Quasi-robust control of biochemical reaction networks via stochastic morphing

One of the main objectives of synthetic biology is the development of molecular controllers that can manipulate the dynamics of a given biochemical network that is at most partially known. When integrated into smaller compartments, such as living or synthetic cells, controllers have to be calibrated to factor in the intrinsic noise. In this context, biochemical controllers put forward in the literature have focused on manipulating the mean (first moment) and reducing the variance (second moment) of the target molecular species. However, many critical biochemical processes are realized via higher-order moments, particularly the number and configuration of the probability distribution modes (maxima). To bridge the gap, we put forward the stochastic morpher controller that can, under suitable timescale separations, morph the probability distribution of the target molecular species into a predefined form. The morphing can be performed at a lower-resolution, allowing one to achieve desired multi-modality/multi-stability, and at a higher-resolution, allowing one to achieve arbitrary probability distributions. Properties of the controller, such as robustness and convergence, are rigorously established, and demonstrated on various examples. Also proposed is a blueprint for an experimental implementation of stochastic morpher.     

On tandem stochastic networks with time-deteriorating product quality

We consider an n-site tandem stochastic production network where each product moves sequentially through the sites, and the product's quality deteriorates with its sojourn time in the system. At each site the product goes through two stages: the first stage is a processing operation with a generally-distributed random duration. This operation either does or does not conclude successfully; in the latter case, the operation is repeated immediately. Once the processing operation concludes successfully, the product goes through an inspection stage lasting a generally-distributed random duration. At the end of the inspection the product's state is determined as follows: either (i) it requires additional processing and moves forward to the next site; or (ii) it is found ‘good’ and exits the network with quality value depending on its total sojourn time in the system; or (iii) it is declared ‘failed’, discarded, and exits the network with zero quality value. Two scenarios are analysed: (i) a new product enters the system only after the preceding product has exited and (ii) the network is a tandem Jackson-type system. For each scenario, we construct both time-dependent and quality-dependent performance measures. In the case where the sites can be arranged in an arbitrary order, we derive easy to implement optimal index-type policies of ordering the sites so as to maximise the quality rate of the production network.     

Transient analysis of stochastic switches and trajectories with applications to gene regulatory networks

Many gene regulatory networks are modelled at the mesoscopic scale, where chemical populations change according to a discrete state (jump) Markov process. The chemical master equation (CME) for such a process is typically infinite dimensional and unlikely to be computationally tractable without reduction. The recently proposed finite state projection (FSP) technique allows for a bulk reduction of the CME while explicitly keeping track of its own approximation error. In previous work, this error has been reduced in order to obtain more accurate CME solutions for many biological examples. Here, it is shown that this dasiaerrordasia has far more significance than simply the distance between the approximate and exact solutions of the CME. In particular, the original FSP error term serves as an exact measure of the rate of first transition from one system region to another. As such, this term enables one to (i) directly determine the statistical distributions for stochastic switch rates, escape times, trajectory periods and trajectory bifurcations, and (ii) evaluate how likely it is that a system will express certain behaviours during certain intervals of time. This article also presents two systems-theory based FSP model reduction approaches that are particularly useful in such studies. The benefits of these approaches are illustrated in the analysis of the stochastic switching behaviour of Gardnerdasias genetic toggle switch.     

A new approach to dynamic fuzzy modeling of genetic regulatory networks

In this paper, the dynamic fuzzy modeling approach is applied for modeling genetic regulatory networks from gene expression data. The parameters of the dynamic fuzzy model and the optimal number of fuzzy rules for the fuzzy gene network can be obtained via the proposed modeling approach from the measured gene expression data. One of the main features of the proposed approach is that the prior qualitative knowledge on the network structure can be easily incorporated in the proposed identification algorithm, so that the faster learning convergence of the algorithm can be achieved. Two sets of data, one the synthetic data, and the other the experimental SOS DNA repair network data with structural knowledge, have been used to validate the proposed modeling approach. It is shown that the proposed approach is effective in modeling genetic regulatory networks.     

基于随机学习的异构蜂窝网络离散功率控制机制

针对宏基站和低功率小基站重叠覆盖共享频谱的异构网络中干扰抑制问题,提出了一种基于随机学习理论的基站下行离散功率控制机制,以便在保证宏基站传输的最低传输质量要求下,最大化网络满足传输质量要求的小基站传输个数。该方法将每个小基站作为随机学习自动机,维持一个概率向量用于传输功率选择。算法迭代过程中,小基站独立地基于自身选择的传输功率以及网络反馈的信息,即满足传输质量要求的小基站传输的个数,来更新概率向量,调整传输功率,直到系统达到均衡状态。仿真结果表明,基于随机学习的离散功率控制方法具有很好的收敛性和寻优性能,能有效提高系统可支持的满足传输质量要求的小基站传输数量,适用实际系统。     

Business process modelling with stochastic networks

Modelling and analysis of business processes is critical to identify current business processes and to understand the contributions of new processes to the system. The quality of the results obtained by modelling and analysis significantly influences the success of business process reengineering (BPR). Therefore, a constant development in techniques used in business process modelling (BPM) and business process analysis (BPA) is necessary. However, when these proposed techniques are analysed it becomes obvious that they repeat the same basic approach, although a few offer different visions. In BPM development studies, the use of time-activity scheduling is often considered secondary (even neglected). The reason for this is that process modelling may be considered as project management and remain under this label. Many organizations may use these techniques in managing their daily activities if the maturity level and the simplicity of project management techniques are considered. It also enables the modelling of stochastic situations, otherwise not possible to do by any BPM method. In this study an existing business process with network properties is analysed using project scheduling techniques. Thus, business processes are described as networks, modelled and timed by network properties and stochastically analysed using GERT, a project based process scheduling method. Finally the results obtained by GERT are examined using the PERT-path approach.     

Control, responses and modularity of cellular regulatory networks: a control analysis perspective

Cells adapt to changes in environmental conditions through the concerted action of signalling, gene expression and metabolic subsystems. The authors will discuss a theoretical framework addressing such integrated systems. This 'hierarchical analysis' was first developed as an extension to a metabolic control analysis. It builds on the phenomenon that often the communication between signalling, gene expression and metabolic subsystems is almost exclusively via regulatory interactions and not via mass flow interactions. This allows for the treatment of the said subsystems as 'levels' in a hierarchical view of the organisation of the molecular reaction network of cells. Such a hierarchical approach has as a major advantage that levels can be analysed conceptually in isolation of each other (from a local intra-level perspective) and at a later stage integrated via their interactions (from a global inter-level perspective). Hereby, it allows for a modular approach with variable scope. A number of different approaches have been developed for the analysis of hierarchical systems, for example hierarchical control analysis and modular response analysis. The authors, here, review these methods and illustrate the strength of these types of analyses using a core model of a system with gene expression, metabolic and signal transduction levels.     

Reverse engineering of gene regulatory networks

Systems biology is a multi-disciplinary approach to the study of the interactions of various cellular mechanisms and cellular components. Owing to the development of new technologies that simultaneously measure the expression of genetic information, systems biological studies involving gene interactions are increasingly prominent. In this regard, reconstructing gene regulatory networks (GRNs) forms the basis for the dynamical analysis of gene interactions and related effects on cellular control pathways. Various approaches of inferring GRNs from gene expression profiles and biological information, including machine learning approaches, have been reviewed, with a brief introduction of DNA microarray experiments as typical tools for measuring levels of messenger ribonucleic acid (mRNA) expression. In particular, the inference methods are classified according to the required input information, and the main idea of each method is elucidated by comparing its advantages and disadvantages with respect to the other methods. In addition, recent developments in this field are introduced and discussions on the challenges and opportunities for future research are provided     

On approximate constitutive equations in nonlinear viscoelasticity

Summary In this paper a simplified constitutive equation for nonlinear slightly viscoelastic materials is derived by a method similar to that ofColeman andNoll. This equation is also valid for short times, slow motions, or small deformations superposed on a large steady deformation for all viscoelastic materials. An experimental method for determining the material parameters contained in this constitutive equation for dynamic conditions is also presented.

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Über genäherte Materialgleichungen in der nichtlinearen Viskoelastizität

Zusammenfassung Mittels einer Methode ähnlich der vonColeman undNoll wird eine vereinfachte Materialgleichung für nichtlineare, schwach viskoelastische Stoffe hergeleitet. Diese Gleichung gilt auch für das Kurzzeitverhalten, für langsame Bewegungen, oder für die Überlagerung kleiner Deformationen auf große stationäre Verformungen bei allen viskoelastischen Materialien. Eine experimentelle Methode zur Bestimmung der in der Materialgleichung auftretenden Stoffkonstanten für dynamische Bedingungen wird gleichfalls angegeben.

     

Tools for intelligent control: fuzzy controllers,neural networks and genetic algorithms

The goal of this expository paper is to bring forth the basic current elements of soft computing (fuzzy logic, neural networks, genetic algorithms and genetic programming) and the current applications in intelligent control. Fuzzy sets and fuzzy logic and their applications to control systems have been documented. Other elements of soft computing, such as neural networks and genetic algorithms, are also treated for the novice reader. Each topic will have a number of relevant references of as many key contributors as possible.     

Fast approximate methods for the reliability analysis of computer networks

The complexity of computer communication networks has taken a dramatic upswing, following significant developments in electronic technology such as medium and large scale integrated circuits and microprocessors. Although components of a computer communication network are broadly classified into software, hardware and communications, the most important problem is that of ensuring the reliable flow of information from source to destination. An important parameter in the analysis of these networks is to find the probability of obtaining a situation in which each node in the network communicates with all other remaining communication centres (nodes). This probability, termed as overall reliability, can be determined using the concept of spanning trees. As the exact reliability evaluation becomes unmanageable even for a reasonable sized system, we present an approximate technique using clustering methods. It has been shown that when component reliability ⩾ 0.9, the suggested technique gives results quite close to those obtained by exact methods with an enormous saving in computation time and memory usage. For still quicker reliability analysis while designing the topological configuration of real-time computer systems, an empirical form of the reliability index is proposed which serves as a fairly good indicator of overall reliability and can be easily incorporated in a design procedure, such as local search, to design maximally reliable computer communication network.     

On physical layer-oriented routing with power control in ad hoc wireless networks

Routing in ad hoc wireless networks does not simply consist in finding a route with shortest length (as in wired networks with virtually error-free communication links), but it requires the creation of a stable and good quality communication route to avoid any unnecessary packet loss. In this paper,we discuss physical layer-oriented routing in ad hoc wireless networks, and we analyse the potential advantages of combining the use of power control (PC) with the chosen routing strategy. More precisely, we propose a modified ad hoc on-demand distance vector (MAODV) routing protocol, with and without PC, derived from the AODV-routing protocol by considering the bit error rate at the end of a multi-hop path as the metric to be minimised for route selection. In other words, we consider routing with a physical layer-oriented quality of service criterion, and we analyse the system performance in scenarios with either strong line-of-sight (LOS) or shadowed communications. Although in a scenario with strong LOS communications there are a few cases where the MAODV-PC protocol offers the best performance, in the presence of shadowed communications the proposed physical layer-oriented strategy is not attractive.     

Optimal approximate designs for comparison with control in dose-escalation studies

Consider an experiment, in which a new drug is tested for the first time on human subjects, namely healthy volunteers. Such experiments are often performed as dose-escalation studies: a set of increasing doses is preselected; individuals are grouped into cohorts; and in each cohort, dose number i can be administered only if dose number \(i-1\) has already been tested in the previous cohort. If an adverse effect of a dose is observed, the experiment is stopped, and thus, no subjects are exposed to higher doses. In this paper, we assume that the response is affected both by the dose or placebo effects and by the cohort effects. We provide optimal approximate designs for estimating the effects of the drug doses compared with the placebo with respect to selected optimality criteria (E-, MV- and LV-optimality). In particular, we prove the optimality of the so-called Senn designs with respect to all of the studied optimality criteria, and we provide optimal extensions of these designs for selected criteria.     

Proximity of intracellular regulatory networks to monotone systems

Networks that contain only sign-consistent loops, such as positive feedforward and feedback loops, function as monotone systems. Simulated using differential equations, monotone systems display well-ordered behaviour that excludes the possibility for chaotic dynamics. Perturbations of such systems have unambiguous global effects and a predictability characteristic that confers robustness and adaptability. The authors assess whether the topology of biological regulatory networks is similar to the topology of monotone systems. For this, three intracellular regulatory networks are analysed where links are specified for the directionality and the effects of interactions. These networks were assembled from functional studies in the experimental literature. It is found that the three biological networks contain far more positive 'sign-consistent' feedback and feedforward loops than negative loops. Negative loops can be 'eliminated' from the real networks by the removal of fewer links as compared with the corresponding shuffled networks. The abundance of positive feedforward and feedback loops in real networks emerges from the presence of hubs that are enriched with either negative or positive links. These observations suggest that intracellular regulatory networks are 'close-to-monotone', a characteristic that could contribute to the dynamical stability observed in cellular behaviour.     

Autonomous Boolean modelling of developmental gene regulatory networks

During early embryonic development, a network of regulatory interactions among genes dynamically determines a pattern of differentiated tissues. We show that important timing information associated with the interactions can be faithfully represented in autonomous Boolean models in which binary variables representing expression levels are updated in continuous time, and that such models can provide a direct insight into features that are difficult to extract from ordinary differential equation (ODE) models. As an application, we model the experimentally well-studied network controlling fly body segmentation. The Boolean model successfully generates the patterns formed in normal and genetically perturbed fly embryos, permits the derivation of constraints on the time delay parameters, clarifies the logic associated with different ODE parameter sets and provides a platform for studying connectivity and robustness in parameter space. By elucidating the role of regulatory time delays in pattern formation, the results suggest new types of experimental measurements in early embryonic development.     

Comments on the pore radius distribution in near-planar stochastic fibre networks

The pore radius distribution in near-planar stochastic fibre networks is known to be influenced by changes in the mean number of fibres per unit area and their distribution in the plane. Experimental data is presented that confirms the established result that the standard deviation of pore radii is proportional to the mean. The data shows also that this proportionality is the same for changes in the number of fibres per unit area and for changes in the uniformity of their in-plane distribution. Data from the literature suggests that processes that increase the mean pore radius, increase also the coefficient of variation of pore radii. Theoretical considerations and experimental data are presented that show that the coefficient of variation of pore radii is in fact constant for near-random and non-random stochastic fibre networks.