Unconventional Fusion and Braiding of Topological Defects in a Lattice Model

We demonstrate the semiclassical nature of symmetry twist defects that differ from quantum deconfined anyons in a true topological phase by examining non-abelian crystalline defects in an abelian lattice model. An underlying non-dynamical ungauged S3-symmetry labels the quasi-extensive defects by group elements and gives rise to order dependent fusion. A central subgroup of local Wilson observables distinguishes defect-anyon composites by species, which can mutate through abelian anyon tunneling by tuning local defect phase parameters. We compute a complete consistent set of primitive basis transformations, or F-symbols, and study braiding and exchange between commuting defects. This suggests a modified spin-statistics theorem for defects and non-modular group structures unitarily represented by the braiding S and exchange T matrices. Non-abelian braiding operations in a closed system represent the sphere braid group projectively by a non-trivial central extension that relates the underlying symmetry.Comment: 44 pages, 43 figure

Braiding Statistics and Congruent Invariance of Twist Defects in Bosonic Bilayer Fractional Quantum Hall States

We describe the braiding statistics of topological twist defects in abelian bosonic bilayer (mmn) fractional quantum Hall (FQH) states, which reduce to the Z_n toric code when m=0. Twist defects carry non-abelian fractional Majorana-like characteristics. We propose local statistical measurements that distinguish the fractional charge, or species, of a defect-quasiparticle composite. Degenerate ground states and basis transformations of a multi-defect system are characterized by a consistent set of fusion properties. Non-abelian unitary exchange operations are determined using half braids between defects, and projectively represent the sphere braid group in a closed system. Defect spin statistics are modified by equating exchange with 4\pi rotation. The braiding S matrix is identified with a Dehn twist (instead of a \pi/2 rotation) on a torus decorated with a non-trivial twofold branch cut, and represents the congruent subgroup \Gamma_0(2) of modular transformations.Comment: 6 pages, 3 figure

From orbifolding conformal field theories to gauging topological phases

Topological phases of matter in (2+1) dimensions are commonly equipped with global symmetries, such as electric-magnetic duality in gauge theories and bilayer symmetry in fractional quantum Hall states. Gauging these symmetries into local dynamical ones is one way of obtaining exotic phases from conventional systems. We study this using the bulk-boundary correspondence and applying the orbifold construction to the (1+1) dimensional edge described by a conformal field theory (CFT). Our procedure puts twisted boundary conditions into the partition function, and predicts the fusion, spin and braiding behavior of anyonic excitations after gauging. We demonstrate this for the electric-magnetic self-dual $\mathbb{Z}_N$ gauge theory, the twofold symmetric $SU(3)_1$, and the $S_3$-symmetric $SO(8)_1$ Wess-Zumino-Witten theories.Comment: 23 pages, 1 figur

SourcererCC: Scaling Code Clone Detection to Big Code

Despite a decade of active research, there is a marked lack in clone detectors that scale to very large repositories of source code, in particular for detecting near-miss clones where significant editing activities may take place in the cloned code. We present SourcererCC, a token-based clone detector that targets three clone types, and exploits an index to achieve scalability to large inter-project repositories using a standard workstation. SourcererCC uses an optimized inverted-index to quickly query the potential clones of a given code block. Filtering heuristics based on token ordering are used to significantly reduce the size of the index, the number of code-block comparisons needed to detect the clones, as well as the number of required token-comparisons needed to judge a potential clone. We evaluate the scalability, execution time, recall and precision of SourcererCC, and compare it to four publicly available and state-of-the-art tools. To measure recall, we use two recent benchmarks, (1) a large benchmark of real clones, BigCloneBench, and (2) a Mutation/Injection-based framework of thousands of fine-grained artificial clones. We find SourcererCC has both high recall and precision, and is able to scale to a large inter-project repository (250MLOC) using a standard workstation.Comment: Accepted for publication at ICSE'16 (preprint, unrevised

PIAAC’s role in global food security: Evidence from machine learning-based feature selection across three major food security indicators

The PIAAC country dataset for 36 countries is explored to understand its role in global food security, adding to its significance in sustainable development goal four, zero hunger