Synthesis of optimal TANT networks

A new synthesis algorithm is developed for TANT networks, i.e. three-level NAND-gate combinational switching networks having only uncomplemented inputs. Pertinent theorems are introduced at the outset to provide a firm theoretical basis for the developed procedure. Thereafter, a detailed discussion of the synthesis algorithm is given in flowchart form for step-by-step instructions. Three examples are provided to illustrate the basic design procedure. A computer-aided design (CAD) software package exists for this algorithm, and its extension for handling hazardless and/or multiple-output TANT networks is suggested. The need for extending the problem definition for sequential TANT network synthesis is identified.     

Stochastic projective methods for simulating stiff chemical reacting systems

In this paper, stochastic projective methods are proposed to improve the stability and efficiency in simulating stiff chemical reacting systems. The efficiency of existing explicit tau-leaping methods can often severely be limited by the stiffness in the system, forcing the use of small time steps to maintain stability. The methods presented in this paper, namely stochastic projective (SP) and telescopic stochastic projective (TSP) method, can be considered as more general stochastic versions of the recently developed stable projective numerical integration methods for deterministic ordinary differential equations. SP and TSP method are developed by fully re-interpreting and extending the key projective integration steps in the deterministic regime under a stochastic context. These new stochastic methods not only automatically reduce to the original deterministic stable methods when applied to simulating ordinary differential equations, but also carry the enhanced stability property over to the stochastic regime. In some sense, the proposed methods are stochastic generalizations to their deterministic counterparts. As such, SP and TSP method can adopt a much larger effective time step than is allowed for explicit tau-leaping, leading to noticeable runtime speedup. The explicit nature of the proposed stochastic simulation methods relaxes the need for solving any coupled nonlinear systems of equations at each leaping step, making them more efficient than the implicit tau-leaping method with similar stability characteristics. The efficiency benefits of SP and TSP method over the implicit tau-leaping is expected to grow even more significantly for large complex stiff chemical systems involving hundreds of active species and beyond.     

Functional abilities of a stochastic logic neural network

The authors have studied the information processing ability of stochastic logic neural networks, which constitute one of the pulse-coded artificial neural network families. These networks realize pseudoanalog performance with local learning rules using digital circuits, and therefore suit silicon technology. The synaptic weights and the outputs of neurons in stochastic logic are represented by stochastic pulse sequences. The limited range of the synaptic weights reduces the coding noise and suppresses the degradation of memory storage capacity. To study the effect of the coding noise on an optimization problem, the authors simulate a probabilistic Hopfield model (Gaussian machine) which has a continuous neuron output function and probabilistic behavior. A proper choice of the coding noise amplitude and scheduling improves the network's solutions of the traveling salesman problem (TSP). These results suggest that stochastic logic may be useful for implementing probabilistic dynamics as well as deterministic dynamics.     

General decomposition of incompletely specified sequential machines with multi-state behavior realization

This paper is devoted to decomposition of sequential machines, discrete functions and relations. Sequential machine decomposition consists in representation of a given machine as a network of collaborating partial machines that together realize behavior of the given machine. A good understanding of possible decomposition structures and of conditions under which the corresponding structures exist is a prerequisite for any adequate circuit or system synthesis. The paper discusses the theory of general decomposition of incompletely specified sequential machines with multi-state behavior realization. The central point of this theory is a constructive theorem on the existence of the general decomposition structures and conditions under which the corresponding structures exist. The theory of general decomposition presented in this paper is the most general known theory of the binary, multi-valued and symbolic sequential and combinational discrete network structures. The correct circuit generator defined by the general decomposition theorem covers all other known structural models of sequential and combinational circuits as its special cases. Using this theory, in recent years we developed a number of effective and efficient methods and EDA tools for sequential and combinational circuit synthesis that consistently construct much better circuits than other academic and commercial state-of-the-art synthesis tools. This demonstrates the practical soundness of our theory. This theory can be applied to any sort of binary, multi-valued and symbolic systems expressed as networks of relations, functions or sequential machines, and can be very useful in such fields as circuit and architecture synthesis of VLSI systems, knowledge engineering, machine learning, neural network training, pattern analysis, etc.     

A Review of Classification Schemes for Computer Communication Networks

Classification of computer communication networks often depends upon the point of view and background of the person doing the classifying. Network designers, for example, tend to categorize the network according to its switching functioc–rcuit switching, message switch-or packet switching. Managers, who are occupied with economic considerations, look at the topological aspects of a network as centralized, decentralized, or distributed. Finally, network operators are interested in the use of deterministic, stochastic, or flow control routing algorithms, which are methods of routing the message or other communication entity across the network.     

Finite difference solution of differential equations with stochastic inputs

This paper discusses application of two numerical methods (central difference and predictor corrector) for the solution of differential equations with deterministic as well as stochastic inputs. The methods are applied to a second order linear differential equation representing a series RLC netowrk with step function, sinusoidal and stochastic inputs. It is shown that both methods give correct answers for the step function and sinusoidal inputs. However, the central-difference method of solution is recommended for stochastic inputs. This statement is justified by comparing the auto-correlation and cross-correlation functions of the central-difference solution (with stochastic inputs) with the corresponding theoretical values of a continuous system. It is further shown that the more common predictor-corrector methods, although suitable for solution of differential equations with regular inputs, diverge for stochastic inputs. The reason is that these methods, by the application of several point integral formulas, use a high degree of smoothing on the variable and its derivatives. Inherent in the derivation of these integral formulas is the assumption of the continuity of the variable and its derivatives, a condition which is not satisfied in problems with stochastic inputs.Note that the second order differential equation chosen here for numerical experiments can be solved by classical methods for all of the given inputs, including the probabilistic inputs. The classical methods, however, unlike the numerical solutions, can not be extended to nonlinear differential equations which frequently arise in the digital simulation of engineering problems.     

A stochastic optimization model for integrated forward/reverse logistics network design

In this paper, we develop a stochastic programming model for an integrated forward/reverse logistics network design under uncertainty. First, an efficient deterministic mixed integer linear programming model is developed for integrated logistics network design to avoid the sub-optimality caused by the separate design of the forward and reverse networks. Then the stochastic counterpart of the proposed MILP model is developed by using scenario-based stochastic approach. Numerical results show the power of the proposed stochastic model in handling data uncertainty.     

Consensus problems in networks of agents with switching topology and time-delays

In this paper, we discuss consensus problems for networks of dynamic agents with fixed and switching topologies. We analyze three cases: 1) directed networks with fixed topology; 2) directed networks with switching topology; and 3) undirected networks with communication time-delays and fixed topology. We introduce two consensus protocols for networks with and without time-delays and provide a convergence analysis in all three cases. We establish a direct connection between the algebraic connectivity (or Fiedler eigenvalue) of the network and the performance (or negotiation speed) of a linear consensus protocol. This required the generalization of the notion of algebraic connectivity of undirected graphs to digraphs. It turns out that balanced digraphs play a key role in addressing average-consensus problems. We introduce disagreement functions for convergence analysis of consensus protocols. A disagreement function is a Lyapunov function for the disagreement network dynamics. We proposed a simple disagreement function that is a common Lyapunov function for the disagreement dynamics of a directed network with switching topology. A distinctive feature of this work is to address consensus problems for networks with directed information flow. We provide analytical tools that rely on algebraic graph theory, matrix theory, and control theory. Simulations are provided that demonstrate the effectiveness of our theoretical results.     

Controlling activity fluctuations in large, sparsely connected random networks

Controlling activity in recurrent neural network models of brain regions is essential both to enable effective learning and to reproduce the low activities that exist in some cortical regions such as hippocampal region CA3. Previous studies of sparse, random, recurrent networks constructed with McCulloch-Pitts neurons used probabilistic arguments to set the parameters that control activity. Here, we extend this work by adding an additional, biologically appropriate, parameter to control the magnitude and stability of activity oscillations. The new constant can be considered to be the rest conductance in a shunting model or the threshold when subtractive inhibition is used. This new parameter is critical for large networks run at low activity levels. Importantly, extreme activity fluctuations that act to turn large networks totally on or totally off can now be avoided. We also show how the size of external input activity interacts with this parameter to affect network activity. Then the model based on fixed weights is extended to estimate activities in networks with distributed weights. Because the theory provides accurate control of activity fluctuations, the approach can be used to design a predictable amount of pseudorandomness into deterministic networks. Such nonminimal fluctuations improve learning in simulations trained on the transitive inference problem.     

Modeling and performance evaluation of supply chains using batch deterministic and stochastic Petri nets

Batch deterministic and stochastic Petri nets are introduced as a tool for modeling and performance evaluation of supply chains. The new model is developed by enhancing deterministic and stochastic Petri nets (DSPNs) with batch places and batch tokens. By incorporating stochastic Petri nets (SPNs) with the batch features, inhibitor arcs, and marking-dependent weights, operational policies of supply chains such as inventory policies can be easily described in the model. Methods for structural and performance analysis of the model are developed by extending existing ones for DSPNs. As applications, an inventory system and an industrial supply chain are modeled and their performances are evaluated analytically and by simulation, respectively, using this BSPN model. The applications demonstrate that our model and associated methods can solve some important supply chain modeling and analysis issues. Note to Practitioners-This paper was motivated by the problem of performance analysis and optimization of supply chains but it also applies to other discrete event systems where materials are processed in finite discrete quantities (batches) and operations are performed in a batch way because of batch inputs and/or in order to take advantages of the economies of scale. Existing Petri net modeling and analysis tools for such systems ignore their batch features, making their modeling complicated. This paper suggests a new model called batch deterministic and stochastic Petri nets (BDSPNs) by enhancing deterministic and stochastic Petri nets with batch places and batch tokens. Methods for structural and performance analysis of the model are developed. We then show how an inventory system and a real-life supply chain can be modeled and their performances can be evaluated analytically and by simulation respectively based on the model. The model and associated analysis methods therefore provide a promising tool for modeling and performance evaluation of supply chains.     

Fundamental calculus on generalized stochastically bounded bursty traffic for communication networks

Since many applications and networks do not require or provide deterministic service guarantees, stochastic service guarantee analysis is becoming increasingly important and has attracted a lot of research attention in recent years. For this, several stochastic versions of deterministic traffic models have been proposed in the literature. Unlike previous stochastic models that are based on the traffic amount property of an input process, we present another stochastic model, generalized Stochastically Bounded Burstiness (gSBB), which is based on the virtual backlog property of the input process. We show the advantages of this approach. We study the superposition of gSBB traffic, and set up the input–output relation. Under various service disciplines, we characterize the output process for each source and investigate probabilistic upper bound on delay. Finally, we introduce a stochastic ordering monotonicity property of gSBB. With this property, we show that many well-known traffic models can be readily represented using the proposed gSBB model. These results set up the basis for a network calculus for gSBB traffic.     

Probabilistic dual heuristic programming-based adaptive critic

Adaptive critic (AC) methods have common roots as generalisations of dynamic programming for neural reinforcement learning approaches. Since they approximate the dynamic programming solutions, they are potentially suitable for learning in noisy, non-linear and non-stationary environments. In this study, a novel probabilistic dual heuristic programming (DHP)-based AC controller is proposed. Distinct to current approaches, the proposed probabilistic (DHP) AC method takes uncertainties of forward model and inverse controller into consideration. Therefore, it is suitable for deterministic and stochastic control problems characterised by functional uncertainty. Theoretical development of the proposed method is validated by analytically evaluating the correct value of the cost function which satisfies the Bellman equation in a linear quadratic control problem. The target value of the probabilistic critic network is then calculated and shown to be equal to the analytically derived correct value. Full derivation of the Riccati solution for this non-standard stochastic linear quadratic control problem is also provided. Moreover, the performance of the proposed probabilistic controller is demonstrated on linear and non-linear control examples.     

Stochastic Boolean Satisfiability

Satisfiability problems and probabilistic models are core topics of artificial intelligence and computer science. This paper looks at the rich intersection between these two areas, opening the door for the use of satisfiability approaches in probabilistic domains. The paper examines a generic stochastic satisfiability problem, SSAT, which can function for probabilistic domains as SAT does for deterministic domains. It shows the connection between SSAT and well-studied problems in belief network inference and planning under uncertainty, and defines algorithms, both systematic and stochastic, for solving SSAT instances. These algorithms are validated on random SSAT formulae generated under the fixed-clause model. In spite of the large complexity gap between SSAT (PSPACE) and SAT (NP), the paper suggests that much of what we have learned about SAT transfers to the probabilistic domain.     

Representation of Nonlinear Random Transformations by Non-Gaussian Stochastic Neural Networks

The learning capability of neural networks is equivalent to modeling physical events that occur in the real environment. Several early works have demonstrated that neural networks belonging to some classes are universal approximators of input-output deterministic functions. Recent works extend the ability of neural networks in approximating random functions using a class of networks named stochastic neural networks (SNN). In the language of system theory, the approximation of both deterministic and stochastic functions falls within the identification of nonlinear no-memory systems. However, all the results presented so far are restricted to the case of Gaussian stochastic processes (SPs) only, or to linear transformations that guarantee this property. This paper aims at investigating the ability of stochastic neural networks to approximate nonlinear input-output random transformations, thus widening the range of applicability of these networks to nonlinear systems with memory. In particular, this study shows that networks belonging to a class named non-Gaussian stochastic approximate identity neural networks (SAINNs) are capable of approximating the solutions of large classes of nonlinear random ordinary differential transformations. The effectiveness of this approach is demonstrated and discussed by some application examples.     

A method to evaluate the spatial extensibility of a switching unit and network

Switching units and networks have been analyzed as extensible fabrics,mostly in terms of their scheduling algorithms.The traditional literature on switching extensibility has provided complexity theory only relating to the total numbers of inputs(or outputs)and exchange lines.This paper analyzes switching extensibility in terms of not only the scheduling algorithm and also the fabric itself.It is found that determining extensibility from soft complexity related to the number of inputs(or outputs)of the scheduling algorithm and the fabric extensibility in previous studies without quantization is a flawed conception.A method is thus proposed to express the spatial extensibility of a switching unit or network in terms of the connections of a switching resource and capacity.The method calculates parameter ES(the efciency of switching)of an m×n switching unit and obtains two functions of the switching unit to describe spatial extensibility along with the number of unilateral inputs or outputs.It is found that the range of ES is(0,1]and three types of switching unit and two types of crosspoint networks have ES=1.ES is calculated for banyan,Clos,parallel packet,fully interconnected and recirculation switching networks.The ES value for the banyan switching network is larger than that for other networks,and switching networks are classified into three types that have absolute/linear/denied spatial extensibility according to the limES value.It is demonstrated that a switching network has the largest ES value when it contains only the five types of switching unit for which ES=1.Finally,a group-switching-first self-routing banyan switching network with lower blocking probability and time delay is deduced,and the ES method is contrasted with two other methods of evaluating spatial extensibility in terms of their mathematical expressions and intuitive graphics,for the five types of switching network listed above.     

Generating probabilistic Boolean networks from a prescribed stationary distribution

Modeling gene regulation is an important problem in genomic research. Boolean networks (BN) and its generalization probabilistic Boolean networks (PBNs) have been proposed to model genetic regulatory interactions. BN is a deterministic model while PBN is a stochastic model. In a PBN, on one hand, its stationary distribution gives important information about the long-run behavior of the network. On the other hand, one may be interested in system synthesis which requires the construction of networks from the observed stationary distribution. This results in an inverse problem which is ill-posed and challenging. Because there may be many networks or no network having the given properties and the size of the inverse problem is huge. In this paper, we consider the problem of constructing PBNs from a given stationary distribution and a set of given Boolean Networks (BNs). We first formulate the inverse problem as a constrained least squares problem. We then propose a heuristic method based on Conjugate Gradient (CG) algorithm, an iterative method, to solve the resulting least squares problem. We also introduce an estimation method for the parameters of the PBNs. Numerical examples are then given to demonstrate the effectiveness of the proposed methods.     

带有时滞的随机区间Hopfield神经网络的指数稳定性

讨论了带有可变时滞的随机区间Hopfield神经网络的指数稳定性, 利用It^o公式和Lyapunov函数, 得到了几个关于其指数稳定时滞无关和时滞相关的充分性条件, 推广了现有文献中关于定常时滞随机神经网络及其确定形式的许多结果.     

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.