A Class of Quantum LDPC Codes Constructed From Finite Geometries

Low-density parity check (LDPC) codes are a significant class of classical codes with many applications. Several good LDPC codes have been constructed using random, algebraic, and finite geometries approaches, with containing cycles of length at least six in their Tanner graphs. However, it is impossible to design a self-orthogonal parity check matrix of an LDPC code without introducing cycles of length four. In this paper, a new class of quantum LDPC codes based on lines and points of finite geometries is constructed. The parity check matrices of these codes are adapted to be self-orthogonal with containing only one cycle of length four. Also, the column and row weights, and bounds on the minimum distance of these codes are given. As a consequence, the encoding and decoding algorithms of these codes as well as their performance over various quantum depolarizing channels will be investigated.Comment: 5pages, 2 figure

Solving reaction-diffusion equations 10 times faster

The most popular numerical method for solving systems of reaction-diffusion equations continues to be a low order finite-difference scheme coupled with low order Euler time stepping. This paper extends previous 1D work and reports experiments that show that with high--order methods one can speed up such simulations for 2D and 3D problems by factors of 10--100. A short MATLAB code (2/3D) that can serve as a template is included.\ud \ud This work was supported by the Engineering and Physical Sciences Research Council (UK) and by the MathWorks, Inc

Facing the growing problem of the electric power consumption in Egyptian residential building using building performance simulation program

Egypt has been experiencing recurrent power cuts especially at the summer, with the problem being made worse by the extra demands placed on the electrical grid by the advent of the holy month of Ramadan. Electricity shortages are now a problem in Cairo, Alexandria, Sohag, Qena, Luxor, Aswan, and Nubia, as well as in the Nile Delta governorates of Beheira and Qalioubiya. The aim of this study is to develop a model for the Egyptian residential building using Building Performance Simulation Program and make sensitivity analysis on some variables effecting the electric power consumption in order to help faceting the growing problem in Egypt. The model was created using the IES-VE 2012 (Integrated Environmental Solution ). The simulation model was verified against the survey data for the Egyptian apartment and same model simulated using energy Plus simulation tool. The results of the program describing different situations for energy using profile for the air conditions, lighting and equipments in respect to building layout and construction climate and pattern of use. This model can be used in the future to help in reducing the electric power consumption in the residential building

Error bounds for small jumps of L\'evy processes

The pricing of options in exponential Levy models amounts to the computation of expectations of functionals of Levy processes. In many situations, Monte-Carlo methods are used. However, the simulation of a Levy process with infinite Levy measure generally requires either to truncate small jumps or to replace them by a Brownian motion with the same variance. We will derive bounds for the errors generated by these two types of approximation.Comment: 21 p