing the field theory on the fuzzy sphere background with the compactification of the 'deconstructed' (higher dimensional) field theory.Comment: Invited contribution to special issue of SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) "Noncommutative Spaces and Fields

More on the scalar-tensor B-F theory

This work is based on an earlier proposal \cite{hs} that the membrane B-F theory consists of matter fields alongwith Chern-Simons fields as well as the auxiliary pairs of scalar and tensor fields. We especially discuss the supersymmetry aspects of such a membrane theory. It is concluded that the theory possesses maximal supersymmetry and it is related to the L-BLG theory via a field map. We obtain fuzzy-sphere solution and corresponding tensor field configuration is given.Comment: 19 pages; v2 typo corrected and more reference

Complex (super)-matrix models with external sources and qq-ensembles of Chern-Simons and ABJ(M) type

The Langmann-Szabo-Zarembo (LSZ) matrix model is a complex matrix model with a quartic interaction and two external matrices. The model appears in the study of a scalar field theory on the non-commutative plane. We prove that the LSZ matrix model computes the probability of atypically large fluctuations in the Stieltjes-Wigert matrix model, which is a $q$-ensemble describing $U(N)$ Chern-Simons theory on the three-sphere. The correspondence holds in a generalized sense: depending on the spectra of the two external matrices, the LSZ matrix model either describes probabilities of large fluctuations in the Chern-Simons partition function, in the unknot invariant or in the two-unknot invariant. We extend the result to supermatrix models, and show that a generalized LSZ supermatrix model describes the probability of atypically large fluctuations in the ABJ(M) matrix model.Comment: 30 pages, 2 figures. v2: A correction made and several new results added; title changed. v3: Presentation reorganized, new results and references added, final versio

A Method Non-Deterministic and Computationally Viable for Detecting Outliers in Large Datasets

This paper presents an outlier detection method that is based on a Variable Precision Rough Set Model (VPRSM). This method generalizes the standard set inclusion relation, which is the foundation of the Rough Sets Basic Model (RSBM). The main contribution of this research is an improvement in the quality of detection because this generalization allows us to classify when there is some degree of uncertainty. From the proposed method, a computationally viable algorithm for large volumes of data is also introduced. The experiments performed in a real scenario and a comparison of the results with the RSBM-based method demonstrate the efficiency of both the method and the algorithm in diverse contexts that involve large volumes of data.This work has been supported by grant TIN2016-78103-C2-2-R, and University of Alicante projects GRE14-02 and Smart University