Identifying time-delayed gene regulatory networks via an evolvable hierarchical recurrent neural network

BACKGROUND

The modeling of genetic interactions within a cell is crucial for a basic understanding of physiology and for applied areas such as drug design. Interactions in gene regulatory networks (GRNs) include effects of transcription factors, repressors, small metabolites, and microRNA species. In addition, the effects of regulatory interactions are not always simultaneous, but can occur after a finite time delay, or as a combined outcome of simultaneous and time delayed interactions. Powerful biotechnologies have been rapidly and successfully measuring levels of genetic expression to illuminate different states of biological systems. This has led to an ensuing challenge to improve the identification of specific regulatory mechanisms through regulatory network reconstructions. Solutions to this challenge will ultimately help to spur forward efforts based on the usage of regulatory network reconstructions in systems biology applications.

METHODS

We have developed a hierarchical recurrent neural network (HRNN) that identifies time-delayed gene interactions using time-course data. A customized genetic algorithm (GA) was used to optimize hierarchical connectivity of regulatory genes and a target gene. The proposed design provides a non-fully connected network with the flexibility of using recurrent connections inside the network. These features and the non-linearity of the HRNN facilitate the process of identifying temporal patterns of a GRN.

RESULTS

Our HRNN method was implemented with the Python language. It was first evaluated on simulated data representing linear and nonlinear time-delayed gene-gene interaction models across a range of network sizes and variances of noise. We then further demonstrated the capability of our method in reconstructing GRNs of the Saccharomyces cerevisiae synthetic network for in vivo benchmarking of reverse-engineering and modeling approaches (IRMA). We compared the performance of our method to TD-ARACNE, HCC-CLINDE, TSNI and ebdbNet across different network sizes and levels of stochastic noise. We found our HRNN method to be superior in terms of accuracy for nonlinear data sets with higher amounts of noise.

CONCLUSIONS

The proposed method identifies time-delayed gene-gene interactions of GRNs. The topology-based advancement of our HRNN worked as expected by more effectively modeling nonlinear data sets. As a non-fully connected network, an added benefit to HRNN was how it helped to find the few genes which regulated the target gene over different time delays.

A series of population models for Hyphantria cunea with delay and seasonality

In this paper, we establish and study a basic stage-structured model for the population of Hyphantria cunea, a delay differential equation model and a model incorporating the resource and seasonality. By introducing the population reproduction number R₀, we show that R₀ acts as a threshold parameter for the existence and stability of equilibria. The trivial equilibria of the above models are all globally asymptotically stable when R₀<1; the basic model and the delay-differential model have a unique positive equilibrium respectively, and they are both locally asymptotically stable when R₀>1; the model with periodic season is uniformly persistent and admits a positive periodic solution if R₀>1. Numerical simulations are carried out to illustrate the theoretical results. In addition, we consider the effect of temperature and season on the population of Hyphantria cunea.

Adaptive fuzzy wavelet network control of second order multi-agent systems with unknown nonlinear dynamics

In this paper, consensus problem is considered for second order multi-agent systems with unknown nonlinear dynamics under undirected graphs. A novel distributed control strategy is suggested for leaderless systems based on adaptive fuzzy wavelet networks. Adaptive fuzzy wavelet networks are employed to compensate for the effect of unknown nonlinear dynamics. Moreover, the proposed method is developed for leader following systems and leader following systems with state time delays. Lyapunov functions are applied to prove uniformly ultimately bounded stability of closed loop systems and to obtain adaptive laws. Three simulation examples are presented to illustrate the effectiveness of the proposed control algorithms.

Imitation dynamics with time delay

Based on the classic imitation dynamics (Hofbauer and Sigmund, 1998, Evolutionary Games and Population Dynamics, Cambridge University Press), the imitation dynamics with time delay is investigated, where the probability that an individual will imitate its opponent's own strategy is assumed to depend on the comparison between the past expected payoff of this individual's own strategy and the past expected payoff of its opponent's own strategy, i.e. there is a time delay effect. For the two-phenotype model, we show that if the system has an interior equilibrium and this interior equilibrium is stable when there is no time delay, then there must be a critical value of time delay such that the system tends to a stable periodic solution when the time delay is larger than the critical value. On the other hand, for three-phenotype (rock-scissors-paper) model, the numerical analysis shows that for the stable periodic solution induced by the time delay, the amplitude and the period will increase with the increase of the time delay. These results should help to understand the evolution of behavior based on the imitation dynamics with time delay.

Predictor-based control for an inverted pendulum subject to networked time delay

The inverted pendulum is considered as a special class of underactuated mechanical systems with two degrees of freedom and a single control input. This mechanical configuration allows to transform the underactuated system into a nonlinear system that is referred to as the normal form, whose control design techniques for stabilization are well known. In the presence of time delays, these control techniques may result in inadequate behavior and may even cause finite escape time in the controlled system. In this paper, a constructive method is presented to design a controller for an inverted pendulum characterized by a time-delayed balance control. First, the partial feedback linearization control for the inverted pendulum is modified and coupled with a state predictor to compensate for the delay. Several coordinate transformations are processed to transform the estimated partial linearized system into an upper-triangular form. Second, nested saturation and backstepping techniques are combined to derive the control law of the transformed system that would complete the design of the whole control input. The effectiveness of the proposed technique is illustrated by numerical simulations.

Improved PI-PD control design using predictive functional optimization for temperature model of a fluidized catalytic cracking unit

Proportional-integral-derivative (PID) control is widely used in industry because of its simple structure and convenient implementation. However, PID control is suitable for small time delay systems; while if too large delay is encountered, PID control may not obtain the desired performance. Proportional-integral-proportional-derivative (PI-PD) control is a modified of PID control and can get improved control performance; however, due to the complex controller parameter tuning, the PI-PD control is used in a limited scope. Inspired by the advantage of predictive functional control (PFC), a new PI-PD control design using PFC optimization is proposed in this paper. The proposed method not only inherits the advantage of PFC, which does well in coping with the time delay, but also has the same structure as the PI-PD controller. The proposed method is tested on the preheated temperature control of crude oil in a fluidized catalytic cracking unit. The results show that the proposed controller improves control performance compared with typical PID control and PI-PD control.

Dissipativity and stability analysis of fractional-order complex-valued neural networks with time delay

As we know, the notion of dissipativity is an important dynamical property of neural networks. Thus, the analysis of dissipativity of neural networks with time delay is becoming more and more important in the research field. In this paper, the authors establish a class of fractional-order complex-valued neural networks (FCVNNs) with time delay, and intensively study the problem of dissipativity, as well as global asymptotic stability of the considered FCVNNs with time delay. Based on the fractional Halanay inequality and suitable Lyapunov functions, some new sufficient conditions are obtained that guarantee the dissipativity of FCVNNs with time delay. Moreover, some sufficient conditions are derived in order to ensure the global asymptotic stability of the addressed FCVNNs with time delay. Finally, two numerical simulations are posed to ensure that the attention of our main results are valuable.

Discrete sliding mode controller with reaching phase elimination for TITO systems

Sliding mode control (SMC) is emerged as a powerful robust controller for the process control application. However, it does not posses robustness properties during reaching phase and suffers from chattering, which is undesirable. In this paper, a chatter free discrete sliding mode controller (DSMC) with reaching phase elimination is proposed. The issue of existence of reaching phase due to physical constraints such as saturation of actuating devices is also addressed. The two-input-two-output (TITO) system is decoupled into two single-input-single-output (SISO) systems using ideal decoupler. The DSMCs are separately designed for two decoupled SISO systems. The stability is ensured via Lyapunov approach. Simulation study and experimentation on real life interacting two tank liquid level system are included to demonstrate effectiveness and applicability of the proposed controller.

Leader-following consensus of the second-order multi-agent systems under directed topology

This paper investigates the consensus problem for second-order multi-agent systems with a dynamical leader. A simple and novel protocol based on the relative state of the neighboring agents is proposed. Using the linear matrix inequality method, sufficient conditions are derived to ensure the consensus for both the cases without and with communication delay in the multi-agent systems. Some numerical simulations are also given to show the effectiveness of the proposed results.

Mean-square exponential input-to-state stability of delayed Cohen-Grossberg neural networks with Markovian switching based on vector Lyapunov functions

This paper studies the mean-square exponential input-to-state stability of delayed Cohen-Grossberg neural networks with Markovian switching. By using the vector Lyapunov function and property of M-matrix, two generalized Halanay inequalities are established. By means of the generalized Halanay inequalities, sufficient conditions are also obtained, which can ensure the exponential input-to-state stability of delayed Cohen-Grossberg neural networks with Markovian switching. Two numerical examples are given to illustrate the efficiency of the derived results.

Epidemic spreading on adaptively weighted scale-free networks

We introduce three modified SIS models on scale-free networks that take into account variable population size, nonlinear infectivity, adaptive weights, behavior inertia and time delay, so as to better characterize the actual spread of epidemics. We develop new mathematical methods and techniques to study the dynamics of the models, including the basic reproduction number, and the global asymptotic stability of the disease-free and endemic equilibria. We show the disease-free equilibrium cannot undergo a Hopf bifurcation. We further analyze the effects of local information of diseases and various immunization schemes on epidemic dynamics. We also perform some stochastic network simulations which yield quantitative agreement with the deterministic mean-field approach.

Sensor-less force-reflecting macro-micro telemanipulation systems by piezoelectric actuators

This paper establishes a novel control strategy for a nonlinear bilateral macro-micro teleoperation system with time delay. Besides position and velocity signals, force signals are additionally utilized in the control scheme. This modification significantly improves the poor transparency during contact with the environment. To eliminate external force measurement, a force estimation algorithm is proposed for the master and slave robots. The closed loop stability of the nonlinear micro-micro teleoperation system with the proposed control scheme is investigated employing the Lyapunov theory. Consequently, the experimental results verify the efficiency of the new control scheme in free motion and during collision between the slave robot and the environment of slave robot with environment, and the efficiency of the force estimation algorithm.

Mathematical analysis of a nutrient-plankton system with delay

A mathematical model describing the interaction of nutrient–plankton is investigated in this paper. In order to account for the time needed by the phytoplankton to mature after which they can release toxins, a discrete time delay is incorporated into the system. Moreover, it is also taken into account discrete time delays which indicates the partially recycled nutrient decomposed by bacteria after the death of biomass. In the first part of our analysis the sufficient conditions ensuring local and global asymptotic stability of the model are obtained. Next, the existence of the Hopf bifurcation as time delay crosses a threshold value is established and, meanwhile, the phenomenon of stability switches is found under certain conditions. Numerical simulations are presented to illustrate the analytical results.

Tuning of IMC based PID controllers for integrating systems with time delay

Design of Proportional Integral and Derivative (PID) controllers based on IMC principles for various types of integrating systems with time delay is proposed. PID parameters are given in terms of process model parameters and a tuning parameter. The tuning parameter is IMC filter time constant. In the present work, the IMC filter (Q) is chosen in such a manner that the order of the denominator of IMC controller is one less than the order of the numerator. The IMC filter time constant (λ) is tuned in such a way that a good compromise is made between performance and robustness for both servo and regulatory problems. To improve servo response of the controller a set point filter is designed such that the closed loop response is similar to that of first order plus time delay system. The proposed controller design method is applied to various transfer function models and to the non-linear model equations of jacketed CSTR to demonstrate its applicability and effectiveness. The performance of the proposed controller is compared with the recently reported methods in terms of IAE and ITAE. The smooth functioning of the controller is determined in terms of total variation and compared with recently reported methods. Simulation studies are carried out on various integrating systems with time delay to show the effectiveness and superiority of the proposed controllers.

The effects of visual feedback during a rhythmic weight-shifting task in patients with Parkinson's disease

Augmented visual feedback (VF) may offer benefits similar to those of rhythmic external cues in alleviating some mobility-related difficulties in individuals with Parkinson's disease (PD). However, due to an impaired ability to reweigh sensory information under changing circumstances, subjects with PD may be rather vulnerable to incongruity of visual information. In the present study, we investigated whether VF is indeed effective in improving motor functioning in a weight-shifting task during upright stance, and whether subjects with PD are affected more by incongruent VF than healthy controls. Participants performed sideways swaying motions based on tracking of real-time and delayed VF - the first providing congruent, and hence more accurate, visual information than the latter. We analyzed center-of-pressure signals patterns for 28 individuals with PD and 16 healthy, age- and gender-matched controls by estimating task accuracy, movement pattern variability, and normalized movement amplitude. For conditions without feedback and with real-time feedback, subjects with PD performed lateral swaying motions with greater error (F(1, 42)=12.065, p=.001) and with more variable movement patterns than healthy controls (F(1, 24)=113.086, p<.001). Error change scores revealed that patients with PD were nevertheless still able to use VF to improve tracking performance (t(24)=-2.366, p=.026). However, whereas controls were able to adapt to a certain amount of visual incongruity, patients with PD were not. Instead, movement amplitude was significantly reduced in this group (F(1.448, 60.820)=17.639, p<.001). By reducing movement amplitude, subjects with PD appear to resort to a 'conservative' strategy to minimize performance breakdown.

Discrete-time domain two-degree-of-freedom control design for integrating and unstable processes with time delay

A discrete-time domain two-degree-of-freedom (2DOF) design method is proposed for integrating and unstable processes with time delay. Based on a 2DOF control structure recently developed, a controller is analytically designed in terms of the H2 optimal control performance specification for the set-point tracking, and another controller is derived by proposing the desired closed-loop transfer function for load disturbance rejection. Both controllers can be tuned relatively independent to realize control optimization. Analytical expression of the set-point response is given for quantitatively tuning the single adjustable parameter in the set-point tracking controller. At the meantime, sufficient and necessary conditions for holding robust stability of the closed-loop control system are established for tuning another adjustable parameter in the disturbance rejection controller, along with numerical tuning guidelines. Illustrative examples from the literature are used to demonstrate the effectiveness of the proposed method.

The similarity analysis of financial stocks based on information clustering

Similarity in time series is an important feature of dynamical systems such as financial systems, with potential use for clustering of series in system. Here, we mainly introduce a novel method: the reconstructed phase space information clustering method to analyze the financial markets. The method is used to examine the similarity of different sequences by calculating the distances between them, which the main difference from previous method is the way to map the original time series to symbolic sequences. Here we make use of the state space reconstruction to construct the symbolic sequences and quantify the similarity of different stock markets and exchange rate markets considering the chaotic behavior between the complex time series. And we compare the results of similarity of artificial and real data using the modified method, information categorization method and system clustering method. We conclude that the reconstructed phase space information clustering method is effective to research the close relationship in time series and for short time series especially. Besides, we report the results of similarity of different exchange rate time series in different periods and find the effect of the exchange rate regime in 2008 on the time series. Also we acquire some characteristics of exchange rate time series in China market, especially for the top four trading partners of China.

Delay driven spatiotemporal chaos in single species population dynamics models

Questions surrounding the prevalence of complex population dynamics form one of the central themes in ecology. Limit cycles and spatiotemporal chaos are examples that have been widely recognised theoretically, although their importance and applicability to natural populations remains debatable. The ecological processes underlying such dynamics are thought to be numerous, though there seems to be consent as to delayed density dependence being one of the main driving forces. Indeed, time delay is a common feature of many ecological systems and can significantly influence population dynamics. In general, time delays may arise from inter- and intra-specific trophic interactions or population structure, however in the context of single species populations they are linked to more intrinsic biological phenomena such as gestation or resource regeneration. In this paper, we consider theoretically the spatiotemporal dynamics of a single species population using two different mathematical formulations. Firstly, we revisit the diffusive logistic equation in which the per capita growth is a function of some specified delayed argument. We then modify the model by incorporating a spatial convolution which results in a biologically more viable integro-differential model. Using the combination of analytical and numerical techniques, we investigate the effect of time delay on pattern formation. In particular, we show that for sufficiently large values of time delay the system's dynamics are indicative to spatiotemporal chaos. The chaotic dynamics arising in the wake of a travelling population front can be preceded by either a plateau corresponding to dynamical stabilisation of the unstable equilibrium or by periodic oscillations.

Delay-dependent guaranteed-cost control based on combination of Smith predictor and equivalent-input-disturbance approach

This paper presents a new system configuration and a design method to improve control performance for a system with an input time delay and disturbances. The equivalent-input-disturbance approach is extended to handle a time-delay system. It is combined with the Smith predictor to reject disturbances. A delay-dependent stability condition is devised in terms of a matrix inequality by using the free-weighting matrix approach. The gain of the observer is designed by applying the cone complementary linearization method to the matrix inequality. A numerical example demonstrates the validity of the method.

Temperature control in a solar collector field using Filtered Dynamic Matrix Control

This paper presents the output temperature control of a solar collector field of a desalinization plant using the Filtered Dynamic Matrix Control (FDMC). The FDMC is a modified controller based on the Dynamic Matrix Control (DMC), a predictive control strategy widely used in industry. In the FDMC, a filter is used in the prediction error, which allows the modification of the robustness and disturbance rejection characteristics of the original algorithm. The implementation and tuning of the FDMC are simple and maintain the advantages of DMC. Several simulation results using a validated model of the solar plant are presented considering different scenarios. The results are also compared to nonlinear control techniques, showing that FDMC, if properly tuned, can yield similar results to more complex control algorithms.

Independent motion control of a tower crane through wireless sensor and actuator networks

The problem of independent control of the performance variables of a tower crane through a wireless sensor and actuator network is investigated. The complete nonlinear mathematical model of the tower crane is developed. Based on appropriate data driven norms an accurate linear approximant of the system, including an upper bound of the communication delays, is derived. Using this linear approximant, a dynamic measurable output multi delay controller for independent control of the performance outputs of the system is proposed. The controller performs satisfactory despite the nonlinearities of the model and the communication delays of the wireless network.

An optimal PID controller via LQR for standard second order plus time delay systems

An improved tuning methodology of PID controller for standard second order plus time delay systems (SOPTD) is developed using the approach of Linear Quadratic Regulator (LQR) and pole placement technique to obtain the desired performance measures. The pole placement method together with LQR is ingeniously used for SOPTD systems where the time delay part is handled in the controller output equation instead of characteristic equation. The effectiveness of the proposed methodology has been demonstrated via simulation of stable open loop oscillatory, over damped, critical damped and unstable open loop systems. Results show improved closed loop time response over the existing LQR based PI/PID tuning methods with less control effort. The effect of non-dominant pole on the stability and robustness of the controller has also been discussed.

Synchronization transitions induced by the fluctuation of adaptive coupling strength in delayed Newman-Watts neuronal networks

Introducing adaptive coupling in delayed neuronal networks and regulating the dissipative parameter (DP) of adaptive coupling by noise, we study the effect of fluctuations of the changing rate of adaptive coupling on the synchronization of the neuronal networks. It is found that time delay can induce synchronization transitions for intermediate DP values, and the synchronization transitions become strongest when DP is optimal. As the intensity of DP noise is varied, the neurons can also exhibit synchronization transitions, and the phenomenon is delay-dependent and is enhanced for certain time delays. Moreover, the synchronization transitions change with the change of DP and become strongest when DP is optimal. These results show that randomly changing adaptive coupling can considerably change the synchronization of the neuronal networks, and hence could play a crucial role in the information processing and transmission in neural systems.

On avian influenza epidemic models with time delay

After the outbreak of the first avian influenza A virus (H5N1) in Hong Kong in 1997, another avian influenza A virus (H7N9) crossed the species barrier in mainland China in 2013 and 2014 and caused more than 400 human cases with a death rate of nearly 40%. In this paper, we take account of the incubation periods of avian influenza A virus and construct a bird-to-human transmission model with different time delays in the avian and human populations combining the survival probability of the infective avian and human populations at the latent time. By analyzing the dynamical behavior of the model, we obtain a threshold value for the prevalence of avian influenza and investigate local and global asymptotical stability of equilibria of the system.