Flux-fusion anomaly test and bosonic topological crystalline insulators

We introduce a method, dubbed the flux-fusion anomaly test, to detect certain anomalous symmetry fractionalization patterns in two-dimensional symmetry enriched topological (SET) phases. We focus on bosonic systems with Z2 topological order, and symmetry group of the form G = U(1) $\rtimes$ G', where G' is an arbitrary group that may include spatial symmetries and/or time reversal. The anomalous fractionalization patterns we identify cannot occur in strictly d=2 systems, but can occur at surfaces of d=3 symmetry protected topological (SPT) phases. This observation leads to examples of d=3 bosonic topological crystalline insulators (TCIs) that, to our knowledge, have not previously been identified. In some cases, these d=3 bosonic TCIs can have an anomalous superfluid at the surface, which is characterized by non-trivial projective transformations of the superfluid vortices under symmetry. The basic idea of our anomaly test is to introduce fluxes of the U(1) symmetry, and to show that some fractionalization patterns cannot be extended to a consistent action of G' symmetry on the fluxes. For some anomalies, this can be described in terms of dimensional reduction to d=1 SPT phases. We apply our method to several different symmetry groups with non-trivial anomalies, including G = U(1) X Z2T and G = U(1) X Z2P, where Z2T and Z2P are time-reversal and d=2 reflection symmetry, respectively.Comment: 18+13 pages, 4 figures. Significant changes to introduction, and other changes to improve presentation. Title shortene

Linear matching method on the evaluation of cyclic behaviour with creep effect

This paper describes a new Linear Matching Method (LMM) technique for the direct evaluation of cyclic behaviour with creep effects of structures subjected to a general load condition in the steady cyclic state. The creep strain and plastic strain range for use in creep damage and fatigue assessments, respectively, are obtained. A benchmark example of a Bree cylinder subjected to cyclic thermal load and constant mechanical load is analysed to verify the applicability of the new LMM to deal with the creep fatigue damage. The cyclic responses for different loading conditions and dwell time periods within the Bree boundary are obtained. To demonstrate the efficiency and effectiveness of the method for more complex structures, a 3D holed plate subjected to cyclic thermal loads and constant axial tension is analysed. The results of both examples show that with the presence of creep the cyclic responses change significantly. The new LMM procedure provides a general purpose technique for the evaluation of cyclic behaviour, the plastic strain range and creep strain for the creep fatigue damage assessment with creep fatigue interaction

Corporate Governance and the Cost of Debt: Evidence from Director Limited Liability and Indemnification Provisions

We find that firms that provide limited liability and indemnification for their directors enjoy higher credit ratings and lower yield spreads. We argue that such provisions insulate corporate directors from the discipline from potential litigation, and allow them to pursue their own interests by adopting low-risk, self-serving operating strategies, which coincidentally redound to the benefit of corporate bondholders. Our evidence further suggests that the reduction in the cost of debt may offset the costs of directorial shirking and suboptimal corporate policies occasioned by this insulation, which may explain why stockholders have little incentive to rescind these legal protections

Relating AdS6_6 solutions in type IIB supergravity

In this note we show that the IIB supergravity solutions of the form AdS$_6\times M_4$ found by Apruzzi et al. are related to the local solutions found by D'Hoker et al. We also discuss how the global regular solutions found by D'Hoker et al. are mapped to the parameterization of Apruzzi et al.Comment: 22 pages, 10 figure

KdV-like solitary waves in two-dimensional FPU-lattices

We prove the existence of solitary waves in the KdV limit of two-dimensional FPU-type lattices using asymptotic analysis of nonlinear and singularly perturbed integral equations. In particular, we generalize the existing results by Friesecke and Matthies since we allow for arbitrary propagation directions and non-unidirectional wave profiles.Comment: revised version with several changes in the presentation of the technical details; 25 pages, 15 figure

Symmetry fractionalization and anomaly detection in three-dimensional topological phases

In a phase with fractional excitations, topological properties are enriched in the presence of global symmetry. In particular, fractional excitations can transform under symmetry in a fractionalized manner, resulting in different Symmetry Enriched Topological (SET) phases. While a good deal is now understood in $2D$ regarding what symmetry fractionalization patterns are possible, the situation in $3D$ is much more open. A new feature in $3D$ is the existence of loop excitations, so to study $3D$ SET phases, first we need to understand how to properly describe the fractionalized action of symmetry on loops. Using a dimensional reduction procedure, we show that these loop excitations exist as the boundary between two $2D$ SET phases, and the symmetry action is characterized by the corresponding difference in SET orders. Moreover, similar to the $2D$ case, we find that some seemingly possible symmetry fractionalization patterns are actually anomalous and cannot be realized strictly in $3D$. We detect such anomalies using the flux fusion method we introduced previously in $2D$. To illustrate these ideas, we use the $3D$ $Z_2$ gauge theory with $Z_2$ global symmetry as an example, and enumerate and describe the corresponding SET phases. In particular, we find four non-anomalous SET phases and one anomalous SET phase, which we show can be realized as the surface of a $4D$ system with symmetry protected topological order.Comment: 19 pages, 8 figure

Development of modularity in the neural activity of children's brains

We study how modularity of the human brain changes as children develop into adults. Theory suggests that modularity can enhance the response function of a networked system subject to changing external stimuli. Thus, greater cognitive performance might be achieved for more modular neural activity, and modularity might likely increase as children develop. The value of modularity calculated from fMRI data is observed to increase during childhood development and peak in young adulthood. Head motion is deconvolved from the fMRI data, and it is shown that the dependence of modularity on age is independent of the magnitude of head motion. A model is presented to illustrate how modularity can provide greater cognitive performance at short times, i.e.\ task switching. A fitness function is extracted from the model. Quasispecies theory is used to predict how the average modularity evolves with age, illustrating the increase of modularity during development from children to adults that arises from selection for rapid cognitive function in young adults. Experiments exploring the effect of modularity on cognitive performance are suggested. Modularity may be a potential biomarker for injury, rehabilitation, or disease.Comment: 29 pages, 11 figure