Commuting-projector Hamiltonians for chiral topological phases built from parafermions

We introduce a family of commuting-projector Hamiltonians whose degrees of freedom involve $\mathbb{Z}_{3}$ parafermion zero modes residing in a parent fractional-quantum-Hall fluid. The two simplest models in this family emerge from dressing Ising-paramagnet and toric-code spin models with parafermions; we study their edge properties, anyonic excitations, and ground-state degeneracy. We show that the first model realizes a symmetry-enriched topological phase (SET) for which $\mathbb{Z}_2$ spin-flip symmetry from the Ising paramagnet permutes the anyons. Interestingly, the interface between this SET and the parent quantum-Hall phase realizes symmetry-enforced $\mathbb{Z}_3$ parafermion criticality with no fine-tuning required. The second model exhibits a non-Abelian phase that is consistent with $\text{SU}(2)_{4}$ topological order, and can be accessed by gauging the $\mathbb{Z}_{2}$ symmetry in the SET. Employing Levin-Wen string-net models with $\mathbb{Z}_{2}$-graded structure, we generalize this picture to construct a large class of commuting-projector models for $\mathbb{Z}_{2}$ SETs and non-Abelian topological orders exhibiting the same relation. Our construction provides the first commuting-projector-Hamiltonian realization of chiral bosonic non-Abelian topological order.Comment: 29+18 pages, 25 figure

Mass Predictions of Open-Flavour Hybrid Mesons from QCD Sum Rules

Within QCD, colourless states may be constructed corresponding to exotic matter outside of the traditional quark model. Experiments have recently observed tetraquark and pentaquark states, but no definitive hybrid meson signals have been observed. With the construction of the PANDA experiment at FAIR, and with full commissioning of the GlueX experiment at JLab expected to be completed this year, the opportunity for the observation of hybrid mesons has greatly increased. However, theoretical calculations are necessary to ascertain the identity of any experimental resonances that may be observed. We present selected QCD sum rule results from a full range of quantum numbers for open-flavour hybrid mesons with heavy valence quark content, including non-perturbative condensate contributions up to six-dimensions.Comment: Formatted from poster presented at 38th International Conference on High Energy Physics, 3-10 August 2016, Chicago, USA. 4 pages, 1 table and 2 figures. Submitted for publication in Proceedings of Science as PoS(ICHEP2016)849. Original poster attache

Characterization of the Critical Sets of Quantum Unitary Control Landscapes

This work considers various families of quantum control landscapes (i.e. objective functions for optimal control) for obtaining target unitary transformations as the general solution of the controlled Schr\"odinger equation. We examine the critical point structure of the kinematic landscapes J_F (U) = ||(U-W)A||^2 and J_P (U) = ||A||^4 - |Tr(AA'W'U)|^2 defined on the unitary group U(H) of a finite-dimensional Hilbert space H. The parameter operator A in B(H) is allowed to be completely arbitrary, yielding an objective function that measures the difference in the actions of U and the target W on a subspace of state space, namely the column space of A. The analysis of this function includes a description of the structure of the critical sets of these kinematic landscapes and characterization of the critical points as maxima, minima, and saddles. In addition, we consider the question of whether these landscapes are Morse-Bott functions on U(H). Landscapes based on the intrinsic (geodesic) distance on U(H) and the projective unitary group PU(H) are also considered. These results are then used to deduce properties of the critical set of the corresponding dynamical landscapes.Comment: 15 pages, 3 figure

Commuting-projector Hamiltonians for two-dimensional topological insulators: Edge physics and many-body invariants

Inspired by a recently constructed commuting-projector Hamiltonian for a two-dimensional (2D) time-reversal-invariant topological superconductor [Z. Wang et al., Phys. Rev. B 98, 094502 (2018)], we introduce a commuting-projector model that describes an interacting yet exactly solvable 2D topological insulator. We explicitly show that both the gapped and gapless boundaries of our model are consistent with those of band-theoretic, weakly interacting topological insulators. Interestingly, on certain lattices our time-reversal-symmetric models also enjoy CP symmetry, leading to intuitive interpretations of the bulk invariant for a CP-symmetric topological insulator upon putting the system on a Klein bottle. We also briefly discuss how these many-body invariants may be able to characterize models with only time-reversal symmetry

Ising Anyons in Frustration-Free Majorana-Dimer Models

Dimer models have long been a fruitful playground for understanding topological physics. Here we introduce a new class - termed Majorana-dimer models - wherein bosonic dimers are decorated with pairs of Majorana modes. We find that the simplest examples of such systems realize an intriguing, intrinsically fermionic phase of matter that can be viewed as the product of a chiral Ising theory, which hosts deconfined non-Abelian quasiparticles, and a topological $p_x - ip_y$ superconductor. While the bulk anyons are described by a single copy of the Ising theory, the edge remains fully gapped. Consequently, this phase can arise in exactly solvable, frustration-free models. We describe two parent Hamiltonians: one generalizes the well-known dimer model on the triangular lattice, while the other is most naturally understood as a model of decorated fluctuating loops on a honeycomb lattice. Using modular transformations, we show that the ground-state manifold of the latter model unambiguously exhibits all properties of the $\text{Ising} \times (p_x-ip_y)$ theory. We also discuss generalizations with more than one Majorana mode per site, which realize phases related to Kitaev's 16-fold way in a similar fashion

The Epidemiology of Stargardt Disease in the United Kingdom

The authors thank the British Ophthalmological Surveillance Unit (BOSU) for the support received, as well as Mr Barnaby Foot, research coordinator for BOSU, for his help and advice on this project. The authors thank the following ophthalmologists who assisted with data collection for this study: N. Acharya, S. Anwar, V. Bansal, P.N. Bishop, D. Byles, J.S. Chawla, A. Churchill, M. Clarke, B. Dhillon, M. Ekstein, S. George, J. Gillian, J.T. Gillow, D. Gilmour, R. Gray, P.T.S. Gregory, R. Gupta, S.P. Kelly, I.C. Lloyd, A. Lotery, M. McKibbin, R. MacLaren, G. Menon, A.T. Moore, A. Mulvihill, Y. Osoba, R. Pilling, H. Porooshani, A. Raghu Ram, T. Rimmer, I. Russell-Eggitt, M. Sarhan, R. Savides, S. Shafquat, A. Smith, A. Tekriwal, P. Tesha, P. Watts.Peer reviewedPublisher PD

Birth/birth-death processes and their computable transition probabilities with biological applications

Birth-death processes track the size of a univariate population, but many biological systems involve interaction between populations, necessitating models for two or more populations simultaneously. A lack of efficient methods for evaluating finite-time transition probabilities of bivariate processes, however, has restricted statistical inference in these models. Researchers rely on computationally expensive methods such as matrix exponentiation or Monte Carlo approximation, restricting likelihood-based inference to small systems, or indirect methods such as approximate Bayesian computation. In this paper, we introduce the birth(death)/birth-death process, a tractable bivariate extension of the birth-death process. We develop an efficient and robust algorithm to calculate the transition probabilities of birth(death)/birth-death processes using a continued fraction representation of their Laplace transforms. Next, we identify several exemplary models arising in molecular epidemiology, macro-parasite evolution, and infectious disease modeling that fall within this class, and demonstrate advantages of our proposed method over existing approaches to inference in these models. Notably, the ubiquitous stochastic susceptible-infectious-removed (SIR) model falls within this class, and we emphasize that computable transition probabilities newly enable direct inference of parameters in the SIR model. We also propose a very fast method for approximating the transition probabilities under the SIR model via a novel branching process simplification, and compare it to the continued fraction representation method with application to the 17th century plague in Eyam. Although the two methods produce similar maximum a posteriori estimates, the branching process approximation fails to capture the correlation structure in the joint posterior distribution

Anomalous morphology in left hemisphere motor and premotor cortex of children who stutter

Stuttering is a neurodevelopmental disorder that affects the smooth flow of speech production. Stuttering onset occurs during a dynamic period of development when children first start learning to formulate sentences. Although most children grow out of stuttering naturally, ∼1% of all children develop persistent stuttering that can lead to significant psychosocial consequences throughout one’s life. To date, few studies have examined neural bases of stuttering in children who stutter, and even fewer have examined the basis for natural recovery versus persistence of stuttering. Here we report the first study to conduct surface-based analysis of the brain morphometric measures in children who stutter. We used FreeSurfer to extract cortical size and shape measures from structural MRI scans collected from the initial year of a longitudinal study involving 70 children (36 stuttering, 34 controls) in the 3–10-year range. The stuttering group was further divided into two groups: persistent and recovered, based on their later longitudinal visits that allowed determination of their eventual clinical outcome. A region of interest analysis that focused on the left hemisphere speech network and a whole-brain exploratory analysis were conducted to examine group differences and group × age interaction effects. We found that the persistent group could be differentiated from the control and recovered groups by reduced cortical thickness in left motor and lateral premotor cortical regions. The recovered group showed an age-related decrease in local gyrification in the left medial premotor cortex (supplementary motor area and and pre-supplementary motor area). These results provide strong evidence of a primary deficit in the left hemisphere speech network, specifically involving lateral premotor cortex and primary motor cortex, in persistent developmental stuttering. Results further point to a possible compensatory mechanism involving left medial premotor cortex in those who recover from childhood stuttering.This study was supported by Award Numbers R01DC011277 (SC) and R01DC007683 (FG) from the National Institute on Deafness and other Communication Disorders (NIDCD). The content is solely the responsibility of the authors and does not necessarily represent the official views of the NIDCD or the National Institutes of Health. (R01DC011277 - National Institute on Deafness and other Communication Disorders (NIDCD); R01DC007683 - National Institute on Deafness and other Communication Disorders (NIDCD))Accepted manuscrip

On the impact of heterogeneity and back-end scheduling in load balancing designs

Load balancing is a common approach for task assignment in distributed architectures. In this paper, we show that the degree of inefficiency in load balancing designs is highly dependent on the scheduling discipline used at each of the backend servers. Traditionally, the back-end scheduler can be modeled as Processor Sharing (PS), in which case the degree of inefficiency grows linearly with the number of servers. However, if the back-end scheduler is changed to Shortest Remaining Processing Time (SRPT), the degree of inefficiency can be independent of the number of servers, instead depending only on the heterogeneity of the speeds of the servers. Further, switching the back-end scheduler to SRPT can provide significant improvements in the overall mean response time of the system as long as the heterogeneity of the server speeds is small