Synchronization In Mobile Ad-hoc Network And Modeling Core Regulatory Gene Network In Osteoporosis

The research of complex networks has been rapidly developed in the past decade, which incorporates many traditional disciplines, such as physics, biology, medicine, engineering, sociology, and economics, etc. It is believed that a new inter-disciplinary science-network science-has been formed, which has great significance in both theory and applications. In this thesis, we investigate two issues in the field of complex net-works:the phase synchronization in Ad-hoc network, and modeling a core regulatory gene network in osteoporosis.1. The phase synchronization in Ad-hoc network. We study the phase synchroniza-tion in a mobile Ad-hoc network whose topology changes dynamically. As the network size or the communication radius of individual oscillator increases, the network gradu-ally approaches connectivity via a second-order percolation transition. It is shown that the mobility of oscillators generally enhances the coherence in such networks. In par-ticular, we find a new type of phase synchronization/clustering, namely, the shuttle-run synchronization. In such coherent state, the phases of oscillators distribute in a certain narrow range, while their instantaneous frequencies change signs frequently, leading to the shuttle-run-like motion of oscillators in phase space. We conduct theoretical analysis to explain the mechanism of such synchronization, and analytically obtain the critical transition point. In addition, we also study the explosive synchronization in Ad-hoc net-work. It is found that both frequency-weighted Kuramoto model and adaptive Kuramoto model can exhibit explosive synchronization. These results help deepen our understand-ings of synchronization in the time-varying networks.2. Modeling core regulatory gene network in osteoporosis. Osteoporosis is a preva-lent aging related disease whose molecular mechanism remains unclear so far. Although inflammation is shown to be related to osteoporosis, there is no simple causality between them. In this work, we identify that at molecular level, hormonal signaling is governed by a complex network, including estrogen signaling, glucocorticoid signaling, retinoic acid signaling, peroxisome proliferator-activated receptor signaling and vitamin D receptor signaling pathways. In this way, the main effect of estrogen can be understood as chang-ing the inherent robust state of the network. The structure of this network manifests that the osteoporosis phenotype may be induced by interrupting either single or multiple com-ponents of the network. We carry out experiments for three groups of rats, i.e., the sham-operated rats, the ovariectomized (OVX) rats, and the OVX rats treated with strontium gluconate (GluSr). The results of transmission electron microscopy (TEM) and microar-ray experiments support our argument. For example, TEM demonstrates that osteocytes exhibit different morphologies, implying that the abnormality of osteocytes might be one leading reason for osteoporosis. The microarray data show significantly altered pattern in glucocorticoids and vitamin D inducible genes, supporting cross-talk among signaling pathways. Based on literatures of molecular biology and biochemical experiments, we identify a regulatory gene network among estrogen, retinoic acids, glucocorticoids, fatty acids and vitamin D regulations. By dynamical analysis, we demonstrate that both physi-ological and osteoporosis profiles correspond to the different robust states of the network. These findings indicate that this network might be a systematic regulatory architecture on osteocytes. This work help provide new insights in understanding the pathology of os-teoporosis as well as the possibility of new therapies.