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 $C$ nonzero 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 $q$-dependencies in the cases of C=2 and $C \ge 3$; the analytical solutions are in agreement with simulation results, providing a quantitative measure to the improvement in performance obtained using non-binary alphabets.Comment: 7 pages, 1 figur

Mathematical methods of market risk valuation in application to Russian stock market

This work is dedicated to comparative analysis and estimation of quantitative methods of risk valuation in application to Russian stock market, which include historical simulation, exponentially-weighted historical simulation, variance-covariance models with adaptive covariance matrix, variance-covariance models with exponentially-weighted adaptive covariance matrix, models based on GARCH(1,1), and Monte-Carlo Models. For the purpose of implementation of these models, algorithms of risk valuation have been developed on the basis of Value-at-Risk methodic as one of the most widely used and in accordance to RiskMetrics standards. Algorithms are implemented with usage of development environment of specialized decision support system software “Prognoz. Market risk†based on “Prognoz†analytical suite. The Decision support system mentioned above allows using different methods of risk measures calculation including standard and complex non-trivial methods. It also provides a capability to be individually tuned to better suit users’ requirements. For the purpose of backtesting of developed algorithms market risk measures were calculated using open data from Russian stock market (MICEX). For mentioned risk measures figures of quality and effectiveness were calculated, including average VaR exception value, average uncovered losses to VaR ratio, maximum loss to VaR ratio, average unused reserves, and multiplier to obtain coverage. Acquired results allowed distinguishing models which are insufficiently adequate if used in current situation on Russian stock market: models which use exponentially weighted historical simulation and some of models using variance-covariance approach. Other models can be taken as adequate with the significance level of 1% and 5%

Quantitative Genetics and Functional-Structural Plant Growth Models: Simulation of Quantitative Trait Loci Detection for Model Parameters and Application to Potential Yield Optimization

Background and Aims: Prediction of phenotypic traits from new genotypes under untested environmental conditions is crucial to build simulations of breeding strategies to improve target traits. Although the plant response to environmental stresses is characterized by both architectural and functional plasticity, recent attempts to integrate biological knowledge into genetics models have mainly concerned specific physiological processes or crop models without architecture, and thus may prove limited when studying genotype x environment interactions. Consequently, this paper presents a simulation study introducing genetics into a functional-structural growth model, which gives access to more fundamental traits for quantitative trait loci (QTL) detection and thus to promising tools for yield optimization. Methods: The GreenLab model was selected as a reasonable choice to link growth model parameters to QTL. Virtual genes and virtual chromosomes were defined to build a simple genetic model that drove the settings of the species-specific parameters of the model. The QTL Cartographer software was used to study QTL detection of simulated plant traits. A genetic algorithm was implemented to define the ideotype for yield maximization based on the model parameters and the associated allelic combination. Key Results and Conclusions: By keeping the environmental factors constant and using a virtual population with a large number of individuals generated by a Mendelian genetic model, results for an ideal case could be simulated. Virtual QTL detection was compared in the case of phenotypic traits - such as cob weight - and when traits were model parameters, and was found to be more accurate in the latter case. The practical interest of this approach is illustrated by calculating the parameters (and the corresponding genotype) associated with yield optimization of a GreenLab maize model. The paper discusses the potentials of GreenLab to represent environment x genotype interactions, in particular through its main state variable, the ratio of biomass supply over demand