Exact solution of mean geodesic distance for Vicsek fractals

The Vicsek fractals are one of the most interesting classes of fractals and the study of their structural properties is important. In this paper, the exact formula for the mean geodesic distance of Vicsek fractals is found. The quantity is computed precisely through the recurrence relations derived from the self-similar structure of the fractals considered. The obtained exact solution exhibits that the mean geodesic distance approximately increases as an exponential function of the number of nodes, with the exponent equal to the reciprocal of the fractal dimension. The closed-form solution is confirmed by extensive numerical calculations.Comment: 4 pages, 3 figure

A general comparison theorem for 1-dimensional anticipated BSDEs

Anticipated backward stochastic differential equation (ABSDE) studied the first time in 2007 is a new type of stochastic differential equations. In this paper, we establish a general comparison theorem for 1-dimensional ABSDEs with the generators depending on the anticipated term of $Z$.Comment: 8 page

Evolution of worldwide stock markets, correlation structure and correlation based graphs

We investigate the daily correlation present among market indices of stock exchanges located all over the world in the time period Jan 1996 - Jul 2009. We discover that the correlation among market indices presents both a fast and a slow dynamics. The slow dynamics reflects the development and consolidation of globalization. The fast dynamics is associated with critical events that originate in a specific country or region of the world and rapidly affect the global system. We provide evidence that the short term timescale of correlation among market indices is less than 3 trading months (about 60 trading days). The average values of the non diagonal elements of the correlation matrix, correlation based graphs and the spectral properties of the largest eigenvalues and eigenvectors of the correlation matrix are carrying information about the fast and slow dynamics of correlation of market indices. We introduce a measure of mutual information based on link co-occurrence in networks, in order to detect the fast dynamics of successive changes of correlation based graphs in a quantitative way.Comment: 8 pages, 11 figure

Epitaxial growth and planar dielectric properties of compositionally graded (Ba[sub 1-x]Sr[sub x])TiO₃ thin films prepared by pulsed-laser deposition

2001-2002 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Scaling on hysteresis dispersion in ferroelectric systems

Author name used in this publication: Z. G. LiuAuthor name used in this publication: N. B. MingAuthor name used in this publication: H. L. W. ChanAuthor name used in this publication: C. L. Choy2000-2001 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Objective measurement for surgical skill evaluation

The purpose of this study was to identify measurable parameters that can be used to quantitatively assess psychomotor skills, specifically for surgical skills assessment. Sixteen participants were recruited from two groups: surgeon (N = 5) and non-surgeon (N = 11). Both groups underwent a psychomotor test using a custom developed ‘Green Target’ module which was designed using a virtual reality system. Six parameters were used to compare the psychomotor skills between the two groups. The results showed that surgeons outperformed the non-surgeons in five out of six parameters investigated and the difference was statistically significant. The average normalised comparison values for surgeons and non-surgeons for motion path accuracy, motion path precision, economy of movement, end-point accuracy and end-point precision were 0.13±0.12 and 0.17±0.12, 0.08±0.11 and 0.10±0.10, 3.76±1.76 and 4.08±2.24, 0.12±0.10 and 0.17±0.11, 0.04±0.10 and 0.07±s0.10 respectively, p < 0.05). These parameters can potentially be used to objectively assess the performance of surgical skill

Coexisting Kondo singlet state with antiferromagnetic long-range order: A possible ground state for Kondo insulators

The ground-state phase diagram of a half-filled anisotropic Kondo lattice model is calculated within a mean-field theory. For small transverse exchange coupling $J_{\perp}<J_{\perp c1}$, the ground state shows an antiferromagnetic long-range order with finite staggered magnetizations of both localized spins and conduction electrons. When $J_{\perp}>J_{\perp c2}$, the long-range order is destroyed and the system is in a disordered Kondo singlet state with a hybridization gap. Both ground states can describe the low-temperature phases of Kondo insulating compounds. Between these two distinct phases, there may be a coexistent regime as a result of the balance between local Kondo screening and magnetic interactions.Comment: four pages, Revtex, one figure; to be published in Phys. Rev. B, 1 July issue, 200

Operator Quantum Geometric Tensor and Quantum Phase Transitions

We extend the quantum geometric tensor from the state space to the operator level,and investigate its properties like the additivity for factorizable models and the splitting of two kinds contributions for the case of stationary reference states. This operator-quantum-geometric tensor (OQGT) is shown to reflect the sensitivity of unitary operations against perturbations of multi parameters. General results for the cases of time evolutions with given stationary reference states are obtained. By this approach, we get exact results for the rotated XY models, and show relations between the OQGT and quantum criticality.Comment: One more reference added. 6 pages,2 figs. Accepted by EP

Partially incoherent optical vortices in self-focusing nonlinear media

We observe stable propagation of spatially localized single- and double-charge optical vortices in a self-focusing nonlinear medium. The vortices are created by self-trapping of partially incoherent light carrying a phase dislocation, and they are stabilized when the spatial incoherence of light exceeds a certain threshold. We confirm the vortex stabilization effect by numerical simulations and also show that the similar mechanism of stabilization applies to higher-order vortices.Comment: 4 pages and 6 figures (including 3 experimental figures

Epitaxial growth, dielectric response, and microstructure of compositionally graded (Ba,Sr)TiO₃ thin films grown on (100) MgO substrates by pulsed laser deposition

2007-2008 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe