Self-sustained oscillations of complex genomic regulatory networks

Recently, self-sustained oscillations in complex networks consisting of non-oscillatory nodes have attracted great interest in diverse natural and social fields. Oscillatory genomic regulatory networks are one of the most typical examples of this kind. Given an oscillatory genomic network, it is important to reveal the central structure generating the oscillation. However, if the network consists of large numbers of genes and interactions, the oscillation generator is deeply hidden in the complicated interactions. We apply the dominant phase-advanced driving path method proposed in Qian et al. (2010) [1] to reduce complex genomic regulatory networks to one-dimensional and unidirectionally linked network graphs where negative regulatory loops are explored to play as the central generators of the oscillations, and oscillation propagation pathways in the complex networks are clearly shown by tree branches radiating from the loops. Based on the above understanding we can control oscillations of genomic networks with high efficiency.     

Excitation of the chaotic oscillations in millimeter BWO

In the paper the characteristic properties of the chaotic oscillation excitation in millimeter Backward-Wave Oscillators are investigated. To enhance the interaction efficiency and provide the strong nonlinear working regimes of the oscillator the weak-resonant oscillatory system with large electrical length is proposed to use. It is shown, that in this case the oscillation automodulation with complicated power spectrum are developed for the smaller values of the working current to starting current ratio in comparison with BWO having matched oscillatory system. This allows to oscillate with high efficiency the continuous millimeter chaotic (noise) signals which have a wide enough power spectrum and integral power of about several watts.     

Dominant phase-advanced driving analysis of self-sustained oscillations in biological networks

Oscillatory behaviors can be ubiquitously observed in various systems. Biological rhythms are significant in governing living activities of all units. The emergence of biological rhythms is the consequence of large numbers of units. In this paper we discuss several important examples of sustained oscillations in biological media, where the unit composed in the system does not possess the oscillation behavior. The dominant phase-advanced driving method is applied to study the skeletons and oscillatory organizing motifs in excitable networks and gene regulatory networks.     

Nonlinear dynamics of the membrane potential of a bursting pacemaker cell

This article presents the results of an exploration of one two-parameter space of the Chay model of a cell excitable membrane. There are two main regions: a peripheral one, where the system dynamics will relax to an equilibrium point, and a central one where the expected dynamics is oscillatory. In the second region, we observe a variety of self-sustained oscillations including periodic oscillation, as well as bursting dynamics of different types. These oscillatory dynamics can be observed as periodic oscillations with different periodicities, and in some cases, as chaotic dynamics. These results, when displayed in bifurcation diagrams, result in complex bifurcation structures, which have been suggested as relevant to understand biological cell signaling.     

Nonlinear Neutral Delay Differential Equations of Fourth-Order: Oscillation of Solutions

The objective of this paper is to study oscillation of fourth-order neutral differential equation. By using Riccati substitution and comparison technique, new oscillation conditions are obtained which insure that all solutions of the studied equation are oscillatory. Our results complement some known results for neutral differential equations. An illustrative example is included.     

Nonlinear fluctuation,frequency and stability analyses in free vibration of circular sector oscillation systems

In the present paper, the modified homotopy perturbation method (MHPM) is employed to investigate about both nonlinear swinging oscillation and the stability of circular sector oscillation systems. The sensitivity study performed for frequency analysis of the mentioned oscillatory circular sector body shows that frequency of nonlinear oscillation depends on some specific parameters and can be optimized. Furthermore onset of the instability is dependent to angle α and initial amplitude.Comparisons made among the results of the present closed-form analytical solution and the traditional numerical iterative time integration solution confirms the accuracy and efficiency of the presented analytical solution.In contrast to the available numerical methods, the present analytical method is free from the numerical damping and the time integration accumulated errors. Moreover, in comparison with the traditional multistep numerical iterative time integration methods, a much less computational time is required for the present analytical method. Responses of the dynamical systems to some extent are affected by the natural frequencies. Results reveal that for nonlinear systems, the natural frequency is remarkably affected by the initial conditions.     

Application of a modified rational harmonic balance method for a class of strongly nonlinear oscillators

An analytical approximate technique for conservative nonlinear oscillators is proposed. This method is a modification of the rational harmonic balance method in which analytical approximate solutions have rational form. This approach gives us the frequency of the motion as a function of the amplitude of oscillation. We find that this method works very well for the whole range of parameters, and excellent agreement of the approximate frequencies with the exact one has been demonstrated and discussed. The most significant features of this method are its simplicity and its excellent accuracy for the whole range of oscillation amplitude values and the results reveal that this technique is very effective and convenient for solving conservative truly nonlinear oscillatory systems with complex nonlinearities.     

Synchronization between different motifs

In this paper,we study the synchronization between different motifs.First,the synchronization between two networks with different topology structures and different dynamical behaviours is studied.With the open-plus-closed-loop(OPCL) method,conditions for two different networks to realize synchronization are given.Then based on the theoretical results achieved,the synchronization between different motifs is studied,which verifies the effectiveness and feasibility of the synchronization scheme.     

Reflections Influence on the Gyrotron Oscillation Regimes

Influence of some types of reflections on oscillatory processes in gyrotrons has been studied. Estimations of the conditions for oscillation stability in the presence of a reflected signal are given. The processes in a gyrotron with a fixed structure of the RF field have been modeled numerically, and enhancement of the spectrum signal in the presence of reflections has been studied.     

Prediction of Time Series Gene Expression and Structural Analysis of Gene Regulatory Networks Using Recurrent Neural Networks

Methods for time series prediction and classification of gene regulatory networks (GRNs) from gene expression data have been treated separately so far. The recent emergence of attention-based recurrent neural network (RNN) models boosted the interpretability of RNN parameters, making them appealing for the understanding of gene interactions. In this work, we generated synthetic time series gene expression data from a range of archetypal GRNs and we relied on a dual attention RNN to predict the gene temporal dynamics. We show that the prediction is extremely accurate for GRNs with different architectures. Next, we focused on the attention mechanism of the RNN and, using tools from graph theory, we found that its graph properties allow one to hierarchically distinguish different architectures of the GRN. We show that the GRN responded differently to the addition of noise in the prediction by the RNN and we related the noise response to the analysis of the attention mechanism. In conclusion, this work provides a way to understand and exploit the attention mechanism of RNNs and it paves the way to RNN-based methods for time series prediction and inference of GRNs from gene expression data.     

Novel magneto-oscillatory behavior of confined electrons at a twin boundary in ZnSe and at an interface in GaAs/AlGaAs heterostructures

Electronic properties of confined electrons at naturally formed twin boundaries in ZeSe have been investigated by microwave absorption measurements. Cyclotron resonance signal of the confined electrons was observed. On the cyclotron resonance peak, novel oscillation of the absorption intensity was observed. Similar oscillatory behavior was also observed in GaAs/AlGaAs heterostructures near cyclotron resonance filed at which new Shubnikov–de Haas-like oscillation was observed by Zudov. The oscillatory structure has a period not in inverse magnetic field but magnetic field. The origin of the oscillation observed is caused by Rayleigh interference of two-dimensional electron gas.     

液封液桥内振荡热毛细对流的三维数值模拟

为了了解微重力下液封液桥内热毛细对流的基本特性,利用有限差分法进行了非稳态三维数值模拟,液桥高为(1-3)mm,直径为2mm和3 mm,液封外直径为(4-7)mm。模拟结果表明,当Marangoni数较小时,液封液桥内的热毛细对流为稳定的轴对称运动,当Marangoni数超过某一临界值后,流动将转化为三维振荡流动;为此,确定了发生振荡的临界Marangoni数,分析了各种条件下热毛细对流的振荡特性,计算了相应的振荡频率。     

Shock oscillation in highly underexpanded jets

The oscillatory motions of shocks in highly underexpanded jets with nozzle pressure ratios of 5.60, 7.47, 9.34, and11.21 are quantitatively studied by using large eddy simulation. Two types of shock oscillations are observed: one is the Mach disk oscillation in the streamwise direction and the other is the shock oscillation in the radial direction. It is found that the Mach disk moves quickly in the middle of the oscillatory region but slowly at the top or bottom boundaries. The oscillation cycles of Mach disk are the same for different cases, and are all dominated by an axisymmetric mode of 5.298 k Hz. For the oscillation in the radial direction, the shocks oscillate more toward the jet centerline but less in the jet shear layer, and the oscillation magnitude is an increasing function of screech amplitude. The cycles of the radial shock oscillation switch randomly between the two screech frequencies for the first two cases. However, the oscillation periodicity is more complex for the jets with high nozzle pressure ratios of 9.34 and 11.21 than for the jets with the low nozzle pressure ratios of 5.6 and 7.47. In addition, the shock oscillation characteristics are also captured by coarse mesh and Smagorinsky model,but the coarse mesh tends to predict a slower and weaker shock oscillation.     

Cooperative Effects of Noise and Coupling on Stochastic Dynamics of a Membrane-Bulk Coupling Model

Based on a membrane-bulk coupling cell model proposed by Gomez-Marin et al. [ Phys. Rev. Lett. 98 （2007） 168303], the cooperative effects of noise and coupling on the stochastic dynamical behavior are investigated. For parameters in a certain region, the oscillation can be induced by the cooperative effect of noise and coupling. Whether considering the coupling or not, corresponding coherence resonance phenomena are observed. Furthermore, the effects of two coupling parameters, cell size L and coupling intensity k, on the noise-induced oscillation of membranes are studied. Contrary effects of noise are found in and out of the deterministic oscillatory regions.     

Periodic oscillatory solution of bidirectional associative memory networks with delays

Periodic oscillatory phenomena of bidirectional associative memory (BAM) networks with axonal signal transmission delays are investigated by constructing suitable Lyapunov functionals and some analysis techniques. Some simple sufficient conditions are derived ensuring the existence and uniqueness of periodic oscillatory solutions of the BAM with delays, and all other solutions of the BAM converge exponentially to a periodic oscillatory solution. These conditions are presented in terms of system parameters, and have an important leading significance in the design and applications of periodic oscillatory neural circuits for the BAM with delays.     

Onset of oscillatory binary fluid convection in finite containers

The onset of oscillatory convection in binary fluid mixtures in a two-dimensional domain with realistic boundary conditions on all boundaries is determined as a function of the fluid parameters and the aspect ratio Gamma of the container. The first unstable mode has either odd or even parity under left-right reflection. Depending on Gamma and the separation ratio S, this mode has the form of a standing wave, or a "chevron," consisting of a pair of waves propagating outwards from the cell center (or, in some cases, inwards towards it). Codimension--two points at which odd and even parity modes are simultaneously marginally stable are determined, as are various Takens-Bogdanov points. For fixed Sinfinity, and to the gap (in Rayleigh number and oscillation frequency) between successively unstable modes. The results quantify the parameter regime in which the weakly nonlinear dynamics of the system can be described in terms of the interaction of the first odd and even parity oscillatory modes.     

Probabilistic analysis of the frequencies of amino acid pairs within characterized protein sequences

Here, we describe a unique probabilistic evaluation of the 20, naturally occurring, amino acids and their distributions within the Swiss-Prot and Complete Human Genebank databases. We have developed a computational technique that imparts both directionality and length constraints into searches for unique combinations of amino acids within protein sequences. Using statistical approaches, we have carried out searches of all possible two- and three-residue motifs contained within these databases. This technique is based on the unusually high occurrence of a small number of these motifs when compared to the expected probability of finding a specific residue grouping within a given database. Subsequent filtering of this search to identify such unique combinations has provided several examples that can be used as markers to identify particular proteins within or across databases. We focus on three of these motifs, which were found to be of greatest interest to us. The CC, CM and a combination of the two, CCM motifs all occur either more or less frequently than would be predicted based on standard amino acid distributions within the entire human proteome.     

Oscillatory disturbance in force calibration of optical tweezers

In the calibration of the optical trap stiffness, it is found that there appears an attenuating oscillation as an oscillatory disturbance added to the trapped bead movement, when the scanner is driven by a triangular wave input.An equivalent oscillator model is put forward to explain the mechanism of the oscillatory disturbance. Both the measurements and calculations show that the attenuating oscillation comes from the oscillation of the scanner and the triangular wave drive causes this additional oscillation of the scanner. Furthermore, the analysis indicates that the oscillatory disturbance will become stronger, when the stiffness of the trap increases or the natural frequency of the scanner decreases. We adopt another driving way, i.e. a sinusoidal wave input is used instead of the triangular wave input. Our experiment has verified that in this case the oscillatory disturbance is eliminated completely.     

Oscillatory and Asymptotic Behavior of a Second-Order Nonlinear Functional Differential Equations

This paper is concerned with oscillatory and asymptotic behavior of solutions of a class of second order nonlinear functional differential equations. By using the generalized Riccati transformation and the integral averaging technique, new oscillation criteria and asymptotic behavior are obtained for all solutions of the equation. Our results generalize and improve some known theorems.     

Study of oscillatory behavior of recording process arising from electron–hole competition in strongly oxidized LiNbO3:Ce:Cu

We have investigated ultraviolet (UV) photorefractive effect of lithium niobate doubly doped with Ce and Cu. It is found the diffraction efficiency shows oscillating behavior under UV-light-recording. A model in which electrons and holes can be excited from impurity centers in the UV region is proposed to study the oscillatory behavior of the diffraction efficiency. On the basis of the material equations and the coupled-wave equations, we found that the oscillatory behavior is due to the oscillation of the relative spatial phase shift Φ. And the electron–hole competition may cause the oscillation of the relative spatial phase shift. A switch point from electron grating to hole grating is chosen to realize nonvolatile readout by a red light with high sensitivity (0.4 cm/J).