Error-correcting codes on a Bethe-like lattice

We analyse Gallager codes by employing a simple mean-field approximation that distorts the model geometry and preserves important interactions between sites. The method naturally recovers the probability propagation decoding algorithm as a minimization of a proper free-energy. We find a thermodynamical phase transition that coincides with information theoretical upper-bounds and explain the practical code performance in terms of the free-energy landscape.

Dominions apart:scandal and sporting mismatch in Australian-South African association football encounters, 1947-1955

South Africa, Australia and New Zealand participated in numerous sporting contests prior to World War Two. These encounters were primarily on cricket pitches and rugby fields. After nearly four decades of negotiations the first Association football matches were played between the three countries in 1947. The first tour of South Africa to Australia and New Zealand was plagued by scandals on and off the pitch, but despite this Australia returned the favour and toured South Africa three years later. Another five years would pass before South African returned to Australia, by which time it was clear that a large gulf had emerged between the two nations in terms of sporting ability and organisational efficiency. This article focuses on the three tours of 1947, 1950 and 1955, dissecting each as they occurred against a backdrop of scandal, organisational inefficiency and sporting mismatch.

Lattice approach to the dynamics of phase-coded soliton trains

We address the collective dynamics of a soliton train propagating in a medium described by the nonlinear Schrödinger equation. Our approach uses the reduction of train dynamics to the discrete complex Toda chain (CTC) model for the evolution of parameters for each train constituent: such a simplification allows one to carry out an approximate analysis of the dynamics of positions and phases of individual interacting pulses. Here, we employ the CTC model to the problem which has relevance to the field of fibre optics communications where each binary digit of transmitted information is encoded via the phase difference between the two adjacent solitons. Our goal is to elucidate different scenarios of the train distortions and the subsequent information garbling caused solely by the intersoliton interactions. First, we examine how the structure of a given phase pattern affects the initial stage of the train dynamics and explain the general mechanisms for the appearance of unstable collective soliton modes. Then we further discuss the nonlinear regime concentrating on the dependence of the Lax scattering matrix on the input phase distribution; this allows one to classify typical features of the train evolution and determine the distance where the soliton escapes from its slot. In both cases, we demonstrate deep mathematical analogies with the classical theory of crystal lattice dynamics.

Collective behaviour in a square lattice of driven Duffing resonators coupled to van der Pol oscillators

The global and local synchronisation of a square lattice composed of alternating Duffing resonators and van der Pol oscillators coupled through displacement is studied. The lattice acts as a sensing device in which the input signal is characterised by an external driving force that is injected into the system through a subset of the Duffing resonators. The parameters of the system are taken from MEMS devices. The effects of the system parameters, the lattice architecture and size are discussed.

A preliminary study into emergent behaviours in a lattice of interacting nonlinear resonators and oscillators

Future sensor arrays will be composed of interacting nonlinear components with complex behaviours with no known analytic solutions. This paper provides a preliminary insight into the expected behaviour through numerical and analytical analysis. Specically, the complex behaviour of a periodically driven nonlinear Duffing resonator coupled elastically to a van der Pol oscillator is investigated as a building block in a 2D lattice of such units with local connectivity. An analytic treatment of the 2-device unit is provided through a two-time-scales approach and the stability of the complex dynamic motion is analysed. The pattern formation characteristics of a 2D lattice composed of these units coupled together through nearest neighbour interactions is analysed numerically for parameters appropriate to a physical realisation through MEMS devices. The emergent patterns of global and cluster synchronisation are investigated with respect to system parameters and lattice size.

Studies of the effects of molecular encounters on N.M.R. spin-lattice relaxation times

This thesis is concerned with investigations of the effects of molecular encounters on nuclear magnetic resonance spin-lattice relaxation times, with particular reference to mesitylene in mixtures with cyclohexane and TMS. The purpose of the work was to establish the best theoretical description of T1 and assess whether a recently identified mechanism (buffeting), that influences n.m.r. chemical shifts, governs Tl also. A set of experimental conditions are presented that allow reliable measurements of Tl and the N. O. E. for 1H and 13C using both C. W. and F.T. n.m.r. spectroscopy. Literature data for benzene, cyclohexane and chlorobenzene diluted by CC14 and CS2 are used to show that the Hill theory affords the best estimation of their correlation times but appears to be mass dependent. Evaluation of the T1 of the mesitylene protons indicates that a combined Hill-Bloembergen-Purcell-Pound model gives an accurate estimation of T1; subsequently this was shown to be due to cancellation of errors in the calculated intra and intemolecular components. Three experimental methods for the separation of the intra and intermolecular relaxation times are described. The relaxation times of the 13C proton satellite of neat bezene, 1,4 dioxane and mesitylene were measured. Theoretical analyses of the data allow the calculation of Tl intra. Studies of intermolecular NOE's were found to afford a general method of separating observed T1's into their intra and intermolecular components. The aryl 1H and corresponding 13C T1 values and the NOE for the ring carbon of mesitylene in CC14 and C6H12-TMS have been used in combination to determine T1intra and T1inter. The Hill and B.P.P. models are shown to predict similarly inaccurate values for T1linter. A buffeting contribution to T1inter is proposed which when applied to the BPP model and to the Gutowsky-Woessner expression for T1inter gives an inaccuracy of 12% and 6% respectively with respect to theexperimentally based T1inter.

Universities and the user community:marriage or mismatch?

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Lattice approach to the dynamics of phase-coded soliton trains

We address the collective dynamics of a soliton train propagating in a medium described by the nonlinear Schrödinger equation. Our approach uses the reduction of train dynamics to the discrete complex Toda chain (CTC) model for the evolution of parameters for each train constituent: such a simplification allows one to carry out an approximate analysis of the dynamics of positions and phases of individual interacting pulses. Here, we employ the CTC model to the problem which has relevance to the field of fibre optics communications where each binary digit of transmitted information is encoded via the phase difference between the two adjacent solitons. Our goal is to elucidate different scenarios of the train distortions and the subsequent information garbling caused solely by the intersoliton interactions. First, we examine how the structure of a given phase pattern affects the initial stage of the train dynamics and explain the general mechanisms for the appearance of unstable collective soliton modes. Then we further discuss the nonlinear regime concentrating on the dependence of the Lax scattering matrix on the input phase distribution; this allows one to classify typical features of the train evolution and determine the distance where the soliton escapes from its slot. In both cases, we demonstrate deep mathematical analogies with the classical theory of crystal lattice dynamics.

Structure and physical properties of [µ-Tris(1,4-bis(tetrazol-1-yl)butane-N4,N4‘')iron(II)] Bis(hexafluorophosphate), a new Fe(II) spin-crossover compound with a three-dimensional threefold interlocked crystal lattice

[μ-Tris(1,4-bis(tetrazol-1-yl)butane-N4,N4‘)iron(II)] bis(hexafluorophosphate), [Fe(btzb)3](PF6)2, crystallizes in a three-dimensional 3-fold interlocked structure featuring a sharp two-step spin-crossover behavior. The spin conversion takes place between 164 and 182 K showing a discontinuity at about T1/2 = 174 K and a hysteresis of about 4 K between T1/2 and the low-spin state. The spin transition has been independently followed by magnetic susceptibility measurements, 57Fe-Mössbauer spectroscopy, and variable temperature far and midrange FTIR spectroscopy. The title compound crystallizes in the trigonal space group P30¯(No. 147) with a unit cell content of one formula unit plus a small amount of disordered solvent. The lattice parameters were determined by X-ray diffraction at several temperatures between 100 and 300 K. Complete crystal structures were resolved for 9 of these temperatures between 100 (only low spin, LS) and 300 K (only high spin, HS), Z = 1 [Fe(btzb)3](PF  6)2:  300 K (HS), a = 11.258(6) Å, c = 8.948(6) Å, V = 982.2(10) Å3; 100 K (LS), a = 10.989(3) Å, c = 8.702(2) Å, V = 910.1(4) Å3. The molecular structure consists of octahedral coordinated iron(II) centers bridged by six N4,N4‘ coordinating bis(tetrazole) ligands to form three 3-dimensional networks. Each of these three networks is symmetry related and interpenetrates each other within a unit cell to form the interlocked structure. The Fe−N bond lengths change between 1.993(1) Å at 100 K in the LS state and 2.193(2) Å at 300 K in the HS state. The nearest Fe separation is along the c-axis and identical with the lattice parameter c.

Intuitive mobile image browsing on a hexagonal lattice

Following miniaturisation of cameras and their integration into mobile devices such as smartphones combined with the intensive use of the latter, it is likely that in the near future the majority of digital images will be captured using such devices rather than using dedicated cameras. Since many users decide to keep their photos on their mobile devices, effective methods for managing these image collections are required. Common image browsers prove to be only of limited use, especially for large image sets [1].

Appetite regulatory mechanisms and food intake in mice are sensitive to mismatch in diets between pregnancy and postnatal periods

Human and animal studies suggest that obesity in adulthood may have its origins partly during prenatal development. One of the underlying causes of obesity is the perturbation of hypothalamic mechanisms controlling appetite. We determined mRNA levels of genes that regulate appetite, namely neuropeptide Y (NPY), pro-opiomelanocortin (POMC) and the leptin receptor isoform Ob-Rb, in the hypothalamus of adult mouse offspring from pregnant dams fed a protein-restricted diet, and examined whether mismatched post-weaning high-fat diet altered further expression of these gene transcripts. Pregnant MF1 mice were fed either normal protein (C, 18% casein) or protein-restricted (PR, 9% casein) diet throughout pregnancy. Weaned offspring were fed to adulthood a high-fat (HF; 45% kcal fat) or standard chow (21% kcal fat) diet to generate the C/HF, C/C, PR/HF and PR/C groups. Food intake and body weight were monitored during this period. Hypothalamic tissues were collected at 16 weeks of age for analysis of gene expression by real time RT-PCR. All HF-fed offspring were observed to be heavier vs. C groups regardless of the maternal diet during pregnancy. In the PR/HF males, but not in females, daily energy intake was reduced by 20% vs. the PR/C group (p <0.001). In PR/HF males, hypothalamic mRNA levels were lower vs. the PR/C group for NPY (p <0.001) and Ob-Rb (p <0.05). POMC levels were similar in all groups. In females, mRNA levels for these transcripts were similar in all groups. Our results suggest that adaptive changes during prenatal development in response to maternal dietary manipulation may have long-term sex-specific consequences on the regulation of appetite and metabolism following post-weaning exposure to an energy-rich nutritional environment. © 2008 Elsevier B.V. All rights reserved.

Abnormality of mismatch negativity in response to tone omission in dyslexic adults

Evidence of abnormalities in the perception of rapidly presented sounds in dyslexia has been interpreted as evidence of a prolonged time window within which sounds can influence the perception of temporally surrounding sounds. We recorded the magnetic mismatch negativity (MMNm) to infrequent tone omissions in a group of six dyslexic adults and six IQ and age-matched controls. An MMNm is only elicited in response to a complete stimulus omission when successive inputs fall within the temporal window of integration (stimulus onset asynchrony (SOA) ∼160 ms). No MMNm responses were recorded in either experimental group when stimuli were presented at SOAs falling just outside the temporal window of integration (SOA = 175 ms). However, while presentation rates of 100 ms resulted in MMNm responses for all control participants, the same stimulus omissions elicited an MMNm response in only one of the six dyslexic participants. These results cannot support the hypothesis of a prolonged time window of integration, but rather indicate auditory grouping deficits in the dyslexic population. © 2006 Elsevier B.V. All rights reserved.