Wiener and Kalman Detection Methods for Molecular Communications.

Diffusion-based molecular communication system (DBMC) is a system in which information-carrying molecules are sent from the transmitter and passively transported to the receiver in a fluid environment. Nanomachines, which are the main part of this system, have limited processing capacity. Besides, at the receiver, high inter-symbol interference (ISI) occurs due to free movement of molecules and the variance of the observation noise is signal dependent. Hence, it is important to design high-performance and low complexity receiver detection methods. In this paper, finite impulse response (FIR) Wiener filter is introduced for the first time, which has considerably less computational complexity compared to the minimum mean square error (MMSE) algorithm proposed in the literature. Moreover, extended Kalman filter is introduced for the first time to DBMC as a receiver detection method. Finally, Viterbi algorithm is modified and used as a benchmark for performance evaluation.

Aggregation for Computing Multi-Modal Stationary Distributions in 1-D Gene Regulatory Networks.

This paper proposes aggregation-based, three-stage algorithms to overcome the numerical problems encountered in computing stationary distributions and mean first passage times for multi-modal birth-death processes of large state space sizes. The considered birth-death processes which are defined by Chemical Master Equations are used in modeling stochastic behavior of gene regulatory networks. Computing stationary probabilities for a multi-modal distribution from Chemical Master Equations is subject to have numerical problems due to the probability values running out of the representation range of the standard programming languages with the increasing size of the state space. The aggregation is shown to provide a solution to this problem by analyzing first reduced size subsystems in isolation and then considering the transitions between these subsystems. The proposed algorithms are applied to study the bimodal behavior of the lac operon of E. coli described with a one-dimensional birth-death model. Thus, the determination of the entire parameter range of bimodality for the stochastic model of lac operon is achieved.