Longitudinal Genetic Analysis of Plasma Lipids

The consensus from published studies is that plasma lipids are each influenced by genetic factors, and that this contributes to genetic variation in risk of cardiovascular disease. Heritability estimates for lipids and lipoproteins are in the range .48 to .87, when measured once per study participant. However, this ignores the confounding effects of biological variation measurement error and ageing, and a truer assessment of genetic effects on cardiovascular risk may be obtained from analysis of longitudinal twin or family data. We have analyzed information on plasma high-density lipoprotein (HDL) and low-density lipoprotein (LDL) cholesterol, and triglycerides, from 415 adult twins who provided blood on two to five occasions over 10 to 17 years. Multivariate modeling of genetic and environmental contributions to variation within and across occasions was used to assess the extent to which genetic and environmental factors have long-term effects on plasma lipids. Results indicated that more than one genetic factor influenced HDL and LDL components of cholesterol, and triglycerides over time in all studies. Nonshared environmental factors did not have significant long-term effects except for HDL. We conclude that when heritability of lipid risk factors is estimated on only one occasion, the existence of biological variation and measurement errors leads to underestimation of the importance of genetic factors as a cause of variation in long-term risk within the population. In addition our data suggest that different genes may affect the risk profile at different ages.

Temporal dynamics of rabbit haemorrhagic disease virus infection in a low-density population of wild rabbits (Oryctolagus cuniculus) in New Zealand

A longitudinal capture-mark-recapture study was conducted to determine the temporal dynamics of rabbit haemorrhagic disease (RHD) in a European rabbit (Oryctolagus cuniculus) population of low to moderate density on sand-hill country in the lower North Island of New Zealand. A combination of sampling ( trapping and radio-tracking) and diagnostic (cELISA, PCR and isotype ELISA) methods was employed to obtain data weekly from May 1998 until June 2001. Although rabbit haemorrhagic disease virus ( RHDV) infection was detected in the study population in all 3 years, disease epidemics were evident only in the late summer or autumn months in 1999 and 2001. Overall, 20% of 385 samples obtained from adult animals older than 11 weeks were seropositive. An RHD outbreak in 1999 contributed to an estimated population decline of 26%. A second RHD epidemic in February 2001 was associated with a population decline of 52% over the subsequent month. Following the outbreaks, the seroprevalence in adult survivors was between 40% and 50%. During 2000, no deaths from RHDV were confirmed and mortalities were predominantly attributed to predation. Influx of seronegative immigrants was greatest in the 1999 and 2001 breeding seasons, and preceded the RHD epidemics in those years. Our data suggest that RHD epidemics require the population immunity level to fall below a threshold where propagation of infection can be maintained through the population.

Statistical physics of irregular low-density parity-check codes

Low-density parity-check codes with irregular constructions have recently been shown to outperform the most advanced error-correcting codes to date. In this paper we apply methods of statistical physics to study the typical properties of simple irregular codes. We use the replica method to find a phase transition which coincides with Shannon's coding bound when appropriate parameters are chosen. The decoding by belief propagation is also studied using statistical physics arguments; the theoretical solutions obtained are in good agreement with simulation results. We compare the performance of irregular codes with that of regular codes and discuss the factors that contribute to the improvement in performance.

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.

Statistical physics of low density parity check error correcting codes

We study the performance of Low Density Parity Check (LDPC) error-correcting codes using the methods of statistical physics. LDPC codes are based on the generation of codewords using Boolean sums of the original message bits by employing two randomly-constructed sparse matrices. These codes can be mapped onto Ising spin models and studied using common methods of statistical physics. We examine various regular constructions and obtain insight into their theoretical and practical limitations. We also briefly report on results obtained for irregular code constructions, for codes with non-binary alphabet, and on how a finite system size effects the error probability.

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.

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.

Average error exponent in Gallager low-density parity-check codes

We present a theoretical method for a direct evaluation of the average error exponent in Gallager error-correcting codes using methods of statistical physics. Results for the binary symmetric channel(BSC)are presented for codes of both finite and infinite connectivity.

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.

Average and reliability error exponents in low-density parity-check codes

We present a theoretical method for a direct evaluation of the average and reliability error exponents in low-density parity-check error-correcting codes using methods of statistical physics. Results for the binary symmetric channel are presented for codes of both finite and infinite connectivity.

Analysis of common attacks in public-key cryptosystems based on low-density parity-check codes

The security and reliability of a class of public-key cryptosystems against attacks by unauthorized parties, who had acquired partial knowledge of one or more of the private key components and/or of the message, were discussed. The standard statistical mechanical methods of dealing with diluted spin systems with replica symmetric considerations were analyzed. The dynamical transition which defined decryption success in practical situation was studied. The phase diagrams which showed the dynamical threshold as a function of the partial acquired knowledge of the private key were also presented.

Statistical mechanics of broadcast channels using low-density parity-check codes

We investigate the use of Gallager's low-density parity-check (LDPC) codes in a degraded broadcast channel, one of the fundamental models in network information theory. Combining linear codes is a standard technique in practical network communication schemes and is known to provide better performance than simple time sharing methods when algebraic codes are used. The statistical physics based analysis shows that the practical performance of the suggested method, achieved by employing the belief propagation algorithm, is superior to that of LDPC based time sharing codes while the best performance, when received transmissions are optimally decoded, is bounded by the time sharing limit.