32,785 research outputs found
Notes on nonabelian (0,2) theories and dualities
In this paper we explore basic aspects of nonabelian (0,2) GLSM's in two
dimensions for unitary gauge groups, an arena that until recently has largely
been unexplored. We begin by discussing general aspects of (0,2) theories,
including checks of dynamical supersymmetry breaking, spectators and weak
coupling limits, and also build some toy models of (0,2) theories for bundles
on Grassmannians, which gives us an opportunity to relate physical anomalies
and trace conditions to mathematical properties. We apply these ideas to study
(0,2) theories on Pfaffians, applying recent perturbative constructions of
Pfaffians of Jockers et al. We discuss how existing dualities in (2,2)
nonabelian gauge theories have a simple mathematical understanding, and make
predictions for additional dualities in (2,2) and (0,2) gauge theories.
Finally, we outline how duality works in open strings in unitary gauge
theories, and also describe why, in general terms, we expect analogous
dualities in (0,2) theories to be comparatively rare.Comment: 93 pages, LaTeX; v2: typos fixe
DPCA: Dimensionality Reduction for Discriminative Analytics of Multiple Large-Scale Datasets
Principal component analysis (PCA) has well-documented merits for data
extraction and dimensionality reduction. PCA deals with a single dataset at a
time, and it is challenged when it comes to analyzing multiple datasets. Yet in
certain setups, one wishes to extract the most significant information of one
dataset relative to other datasets. Specifically, the interest may be on
identifying, namely extracting features that are specific to a single target
dataset but not the others. This paper develops a novel approach for such
so-termed discriminative data analysis, and establishes its optimality in the
least-squares (LS) sense under suitable data modeling assumptions. The
criterion reveals linear combinations of variables by maximizing the ratio of
the variance of the target data to that of the remainders. The novel approach
solves a generalized eigenvalue problem by performing SVD just once. Numerical
tests using synthetic and real datasets showcase the merits of the proposed
approach relative to its competing alternatives.Comment: 5 pages, 2 figure
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