A lower bound for the optimal crossing-free Hamiltonian cycle problem

Consider a drawing in the plane ofK _n , the complete graph onn vertices. If all edges are restricted to be straight line segments, the drawing is called rectilinear. Consider a Hamiltonian cycle in a drawing ofK _n . If no pair of the edges of the cycle cross, it is called a crossing-free Hamiltonian cycle (cfhc). Let (n) represent the maximum number of cfhc's of any drawing ofK _n , and (n) the maximum number of cfhc's of any rectilinear drawing ofK _n . The problem of determining (n) and (n), and determining which drawings have this many cfhc's, is known as the optimal cfhc problem. We present a brief survey of recent work on this problem, and then, employing a recursive counting argument based on computer enumeration, we establish a substantially improved lower bound for (n) and (n). In particular, it is shown that (n) is at leastk × 3.2684 ⁿ . We conjecture that both (n) and (n) are at mostc × 4.5 ⁿ .This research, part of which was conducted at Queen's University, was supported by an N.S.E.R.C. postgraduate scholarship.     

Cooperative luminescence and absorption in ytterbium doped aluminosilicate glass optical fibres and preforms

The cooperative luminescence and absorption properties of Yb³⁺ doped aluminosilicate glass optical fibres and preforms are investigated in detail. In accordance with previous investigations, both the visible cooperative luminescence and the infrared luminescence decay measurements have been resolved into a single exponential decay component. We show that for a glass with similar Yb³⁺ dopant concentration but more Al³⁺, the glass emits less visible luminescence. Absorption loss measurements completed on fibre samples revealed a broad absorption in the 350-500 nm range, which we propose is due to a combination of Yb²⁺ absorption and cooperative absorption from Yb³⁺ ion pairs.     

Local spin correlations in partially frustrated amorphous Fe-Mn

Mössbauer measurements in a-(Fe_0.765Mn_0.235)₇₈Sn₂Si₆B₁₄ have been performed with⁵⁷Fe and¹¹⁹Sn. Both hyperfine fields show a kink near 70 K, indicating a freezing of the transverse spins. The ratio of the two hyperfine fields contains information about the correlation of the transverse spins. The ratioB _hf(Sn)/B _hf(Fe) stays constant aboveT _xy and rises belowT _xy . This indicates an alignment of the transverse spins on a local scale, as was also found inAuFe and a-FeZr.     

Anechoic chamber qualification: traverse method,inverse square law analysis method,and nature of test signal

Qualification of anechoic chambers is intended to demonstrate that the chamber supports the intended free-field environment within some permissible tolerance bounds. Key qualification issues include the method used to obtain traverse data, the analysis method for the data, and the use of pure tone or broadband noise as the chamber excitation signal. This paper evaluates the relative merits of continuous versus discrete traverses, of fixed versus optimal reference analysis of the traverse data, and of the use of pure tone versus broadband signals. The current practice of using widely space discrete sampling along a traverse is shown to inadequately sample the complexity of the sound field extant with pure tone traverses, but is suitable for broadband traverses. Continuous traverses, with spatial resolution on the order of 15% of the wavelength at the frequency of interest, are shown to be necessary to fully resolve the spatial complexity of pure tone qualifications. The use of an optimal reference method for computing the deviations from inverse square law is shown to significantly improve the apparent performance of the chamber for pure tone qualifications. Finally, the use of broadband noise as the test signal, as compared to pure tone traverses over the same span, is demonstrated to be a marginal indicator of chamber performance.     

Continuous-wave mid-infrared frequency conversion in silicon nanowaveguides

We report the first demonstration of cw wavelength conversion from the telecommunications band to the mid-IR (MIR) region via four-wave mixing in silicon nanowaveguides. We measure a parametric bandwidth of 748 nm by converting a 1636 nm signal to produce a 2384 nm idler and show continuously tunable wavelength conversion from 1792 to 2116 nm. This report indicates that the advantages of silicon photonics may be leveraged to create devices for a large range of MIR applications that require cw operation.     

Demonstration of sufficient control for two rounds of quantum error correction in a solid state ensemble quantum information processor

We report the implementation of a 3-qubit quantum error-correction code on a quantum information processor realized by the magnetic resonance of carbon nuclei in a single crystal of malonic acid. The code corrects for phase errors induced on the qubits due to imperfect decoupling of the magnetic environment represented by nearby spins, as well as unwanted evolution under the internal Hamiltonian. We also experimentally demonstrate sufficiently high-fidelity control to implement two rounds of quantum error correction. This is a demonstration of state-of-the-art control in solid state nuclear magnetic resonance, a leading test bed for the implementation of quantum algorithms.     

Development of a cryopreservation protocol for the microcyclic rust-fungus Puccinia spegazzinii

The rust fungus Puccinia spegazzinii (Basidiomycotina: Uredinales) has been identified as a potential classical biological control agent for the invasive weed Mikania micrantha (Asteraceae). Long-term, live storage of this pathogen is required for reference. As biotrophs, almost all rusts species cannot be preserved by traditional cryopreservation protocols, which rely on in vitro culture techniques. In addition, the embedded teliospores and delicate basidiospores of this microcyclic rust are not amenable to direct plunge freezing. Continuous culture of the rust on living plants is both laborious and expensive, so a variety of approaches for cryopreservation and storage were tested. These methods included traditional approaches to fungal cryopreservation such as variation of cooling rate regime and alginate encapsulation techniques. However, an in situ cryopreservation technique was the only method identified as having any potential for the long-term cryopreservation of the 10 isolates tested. Material from either petiole or stem tissue remained viable after cryopreservation, determined by the ability of the material to produce basidiospores. However, despite great progress being made in developing an optimal cryopreservation method, infection of the host plant by basidiospores produced from previously cryopreserved teliospores, embedded in leaf petioles, was not achieved.