Almost all self-dual codes are rigid

We prove that almost every binary self-dual code has trivial automorphism group. We also construct a self-dual code with trivial automorphism group.     

Blind SNR estimation for limited time series

A blind SNR estimation method for discrete data is presented. The original noise-free data is assumed to follow a known signal model with an unknown attenuation. The SNR in noisy data is estimated using a polynomial fit obtained from the correlative characteristics between SNR and variance fractal dimension values. The bias and the “standard error” (root mean square error) of the estimator are used as performance measures. The simulated performance of the estimator for a specific signal model with real additive white Gaussian noise assumption is compared to that of a published decision-aided (nonblind) SNR estimator.     

Mathematical analysis of a shuttle system based on two interdependent queues

This is an analysis of a multishuttle system, using a car ferry as the example, to develop mathematical models of shuttle systems. Poisson-exponential mathematical models for the single- and two-shuttle systems are formulated as interdependent queueing systems. The vector (X_A, X_B) representing the number of cars waiting at shore A and shore B respectively, at the end of an unloading at one of the shores is shown to form a bivariate Markov chain; thus the long run probability distributions of (X_A, X_B) can be evaluated using classical Markov chain theory.     

Multinomial tau-leaping method for stochastic kinetic simulations

We introduce the multinomial tau-leaping (MtauL) method for general reaction networks with multichannel reactant dependencies. The MtauL method is an extension of the binomial tau-leaping method where efficiency is improved in several ways. First, tau-leaping steps are determined simply and efficiently using a priori information and Poisson distribution-based estimates of expectation values for reaction numbers over a tentative tau-leaping step. Second, networks are partitioned into closed groups of reactions and corresponding reactants in which no group reactant set is found in any other group. Third, product formation is factored into upper-bound estimation of the number of times a particular reaction occurs. Together, these features allow larger time steps where the numbers of reactions occurring simultaneously in a multichannel manner are estimated accurately using a multinomial distribution. Furthermore, we develop a simple procedure that places a specific upper bound on the total reaction number to ensure non-negativity of species populations over a single multiple-reaction step. Using two disparate test case problems involving cellular processes--epidermal growth factor receptor signaling and a lactose operon model--we show that the tau-leaping based methods such as the MtauL algorithm can significantly reduce the number of simulation steps thus increasing the numerical efficiency over the exact stochastic simulation algorithm by orders of magnitude.     

Photoionization cross section and refractive-index change of hydrogenic impurities in a CdS-SiO<Subscript>2</Subscript> spherical quantum dot

In this study, we calculate the photoionization cross section and refractive-index change of an on-center hydrogenic impurity in a CdS-SiO₂ spherical quantum dot. In numerical calculations, both the finite- and infinite-confinement cases are considered and a variational scheme is adopted to determine the energy eigenvalues for the impurity. The variations of the photoionization cross section with the dot radius, the refractive-index change, and the normalized photon energy are investigated, and the effect of the potential-barrier height on the cross section is discussed. The results obtained show that the photoionization cross section and the refractive-index change in CdS-SiO₂ spherical quantum dots are sensitively dependent on the incident optical intensity and on the dot sizes.