New results on adaptive fixed-time control for convex-delayed neural networks.

This paper studies the adaptive fixed-time synchronization issue for convex-delayed neural networks. First, the convex delay is introduced to address the state delay of neural networks in order to reflect the impacts of multiple delay components such as input transition time and switching communication. Then, a new fixed-time control method is presented to adaptively determine multi-control gains with a unified update law. Afterward, some sufficient criteria are figured out by using Lyapunov stability theorem to ensure that the delayed neural networks are fixed-timely stable. Finally, simulated examples are adopted to validate our theoretical results.

Mean field theory for biology inspired duplication-divergence network model.

The duplication-divergence network model is generally thought to incorporate key ingredients underlying the growth and evolution of protein-protein interaction networks. Properties of the model have been elucidated through numerous simulation studies. However, a comprehensive theoretical study of the model is lacking. Here, we derived analytic expressions for quantities describing key characteristics of the network-the average degree, the degree distribution, the clustering coefficient, and the neighbor connectivity-in the mean-field, large-N limit of an extended version of the model, duplication-divergence complemented with heterodimerization and addition. We carried out extensive simulations and verified excellent agreement between simulation and theory except for one partial case. All four quantities obeyed power-laws even at moderate network size ( N∼10(4)), except the degree distribution, which had an additional exponential factor observed to obey power-law. It is shown that our network model can lead to the emergence of scale-free property and hierarchical modularity simultaneously, reproducing the important topological properties of real protein-protein interaction networks.

Pinning synchronization of hybrid-coupled directed delayed dynamical network via intermittent control.

This paper concerns the problem of exponential synchronization for a class of general delayed dynamical networks with hybrid coupling via pinning periodically intermittent control. Both the internal delay and coupling delay are taken into account in the network model. Meanwhile, the transmission delay and self-feedback delay are involved in the delayed coupling term. By establishing a new differential inequality, several simple and useful exponential synchronization criteria are derived analytically. It is shown that the controlled synchronization state can vary in comparison with the conventional synchronized solution, and the degree of the node and the inner delayed coupling matrix play important roles in the controlled synchronization state. By choosing different inner delayed coupling matrices and the degrees of the node, different controlled synchronization states can be obtained. Furthermore, the detail pinning schemes deciding what nodes should be chosen as pinned candidates and how many nodes are needed to be pinned for a fixed coupling strength are provided. The simple procedures illuminating how to design suitable intermittent controllers in real application are also given. Numerical simulations, including an undirected scale-free network and a directed small-world network, are finally presented to demonstrate the effectiveness of the theoretical results.

Functional characteristics of a double negative feedback loop mediated by microRNAs.

MicroRNAs (miRNAs) are a class of small, noncoding RNAs that play crucial roles in almost all cellular processes. As key post-transcriptional regulators of gene expression, miRNAs mainly induce mRNA degradation or translational repression. Recently computational and experimental studies have identified an abundance of motifs involving miRNAs and transcriptional factors (TFs). Here, we study the functional characteristics of one such motif, a two-node miRNA-mediated double negative feedback loop (MDNFL) in which a TF suppresses an miRNA and the TF itself is negatively regulated by the miRNA. Several examples of this motif are described from the literature. We propose a general computational model for the MDNFL based on biochemical regulations and explore its dynamics by using bifurcation analysis. Our results show that the MDNFL can behave as a bistable switch. This functional feature is in agreement with experimental observations of the widespread appearance of miRNAs in fate decisions such as differentiation during development. Importantly, it is found that under the interplay of a TF and an miRNA, the MDNFL model can behave as switches for wide ranges of parameters even without cooperative binding of the TF. In addition, we also investigate how extrinsic noise affects dynamic behavior of the MDNFL. Interestingly, it is found that when the MDNFL is in the bistable region, by choosing the appropriate extrinsic noise source, the MDNFL system can switch from one steady state to the other and meanwhile the production of either miRNA or protein is amplified significantly. From an engineering perspective, this noise-based switch and amplifier for gene expression is very easy to control. It is hoped that the results presented here would provide a new insight on how gene expression is regulated by miRNAs and further guidance for experiments.

Mechanisms generating bistability and oscillations in microRNA-mediated motifs.

The importance of post-transcriptional regulation by microRNAs (miRNAs) has recently been recognized in almost all cellular processes. When participating in cellular processes, miRNAs mainly mediate mRNA degradation or translational repression. Recently computational and experimental studies have identified an abundance of motifs involving miRNAs and transcriptional factors (TFs). The simplest motif is a two-node miRNA-mediated feedback loop (MFL) in which a TF regulates an miRNA and the TF itself is negatively regulated by the miRNA. In this paper we present a general computational model for the MFL based on biochemical regulations and explore its dynamics by using bifurcation analysis. Our results show that the MFL can behave either as switches or as oscillators, depending on the TF as a repressor or an activator. These functional features are consistent with the widespread appearance of miRNAs in fate decisions such as proliferation, differentiation, and apoptosis during development. We found that under the interplay of a TF and an miRNA, the MFL model can behave as switches for wide ranges of parameters even without cooperative binding of the TF. In addition, oscillations induced by the miRNA in the MFL model require neither an additional positive feedback loop, nor self-activation of the gene, nor cooperative binding of the TF, nor saturated degradation. Therefore, the MFL may provide a general network structure to induce bistability or oscillations. It is hoped that the results presented here will provide a new view on how gene expression is regulated by miRNAs and further guidance for experiments. Moreover, the insight gained from this study is also expected to provide a basis for the investigation of more complex networks assembled by simple building blocks.

Exponential synchronization of chaotic systems with time-varying delays and parameter mismatches via intermittent control.

This paper studies the synchronization of coupled chaotic systems with time-varying delays in the presence of parameter mismatches by means of periodically intermittent control. Some novel and useful quasisynchronization criteria are obtained by using the methods which are different from the techniques employed in the existing works, and the derived results are less conservative. Especially, a strong constraint on the control width that the control width should be larger than the time delay imposed by the current references is released in this paper. Moreover, our results show that the synchronization criteria depend on the ratio of control width to control period, but not the control width or the control period. Finally, some numerical simulations are given to show the effectiveness of the theoretical results.

The interaction between multiplex community networks.

Multiplex community networks, consisting of several different types of simplex networks and interconnected among them, are ubiquitous in the real world. In this paper, we carry out a quantitative discussion on the interaction among these diverse simplex networks. First, we define two measures, mutual-path-strength and proximity-node-density, based on twoplex community networks and then propose an impact-strength-index (ISI) to describe the influence of a simplex network on the other one. Finally, we apply the measure ISI to make an explanation for the challenge system of social relations from the viewpoint of network theory. Numerical simulations show that the measure ISI can describe the interaction between multiplex community networks perfectly.

Emergence of modularity and disassortativity in protein-protein interaction networks.

In this paper, we present a simple evolution model of protein-protein interaction networks by introducing a rule of small-preference duplication of a node, meaning that the probability of a node chosen to duplicate is inversely proportional to its degree, and subsequent divergence plus nonuniform heterodimerization based on some plausible mechanisms in biology. We show that our model cannot only reproduce scale-free connectivity and small-world pattern, but also exhibit hierarchical modularity and disassortativity. After comparing the features of our model with those of real protein-protein interaction networks, we believe that our model can provide relevant insights into the mechanism underlying the evolution of protein-protein interaction networks.