Delaying mismatched field multiplications in pairing computations

Miller’s algorithm for computing pairings involves perform- ing multiplications between elements that belong to different finite fields. Namely, elements in the full extension field Fpk are multiplied by elements contained in proper subfields F pk/d , and by elements in the base field Fp . We show that significant speedups in pairing computations can be achieved by delaying these “mismatched” multiplications for an optimal number of iterations. Importantly, we show that our technique can be easily integrated into traditional pairing algorithms; implementers can exploit the computational savings herein by applying only minor changes to existing pairing code.

Lie group symmetry analysis for granular media stress equations

The Airy stress function, although frequently employed in classical linear elasticity, does not receive similar usage for granular media problems. For plane strain quasi-static deformations of a cohesionless Coulomb–Mohr granular solid, a single nonlinear partial differential equation is formulated for the Airy stress function by combining the equilibrium equations with the yield condition. This has certain advantages from the usual approach, in which two stress invariants and a stress angle are introduced, and a system of two partial differential equations is needed to describe the flow. In the present study, the symmetry analysis of differential equations is utilised for our single partial differential equation, and by computing an optimal system of one-dimensional Lie algebras, a complete set of group-invariant solutions is derived. By this it is meant that any group-invariant solution of the governing partial differential equation (provided it can be derived via the classical symmetries method) may be obtained as a member of this set by a suitable group transformation. For general values of the parameters (angle of internal friction and gravity g) it is found there are three distinct classes of solutions which correspond to granular flows considered previously in the literature. For the two limiting cases of high angle of internal friction and zero gravity, the governing partial differential equation admit larger families of Lie point symmetries, and from these symmetries, further solutions are derived, many of which are new. Furthermore, the majority of these solutions are exact, which is rare for granular flow, especially in the case of gravity driven flows.

Interocular symmetry in myopic anisometropia

Purpose: To investigate the interocular symmetry of optical, biometric and biomechanical characteristics between the fellow eyes of myopic anisometropes. Methods: Thirty-four young, healthy myopic anisometropic adults (≥ 1 D spherical equivalent difference between eyes) without amblyopia or strabismus were recruited. A range of biometric and optical parameters were measured in both eyes of each subject including; axial length, ocular aberrations, intraocular pressure (IOP), corneal topography and biomechanics. Ocular sighting dominance was also measured. Results: Mean absolute spherical equivalent anisometropia was 1.70 ± 0.74 D and there was a strong correlation between the degree of anisometropia and the interocular difference in axial length (r = 0.81, p < 0.001). The more and less myopic eyes displayed a high degree of interocular symmetry for the majority of biometric, biomechanical and optical parameters measured. When the level of anisometropia exceeded 1.75 D, the more myopic eye was more likely to be the dominant sighting eye than for lower levels of anisometropia (p=0.002). Subjects with greater levels of anisometropia (> 1.75 D) also showed high levels of correlation between the dominant and non-dominant eyes in their biometric, biomechanical and optical characteristics. Conclusions: Although significantly different in axial length, anisometropic eyes display a high degree of interocular symmetry for a range of anterior eye biometrics and optical parameters. For higher levels of anisometropia, the more myopic eye tends to be the dominant sighting eye.

Symmetry of in-shoe force signatures in athletes under field conditions : an application for injury prevention

The aetiology behind overuse injuries such as stress fractures is complex and multi-factorial. In sporting events where the loading is likely to be uneven (e.g. hurdling and jumps), research has suggested that the frequency of stress fractures seems to favour the athlete’s dominant limb. The tendency for an individual to have a preferred limb for voluntary motor acts makes limb selection a possible factor behind the development of unilateral overuse injuries, particularly when repeatedly used during high loading activities. The event of sprint hurdling is well suited for the study of loading asymmetry as the hurdling technique is repetitive and the limb movement asymmetrical. Of relevance to this study is the high incidence of Navicular Stress Fractures (NSF) in hurdlers, with suggestions there is a tendency for the fracture to develop in the trail leg foot, although this is not fully accepted. The Ground Reaction Force (GRF) with each foot contact is influenced by the hurdle action, with research finding step-to-step loading variations. However, it is unknown if this loading asymmetry extends to individual forefoot joints, thereby influencing stress fracture development. The first part of the study involved a series of investigations using a commercially available matrix style in-shoe sensor system (FscanTM, Tekscan Inc.). The suitability of insole sensor systems and custom made discrete sensors for use in hurdling-related training activities was assessed. The methodology used to analyse foot loading with each technology was investigated. The insole and discrete sensors systems tested proved to be unsuitable for use during full pace hurdling. Instead, a running barrier task designed to replicate the four repetitive foot contacts present during hurdling was assessed. This involved the clearance of a series of 6 barriers (low training hurdles), place in a straight line, using 4 strides between each. The second part of the study involved the analysis of "inter-limb" and "within foot loading asymmetries" using stance duration as well as vertical GRF under the Hallux (T1), the first metatarsal head (M1) and the central forefoot peak pressure site (M2), during walking, running, and running with barrier clearances. The contribution to loading asymmetry that each of the four repetitive foot contacts made during a series of barrier clearances was also assessed. Inter-limb asymmetry, in forefoot loading, occurred at discrete forefoot sites in a non-uniform manner across the three gait conditions. When the individual barrier foot contacts were compared, the stance duration was asymmetrical and the proportion of total forefoot load at M2 was asymmetrical. There were no significant differences between the proportion of forefoot load at M1, compared to M2; for any of the steps involved in the barrier clearance. A case study testing experimental (discrete) sensors during full pace sprinting and hurdling found that during both gait conditions, the trail limb experienced the greater vertical GRF at M1 and M2. During full pace hurdling, increased stance duration and vertical loading was a characteristic of the trail limb hurdle foot contacts. Commercially available in-shoe systems are not suitable for on field assessment of full pace hurdling. For the use of discrete sensor technology to become commonplace in the field, more robust sensors need to be developed.

Subcarrier pairing and relay assignment with improved user fairness in a multi-user cooperative OFDM system

We consider a joint relay selection and subcarrier allocation problem that minimizes the total system power for a multi-user, multi-relay and single source cooperative OFDM based two hop system. The system is constrained to all users having a specific subcarrier requirement (user fairness). However no specific fairness constraints for relays are considered. To ensure the optimum power allocation, the subcarriers in two hops are paired with each other. We obtain an optimal subcarrier allocation for the single user case using a similar method to what is described in [1] and modify the algorithm for multiuser scenario. Although the optimality is not achieved in multiuser case the probability of all users being served fairly is improved significantly with a relatively low cost trade off.

Interocular corneal symmetry in refractive error groups

Purpose: To examine between eye differences in corneal higher order aberrations and topographical characteristics in a range of refractive error groups. Methods: One hundred and seventy subjects were recruited including; 50 emmetropic isometropes, 48 myopic isometropes (spherical equivalent anisometropia ≤ 0.75 D), 50 myopic anisometropes (spherical equivalent anisometropia ≥ 1.00 D) and 22 keratoconics. The corneal topography of each eye was captured using the E300 videokeratoscope (Medmont, Victoria, Australia) and analyzed using custom written software. All left eye data were rotated about the vertical midline to account for enantiomorphism. Corneal height data were used to calculate the corneal wavefront error using a ray tracing procedure and fit with Zernike polynomials (up to and including the eighth radial order). The wavefront was centred on the line of sight by using the pupil offset value from the pupil detection function in the videokeratoscope. Refractive power maps were analysed to assess corneal sphero-cylindrical power vectors. Differences between the more myopic (or more advanced eye for keratoconics) and the less myopic (advanced) eye were examined. Results: Over a 6 mm diameter, the cornea of the more myopic eye was significantly steeper (refractive power vector M) compared to the fellow eye in both anisometropes (0.10 ± 0.27 D steeper, p = 0.01) and keratoconics (2.54 ± 2.32 D steeper, p < 0.001) while no significant interocular difference was observed for isometropic emmetropes (-0.03 ± 0.32 D) or isometropic myopes (0.02 ± 0.30 D) (both p > 0.05). In keratoconic eyes, the between eye difference in corneal refractive power was greatest inferiorly (associated with cone location). Similarly, in myopic anisometropes, the more myopic eye displayed a central region of significant inferior corneal steepening (0.15 ± 0.42 D steeper) relative to the fellow eye (p = 0.01). Significant interocular differences in higher order aberrations were only observed in the keratoconic group for; vertical trefoil C(3,-3), horizontal coma C(3,1) secondary astigmatism along 45 C(4, -2) (p < 0.05) and vertical coma C(3,-1) (p < 0.001). The interocular difference in vertical pupil decentration (relative to the corneal vertex normal) increased with between eye asymmetry in refraction (isometropia 0.00 ± 0.09, anisometropia 0.03 ± 0.15 and keratoconus 0.08 ± 0.16 mm) as did the interocular difference in corneal vertical coma C (3,-1) (isometropia -0.006 ± 0.142, anisometropia -0.037 ± 0.195 and keratoconus -1.243 ± 0.936 μm) but only reached statistical significance for pair-wise comparisons between the isometropic and keratoconic groups. Conclusions: There is a high degree of corneal symmetry between the fellow eyes of myopic and emmetropic isometropes. Interocular differences in corneal topography and higher order aberrations are more apparent in myopic anisometropes and keratoconics due to regional (primarily inferior) differences in topography and between eye differences in vertical pupil decentration relative to the corneal vertex normal. Interocular asymmetries in corneal optics appear to be associated with anisometropic refractive development.

Philanthropy and sociology : a logical pairing

In philanthropic studies we hear about a growing academic discipline of ‘philanthropic psychology’ but arguably there is an equal role for ‘philanthropic sociology’, both from a research and a teaching perspective. This commentary begins by noting the early links between philanthropy and sociology. It then introduces a few Australian studies that show how sociology is enriching an understanding of philanthropy, its institutions and its place in society.

Analysis of bilinear pairing-based accumulator for identity escrowing

An accumulator based on bilinear pairings was proposed at CT-RSA'05. Here, it is first demonstrated that the security model proposed by Lan Nguyen does lead to a cryptographic accumulator that is not collision resistant. Secondly, it is shown that collision-resistance can be provided by updating the adversary model appropriately. Finally, an improvement on Nguyen's identity escrow scheme, with membership revocation based on the accumulator, by removing the trusted third party is proposed.

Symmetry is an organizing principle in neuronal dendrotaxis

Symmetry is a fundamental property found in both the physical and natural worlds. Bilateral symmetry is also present in the organization of the brain, however the degree to which symmetry is also an organizing principal between and within the key constituent elements of the nervous system, neurons, is not known. We compared and contrasted the structural organization of principal neurons (PN) in the three subnuclei of the lateral amygdala (LA) of the rat and for comparison also from the infralimbic cortex (IL)...

Some remarks on the symplectic pairing on the moduli space of representations of the fundamental group of surfaces

This work grew out of an attempt to understand a conjectural remark made by Professor Kyoji Saito to the author about a possible link between the Fox-calculus description of the symplectic structure on the moduli space of representations of the fundamental group of surfaces into a Lie group and pairs of mutually dual sets of generators of the fundamental group. In fact in his paper [3] , Prof. Kyoji Saito gives an explicit description of the system of dual generators of the fundamental group.

Two-dimensional self-assembly of a symmetry-reduced tricarboxylic acid

Investigations of the self-assembly of simple molecules at the solution/solid interface can provide useful insight into the general principles governing supramolecular chemistry in two dimensions. Here, we report on the assembly of 3,4′,5-biphenyl tricarboxylic acid (H3BHTC), a small hydrogen bonding unit related to the much-studied 1,3,5-benzenetricarboxylic acid (trimesic acid, TMA), which we investigate using scanning tunneling microscopy (STM) and density functional theory (DFT) calculations. STM images show that H3BHTC assembles by itself into an offset zigzag chain structure that maximizes the surface molecular density in favor of maximizing the number density of strong cyclic hydrogen bonds between the carboxylic groups. The offset geometry creates “sticky” pores that promote solvent coadsorption. Adding coronene to the molecular solution produces a transformation to a high-symmetry host–guest lattice stabilized by a dimeric/trimeric hydrogen bonding motif similar to the TMA flower structure. Finally, we show that the H3BHTC lattice firmly immobilizes the guest coronene molecules, allowing for high-resolution imaging of the coronene structure.

Watson-Crick pairing, the Heisenberg group and Milnor invariants

We study the secondary structure of RNA determined by Watson-Crick pairing without pseudo-knots using Milnor invariants of links. We focus on the first non-trivial invariant, which we call the Heisenber invariant. The Heisenberg invariant, which is an integer, can be interpreted in terms of the Heisenberg group as well as in terms of lattice paths. We show that the Heisenberg invariant gives a lower bound on the number of unpaired bases in an RNA secondary structure. We also show that the Heisenberg invariant can predict allosteric structures for RNA. Namely, if the Heisenberg invariant is large, then there are widely separated local maxima (i.e., allosteric structures) for the number of Watson-Crick pairs found.

Spontaneous symmetry breaking in twisted noncommutative quantum theories

We analyze aspects of symmetry breaking for Moyal spacetimes within a quantization scheme which preserves the twisted Poincare´ symmetry. Towards this purpose, we develop the Lehmann-Symanzik- Zimmermann (LSZ) approach for Moyal spacetimes. The latter gives a formula for scattering amplitudes on these spacetimes which can be obtained from the corresponding ones on the commutative spacetime. This formula applies in the presence of spontaneous breakdown of symmetries as well. We also derive Goldstone’s theorem on Moyal spacetime. The formalism developed here can be directly applied to the twisted standard model.