Computation with finite stochastic chemical reaction networks

A highly desired part of the synthetic biology toolbox is an embedded chemical microcontroller, capable of autonomously following a logic program specified by a set of instructions, and interacting with its cellular environment. Strategies for incorporating logic in aqueous chemistry have focused primarily on implementing components, such as logic gates, that are composed into larger circuits, with each logic gate in the circuit corresponding to one or more molecular species. With this paradigm, designing and producing new molecular species is necessary to perform larger computations. An alternative approach begins by noticing that chemical systems on the small scale are fundamentally discrete and stochastic. In particular, the exact molecular counts of each molecular species present, is an intrinsically available form of information. This might appear to be a very weak form of information, perhaps quite difficult for computations to utilize. Indeed, it has been shown that error-free Turing universal computation is impossible in this setting. Nevertheless, we show a design of a chemical computer that achieves fast and reliable Turing-universal computation using molecular counts. Our scheme uses only a small number of different molecular species to do computation of arbitrary complexity. The total probability of error of the computation can be made arbitrarily small (but not zero) by adjusting the initial molecular counts of certain species. While physical implementations would be difficult, these results demonstrate that molecular counts can be a useful form of information for small molecular systems such as those operating within cellular environments.

A stochastic model of catalytic reaction networks in protocells

Protocells are supposed to have played a key role in the self-organizing processes leading to the emergence of life. Existing models either (i) describe protocell architecture and dynamics, given the existence of sets of collectively self-replicating molecules for granted, or (ii) describe the emergence of the aforementioned sets from an ensemble of random molecules in a simple experimental setting (e.g. a closed system or a steady-state flow reactor) that does not properly describe a protocell. In this paper we present a model that goes beyond these limitations by describing the dynamics of sets of replicating molecules within a lipid vesicle. We adopt the simplest possible protocell architecture, by considering a semi-permeable membrane that selects the molecular types that are allowed to enter or exit the protocell and by assuming that the reactions take place in the aqueous phase in the internal compartment. As a first approximation, we ignore the protocell growth and division dynamics. The behavior of catalytic reaction networks is then simulated by means of a stochastic model that accounts for the creation and the extinction of species and reactions. While this is not yet an exhaustive protocell model, it already provides clues regarding some processes that are relevant for understanding the conditions that can enable a population of protocells to undergo evolution and selection.     

Variable structure control of stochastic systems

In this paper, the problem of variable structure control of stochastic (SVSC) systems is proposed and the corresponding variable structure control strategies with complete and incomplete state information are established. The concepts of stochastic sliding mode and sliding motion band are introduced which may be regarded as the basic characteristics of SVSC systems. Robustness of SVSC systems is considered and a general design procedure for SVSC systems is presented. The effectiveness of the proposed control method is shown by simulation results.     

Global stability analysis for stochastic coupled systems on networks

This paper considers the global stability problem for some stochastic coupled systems on networks (SCSNs). We provide a systematic method for constructing a global Lyapunov function for these SCSNs, by using graph theory and the Lyapunov second method. Consequently, a new global stability principle, which has a close relation to the topology property of the network, is given. As an application to the results, we employ the principle to two well-known coupled systems in physical and ecology, and then some easy-verified sufficient conditions which guarantee the global stability are obtained.     

Mean square exponential input-to-state stability of stochastic memristive complex-valued neural networks with time varying delay

In this paper, mean square exponential input-to-state stability (exp-ISS) of stochastic memristive complex-valued neural networks (SMCVNNs) is investigated. By utilising Lyapunov functional and stochastic analysis theory, a sufficient criterion is derived to assure the mean square exp-ISS of the SMCVNNs. The obtained results not only generalise the previous works in the literature about real-valued neural networks as special cases, but also can be easily checked by parameters of system. Numerical simulations are given to show the effectiveness of our theoretical results.     

Exponential stability of hybrid stochastic neural networks with mixed time delays and nonlinearity

This paper is concerned with the problem of robust exponential stability for a class of hybrid stochastic neural networks with mixed time-delays and Markovian jumping parameters. In this paper, free-weighting matrices are employed to express the relationship between the terms in the Leibniz–Newton formula. Based on the relationship, a linear matrix inequality (LMI) approach is developed to establish the desired sufficient conditions for the mixed time-delays neural networks with Markovian jumping parameters. Finally, two simulation examples are provided to demonstrate the effectiveness of the results developed.     

Cluster formation in a time-varying multi-agent system

We introduce time-varying parameters in a multi-agent clustering model and we derive necessary and sufficient conditions for the occurrence of clustering behavior with respect to a given cluster structure. For periodically varying parameters the clustering conditions may be formulated in a similar way as for the time-invariant model. The results require the individual weights assigned to the agents to be constant. For time-varying weights we illustrate with an example that the obtained results can no longer be applied.     

Neural networks in stochastic mechanics

Summary  A state of art on the application of neural networks in Stochastic Mechanics is presented. The use of these Artificial Intelligence numerical devices is almost exclusively carried out in combination with Monte Carlo simulation for calculating the probability distributions of response variables, specific failure probabilities or statistical quantities. To that purpose the neural networks are trained with a few samples obtained by conventional Monte Carlo techniques and used henceforth to obtain the responses for the rest of samples. The advantage of this approach over standard Monte Carlo techniques lies in the fast computation of the output samples which is characteristic of neural networks in comparison to the lengthy calculation required by finite element solvers. The paper considers this combined method as applied to three categories of stochastic mechanics problems, namely those modelled with random variables, random fields and random processes. While the first class is suitable to the analysis of static problems under the effect of values of loads and resistances independent from time and space, the second is useful for describing the spatial variability of material properties and the third for dynamic loads producing random vibration. The applicability of some classical and special neural network types are discussed from the points of view of the type of input/output mapping, the accuracy and the numerical efficiency.     

Emergence and disappearance of traffic congestion in weight-evolving networks

A weight-evolving traffic network model, which is based on Barrat–Barthelemy–Vespignani (BBV) model, is developed to study the spreading of traffic congestion in complex networks. In this model, edge weights of networks evolve according to the flow quantity, and then traffic flows can detour congested nodes. This paper simulates and analyzes the process of the emergence and spreading of congestion, which is triggered by adjusting of data generating speed and data sending ability of the network. A recover process of the network from congestion to normal state is also studied, since, in this model, nodes could resume from congestion when the traffic on the network is not busy. Results show that, if the time interval of network’s rush hour last longer than a certain threshold, the congested nodes cannot resume automatically.     

Customer churn prediction by hybrid neural networks

As churn management is a major task for companies to retain valuable customers, the ability to predict customer churn is necessary. In literature, neural networks have shown their applicability to churn prediction. On the other hand, hybrid data mining techniques by combining two or more techniques have been proved to provide better performances than many single techniques over a number of different domain problems. This paper considers two hybrid models by combining two different neural network techniques for churn prediction, which are back-propagation artificial neural networks (ANN) and self-organizing maps (SOM). The hybrid models are ANN combined with ANN (ANN + ANN) and SOM combined with ANN (SOM + ANN). In particular, the first technique of the two hybrid models performs the data reduction task by filtering out unrepresentative training data. Then, the outputs as representative data are used to create the prediction model based on the second technique. To evaluate the performance of these models, three different kinds of testing sets are considered. They are the general testing set and two fuzzy testing sets based on the filtered out data by the first technique of the two hybrid models, i.e. ANN and SOM, respectively. The experimental results show that the two hybrid models outperform the single neural network baseline model in terms of prediction accuracy and Types I and II errors over the three kinds of testing sets. In addition, the ANN + ANN hybrid model significantly performs better than the SOM + ANN hybrid model and the ANN baseline model.     

Approximating the distribution functions in stochastic networks

In this paper an analytical procedure to approximate the distribution functions in stochastic networks is presented. The procedure is efficient in the sense of its accuracy and its computational requirements. Contrary to the existing approximating procedures, it can be applied to large networks. Examples and computational experiences involving large networks are provided.     

Finding the shortest path in stochastic networks

Common network parameters, such as number of nodes and arc lengths are frequently subjected to ambiguity as a result of probability law. A number of authors have discussed the calculation of the shortest path in networks with random variable arc lengths. Generally, only a subset of intermediate nodes chosen in accordance with a given probability law can be used to transition from source node to sink node. The determination of a priori path of the minimal length in an incomplete network is defined as a probabilistic shortest path problem. When arc lengths between nodes are randomly assigned variables in an incomplete network the resulting network is known as an incomplete stochastic network. In this paper, the computation of minimal length in incomplete stochastic networks, when travel times between nodes are allowed to be exponentially distributed random variables, is formulated as a linear programming problem. A practical application of the methodology is demonstrated and the results and process compared to the Kulkarni’s [V.G. Kulkarni, Shortest paths in networks with exponentially distributed arc lengths, Networks 16 (1986) 255–274] method.     

Segmentation of the on-line shopping market using neural networks

The characterization and analysis of on-line customers' needs and expectations, regarding the Internet as a new marketing channel, is considered a prerequisite to the realization of the expected growth of the consumer-oriented electronic commerce market. The aim of the present study is twofold: to carry out an exploratory segmentation of this market that can throw some light upon its structure, and to characterize the on-line shopping adoption process. The Self-Organizing Map (SOM), an unsupervised neural network model devised by Kohonen (Kohonen, T. (1982). Self-organized formation of topologically correct feature maps. Biological Cybernetics, 43(1), 59–69; Kohonen, T., (1995). Self-organizing maps. Berlin: Springer) will be used as part of a tandem approach to segmentation, which involves the factor analysis of the observable variables in the data to be analyzed, prior to clustering. The SOM is shown to be a powerful data visualization tool, able to assist the data analysis, providing supervised methods with useful explanatory capabilities. It is also applied, in a completely unsupervised mode, to discover the clusters or segments that naturally occur in the data. The SOM is proposed as a flexible clustering model able to accommodate both Finer Segmentation and Normative Segmentation approaches. Within the latter, a cluster-partition is proposed and analysed, and high-level customer profiles, of potential interest to on-line marketers, are derived and described in marketing terms.     

Probabilistic self-organizing map and radial basis function networks

We propose in this paper a new learning algorithm probabilistic self-organizing map (PRSOM) using a probabilistic formalism for topological maps. This algorithm approximates the density distribution of the input set with a mixture of normal distributions. The unsupervised learning is based on the dynamic clusters principle and optimizes the likelihood function. A supervised version of this algorithm based on radial basis functions (RBF) is proposed. In order to validate the theoretical approach, we achieve regression tasks on simulated and real data using the PRSOM algorithm. Moreover, our results are compared with normalized Gaussian basis functions (NGBF) algorithm.     

Feature extraction and image segmentation using self-organizing networks

Feature extraction and image segmentation (FEIS) are two primary goals of almost all image-understanding systems. They are also the issues at which we look in this paper. We think of FEIS as a multilevel process of grouping and describing at each level. We emphasize the importance of grouping during this process because we believe that many features and events in real images are only perceived by combining weak evidence of several organized pixels or other low-level features. To realize FEIS based on this formulation, we must deal with such problems as how to discover grouping rules, how to develop grouping systems to integrate grouping rules, how to embed grouping processes into FEIS systems, and how to evaluate the quality of extracted features at various levels. We use self-organizing networks to develop grouping systems that take the organization of human visual perception into consideration. We demonstrate our approach by solving two concrete problems: extracting linear features in digital images and partitioning color images into regions. We present the results of experiments on real images.     

Learning of stable states in stochastic asymmetric networks

Boltzmann-based models with asymmetric connections are investigated. Although they are initially unstable, these networks spontaneously self-stabilize as a result of learning. Moreover, pairs of weights symmetrize during learning; however, the symmetry is not enough to account for the observed stability. To characterize the system it is useful to consider how its entropy is affected by learning and the entropy of the information stream. The stability of an asymmetric network is confirmed with an electronic model.     

Design of a grey-prediction self-organizing fuzzy controller for active suspension systems

Self-organizing fuzzy controllers (SOFCs) have excellent learning capabilities. They have been proposed for the manipulation of active suspension systems. However, it is difficult to select the parameters of an SOFC appropriately, and an SOFC may extensively modify its fuzzy rules during the control process when the parameters selected for it are inappropriate. To eliminate this problem, this study developed a grey-prediction self-organizing fuzzy controller (GPSOFC) for active suspension systems. The GPSOFC introduces a grey-prediction algorithm into an SOFC, in order to pre-correct its fuzzy rules for the control of active suspension systems. This design solves the problem of SOFCs with inappropriately chosen parameters. To evaluate the feasibility of the proposed method, this study applied the GPSOFC to the manipulation of an active hydraulic-servo suspension system, in order to determine its control performance. Experimental results demonstrated that the GPSOFC achieved better control performance than either the SOFC or the passive method of active suspension control.     

Training neural networks by stochastic optimisation

We present a stochastic learning algorithm for neural networks. The algorithm does not make any assumptions about transfer functions of individual neurons and does not depend on a functional form of a performance measure. The algorithm uses a random step of varying size to adapt weights. The average size of the step decreases during learning. The large steps enable the algorithm to jump over local maxima/minima, while the small ones ensure convergence in a local area. We investigate convergence properties of the proposed algorithm as well as test the algorithm on four supervised and unsupervised learning problems. We have found a superiority of this algorithm compared to several known algorithms when testing them on generated as well as real data.