“Chaotic relaxation” in concurrently asynchronous neural networks

In this paper we analyze a fundamental issue which directly impacts the scalability of current theoretical neural network models to applicative embodiments, in both software as well as hardware. This pertains to the inherent and unavoidable concurrent asynchronicity of emerging fine-grained computational ensembles and the consequent chaotic manifestations in the absence of proper conditioning. The latter concern is particularly significant since the computational inertia of neural networks in general and our dynamical learning formalisms manifests itself substantially, only in massively parallel hardward—optical, VLSI or opto-electronic. We introduce a mathematical framework for systematically reconditioning additive-type models and derive a neuro-operator, based on the chaotic relaxation paradigm whose resulting dynamics are neither “concurrently” synchronous nor “sequentially” asynchronous. Necessary and sufficient conditions guaranteeing concurrent asynchronous convergence are established in terms of contracting operators. Lyapunov exponents are also computed to characterize the network dynamics and to ensure that throughput-limiting “emergent computational chaos” behavior in models reconditioned with concurrently asynchronous algorithms was eliminated.     

Basins of attraction in fully asynchronous discrete-time discrete-state dynamic networks

This paper gives a formulation of the basins of fixed point states of fully asynchronous discrete-time discrete-state dynamic networks. That formulation provides two advantages. The first one is to point out the different behaviors between synchronous and asynchronous modes and the second one is to allow us to easily deduce an algorithm which determines the behavior of a network for a given initialization. In the context of this study, we consider networks of a large number of neurons (or units, processors, etc.), whose dynamic is fully asynchronous with overlapping updates . We suppose that the neurons take a finite number of discrete states and that the updating scheme is discrete in time. We make no hypothesis on the activation functions of the nodes, so that the dynamic of the network may have multiple cycles and/or basins. Our results are illustrated on a simple example of a fully asynchronous Hopfield neural network.     

Asynchronous H ∞ Control for Positive Discrete-time Markovian Jump Systems

This paper deals with the asynchronous H∞ control for discrete-time positive Markovian jump systems (PMJSs). In previous results about PMJSs, asynchronous behaviors are always overlooked and the designed controller is based on the synchronization between the system modes and controller modes. Sufficient conditions for stochastic stability are proposed by the use of Lyapunov-Krasovskii functional. The asynchronous controller is designed to ensure the closed-loop system stochastically stable with a prescribed H∞ performance index. All the conditions are given in linear matrix inequality framework. Finally, a pest’s age-structured population dynamic model is illustrated to show the validity of the present design.     

Comments on “direct bilinear routh stability criteria for discrete systems”

The above paper¹ discusses useful Routh-like stability criteria for discrete systems. Unfortunately, however, previous work on the subject escaped the attention of the author. This note co-ordinates previous work with results obtained in the above paper. It also points out some of the more recent developments on the subject.     

Alias types for “environment-aware” computations

In previous work with Bono we introduced a calculus for modelling “environment-aware” computations, that is computations that adapt their behavior according to the capabilities of the environment. The calculus is an imperative, object-based language (with extensible objects and primitives for discriminating the presence or absence of attributes of objects) equipped with a small-step operational semantics.In this paper we define a type and effect system for the calculus. The typing judgements specify, via constraints, the shape of environments which guarantees the correct execution of expressions and the typing rules track the effect of expression evaluation on the environment. The type and effect system is sound w.r.t. the operational semantics of the language.     

Author's reply: “A comment on optimal control of SISO continuous-time systems”

In the above-mentioned comment, the author points out a technical problem with the paper (Wang, Z. Q., & Sznaier, M. (1997). Automatica, 33(1), 85–90). As we show here, this technical problem can be easily solved. Moreover, it affects neither the main formulation nor the results, which remain valid.     

Comments on “Controller Synthesis of Fuzzy-Dynamic Systems Based on Piecewise Lyapunov Functions”

This comment tries to describe a theoretical mistake made in the aforementioned paper [G. Feng, IEEE Trans. Fuzzy Syst., vol. 11, no. 5, pp. 605–612, Oct. 2003] to formulate the inverse of matrices used to construct the piecewise-quadratic Lyapunov functions. Derivation of these inverse matrices is the most critical step toward transforming the design constraints into linear matrix inequalities (LMIs). Therefore, the erroneous formulation essentially affects the validity of the approach and final results. Unfortunately, it seems that there is no simple correction for this problem. However, some close alternative approaches are suggested by the same authors in their other works.      

Stability of iterative learning control with data dropouts via asynchronous dynamical system

In this paper, the stability of iterative learning control with data dropouts is discussed. By the super vector formulation, an iterative learning control (ILC) system with data dropouts can be modeled as an asynchronous dynamical system with rate constraints on events in the iteration domain. The stability condition is provided in the form of linear matrix inequalities (LMIS) depending on the stability of asynchronous dynamical systems. The analysis is supported by simulations.     

Structure-Based Deadlock Checking of Asynchronous Circuits

It is important to verify the absence of deadlocks in asynchronous circuits. Much previous work relies on a reachability analysis of the circuits’ states, with the use of binary decision diagrams (BDDs) or Petri nets to model the behaviors of circuits. This paper presents an alternative approach focusing on the structural properties of well-formed asynchronous circuits that will never suffer deadlocks. A class of data-driven asynchronous pipelines is targeted in this paper, which can be viewed as a network of basic components connected by handshake channels. The sufficient and necessary conditions for a component network consisting of Steer, Merge, Fork and Join are given. The slack elasticity of the channels is analyzed in order to introduce pipelining. As an application, a deadlock checking method is implemented in a syntax-directed asynchronous design tool -- Teak. The proposed method shows a great runtime advantage when compared against previous Petri net based verification tools.     

Access cost for asynchronous Byzantine quorum systems

Summary. Quorum systems have been used to implement many coordination problems in distributed systems. In this paper, we study the cost of accessing quorums in asynchronous systems. We formally define the asynchronous access cost of quorum systems and argue that the asynchronous access cost and not the size of a quorum is the right measure of message complexity of protocols using quorums in asynchronous systems. We show that previous quorum systems proposed in the literature have a very high asynchronous access cost. We propose a reformulation of the definition of Byzantine quorum systems that captures the requirement for non-blocking access to quorums in asynchronous systems. We present new Byzantine quorum systems with low asynchronous access cost whose other performance parameters match those of the best Byzantine quorum systems proposed in the literature. In particular, we present a construction for the disjoint failure pattern that outperforms previously proposed systems for that pattern. Received: September 1999 / Accepted: September 2000     

A comment on “L∞ optimal control of SISO continuous-time systems”

The paper “L_∞ optimal control of SISO continuous-time systems” by Wang and Sznaier (Wang & Sznaier (1997). Automatica, 33 (1), 85–90) studies the problem of designing a controller that optimally minimizes the peak absolute value of system output, due to a fixed input signal. With a newly defined function space A_∞, it was claimed that the set of all L_∞-bounded outputs could be parameterized and that the problem could be transformed to a minimal distance problem on L_∞ space. We believe, however, their formulation has essential flaws.     

Comment on “Facial expression recognition based on two-dimensional discriminant locality preserving projections” [Neurocomputing 71 (2008) 1730-1734]

In this note, we show that the mathematical formulation of the two-dimensional discriminant locality preserving projections (2D-DLPP) proposed in the paper [R. Zhi, Q. Ruan, Facial expression recognition based on two-dimensional discriminant locality preserving projections, Neurocomputing 71 (2008) 1730–1734] is not very sound. The rigorous version is thus given. We also point out that 2D-DLPP can be viewed from the perspective of the discriminant locality preserving projections (DLPP).     

Comments on “self-tuning adaptive control of cement raw material blending”

In a recent paper Keviczky and co-workers (1978) use results of previous papers (Keviczky and Hetthessy, 1977; Hetthessy, Haber and Keviczky (1975) to present the MIMO-ST-MV and the MIMO-ST-MV-RAFT used in cement industries. In this correspondence an algebraic mistake is shown to have taken place in Keviczky and Hetthessy (1977). Accordingly, the representation in Keviczky and co-workers (1978) of the regulator parameter matrix is not of the minimum variance type.     

An “impossibility” theorem on a class of high-order discrete-time nonlinear control systems

A high-order discrete-time nonlinear system with unknown parameters and Gaussian noise is studied in this paper, and it is shown that under a simple algebraic condition concerning the nonlinearity of the system, there does not exist any feedback controller that globally stabilizes the uncertain system. This impossibility result attempts to understand the capability and limitation of feedback mechanism of a high-order discrete-time nonlinear system and continues a series of previous research on similar first-order systems. This result shows that for the high-order discrete-time nonlinear system studied here, a polynomial corresponding to the first-order principle part of the system determines the limit of the feedback mechanism.     

“Vague-to-Crisp” Neural Mechanism of Perception

This brief describes neural modeling fields (NMFs) for object perception, a bio-inspired paradigm. We discuss previous difficulties in object perception algorithms encountered since the 1950s, and describe how NMF overcomes these difficulties. NMF mechanisms are compared to recent experimental neuroimaging observations, which have demonstrated that initial top-down signals are vague and during perception they evolve into crisp representations matching the bottom-up signals from observed objects. Neural and mathematical mechanisms are described and future research directions outlined.      

异步电路验证算法

异步电路因不受时钟偏差的限制而逐渐成为电路设计研究的热点 .发展自动化的验证工具已成为确保大规模异步电路质量和性能的关键 .其核心课题就是建立异步电路的验证算法 .该文整理列举了基于多种数学模型的验证算法 ,如逻辑模型、代数模型、符号模型、数值模型和几何模型的验证算法 ,并从应用的角度将现有的异步电路验证算法分为两类 ,分别是事件时序分析类算法和状态空间搜索类算法 ,从算法的理论基础、应用背景、模型结构、图形描述、适用范围、算法复杂度编程复杂度等多个角度作了比较研究 ,给出了部分代表算法的应用算例 ,最后总结了在实际问题中选择验证算法的原则     

A “static” optimal strategy for a service robot: A one dimensional case

In this paper we present a method for creating a strategy to control the movements of a service robot, servicing thread rewinding machines. The robot moves from one machine to another detecting a dropped or broken thread. When this is detected the robot will restart the machine.

A previous paper considered a number of naive strategies and compared them to the simple strategy of just moving back and forth from one end of the line to the other. In this paper we will propose a new method for determining the strategy and we will examine the effects of this new strategy with the aid of simulation.     

Corrections to “Aggregation Using the Linguistic Weighted Average and Interval Type-2 Fuzzy Sets”

In the previous paper, we have proposed linguistic weighted average (LWA) algorithms that can be used in distributed and hierarchical decision making. The original LWA algorithms were completely based on the representation theorem for interval type-2 fuzzy sets (IT2 FSs). In later usage, we found that when the lower membership functions (LMFs) of the inputs and weights are of different heights, the LMF of the output IT2 FS may be nonconvex and discontinuous. In this letter, a correction to the original LWA algorithms is proposed. The new LWA algorithms are simpler and easier to understand; so, it should facilitate the applications of the LWAs.      

Stability,L2‐gain and asynchronous H ∞ control for continuous‐time switched systems

This paper is concerned with the stability and L₂‐gain problems for a class of continuous‐time linear switched systems with the existed asynchronous behaviors, where ‘asynchronous’ means that the switching of the controllers to be designed has a lag to the switching of the system modes. Firstly, a new sufficient condition on the asymptotic stability and weighted L₂‐gain analysis is obtained by using multiple Lyapunov functions combined with the average dwell time technique. Moreover, a result that is formulated in form of linear matrix inequalities is derived for the problem of asynchronous H _∞ control. Based on the result, the mode‐dependent controllers can be designed. Finally, an illustrative numerical example is presented to show the effectiveness of the obtained results.Copyright © 2013 John Wiley & Sons, Ltd.     

Knowledge Engineering for Rough Sets Based Decision‐Making Models

In this paper, a review of decision‐making models based on the rough set theory is presented. The use of these techniques allows for the presence of uncertainty in computer models that are developed for decision making, and to formulate the decision‐making models using the experiences of previous decisions made. Since the formulation of these models differs from the classical approach of decision‐making models, in this paper, the models are analyzed and a method is proposed for its implementation.