Calculation of propagation loss in photonic crystal waveguides by FDTD technique and Pade approximation

The propagation losses in single-line defect waveguides in a two-dimensional (2D) square-lattice photonic crystal (PC) consisted of infinite dielectric rods and a triangular-lattice photonic crystal slab with air holes are studied by finite-difference time-domain (FDTD) technique and a Pade approximation. The decaying constant beta of the fundamental guided mode is calculated from the mode frequency, the quality factor (Q-factor) and the group velocity v(g) as beta = omega/(2Qv(g)). In the 2D square-lattice photonic crystal waveguide (PCW), the decaying rate ranged from 10(3) to 10(-4) cm(-1) can be reliably obtained from 8 x 10(3)-item FDTD output with the FDTD computing time of 0.386 ps. And at most 1 ps is required for the mode with the Q-factor of 4 x 10(11) and the decaying rate of 10(-7) cm(-1). In the triangular-lattice photonic crystal slab, a 10(4)-item FDTD output is required to obtain a reliable spectrum with the Q-factor of 2.5 x 10(8) and the decaying rate of 0.05 cm(-1). (c) 2004 Elsevier B.V. All rights reserved.

Finite-difference time-domain analysis of deformed square cavity filters with a traveling-wave-like filtering response by mode coupling

An add-drop filter based on a perfect square resonator can realize a maximum of only 25% power dropping because the confined modes are standing-wave modes. By means of mode coupling between two modes with inverse symmetry properties, a traveling-wave-like filtering response is obtained in a two-dimensional single square cavity filter with cut or circular corners by finite-difference time-domain simulation. The optimized deformation parameters for an add-drop filter can be accurately predicted as the overlapping point of the two coupling modes in an isolated deformed square cavity. More than 80% power dropping can be obtained in a deformed square cavity filter with a side length of 3.01 mu m. The free spectral region is decided by the mode spacing between modes, with the sum of the mode indices differing by 1. (c) 2007 Optical Society of America.

BASS CYCLIC UNITS AS FACTORS IN A FREE GROUP IN INTEGRAL GROUP RING UNITS

Marciniak and Sehgal showed that if u is a non-trivial bicyclic unit of an integral group ring then there is a bicyclic unit v such that u and v generate a non-abelian free group. A similar result does not hold for Bass cyclic units of infinite order based on non-central elements as some of them have finite order modulo the center. We prove a theorem that suggests that this is the only limitation to obtain a non-abelian free group from a given Bass cyclic unit. More precisely, we prove that if u is a Bass cyclic unit of an integral group ring ZG of a solvable and finite group G, such that u has infinite order modulo the center of U(ZG) and it is based on an element of prime order, then there is a non-abelian free group generated by a power of u and a power of a unit in ZG which is either a Bass cyclic unit or a bicyclic unit.

SIGMA THEORY AND TWISTED CONJUGACY CLASSES

Using Sigma theory we show that for large classes of groups G there is a subgroup H of finite index in Aut(G) such that for phi is an element of H the Reidemeister number R(phi) is infinite. This includes all finitely generated nonpolycyclic groups G that fall into one of the following classes: nilpotent-by-abelian groups of type FP(infinity); groups G/G `` of finite Prufer rank; groups G of type FP(2) without free nonabelian subgroups and with nonpolycyclic maximal metabelian quotient; some direct products of groups; or the pure symmetric automorphism group. Using a different argument we show that the result also holds for 1-ended nonabelian nonsurface limit groups. In some cases, such as with the generalized Thompson`s groups F(n,0) and their finite direct products, H = Aut(G).

Involutions and free pairs of bicyclic units in integral group rings

If * : G -> G is an involution on the finite group G, then * extends to an involution on the integral group ring Z[G] . In this paper, we consider whether bicyclic units u is an element of Z[G] exist with the property that the group < u, u*> generated by u and u* is free on the two generators. If this occurs, we say that (u, u*)is a free bicyclic pair. It turns out that the existence of u depends strongly upon the structure of G and on the nature of the involution. One positive result here is that if G is a nonabelian group with all Sylow subgroups abelian, then for any involution *, Z[G] contains a free bicyclic pair.

Nest Digging by Leaf-Cutting Ants: Effect of Group Size and Functional Structures.

Leaf-cutting ant workers dig underground chambers, for housing their symbiotic fungus, interconnected by a vast quantity of tunnels whose function is to permit the entrance of food (leaves), gaseous exchanges, andmovement of workers, offspring, and the queen. Digging is a task executed by a group of workers, but little is known about the group effect and group-constructed functional structures. Thus, we analyzed the structures formed by worker groups (5, 10, 20, and 40 individuals) of the leaf-cutting ant, Atta sexdens rubropilosa, for 2 days of excavation. The digging arena was the same for the 4 groups, with each group corresponding to a different density. Our results verified a pattern of tunneling by the workers, but no chamber was constructed. The group effect is well known, since the 40-worker group dug significantly more than the groups of 5, 10, and 20. These groups did not differ statistically from each other. Analysis of load/worker verified that workers of the smallest group carried the greatest load. Our paper demonstrates the group effect on the digging of nests, namely, that excavation is proportional to group size, but without emergence of a functional structure such as a chamber.

Finite Groups as the Union of Proper Subgroups

2000 Mathematics Subject Classification: 20D60,20E15.

Generalized cluster states based on finite groups

We define generalized cluster states based on finite group algebras in analogy to the generalization of the toric code to the Kitaev quantum double models. We do this by showing a general correspondence between systems with CSS structure and finite group algebras, and applying this to the cluster states to derive their generalization. We then investigate properties of these states including their projected entangled pair state representations, global symmetries, and relationship to the Kitaev quantum double models. We also discuss possible applications of these states.

Development of a computer simulation tool for application in adolescent spinal deformity surgery

Scoliosis is a three-dimensional spinal deformity which requires surgical correction in progressive cases. In order to optimize correction and avoid complications following scoliosis surgery, patient-specific finite element models (FEM) are being developed and validated by our group. In this paper, the modeling methodology is described and two clinically relevant load cases are simulated for a single patient. Firstly, a pre-operative patient flexibility assessment, the fulcrum bending radiograph, is simulated to assess the model's ability to represent spine flexibility. Secondly, intra-operative forces during single rod anterior correction are simulated. Clinically, the patient had an initial Cobb angle of 44 degrees, which reduced to 26 degrees during fulcrum bending. Surgically, the coronal deformity corrected to 14 degrees. The simulated initial Cobb angle was 40 degrees, which reduced to 23 degrees following the fulcrum bending load case. The simulated surgical procedure corrected the coronal deformity to 14 degrees. The computed results for the patient-specific FEM are within the accepted clinical Cobb measuring error of 5 degrees, suggested that this modeling methodology is capable of capturing the biomechanical behaviour of a scoliotic human spine during anterior corrective surgery.

Patient-specific computational biomechanics for simulating adolescent scoliosis surgery : predicted vs clinical correction for a preliminary series of six patients

Scoliosis is a spinal deformity that requires surgical correction in progressive cases. In order to optimize surgical outcomes, patient-specific finite element models are being developed by our group. In this paper, a single rod anterior correction procedure is simulated for a group of six scoliosis patients. For each patient, personalised model geometry was derived from low-dose CT scans, and clinically measured intra-operative corrective forces were applied. However, tissue material properties were not patient-specific, being derived from existing literature. Clinically, the patient group had a mean initial Cobb angle of 47.3 degrees, which was corrected to 17.5 degrees after surgery. The mean simulated post-operative Cobb angle for the group was 18.1 degrees. Although this represents good agreement between clinical and simulated corrections, the discrepancy between clinical and simulated Cobb angle for individual patients varied between -10.3 and +8.6 degrees, with only three of the six patients matching the clinical result to within accepted Cobb measurement error of +-5 degrees. The results of this study suggest that spinal tissue material properties play an important role in governing the correction obtained during surgery, and that patient-specific modelling approaches must address the question of how to prescribe patient-specific soft tissue properties for spine surgery simulation.

Improved sensorimotor adaptation after exhaustive exercise is accompanied by altered brain activity

Acute exercise has been shown to exhibit different effects on human sensorimotor behavior; however, the causes and mechanisms of the responses are often not clear. The primary aim of the present study was to determine the effects of incremental running until exhaustion on sensorimotor performance and adaptation in a tracking task. Subjects were randomly assigned to a running group (RG), a tracking group (TG), or a running followed by tracking group (RTG), with 10 subjects assigned to each group. Treadmill running velocity was initially set at 2.0 m s− 1, increasing by 0.5 m s− 1 every 5 min until exhaustion. Tracking consisted of 35 episodes (each 40 s) where the subjects' task was to track a visual target on a computer screen while the visual feedback was veridical (performance) or left-right reversed (adaptation). Resting electroencephalographic (EEG) activity was recorded before and after each experimental condition (running, tracking, rest). Tracking performance and the final amount of adaptation did not differ between groups. However, task adaptation was significantly faster in RTG compared to TG. In addition, increased alpha and beta power were observed following tracking in TG but not RTG although exhaustive running failed to induce significant changes in these frequency bands. Our results suggest that exhaustive running can facilitate adaptation processes in a manual tracking task. Attenuated cortical activation following tracking in the exercise condition was interpreted to indicate cortical efficiency and exercise-induced facilitation of selective central processes during actual task demands.

Impact of passenger group dynamics on an airport evacuation process using an agent-based model

The safety of passengers is a major concern to airports. In the event of crises, having an effective and efficient evacuation process in place can significantly aid in enhancing passenger safety. Hence, it is necessary for airport operators to have an in-depth understanding of the evacuation process of their airport terminal. Although evacuation models have been used in studying pedestrian behaviour for decades, little research has been done in considering the evacuees’ group dynamics and the complexity of the environment. In this paper, an agent-based model is presented to simulate passenger evacuation process. Different exits were allocated to passengers based on their location and security level. The simulation results show that the evacuation time can be influenced by passenger group dynamics. This model also provides a convenient way to design airport evacuation strategy and examine its efficiency. The model was created using AnyLogic software and its parameters were initialised using recent research data published in the literature.

On secure multi-party computation in black-box groups

We study the natural problem of secure n-party computation (in the passive, computationally unbounded attack model) of the n-product function f G (x 1,...,x n ) = x 1 ·x 2 ⋯ x n in an arbitrary finite group (G,·), where the input of party P i is x i  ∈ G for i = 1,...,n. For flexibility, we are interested in protocols for f G which require only black-box access to the group G (i.e. the only computations performed by players in the protocol are a group operation, a group inverse, or sampling a uniformly random group element). Our results are as follows. First, on the negative side, we show that if (G,·) is non-abelian and n ≥ 4, then no ⌈n/2⌉-private protocol for computing f G exists. Second, on the positive side, we initiate an approach for construction of black-box protocols for f G based on k-of-k threshold secret sharing schemes, which are efficiently implementable over any black-box group G. We reduce the problem of constructing such protocols to a combinatorial colouring problem in planar graphs. We then give two constructions for such graph colourings. Our first colouring construction gives a protocol with optimal collusion resistance t < n/2, but has exponential communication complexity O(n*2t+1^2/t) group elements (this construction easily extends to general adversary structures). Our second probabilistic colouring construction gives a protocol with (close to optimal) collusion resistance t < n/μ for a graph-related constant μ ≤ 2.948, and has efficient communication complexity O(n*t^2) group elements. Furthermore, we believe that our results can be improved by further study of the associated combinatorial problems.

Structural analysis and magnetic resonance imaging predict plaque vulnerability: A study comparing symptomatic and asymptomatic individuals

Background: More than half of all cerebral ischemic events are the result of rupture of extracranial plaques. The clinical determination of carotid plaque vulnerability is currently based solely on luminal stenosis; however, it has been increasingly suggested that plaque morphology and biomechanical stress should also be considered. We used finite element analysis based on in vivo magnetic resonance imaging (MRI) to simulate the stress distributions within plaques of asymptomatic and symptomatic individuals. Methods: Thirty nonconsecutive subjects (15 symptomatic and 15 asymptomatic) underwent high-resolution multisequence in vivo MRI of the carotid bifurcation. Stress analysis was performed based on the geometry derived from in vivo MRI of the carotid artery at the point of maximal stenosis. The finite element analysis model considered plaque components to be hyperelastic. The peak stresses within the plaques of symptomatic and asymptomatic individuals were compared. Results: High stress concentrations were found at the shoulder regions of symptomatic plaques, and the maximal stresses predicted in this group were significantly higher than those in the asymptomatic group (508.2 ± 193.1 vs 269.6 ± 107.9 kPa; P = .004). Conclusions: Maximal predicted plaque stresses in symptomatic patients were higher than those predicted in asymptomatic patients by finite element analysis, suggesting the possibility that plaques with higher stresses may be more prone to be symptomatic and rupture. If further validated by large-scale longitudinal studies, biomechanical stress analysis based on high resolution in vivo MRI could potentially act as a useful tool for risk assessment of carotid atheroma. It may help in the identification of patients with asymptomatic carotid atheroma at greatest risk of developing symptoms or mild-to-moderate symptomatic stenoses, which currently fall outside current clinical guidelines for intervention.

Grower group case study on new farming practices in the Herbert region, Australia

Growers working together have proven to be a successful method for improving the utilization of farm resources and accelerating the adoption of the Sugar Yield Decline Joint Venture principles (SYDJV). The Pinnacle Precision Farming Group was formed in 2004 with the aim to bring together the ideas, knowledge and resources of growers in the Herbert region. Along with their common interest in controlled traffic, minimal tillage and crop rotations, the grower group utilize a farm machinery contractor to provide some of their major farming operations. This paper provides an insight into the changes made by the Pinnacle Precision Farming Group and their journey to adopt the new farming system practices. This paper also details the changes made by the group machinery contractor and a comparison of the old and new farming systems used by a group member. A focus point of the document is the impact of the new farming system on the economic, social and environmental components of the farming business. Analysis of the new farming system with a legume crop rotation revealed an increase in the farm gross margin by AU$22 024 and, in addition, a reduction in tractor operation time by 38% across the whole farm. This represents a return on marginal capital of 14.68 times the original capital outlay required by the group member. Using the new farming system without a legume crop will still improve the group members whole of farm gross margin by AU$6 839 and reduce tractor operation time by 43% across the whole farm. The Pinnacle Precision Farming group recognize the need to continually improve their farming businesses and believe that the new farming system principles are critical for the long term viability of the industry. [U$1 = AU$1.19].