A neural network for linear matrix inequality problems

Zhang neural network for online solution of time-varying linear matrix inequality aided with an equality conversion

In this paper, for online solution of time-varying linear matrix inequality (LMI), such an LMI is first converted to a time-varying matrix equation by introducing a time-varying matrix, of which each element is greater than or equal to zero. Then, by employing Zhang et al.'s neural dynamic method, a special recurrent neural network termed Zhang neural network (ZNN) is proposed and investigated for solving online the converted time-varying matrix equation as well as the time-varying LMI. Such a ZNN model showed in an explicit dynamics exploits the time-derivative information of time-varying coefficients. In addition, theoretical analysis and results of the proposed ZNN model are discussed and presented to show its excellent performance on solving the time-varying LMI. Computer simulation results further demonstrate the efficacy of the proposed ZNN model for online solution of the time-varying LMI and the converted time-varying matrix equation.

On the increase in network robustness and decrease in network response ability during the aging process: a systems biology approach via microarray data

Aging, an extremely complex and system-level process, has attracted much attention in medical research, especially since chronic diseases are quite prevalent in the elderly population. These may be the result of both gene mutations that lead to intrinsic perturbations and environmental changes that may stimulate signaling in the body. Therefore, analysis of network robustness to tolerate intrinsic perturbations and network response ability of gene networks to respond to external stimuli during the aging process may provide insight into the systematic changes caused by aging. We first propose novel methods to estimate network robustness and measure network response ability of gene regulatory networks by using their corresponding microarray data in the aging process. Then, we find that an aging-related gene network is more robust to intrinsic perturbations in the elderly than the young, and therefore is less responsive to external stimuli. Finally, we find that the response abilities of individual genes, especially FOXOs, NF-κB, and p53, are significantly different in the young versus the aged subjects. These observations are consistent with experimental findings in the aged population, e.g., elevated incidence of tumorigenesis and diminished resistance to oxidative stress. The proposed method can also be used for exploring and analyzing the dynamic properties of other biological processes via corresponding microarray data to provide useful information on clinical strategy and drug target selection.

New measurement methods of network robustness and response ability via microarray data

"Robustness", the network ability to maintain systematic performance in the face of intrinsic perturbations, and "response ability", the network ability to respond to external stimuli or transduce them to downstream regulators, are two important complementary system characteristics that must be considered when discussing biological system performance. However, at present, these features cannot be measured directly for all network components in an experimental procedure. Therefore, we present two novel systematic measurement methods--Network Robustness Measurement (NRM) and Response Ability Measurement (RAM)--to estimate the network robustness and response ability of a gene regulatory network (GRN) or protein-protein interaction network (PPIN) based on the dynamic network model constructed by the corresponding microarray data. We demonstrate the efficiency of NRM and RAM in analyzing GRNs and PPINs, respectively, by considering aging- and cancer-related datasets. When applied to an aging-related GRN, our results indicate that such a network is more robust to intrinsic perturbations in the elderly than in the young, and is therefore less responsive to external stimuli. When applied to a PPIN of fibroblast and HeLa cells, we observe that the network of cancer cells possesses better robustness than that of normal cells. Moreover, the response ability of the PPIN calculated from the cancer cells is lower than that from healthy cells. Accordingly, we propose that generalized NRM and RAM methods represent effective tools for exploring and analyzing different systems-level dynamical properties via microarray data. Making use of such properties can facilitate prediction and application, providing useful information on clinical strategy, drug target selection, and design specifications of synthetic biology from a systems biology perspective.

A new variant of the Zhang neural network for solving online time-varying linear inequalities

Since March 2001, a special class of recurrent neural networks termed the Zhang neural network (ZNN) has been proposed by Zhang and co-workers for solving online a rich repertoire of time-varying problems. By extending Zhang et al. 's design formula (or say, the ZNN design formula), a (new) variant of the ZNN design formula is proposed and investigated in this paper, which is also based on a matrix/vector-valued indefinite error function. In addition, by employing such a novel design formula, a new variant of the ZNN (NVZNN) is proposed, developed and investigated for online solution of time-varying linear inequalities (LIs). The resultant NVZNN models are depicted in implicit dynamics and methodologically exploit the time-derivative information of time-varying coefficients. Computer simulation results further demonstrate the novelty, efficacy and superiority of the proposed NVZNN models for solving online time-varying LIs.