Statistical mechanics of low-density parity check error-correcting codes over Galois fields

A variation of low-density parity check (LDPC) error-correcting codes defined over Galois fields (GF(q)) is investigated using statistical physics. A code of this type is characterised by a sparse random parity check matrix composed of C non-zero elements per column. We examine the dependence of the code performance on the value of q, for finite and infinite C values, both in terms of the thermodynamical transition point and the practical decoding phase characterised by the existence of a unique (ferromagnetic) solution. We find different q-dependence in the cases of C = 2 and C ≥ 3; the analytical solutions are in agreement with simulation results, providing a quantitative measure to the improvement in performance obtained using non-binary alphabets.

Typical performance of low-density parity-check codes over general symmetric channels

Typical performance of low-density parity-check (LDPC) codes over a general binary-input output-symmetric memoryless channel is investigated using methods of statistical mechanics. The binary-input additive-white-Gaussian-noise channel and the binary-input Laplace channel are considered as specific channel noise models.

Metastable de-excitation spectroscopy and density functional theory study of the selective oxidation of crotyl alcohol over Pd(111)

The extremely surface sensitive technique of metastable de-excitation spectroscopy (MDS) has been utilized to probe the bonding and reactivity of crotyl alcohol over Pd(111) and provide insight into the selective oxidation pathway to crotonaldehyde. Auger de-excitation (AD) of metastable He (23S) atoms reveals distinct features associated with the molecular orbitals of the adsorbed alcohol, corresponding to emission from the hydrocarbon skeleton, the O n nonbonding, and C═C π states. The O n and C═C π states of the alcohol are reversed when compared to those of the aldehyde. Density functional theory (DFT) calculations of the alcohol show that an adsorption mode with both C═C and O bonds aligned somewhat parallel to the surface is energetically favored at a substrate temperature below 200 K. Density of states calculations for such configurations are in excellent agreement with experimental MDS measurements. MDS revealed oxidative dehydrogenation of crotyl alcohol to crotonaldehyde between 200 and 250 K, resulting in small peak shifts to higher binding energy. Intramolecular changes lead to the opposite assignment of the first two MOs in the alcohol versus the aldehyde, in accordance with DFT and UPS studies of the free molecules. Subsequent crotonaldehyde decarbonylation and associated propylidyne formation above 260 K could also be identified by MDS and complementary theoretical calculations as the origin of deactivation and selectivity loss. Combining MDS and DFT in this way represents a novel approach to elucidating surface catalyzed reaction pathways associated with a “real-world” practical chemical transformation, namely the selective oxidation of alcohols to aldehydes.

Typical performance of regular low-density parity-check codes over general symmetric channels

Typical performance of low-density parity-check (LDPC) codes over a general binary-input output-symmetric memoryless channel is investigated using methods of statistical mechanics. Relationship between the free energy in statistical-mechanics approach and the mutual information used in the information-theory literature is established within a general framework; Gallager and MacKay-Neal codes are studied as specific examples of LDPC codes. It is shown that basic properties of these codes known for particular channels, including their potential to saturate Shannon's bound, hold for general symmetric channels. The binary-input additive-white-Gaussian-noise channel and the binary-input Laplace channel are considered as specific channel models.

Do lutein, zeaxanthin, and macular pigment optical density differ with age or age-related maculopathy?

Background and aims Current age-related macular disease (ARMD) treatment includes antioxidant supplementation. Lutein (L) and zeaxanthin (Z) are antioxidants that make up macularpigment within the retina and may reduce the risk of developing ARMD. Ageing and smoking are leading risk factors for developing ARMD. We investigated differences in dietary, supplemental and retinal L and Z, and smoking habits in healthy younger eyes (HY), healthy older eyes (HO) and eyes with an early form of ARMD called age-related maculopathy (ARM). Methods HO, HY and ARM groups were assessed for dietary intakes of L and Z using food diaries. Smoking habits and self-administered quantities of L and Z were obtained via questionnaire. Retinal L and Z levels (macularpigmentopticaldensity, or MPOD) were determined using heterochromatic flicker photometry. Results No significant difference was demonstrated for dietary L and Z intake (?2 = 4.983, p = 0.083) or for MPOD between groups (F = 0.40, p = 0.67). There was a significant difference between the HY (mean ± sd: 1.20 ± 2.99), HO (4.51 ± 7.05) ARM groups (9.15 ± 12.28) for pack years smoked (?2 = 11.61, p = 0.03). Conclusions Our results do not support the theory that ARM develops as a result of L and Z deficiency. Higher pack years smoked may be a factor in disease development. Dietary and supplementary L and Z levels must be obtained when assessing MPOD between groups or over time.

Statistical mechanics of low-density parity-check codes

We review recent theoretical progress on the statistical mechanics of error correcting codes, focusing on low-density parity-check (LDPC) codes in general, and on Gallager and MacKay-Neal codes in particular. By exploiting the relation between LDPC codes and Ising spin systems with multispin interactions, one can carry out a statistical mechanics based analysis that determines the practical and theoretical limitations of various code constructions, corresponding to dynamical and thermodynamical transitions, respectively, as well as the behaviour of error-exponents averaged over the corresponding code ensemble as a function of channel noise. We also contrast the results obtained using methods of statistical mechanics with those derived in the information theory literature, and show how these methods can be generalized to include other channel types and related communication problems.

Finite-connectivity spin-glass phase diagrams and low-density parity check codes

We obtain phase diagrams of regular and irregular finite-connectivity spin glasses. Contact is first established between properties of the phase diagram and the performance of low-density parity check (LDPC) codes within the replica symmetric (RS) ansatz. We then study the location of the dynamical and critical transition points of these systems within the one step replica symmetry breaking theory (RSB), extending similar calculations that have been performed in the past for the Bethe spin-glass problem. We observe that the location of the dynamical transition line does change within the RSB theory, in comparison with the results obtained in the RS case. For LDPC decoding of messages transmitted over the binary erasure channel we find, at zero temperature and rate R=14, an RS critical transition point at pc 0.67 while the critical RSB transition point is located at pc 0.7450±0.0050, to be compared with the corresponding Shannon bound 1-R. For the binary symmetric channel we show that the low temperature reentrant behavior of the dynamical transition line, observed within the RS ansatz, changes its location when the RSB ansatz is employed; the dynamical transition point occurs at higher values of the channel noise. Possible practical implications to improve the performance of the state-of-the-art error correcting codes are discussed. © 2006 The American Physical Society.

An assessment of the performance of high density polyethylene copolymers for natural gas distribution pipes

The total thermoplastics pipe market in west Europe is estimated at 900,000 metric tonnes for 1977 and is projected to grow to some 1.3 million tonnes of predominantly PVC and polyolefins pipe by 1985. By that time, polyethylene for gas distribution pipe and fittings will represent some 30% of the total polyethylene pipe market. The performance characteristics of a high density polyethylene are significantly influenced by both molecular weight and type of comonomer; the major influences being in the long-term hoop stress resistance and the environmental stress cracking resistance. Minor amounts of hexene-1 are more effective than comonomers lower in the homologous series, although there is some sacrifice of density related properties. A synergistic improvement is obtained by combining molecular weight increase with copolymerisation. The Long-term design strength of polyethylene copolymers can be determined from hoop stress measurement at elevated temperatures and by means of a separation factor of approximate value 22, extrapolation can be made to room temperature performance for a water environment. A polyethylene of black composition has a sufficiently improved performance over yellow pigmented pipe to cast doubts on the validity of internationally specifying yellow coded pipe for gas distribution service. The chemical environment (condensate formation) that can exist in natural gas distribution networks has a deleterious effect on the pipe performance the reduction amounting to at least two decades in log time. Desorption of such condensate is very slow and the influence of the more aggressive aromatic components is to lead to premature stress cracking. For natural gas distribution purposes, the design stress rating should be 39 Kg/cm2 for polyethylenes in the molecular weight range of 150 - 200,000 and 55 Kg/cm2 for higher molecular weight materials.

Modelling data and voice traffic over IP networks using continuous-time Markov models

Common approaches to IP-traffic modelling have featured the use of stochastic models, based on the Markov property, which can be classified into black box and white box models based on the approach used for modelling traffic. White box models, are simple to understand, transparent and have a physical meaning attributed to each of the associated parameters. To exploit this key advantage, this thesis explores the use of simple classic continuous-time Markov models based on a white box approach, to model, not only the network traffic statistics but also the source behaviour with respect to the network and application. The thesis is divided into two parts: The first part focuses on the use of simple Markov and Semi-Markov traffic models, starting from the simplest two-state model moving upwards to n-state models with Poisson and non-Poisson statistics. The thesis then introduces the convenient to use, mathematically derived, Gaussian Markov models which are used to model the measured network IP traffic statistics. As one of the most significant contributions, the thesis establishes the significance of the second-order density statistics as it reveals that, in contrast to first-order density, they carry much more unique information on traffic sources and behaviour. The thesis then exploits the use of Gaussian Markov models to model these unique features and finally shows how the use of simple classic Markov models coupled with use of second-order density statistics provides an excellent tool for capturing maximum traffic detail, which in itself is the essence of good traffic modelling. The second part of the thesis, studies the ON-OFF characteristics of VoIP traffic with reference to accurate measurements of the ON and OFF periods, made from a large multi-lingual database of over 100 hours worth of VoIP call recordings. The impact of the language, prosodic structure and speech rate of the speaker on the statistics of the ON-OFF periods is analysed and relevant conclusions are presented. Finally, an ON-OFF VoIP source model with log-normal transitions is contributed as an ideal candidate to model VoIP traffic and the results of this model are compared with those of previously published work.

Improving the repeatability of heterochromatic flicker photometry for measurement of macular pigment optical density

Background: Heterochromatic flicker photometry (HFP) is a psychophysical technique used to measure macular pigment optical density (MPOD). We used the MPS 9000 (MPS) HFP device. Our aim was to determine if the repeatability of the MPS could be improved to make it more suitable for monitoring MPOD over time. Methods: Intra-session repeatability was assessed in 25 participants (aged 20-50 years). The resulting data was explored in detail, e.g., by examining the effect of removal and adjustment of data with less than optimal quality parameters. A protocol was developed for improved overall reliability, which was then tested in terms of inter-session repeatability in a separate group of 27 participants (aged 19-52 years). Results: Removal and adjustment of data reduced the intra-session coefficient of repeatability (CR) by 0.04, on average, and the mean individual standard deviation by 0.004. Raw data observation offered further insight into ways of improving repeatability. The proposed protocol resulted in an inter-session CR of 0.08. Conclusions: Removal and adjustment of less than optimal data improved repeatability, and is therefore recommended. To further improve repeatability, in brief we propose that each patient perform each part of the test twice, and a third time where necessary (described in detail by the protocol). Doing so will make the MPS more useful in research and clinical settings. © 2012 Springer-Verlag.

Impact of co-adsorbed oxygen on crotonaldehyde adsorption over gold nanoclusters:a computational study

Crotonaldehyde (2-butenal) adsorption over gold sub-nanometer particles, and the influence of co-adsorbed oxygen, has been systematically investigated by computational methods. Using density functional theory, the adsorption energetics of crotonaldehyde on bare and oxidised gold clusters (Au , d = 0.8 nm) were determined as a function of oxygen coverage and coordination geometry. At low oxygen coverage, sites are available for which crotonaldehyde adsorption is enhanced relative to bare Au clusters by 10 kJ mol. At higher oxygen coverage, crotonaldehyde is forced to adsorb in close proximity to oxygen weakening adsorption by up to 60 kJ mol relative to bare Au. Bonding geometries, density of states plots and Bader analysis, are used to elucidate crotonaldehyde bonding to gold nanoparticles in terms of partial electron transfer from Au to crotonaldehyde, and note that donation to gold from crotonaldehyde also becomes significant following metal oxidation. At high oxygen coverage we find that all molecular adsorption sites have a neighbouring, destabilising, oxygen adatom so that despite enhanced donation, crotonaldehyde adsorption is always weakened by steric interactions. For a larger cluster (Au, d = 1.1 nm) crotonaldehyde adsorption is destabilized in this way even at a low oxygen coverage. These findings provide a quantitative framework to underpin the experimentally observed influence of oxygen on the selective oxidation of crotyl alcohol to crotonaldehyde over gold and gold-palladium alloys. © 2014 the Partner Organisations.

Density forecasts of crude-oil prices using option-implied and ARCH-type models

The predictive accuracy of competing crude-oil price forecast densities is investigated for the 1994–2006 period. Moving beyond standard ARCH type models that rely exclusively on past returns, we examine the benefits of utilizing the forward-looking information that is embedded in the prices of derivative contracts. Risk-neutral densities, obtained from panels of crude-oil option prices, are adjusted to reflect real-world risks using either a parametric or a non-parametric calibration approach. The relative performance of the models is evaluated for the entire support of the density, as well as for regions and intervals that are of special interest for the economic agent. We find that non-parametric adjustments of risk-neutral density forecasts perform significantly better than their parametric counterparts. Goodness-of-fit tests and out-of-sample likelihood comparisons favor forecast densities obtained by option prices and non-parametric calibration methods over those constructed using historical returns and simulated ARCH processes. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:727–754, 2011

Cs promoted triglyceride transesterification over MgO nanocatalysts

The influence of Cs on the structure and basicity of nanocrystalline MgO was assessed via electron microscopy, CO2 chemisorption, XRD and XPS. Caesium incorporation via co-precipitation under supercritical conditions generates Cs2Mg(CO3)2 nanocrystallites with an enhanced density and strength of surface base sites. Wet impregnation proved less effective for modifying MgO nanocrystals. A strong synergy between Cs and Mg components in the co-precipitated material dramatically enhanced the rate of tributyrin transesterification with methanol relative to undoped MgO and homogeneous Cs2CO3 catalysts. On-stream deactivation of Cs-doped MgO reflects heavy surface carbon deposition and loss of the high activity Cs2Mg(CO3)2 phase due to limited Cs dissolution.

In situ studies of structure-reactivity relations in biodiesel synthesis over nanocrystalline MgO

High temperature processing of solvothermally synthesised MgO nanoparticles promotes striking changes in their morphology, and surface chemical and electronic structure. As-prepared NanoMgO comprised ∼4 nm cubic periclase nanocrystals, interspersed within an amorphous Mg(OH)(OCH3) matrix. These crystallites appear predominantly (1 0 0) terminated, and the overall material exhibits carbonate and hydroxyl surface functionalities of predominantly weak/moderate base character. Heating promotes gradual crystallisation and growth of the MgO nanoparticles, and concomitant loss of Mg(OH)(OCH3). In situ DRIFTS confirms the residual precursor and surface carbonate begin to decompose above 300 °C, while in situ XPS shows these morphological changes are accompanied by the disappearance of surface hydroxyl/methoxide species and genesis of O- centres which enhance both the surface density and basicity of the resulting stepped and defective MgO nanocrystals. The catalytic performance in tributyrin transesterification with methanol is directly proportional to the density of strong surface base sites. © 2010 Elsevier B.V. All rights reserved.

The effect of ocular nutritional supplements on macular pigment optical density

This thesis describes the investigation of the effects of ocular supplements with different levels of nutrients on the macular pigment optical density (MPOD) in participants with healthy eyes. Abstract A review of the literature highlighted that ocular supplements are produced in various combinations of nutrients and concentrations. The ideal concentrations of nutrients such as lutein (L) have not been established. It was unclear whether different stages of eye disease require different concentrations of key nutrients, leading to the design of this study. The primary aim was to determine the effects of ocular supplements with different concentrations of nutrients on the MPOD of healthy participants. The secondary aim was to determine L and zeaxanthin (Z) intake at the start and end of the study through completion of food diaries. The primary study was split into two experiments. Experiment 1 was an exploratory study to determine sample size and experiment 2 the main study. Statistical power was calculated and a sample size of 38 was specified. Block stratification for age, gender and smoking habit was applied and from 101 volunteers 42 completed the study, 31 with both sets of food diaries. Four confounders were accounted for in the design of the study; gender, smoking habit, age and diet. Further factors that could affect comparability of results between studies were identified during the study and were not monitored; ethnicity, gastro-intestinal health, alcohol intake, body mass index and genetics. Comparisons were made between the sample population and the Sheffield general population according to recent demographic results in the public domain. Food diaries were analysed and shown to have no statistical difference when comparing baseline to final results. The average L and Z intake for the 31 participants who returned both sets of food diaries was initially 1.96mg and 1.51mg for the final food diaries. The effect of the two ocular supplements with different levels of xanthophyll (6mg lutein/zeaxanthin and 10mg lutein only) on MPOD was not significantly different over a four-month period.