Higher rank numerical ranges of normal matrices

The higher rank numerical range is closely connected to the construction of quantum error correction code for a noisy quantum channel. It is known that if a normal matrix $A \in M_n$ has eigenvalues $a_1, \..., a_n$, then its higher rank numerical range $\Lambda_k(A)$ is the intersection of convex polygons with vertices $a_{j_1}, \..., a_{j_{n-k+1}}$, where $1 \le j_1 < \... < j_{n-k+1} \le n$. In this paper, it is shown that the higher rank numerical range of a normal matrix with $m$ distinct eigenvalues can be written as the intersection of no more than $\max\{m,4\}$ closed half planes. In addition, given a convex polygon ${\mathcal P}$ a construction is given for a normal matrix $A \in M_n$ with minimum $n$ such that $\Lambda_k(A) = {\mathcal P}$. In particular, if ${\mathcal P}$ has $p$ vertices, with $p \ge 3$, there is a normal matrix $A \in M_n$ with $n \le \max\left\{p+k-1, 2k+2 \right\}$ such that $\Lambda_k(A) = {\mathcal P}$.Comment: 12 pages, 9 figures, to appear in SIAM Journal on Matrix Analysis and Application

Recursive Encoding and Decoding of Noiseless Subsystem and Decoherence Free Subspace

When the environmental disturbace to a quantum system has a wavelength much larger than the system size, all qubits localized within a small area are under action of the same error operators. Noiseless subsystem and decoherence free subspace are known to correct such collective errors. We construct simple quantum circuits, which implement these collective error correction codes, for a small number $n$ of physical qubits. A single logical qubit is encoded with $n=3$ and $n=4$, while two logical qubits are encoded with $n=5$. The recursive relations among the subspaces employed in noiseless subsystem and decoherence free subspace play essential r\^oles in our implementation. The recursive relations also show that the number of gates required to encode $m$ logical qubits increases linearly in $m$.Comment: 9 pages, 3 figure

Light atom quantum oscillations in UC and US

High energy vibrational scattering in the binary systems UC and US is measured using time-of-flight inelastic neutron scattering. A clear set of well-defined peaks equally separated in energy is observed in UC, corresponding to harmonic oscillations of the light C atoms in a cage of heavy U atoms. The scattering is much weaker in US and only a few oscillator peaks are visible. We show how the difference between the materials can be understood by considering the neutron scattering lengths and masses of the lighter atoms. Monte Carlo ray tracing is used to simulate the scattering, with near quantitative agreement with the data in UC, and some differences with US. The possibility of observing anharmonicity and anisotropy in the potentials of the light atoms is investigated in UC. Overall the observed data is well accounted for by considering each light atom as a single atom isotropic quantum harmonic oscillator.Comment: 10 pages, 8 figure

Perceptions of Safety Climate in Construction Projects between Workers and Managers/Supervisors in the Developing Country of Iran

What are the different perceptions on safety climate (SC) by workers and managers/supervisors engaged in the construction industry of developing countries? Reconciling these two differing views is pivotal for mitigating and avoiding both the injured and fatal accidents in the construction industry, especially in those developing countries where safety conditions are poor and unpredictable, and safety measures are inadequate in most cases. To answer this research question, the collective perceptions of 118 construction workers and 123 managers/supervisors on the SC in construction projects in Iran were gleaned and investigated. In particular, these perceptions were initially collected by two different empirical surveys validated by a sample of university professors and construction managers and then analyzed through the Kaiser-Meyer-Olkin (KMO) test and Bartlett’s test of sphericity under factor analysis, together with a one-sample t-test. Results indicated that “workers’ attitudes and perceptions”, “safety knowledge and training”, “working relationships and roles of colleagues”, and “workers’ risk perceptions” are important categories of SC factors perceived by construction workers, whereas “safety rules and management practices” is the essential category of SC factors discerned by managers/supervisors. The difference in perceptions between workers and managers/supervisors is considered to be beneficial for an overall understanding of SC in general and for developing countries in particular. Moreover, a series of effective suggestions for improving SC in the construction industry of developing countries are provided with reference to each category. The views of SC factors are reinforced as a social process combining the synergies of workers and managers/supervisors, as well as proper safety training to be pushed forward as an essential activity that should be incorporated in human resources development of construction organizations so as to improve the existing level of SC, leading to fewer accidents at the industry level

State Transition Algorithm

In terms of the concepts of state and state transition, a new heuristic random search algorithm named state transition algorithm is proposed. For continuous function optimization problems, four special transformation operators called rotation, translation, expansion and axesion are designed. Adjusting measures of the transformations are mainly studied to keep the balance of exploration and exploitation. Convergence analysis is also discussed about the algorithm based on random search theory. In the meanwhile, to strengthen the search ability in high dimensional space, communication strategy is introduced into the basic algorithm and intermittent exchange is presented to prevent premature convergence. Finally, experiments are carried out for the algorithms. With 10 common benchmark unconstrained continuous functions used to test the performance, the results show that state transition algorithms are promising algorithms due to their good global search capability and convergence property when compared with some popular algorithms.Comment: 18 pages, 28 figure

A Study of The Formation of Stationary Localized States Due to Nonlinear Impurities Using The Discrete Nonlinear Schr\"odinger Equation

The Discrete Nonlinear Schr$\ddot{o}$dinger Equation is used to study the formation of stationary localized states due to a single nonlinear impurity in a Caley tree and a dimeric nonlinear impurity in the one dimensional system. The rotational nonlinear impurity and the impurity of the form $-\chi \mid C \mid^{\sigma}$ where $\sigma$ is arbitrary and $\chi$ is the nonlinearity parameter are considered. Furthermore, $\mid C \mid$ represents the absolute value of the amplitude. Altogether four cases are studies. The usual Greens function approach and the ansatz approach are coherently blended to obtain phase diagrams showing regions of different number of states in the parameter space. Equations of critical lines separating various regions in phase diagrams are derived analytically. For the dimeric problem with the impurity $-\chi \mid C \mid^{\sigma}$, three values of $\mid \chi_{cr} \mid$, namely, $\mid \chi_{cr} \mid = 2$, at $\sigma = 0$ and $\mid \chi_{cr} \mid = 1$ and $\frac{8}{3}$ for $\sigma = 2$ are obtained. Last two values are lower than the existing values. Energy of the states as a function of parameters is also obtained. A model derivation for the impurities is presented. The implication of our results in relation to disordered systems comprising of nonlinear impurities and perfect sites is discussed.Comment: 10 figures available on reques

Global Guidelines in Dermatology Mapping Project (GUIDEMAP):a scoping review of dermatology clinical practice guidelines

Background Clinical practice guidelines (CPGs) play a critical role in standardizing and improving treatment outcomes based on the available evidence. It is unclear how many CPGs are available globally to assist clinicians in the management of patients with skin disease. Objectives To search for and identify CPGs for dermatological conditions with the highest burden globally. Methods We adapted a list of 12 dermatological conditions with the highest burden from the Global Burden of Disease (GBD) study 2019. A systematic literature search was done to identify CPGs published between October 2014 to October 2019. The scoping review was conducted and reported in accordance with the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) framework. Results A total of 226 CPGs were included. Melanoma had the greatest representation in the CPGs, followed by dermatitis and psoriasis. Skin cancers had a relatively high CPG representation but with lower GBD disease burden ranking. There was an uneven distribution by geographical region, with resource-poor settings being under-represented. The skin disease categories of the CPGs correlated weakly with the GBD disability-adjusted life-years metrics. Eighty-nine CPGs did not have funding disclosures and 34 CPGs were behind a paywall. Conclusions The global production of dermatology CPGs showed wide variation in geographical representation, article accessibility and reporting of funding. The number of skin disease CPGs were not commensurate with its disease burden. Future work will critically appraise the methodology and quality of dermatology CPGs and lead to the production of an accessible online resource summarizing these findings.Dermatology-oncolog

Optimization of a high work function solution processed vanadium oxide hole-extracting layer for small molecule and polymer organic photovoltaic cells

We report a method of fabricating a high work function, solution processable vanadium oxide (V2Ox(sol)) hole-extracting layer. The atmospheric processing conditions of film preparation have a critical influence on the electronic structure and stoichiometry of the V2Ox(sol), with a direct impact on organic photovoltaic (OPV) cell performance. Combined Kelvin probe (KP) and ultraviolet photoemission spectroscopy (UPS) measurements reveal a high work function, n-type character for the thin films, analogous to previously reported thermally evaporated transition metal oxides. Additional states within the band gap of V2Ox(sol) are observed in the UPS spectra and are demonstrated using X-ray photoelectron spectroscopy (XPS) to be due to the substoichiometric nature of V2Ox(sol). The optimized V2Ox(sol) layer performance is compared directly to bare indium–tin oxide (ITO), poly(ethyleneoxythiophene):poly(styrenesulfonate) (PEDOT:PSS), and thermally evaporated molybdenum oxide (MoOx) interfaces in both small molecule/fullerene and polymer/fullerene structures. OPV cells incorporating V2Ox(sol) are reported to achieve favorable initial cell performance and cell stability attributes