Further results on strongbox secured secret sharing schemes

We extend our earlier work on ways in which defining sets of combinatorial designs can be used to create secret sharing schemes. We give an algorithm for classifying defining sets or designs according to their security properties and summarise the results of this algorithm for many small designs. Finally, we discuss briefly how defining sets can be applied to variations of the basic secret sharing scheme.

Steiner trade spectra of complete partite graphs

The Steiner trade spectrum of a simple graph G is the set of all integers t for which there is a simple graph H whose edges can be partitioned into t copies of G in two entirely different ways. The Steiner trade spectra of complete partite graphs were determined in all but a few cases in a recent paper by Billington and Hoffman (Discrete Math. 250 (2002) 23). In this paper we resolve the remaining cases. (C) 2004 Elsevier B.V. All rights reserved.

A low-complexity lattice-based low-PAR transmission scheme for DSL channels

This paper presents a new low-complexity multicarrier modulation (MCM) technique based on lattices which achieves a peak-to-average power ratio (PAR) as low as three. The scheme can be viewed as a drop in replacement for the discrete multitone (DMT) modulation of an asymmetric digital subscriber line modem. We show that the lattice-MCM retains many of the attractive features of sinusoidal-MCM, and does so with lower implementation complexity, O(N), compared with DMT, which requires O(N log N) operations. We also present techniques for narrowband interference rejection and power profiling. Simulation studies confirm that performance of the lattice-MCM is superior, even compared with recent techniques for PAR reduction in DMT.

Observations of spermiogenesis and epididymal sperm maturation in the rufous hare wallaby, Lagorchestes hirsutus (Metatheria, Mammalia)

Acrosomal development in the early spermatid of the rufous hare wallaby shows evidence of formation of an acrosomal granule, similar to that found in eutherian mammals, the Phascolarctidae and Vombatidae. Unlike the other members of the Macropodidae so far examined, the acrosome of this species appears to be fully compacted at spermiation and extends evenly over 90% of the dorsal aspect of the nucleus. During spermiogenesis, the nucleus of the rufous hare wallaby spermatid showed evidence of uneven condensation of chromatin; this may also be related to the appearance of unusual nucleoplasm evaginations from the surface of the fully condensed spermatid. This study was unable to find evidence of the presence of Sertoli cell spurs or nuclear rotation during spermiogenesis in the rufous hare wallaby. The majority of spermatozoa immediately before spermiation had a nucleus that was essentially perpendicular to the long axis of the sperm tail. Nuclei of spermatozoa found in the process of being released or isolated in the lumen of the seminiferous tubule were rotated almost parallel to the long axis of the flagellum; complete parallel alignment occurred during epididymal maturation. At spermiation spermatozoa have characteristically small cytoplasmic remnants compared to those of other macropods. Unlike the majority of macropodid spermatozoa so far described, the spermatozoa of the rufous hare wallaby showed little evidence of morphological change during epididymal transit. There was no formation of a fibre network around the midpiece or of plasma membrane specializations in this region; the only notable change was a distinctive flattening of midpiece mitochondria and scalloping of the anterior mitochondrial sheath to accommodate the sperm head. Preliminary evidence from spermiogenesis and epididymal sperm maturation supports the classification of the rufous hare wallaby as a separate genus but also indicates that its higher taxonomic position may need to be re-evaluated.

High-pressure adsorption capacity and structure of CO2 in carbon slit pores: Theory and simulation

We present new simulation results for the packing of single-center and three-center models of carbon dioxide at high pressure in carbon slit pores. The former shows a series of packing transitions that are well described by our density functional theory model developed earlier. In contrast, these transitions are absent for the three-center model. Analysis of the simulation results shows that alternations of flat-lying molecules and rotated molecules can occur as the pore width is increased. The presence or absence of quadrupoles has negligible effect on these high-density structures.

Manipulation and growth of birefringent protein crystals in optical tweezers

We report on the trapping, rotation, and in-situ growth of birefringent tetragonal lysozyme crystals in optical tweezers operating at a wavelength of 1070 nm. Variation of the pH and lysozyme concentration of the solution during growth was used to alter the length to width ratio of the crystals, and hence their orientation in the tweezers. Crystals with the optical axis skewed or perpendicular to the trapping-beam axis could be rotated by changing the orientation of linearly polarized light. We observed spontaneous spinning of some asymmetric crystals in the presence of linearly polarized light, due to radiation pressure effects. Addition of protein to the solution in the tweezers permitted real-time observation of crystal growth. (C) 2004 Optical Society of America.

Energy as an entanglement witness for quantum many-body systems

We investigate quantum many-body systems where all low-energy states are entangled. As a tool for quantifying such systems, we introduce the concept of the entanglement gap, which is the difference in energy between the ground-state energy and the minimum energy that a separable (unentangled) state may attain. If the energy of the system lies within the entanglement gap, the state of the system is guaranteed to be entangled. We find Hamiltonians that have the largest possible entanglement gap; for a system consisting of two interacting spin-1/2 subsystems, the Heisenberg antiferromagnet is one such example. We also introduce a related concept, the entanglement-gap temperature: the temperature below which the thermal state is certainly entangled, as witnessed by its energy. We give an example of a bipartite Hamiltonian with an arbitrarily high entanglement-gap temperature for fixed total energy range. For bipartite spin lattices we prove a theorem demonstrating that the entanglement gap necessarily decreases as the coordination number is increased. We investigate frustrated lattices and quantum phase transitions as physical phenomena that affect the entanglement gap.

Embeddings of partial Steiner triple systems

Any partial Steiner triple system of order u can be embedded in a Steiner triple system of order v if v equivalent to 1, 3 (mod 6) and v greater than or equal to 3u - 2. (C) 2004 Elsevier Inc. All rights reserved.

Coherent-state linear optical quantum computing gates using simplified diagonal superposition resource states

In this paper we explore the possibility of fundamental tests for coherent-state optical quantum computing gates [ T. C. Ralph et al. Phys. Rev. A 68 042319 (2003)] using sophisticated but not unrealistic quantum states. The major resource required in these gates is a state diagonal to the basis states. We use the recent observation that a squeezed single-photon state [S(r)∣1⟩] approximates well an odd superposition of coherent states (∣α⟩−∣−α⟩) to address the diagonal resource problem. The approximation only holds for relatively small α, and hence these gates cannot be used in a scalable scheme. We explore the effects on fidelities and probabilities in teleportation and a rotated Hadamard gate.

3-Homogeneous latin trades

Let T be a partial latin square and L be a latin square with T subset of L. We say that T is a latin trade if there exists a partial latin square T' with T' boolean AND T = theta such that (LT) U T' is a latin square. A k-homogeneous latin trade is one which intersects each row, each column and each entry either 0 or k times. In this paper, we construct 3-homogeneous latin trades from hexagonal packings of the plane with circles. We show that 3-homogeneous latin trades of size 3 m exist for each m >= 3. This paper discusses existence results for latin trades and provides a glueing construction which is subsequently used to construct all latin trades of finite order greater than three. Crown Copyright (c) 2005 Published by Elsevier B.V. All rights reserved.

The Bazhanov-Stroganov model from 3D approach

We apply a three-dimensional approach to describe a new parametrization of the L-operators for the two-dimensional Bazhanov-Stroganov (BS) integrable spin model related to the chiral Potts model. This parametrization is based on the solution of the associated classical discrete integrable system. Using a three-dimensional vertex satisfying a modified tetrahedron equation, we construct an operator which generalizes the BS quantum intertwining matrix S. This operator describes the isospectral deformations of the integrable BS model.

Some equitably 3-colourable cycle decompositions of complete equipartite graphs

Let G be a graph in which each vertex has been coloured using one of k colours, say c(1), c(2),.. , c(k). If an m-cycle C in G has n(i) vertices coloured c(i), i = 1, 2,..., k, and vertical bar n(i) - n(j)vertical bar <= 1 for any i, j is an element of {1, 2,..., k}, then C is said to be equitably k-coloured. An m-cycle decomposition C of a graph G is equitably k-colourable if the vertices of G can be coloured so that every m-cycle in W is equitably k-coloured. For m = 3, 4 and 5 we completely settle the existence question for equitably 3-colourable m-cycle decompositions of complete equipartite graphs. (c) 2005 Elsevier B.V. All rights reserved.