Sensitivity analysis is fundamental and essential in analysis and design of any system. This paper proposes a method of sensitivity analysis for rhythm phenomena in gene regulatory networks (GRNs). In particular, we focus on cyclic expression pattern sequences in GRNs and sensitivity of period which plays one of important roles in periodic phenomena. A piecewise-linear differential-equation model is utilized as a model of GRNs. Rhythm phenomena are expressed by using periodic orbits and corresponding expression pattern sequences. Sensitivity analysis of rhythm phenomena is very difficult because rhythms appear autonomously as periodic phenomena in nonlinear systems. and only a few studies have been done. In general, sensitivities of period are calculated by using numerical methods approximately. In this paper, we analytically derive the mathematical expression of period sensitivity of GRNs. It is shown through numerical examples that the proposed method makes it possible to obtain period sensitivity appropriately.

Sensitivity analysis is a basic and essential issue in analysis and design of any system. In this paper, we discuss a method of sensitivity analysis of rhythm phenomena which are found in various systems such as physical systems, biological systems and social systems and so on. Sensitivity analysis of rhythm phenomena is very difficult because rhythms appear autonomously as periodic phenomena in nonlinear dynamical systems and only a few studies have been done. We have already proposed an analysis method of period sensitivities in rhythm phenomena. This paper discusses an analysis method of phase sensitivity in rhythm phenomena. We first define phase for periodic trajectories of nonlinear systems, that is, limit cycles and derive a rigorous mathematical expression of phase sensitivities by introducing Poincaré map. Based on the expression we derive an efficient computer algorithm to calculate the phase sensitivities. It is shown that the proposed analysis method makes it possible to obtain both the period and phase sensitivities efficiently with reasonable accuracy.

Sensitivity analysis is fundamental and essential in analysis and design of any system. This paper proposes a method of sensitivity analysis of rhythm phenomena which are found in various systems. In particular, we propose an analysis method of period sensitivities in rhythm phenomena. Analysis of period sensitivities is very difficult because rhythms appear autonomously as periodic phenomena in nonlinear systems and only a few studies have been done. We already proposed an analysis method of parameter sensitivities of the periods in rhythm phenomena based on the sensitivity equation approach. In this paper, we propose a computationally efficient and accurate method to analyze the period sensitivities by the adjoint equation approach. Comparisons of the proposed method with that based on sensitivity equations are also made.

The purpose of this paper is to propose a method for analyzing the period sensitivities and bifurcations for rhythm phenomena. The authors have already proposed a method for analyzing the sensitivities of the period with respect to parameters, an important characteristic of rhythm phenomena, and computationally efficient algorithms for this purpose. The period sensitivities of rhythm phenomena depend on bifurcations of that phenomena. In this paper, we propose a method and computation algorithms for investigating variations of the period sensitivities and bifurcations for rhythm phenomena by incorporating those algorithms. We also show an example of investigating variations of the period sensitivities and bifurcations by using the developed algorithm and demonstrate what can be revealed by it.

Sensitivity analysis is fundamental and essential in analysis and design in any system. This paper discusses a method of sensitivity analysis of rhythm phenomena which are found in various systems such as physical systems, biological systems and human societies and so on. Sensitivity analysis of rhythm phenomena is very difficult because rhythms appear autonomously as periodic phenomena in nonlinear systems and only few studies have been done. We deal with the periods and propose an analysis method of sensitivities of periods for periodic phenomena. We first derive a strict expression of period sensitivities by introducing Poincaré map. Based on the expression we derive an efficient computer algorithm to calculate period sensitivities. It is shown that the proposed analysis method makes it possible to obtain period sensitivities of not only stable periodic orbits but also unstable periodic orbits embedded in chaos attracters.

Recently, synthesis of gene regulatory networks having desired behavior has become of interest to many researchers and several studies have been done. There exist periodic phenomena in cells and these periodic phenomena are considered to be generated by gene regulatory networks. We already proposed a synthesis method of gene regulatory networks having desired cyclic expression pattern sequences. In this paper, we propose a synthesis method for realizing not only desired cyclic expression pattern sequences but also desired periods. In the proposed method we derive a representation of periods and introduce Poincare map for realizing periodic solution trajectories with desired periods. We also introduce a discrete-time network which represent transition of expression pattern. In the problem, gene regulatory network model is given by differential equations. However, in order to synthesize gene regulatory networks we solve only the discrete-time network. Therefore desired behavior are realized efficiently. Numerical experiments are carried out to illustrate the performance of the proposed method.

This paper presents neural network models for identification and realization of a class of discrete event systems (DESs). We consider a class of DESs which is modeled by using finite state automata. Two neural network models are presented: one is a class of recurrent neural networks and the other is a class of recurrent high-order neural networks. The models are capable of representing the DESs with the network size being smaller than the existing models. We also discuss identification and realization methods of the DESs from a given set of input and output data by training the neural networks. Comparisons are made among the models in terms of abilities of identification and realization of the DESs.

Abstract This paper describes how new learning methods may make it possible for a large‐scale, hierarchical neural network to recognize most Japanese handwritten characters. This is a very large and complex task, as the Japanese character set consists of about 3000 categories which can be written in many different ways. Such a difficult task can lead a neural network to converge very slowly and to yield recognition rates that are uneven between categories. To address these problems we here propose five learning methods as modifications of the conventional back‐propagation learning rule. These methods produce fast convergence, even recognition rates over all categories, and adequate recognition of test samples. We also describe how a large‐scale neural network can be built by dividing the recognition task into several subtasks, with networks for each subtask, and then integrating these subnetworks in a large network with a hierarchical structure. In a hierarchical network, the upper level network directly integrates outputs from each lower level network. Application of that network to handwritten Japanese character recognition has resulted in poor recognition, because lower level networks do not know about unknown input patterns, and the direct integration of ambiguous outputs from many lower level networks confuses the upper level network. We propose a new integration method which provides each subnetwork with more information as to how close an input pattern is to the categories of that subnetwork. This method resulted in high recognition performance for character recognition. We here described the above methods, and report the performance of our implementation of a neural network for the recognition of 71 Hiragana characters, and describe our implementation of this network on a hypercube concurrent computer.