An important factor determining the performance of delay tolerant networks (DTNs) is packet delivery delay. In this paper, we study the block delivery delay of DTN with the epidemic routing scheme based on random linear network coding (RLNC). First, simulations show that the influence of relay buffer size on the delivery delay is not as strong in RLNC-based routing as it is in replica-based routing. With this observation,we can simplify the performance analysis by constraining the buffer of the relay node to just one size. Then we derive the cumulative distribution function (CDF) of block delivery delay with difference equations. Finally, we validate the correctness of our analytical results by simulations.

In this paper, a new set of difference equations is derived for transient analysis of the convergence of adaptive FIR filters using the Sign-Sign Algorithm with Gaussian reference input and additive Gaussian noise. The analysis is based on the assumption that the tap weights are jointly Gaussian distributed. Residual mean squared error after convergence and simpler approximate difference equations are further developed. Results of experiment exhibit good agreement between theoretically calculated convergence and that of simulation for a wide range of parameter values of adaptive filters.

In this paper stochastic aradient adaptive filters using the Sign or Sign-Sign Algorithm are analyzed based upon general assumptions on the reference signal, additive noise and particularly jointly distributed tap errors. A set of difference equations for calculating the convergence process of the mean and covariance of the tap errors is derived with integrals involving characteristic function and its derivative of the tap error distribution. Examples of echo canceller convergence with jointly Gaussian distributed tap errors show an excellent agreement between the empirical results and the theory.

On mutually coupling lines, the transmission signal is dispersively propagated by crosstalk coupling between lines and shows complex propagation characteristics caused by reciprocal reflections. Usually, the differential equation and the integral equation have been applied to analyze the solutions of transmission lines. In this paper, we propose a different analytical method of the propagation characteristics of signal and crosstalk noise. By setting up crosstalk coupling line as a sectionally divided digital transmission network and by using the signal flow graph and the difference equation, the propagation characteristics in the frequency domain, the space domain and the time domain on mutually coupling lines can be obtained. To verify the validity of this method and analyze the complex propagation problems, we first study the crosstalk characteristics of a twisted pair cable via the third circuit by unidirectional coupling. Subsequently we will analyze the coupling theory of bidirectional coupling lines.

We develop a convergence theory of the simple genetic algorithm (SGA) for two-bit problems (Type I TBP and Type II TBP). SGA consists of two operations, reproduction and crossover. These are imitations of selection and recombination in biological systems. TBP is the simplest optimization problem that is devised with an intention to deceive SGA into deviating from the maximum point. It has been believed that, empirically, SGA can deviate from the maximum point for Type II while it always converges to the maximum point for Type I. Our convergence theory is a first mathematical achievement to ensure that the belief is true. Specifically, we demonstrate the following. (a) SGA always converges to the maximum point for Type I, starting from any initial point. (b) SGA converges either to the maximum or second maximum point for Type II, depending upon its initial points. Regarding Type II, we furthermore elucidate a typical sufficient initial condition under which SGA converges either to the maximum or second maximum point. Consequently, our convergence theory establishes a solid foundation for more general GA convergence theory that is in its initial stage of research. Moreover, it can bring powerful analytical techniques back to the research of original biological systems.