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.

Emergence of auto-catalytic structure in stochastic self-reinforcing reaction networks

We consider a chemical reaction network model in which some of the reactions are stochastic and depend on past history. In this chemical reaction network, we found the emergence of autocatalytic sets (ACS) and complex dynamics in which ACS are repeatedly created and destroyed. This work was presented in part at the 7th International Symposium on Artificial Life and Robotics, Oita, Japan, January 16–18, 2002     

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.     

氨合成催化反应中毒模型建立和计算

建立了绝热式氨合成塔的二维非均相数学模型,考察了由硫化氢引起的催化剂中毒对整个床层状态的影响。应用正交配置法及龙格-库塔方法对方程进行求解,获得了床层温度、氨浓度随催化剂中毒深度的变化规律。针对中毒物不同浓度,讨论了床层中各组分及温度所受到的影响和变化。     

A surrogate indicator of criticality for stochastic project networks

The study of the delay that can be caused by any activity of a stochastic project network is a key topic because of the increasing importance of risk and time control in project management. The main concept adopted for this purpose has been the notion of critical activity developed for deterministic project networks but, in this paper, the inadequacy of the concept critical activity for stochastic project networks is shown and a new surrogate indicator of criticality (SIC) is built, using a regression model applied to a large set of generated project networks. This new indicator explains more than 90% of the initial variance estimated for more than 80,000 activities belonging to a wide range of project networks (580 nets), with very different morphological types.     

A multivariate threshold stochastic volatility model

We introduce in this paper a multivariate threshold stochastic volatility model for multiple financial return time series. This model allows the dynamic structure of return and volatility to change according to a threshold model while accounting for the interdependence of financial returns. Through the threshold volatility modeling, we can understand the impact of market news on volatility asymmetry. Estimation of unknown parameters are carried out using Markov chain Monte Carlo techniques. Simulations show that our estimators are reliable in moderately large sample sizes. We apply the model to three market indice data and estimate time-varying correlations among the indice returns.     

A stochastic model of port elevator capacity

This paper uses the results from a queueing model to optimize the inventory to be held at the port when exporting a bulk commodity.     

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.     

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.     

A realization approach to stochastic model reduction

The problem of discrete-time stochastic model reduction (approximation) is considered. Using the canonical correlation analysis approach of Akaike (1975), a new order-reduction algorithm is developed. Furthermore, it is shown that the inverse of the reduced-order realization is asymptotically stable. Next, an explicit relationship between canonical variables and the linear least-squares estimate of the state vector is established. Using this, a more direct approach for order reduction is presented, and also a new design for reduced-order Kalman filters is developed. Finally, the uniqueness and symmetry properties for the new realization—the balanced stochastic realization—along with a simulation result, are presented.     

A transformation approach to stochastic model reduction

A new and direct approach to stochastic model reduction is developed. The order reduction algorithm is obtained by establishing an equivalence between canonical correlation analysis and solutions to algebraic Riccati equations. Also the concept of balanced stochastic realization (BSR) plays a fundamental role. Asymptotic stability of the reduced-order realization is established, and spectral domain interpretations for the BSR are given.     

A stochastic system model of an educational institute

This paper is aimed at the development of a stochastic model for an academic institution. It is argued that many of the parameters of such an institute can only be effectively modelled in a probabilistic sense. It is proposed that all such parameters which cause a deterministic model of the institute to be erroneous can be lumped together as a white noise term in the state variable model. It is shown that the covariance of the noise term as well as the parameters of the deterministic part of the model can be recursively estimated on the basis of the known performance of the institute over a period of post several years. Once the model is identified it is shown that a prediction of the future performance of the institute is possible. The various concepts are illustrated in the paper on the basis of data collected from an existing institute.     

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.     

A two-stage stochastic model of limitations in human visualinformation processing

A stochastic model of perceptual encoding is formulated and derived for the purpose of extending an existing queuing model of the central decision-making stage of visual information processing. The new combined model can account for processing capacity limitations that arise from both perceptual and central processing limitations. The new model provided an acceptable parameter fit to extant data     

Complexity and stochastic evolution of dyadic networks

A strategic model of network formation is developed which permits unreliable links and organizational costs. Finding a connected Nash network which guarantees a given payoff to each player proves to be an NP-hard problem. For the associated evolutionary game with asynchronous updating and logit updating rules, the stochastically stable networks are characterized.     

Improving reinforcement learning in stochastic RAM-based neural networks

RAM-based neural networks are designed to be efficiently implemented in hardware. The desire to retain this property influences the training algorithms used, and has led to the use of reinforcement (reward-penalty) learning. An analysis of the reinforcement algorithm applied to RAM-based nodes has shown the ease with which unlearning can occur. An amended algorithm is proposed which demonstrates improved learning performance compared to previously published reinforcement regimes.