Dynamics of network motifs in genetic regulatory networks

Network motifs hold a very important status in genetic regulatory networks. This paper aims to analyse the dynamical property of the network motifs in genetic regulatory networks. The main result we obtained is that the dynamical property of a single motif is very simple with only an asymptotically stable equilibrium point, but the combination of several motifs can make more complicated dynamical properties emerge such as limit cycles. The above-mentioned result shows that network motif is a stable substructure in genetic regulatory networks while their combinations make the genetic regulatory network more complicated.     

Effects of nonlinear degradation of protein on the oscillatory dynamics in a simple gene regulatory network

Cooperative stability of protein is here defined as the tendency for the oligomers to be more stable than their monomeric components and to perform their physiological functions. In this paper, we incorporate nonlinear degradation of protein induced by cooperative stability into a simple model which has been previously presented in the biological literature. Linear analysis gives a critical time delay beyond which a periodic solution is born in a Hopf bifurcation. Lindstedt’s method is applied to the nonlinear system, resulting in closed form approximate expressions for the amplitude and frequency of oscillation. Our findings indicate that cooperative stability can cause periodic dynamics through reducing the critical time delay. In addition, we show that cooperative stability may increase the amplitude of oscillation. Our study contributes to the theoretical demonstration of the effect of cooperative stability in the simple gene regulatory network.     

Pattern recognition minimizes entropy production in a neural network of electrical oscillators

We investigate the physical principle driving pattern recognition in a previously introduced Hopfield-like neural network circuit (Hölzel and Krischer, 2011 [13]). Effectively, this system is a network of Kuramoto oscillators with a coupling matrix defined by the Hebbian rule. We calculate the average entropy production 〈dS/dt〉$〈\mathrm{d}S/\mathrm{d}t〉$ of all neurons in the network for an arbitrary network state and show that the obtained expression for 〈dS/dt〉$〈\mathrm{d}S/\mathrm{d}t〉$ is a potential function for the dynamics of the network. Therefore, pattern recognition in a Hebbian network of Kuramoto oscillators is equivalent to the minimization of entropy production for the implementation at hand. Moreover, it is likely that all Hopfield-like networks implemented as open systems follow this mechanism.     

遗传优化神经网络的水声信道盲均衡

不需要训练序列的盲均衡技术可以有效地节省水声通信带宽，消除码间干扰，提高水声通信效率和质量。以前馈神经网络（FNN）作为盲均衡器，既适用于最小相位信道，也适用于非最小相位信道，包括非线性信道，但是前馈神经网络在实际的应用中其网络拓扑结构的选取和初始权重的确定缺乏理论依据，且其训练主要依靠BP算法，存在收敛速度慢、容易陷入局部极值及“过学习”的问题。为此，本文提出了一种遗传优化神经网络的水声信道盲均衡算法（GA—BP），对前馈神经网络拓扑结构和网络权重同时优化，有效地克服了传统前馈神经网络盲均衡的缺陷，提高了前馈神经网络盲均衡的泛化性能并加强了跟踪时变信道的能力和对信道突变的适应能力。水池试验结果证明了文中提出的遗传优化神经网络水声信道盲均衡算法的有效性，与直接前馈神经网络盲均衡相比较，均衡性能明显得到了提高。     

On stationary convection and oscillatory motions in ferromagnetic convection in a ferrofluid layer

It is shown analytically that the ‘principle of the exchange of stabilities’ (PES), in general, is not valid in ferromagnetic convection in a ferrofluid layer, for the case of free boundaries and hence a sufficient condition is derived for the validity of the PES. Upper bounds for the complex growth rate are then obtained. It is proved that the complex growth rate σ=σ_r+iσ_i (where σ_r and σ_i are, respectively, the real and imaginary parts of σ) of an arbitrary oscillatory motion of growing amplitude, in ferromagnetic convection in a ferrofluid layer, for the case of free boundaries lies inside a semicircle in the right half of the σ_rσ_i-plane whose center is at the origin and ²(radius)=RM₁/P_r, where R is the Rayleigh number,M₁ is the magnetic number and P_r is the Prandtl number. Further, bounds for the case of rigid ferromagnetic boundaries are also derived separately.     

Polymorphic and regular localized activity structures in a two-dimensional two-component reaction-diffusion lattice with complex threshold excitation

Space-time dynamics of the system modeling collective behaviour of electrically coupled nonlinear units is investigated. The dynamics of a local cell is described by the FitzHugh-Nagumo system with complex threshold excitation. It is shown that such a system supports formation of two distinct kinds of stable two-dimensional spatially localized moving structures without any external stabilizing actions. These are regular and polymorphic structures. The regular structures preserve their shape and velocity under propagation while the shape and velocity as well as other integral characteristics of polymorphic structures show rather complex temporal behaviour. Both kinds of structures represent novel sorts of spatially temporal patterns which have not been observed before in typical two-component reaction-diffusion type systems. It is demonstrated that there exist two types of regular structures: single and bound states and three types of polymorphic structures: periodic, quasiperiodic and even chaotic ones. The partition of the parameter plane into regions corresponding to the existence of these different types of structures is carried out. High multistability of regular structures is indicated. The interaction of regular structures is investigated. The correspondence between the structures and trajectories in multidimensional phase space associated with the system is given. Bifurcation mechanisms leading to the loss of stability of regular structures as well as to a transition from one type of polymorphic structure to another are indicated. The mechanisms of formation of regular and polymorphic structures are discussed.     

A novel hard decision decoding scheme based on genetic algorithm and neural network

A novel hard decision decoding scheme based on a hybrid intelligent algorithm combining genetic algorithm and neural network, named as genetic neural-network decoding (GND), is proposed. GND offsets the reliability loss caused by channel transmission error and hard decision quantization by making full use of the genetic algorithm's optimization capacity and neural network's pattern classification function to optimize the hard decision outputs of received matched filter and restore a more likelihood codeword as the input of hard decision decoder. As can be seen from the theoretical analysis and computer simulation, GND scheme is close to the traditional soft decision decoding in error correction performance, while its complexity, compared with the traditional soft decision decoding, is greatly reduced because its decoding process does not need to use the channel statistical information.     

Existence and stability of steady fronts in bistable coupled map lattices

We prove the existence and we study the stability of the kinklike fixed points in a simple coupled map lattice (CML) for which the local dynamics has two stable fixed points. The condition for the existence allows us to define a critical value of the coupling parameter where a (multi) generalized saddle-node bifurcation occurs and destroys these solutions. An extension of the results to other CMLs in the same class is also displayed. Finally, we emphasize the property of spatial chaos for small coupling.     

Oscillatory and anti-oscillatory motifs in genetic regulatory networks

Recently,self-sustained oscillatory genetic regulatory networks(GRNs) have attracted significant attention in the biological field.Given a GRN,it is important to anticipate whether the network could generate oscillation with proper parameters,and what the key ingredients for the oscillation are.In this paper the ranges of some function-related parameters which are favorable to sustained oscillations are considered.In particular,some oscillatory motifs appearing with high-frequency in most of the oscillatory GRNs are observed.Moreover,there are some anti-oscillatory motifs which have a strong oscillation repressing effect.Some conclusions analyzing these motif effects and constructing oscillatory GRNs are provided.     

Attaining and maintaining criticality in a neuronal network model

We propose a cellular automaton model for neuronal networks that combines short-term synaptic plasticity with long-term metaplasticity. We investigate how these two mechanisms contribute to attaining and maintaining operation at the critical point. We find that short-term plasticity, represented in the model by synaptic depression and synaptic recovery, is sufficient to allow the system to attain the critical state, if the level of plasticity is properly chosen. However, it is not sufficient to maintain the criticality if the system is perturbed. But the long time scale change in the short-term plasticity, a change in the way synaptic efficacy is modified, allows the system to recover from perturbation. Working together, these two time scales of plasticity could help the system to attain and maintain criticality, leading to a self-organized critical state.     

Stability of a complex dynamical network model

In this paper, firstly, we propose a complex dynamical network model, which is always uniformly asymptotically stable about its equilibrium. Then, we give theoretical analysis of its uniform asymptotical stability by using Lyapunov stability theory. Finally, we show a numerical example to verify our theoretical result.     

Oscillatory dynamics in a simple gene regulatory network mediated by small RNAs

More and more experiments show that small RNAs regulate gene expression by repressing translation of messenger RNAs (mRNAs) or degrading mRNAs. In this paper, we incorporate the small RNAs into a simple gene regulatory network and investigate its dynamical behaviors. In addition, we also derive the theoretical results of globally asymptotic stability and provide the sufficient conditions for the oscillation of the simple gene regulatory network, and further demonstrate that the amplitudes against the change of delay in the gene regulatory network are robust.     

Solder joint inspection based on neural network combined with genetic algorithm

To improve the performance of automatic optical inspection (AOI), a neural network combined with genetic algorithm for the diagnosis of solder joint defects on printed circuit boards (PCBs) assembled in surface mounting technology (SMT) is presented. Six types of solder joint have been classified in respect to the reality in the manufacture. The images of solder joint under test are acquired and 14 features are extracted as input features for the classification. The neural network is easily become over-fitting because these input features are not independent of each other, so the genetic algorithm is introduced to select and remove redundant input features. The experimental results have proved that the neural network combined with genetic algorithm reduced the number of input feature and had a satisfying recognition rate.     

Computational study of propagating fronts in a Lattice-gas model

Velocities and other features of propagating fronts in the lattice-gas model analyzed by Bramsonet al. are computed by Monte Carlo simulation. The propagation velocity() is found to converge slowly to its asymptotic dependence on the exchange-rate parameter. The number density of occupied sites in the interaction zone (extending from the forwardmost occupied to the rearmost unoccupied site) appears to converge to 2/3 for large. Spatial profiles of site occupancy and interface number density for finite are compared to the profiles originally computed by Fisher using the differential equation obeyed in the large- limit. Several significant features inferred from the computations have not yet been explained analytically.     

Monomer-dimer model on a scale-free small-world network

The explicit determination of the number of monomer-dimer arrangements on a network is a theoretical challenge, and exact solutions to monomer-dimer problem are available only for few limiting graphs with a single monomer on the boundary, e.g., rectangular lattice and quartic lattice; however, analytical research (even numerical result) for monomer-dimer problem on scale-free small-world networks is still missing despite the fact that a vast variety of real systems display simultaneously scale-free and small-world structures. In this paper, we address the monomer-dimer problem defined on a scale-free small-world network and obtain the exact formula for the number of all possible monomer-dimer arrangements on the network, based on which we also determine the asymptotic growth constant of the number of monomer-dimer arrangements in the network. We show that the obtained asymptotic growth constant is much less than its counterparts corresponding to two-dimensional lattice and Sierpinski fractal having the same average degree as the studied network, which indicates from another aspect that scale-free networks have a fundamentally distinct architecture as opposed to regular lattices and fractals without power-law behavior.     

Infinite hierarchy of exponents in a two-component random resistor network

We have studied the voltage distribution for a two-component random mixture of conductances _a and _b. A scaling theory is developed for the moments of the distribution, which predicts, for small values ofh=_a/_b, an infinite number of crossover exponents, one for each moment, for Euclidean dimensiond >2, and only one crossover exponent ford=2. Monte Carlo results on the square lattice confirm this prediction.     

Stability and bifurcation of delayed bidirectional gene regulatory networks with negative feedback loops

This paper studies the stability and bifurcation of three cases of bidirectional gene regulatory networks with negative feedback loops and time delays. The uniqueness of the positive equilibrium point of the gene regulatory networks is verified. The delay independent stability conditions of the networks are established by analyzing their corresponding characteristic equations. The existence of the Hopf bifurcation of the networks with or without time delays is presented. Numerical simulations demonstrate the correctness of the obtained theoretical results.     

Propagating fronts,chaos and multistability in a cell replication model

Numerical solutions to a model equation that describes cell population dynamics are presented and analyzed. A distinctive feature of the model equation (a hyperbolic partial differential equation) is the presence of delayed arguments in the time (t) and maturation (x) variables due to the nonzero length of the cell cycle. This transport like equation balances a linear convection with a nonlinear, nonlocal, and delayed reaction term. The linear convection term acts to impress the value of u(t,x=0) on the entire population while the death term acts to drive the population to extinction. The rich phenomenology of solution behaviour presented here arises from the nonlinear, nonlocal birth term. The existence of this kinetic nonlinearity accounts for the existence and propagation of soliton-like or front solutions, while the increasing effect of nonlocality and temporal delays acts to produce a fine periodic structure on the trailing part of the front. This nonlinear, nonlocal, and delayed kinetic term is also shown to be responsible for the existence of a Hopf bifurcation and subsequent period doublings to apparent "chaos" along the characteristics of this hyperbolic partial differential equation. In the time maturation plane, the combined effects of nonlinearity, nonlocality, and delays leads to solution behaviour exhibiting spatial chaos for certain parameter values. Although analytic results are not available for the system we have studied, consistency and validation of the numerical results was achieved by using different numerical methods. A general conclusion of this work, of interest for the understanding of any biological system modeled by a hyperbolic delayed partial differential equation, is that increasing the spatio-temporal delays will often lead to spatial complexity and irregular wave propagation. (c) 1996 American Institute of Physics.