The phenomenon of stochastic resonance (SR) in a mono-threshold-system-based detector (MTD) with additive background noise and multiplicative external noise is investigated. On the basis of maximum a posteriori probability (MAP) criterion, we deal with the binary signal transmission in four scenarios. The performance of the MTD is characterized by the probability of error detection, and the effects of system threshold and noise intensity on detectability are discussed in this paper. Similar to prior studies that focus on additive noises, along with increases in noise intensity, we also observe a non-monotone phenomenon in the multiplicative ways. However, unlike the case with the additive noise, optimal multiplicative noises all tend toward infinity for fixed additive noise intensities. The results of our model are potentially useful for the design of a sensor network and can help one to understand the biological mechanism of synaptic transmission.

Identifying the infection sources in a network, including the sponsor of a network rumor, the servers that inject computer virus into a computer network, or the zero-patient in an infectious disease network, plays a critical role in limiting the damage caused by the infection. A two-source estimator is firstly constructed on basis of partitions of infection regions in this paper. Meanwhile, the two-source estimation problem is transformed into calculating the expectation of permitted permutations count which can be simplified to a single-source estimation problem under determined infection region. A heuristic algorithm is also proposed to promote the estimator to general graphs in a Breadth-First-Search (BFS) fashion. Experimental results are provided to verify the performance of our method and illustrate variations of error detection in different networks.