Fully Connected PLL Networks: How Filter Determines the Number of Nodes

Synchronization plays an important role in telecommunication systems, integrated circuits, and automation systems. Formerly, the masterslave synchronization strategy was used in the great majority of cases due to its reliability and simplicity. Recently, with the wireless networks development, and with the increase of the operation frequency of integrated circuits, the decentralized clock distribution strategies are gaining importance. Consequently, fully connected clock distribution systems with nodes composed of phase-locked loops (PLLs) appear as a convenient engineering solution. In this work, the stability of the synchronous state of these networks is studied in two relevant situations: when the node filters are first-order lag-lead low-pass or when the node filters are second-order low-pass. For first-order filters, the synchronous state of the network shows to be stable for any number of nodes. For second-order filter, there is a superior limit for the number of nodes, depending on the PLL parameters. Copyright (C) 2009 Atila Madureira Bueno et al.

FLOWS WITHOUT WANDERING POINTS ON COMPACT CONNECTED SURFACES

Given a compact 2 dimensional manifold M we classify all continuous flows phi without wandering points on M. This classification is performed by finding finitely many pairwise disjoint open phi-invariant subsets {U(1), U(2), ..., U(n)} of M such that U(i=1)(n) (U(i)) over bar = M and each U(i) is either a suspension of an interval exchange transformation, or a maximal open cylinder made up of closed trajectories of phi.

On the basic reproduction number and the topological properties of the contact network: An epidemiological study in mainly locally connected cellular automata

We study the spreading of contagious diseases in a population of constant size using susceptible-infective-recovered (SIR) models described in terms of ordinary differential equations (ODEs) and probabilistic cellular automata (PCA). In the PCA model, each individual (represented by a cell in the lattice) is mainly locally connected to others. We investigate how the topological properties of the random network representing contacts among individuals influence the transient behavior and the permanent regime of the epidemiological system described by ODE and PCA. Our main conclusions are: (1) the basic reproduction number (commonly called R(0)) related to a disease propagation in a population cannot be uniquely determined from some features of transient behavior of the infective group; (2) R(0) cannot be associated to a unique combination of clustering coefficient and average shortest path length characterizing the contact network. We discuss how these results can embarrass the specification of control strategies for combating disease propagations. (C) 2009 Elsevier B.V. All rights reserved.

Reachability of the synchronous state in a mutually connected PLL network

Second-order phase locked loops (PLLs) are devices that are able to provide synchronization between the nodes in a network even under severe quality restrictions in the signal propagation. Consequently, they are widely used in telecommunication and control. Conventional master-slave (M-S) clock-distribution systems are being, replaced by mutually connected (MC) ones due to their good potential to be used in new types of application such as wireless sensor networks, distributed computation and communication systems. Here, by using an analytical reasoning, a nonlinear algebraic system of equations is proposed to establish the existence conditions for the synchronous state in an MC PLL network. Numerical experiments confirm the analytical results and provide ideas about how the network parameters affect the reachability of the synchronous state. The phase-difference oscillation amplitudes are related to the node parameters helping to design PLL neural networks. Furthermore, estimation of the acquisition time depending on the node parameters allows the performance evaluation of time distribution systems and neural networks based on phase-locked techniques. (c) 2008 Elsevier GmbH. All rights reserved.

Mutually connected phase-locked loop networks: dynamical models and design parameters

Distribution of timing signals is an essential factor for the development of digital systems for telecommunication networks, integrated circuits and manufacturing automation. Originally, this distribution was implemented by using the master-slave architecture with a precise master clock generator sending signals to phase-locked loops (PLL) working as slave oscillators. Nowadays, wireless networks with dynamical connectivity and the increase in size and operation frequency of the integrated circuits suggest that the distribution of clock signals could be more efficient if mutually connected architectures were used. Here, mutually connected PLL networks are studied and conditions for synchronous states existence are analytically derived, depending on individual node parameters and network connectivity, considering that the nodes are nonlinear oscillators with nonlinear coupling conditions. An expression for the network synchronisation frequency is obtained. The lock-in range and the transmission error bounds are analysed providing hints to the design of this kind of clock distribution system.

Chaotic Synchronization in Discrete-Time Systems Connected by Bandlimited Channels

Due to the broadband characteristic of chaotic signals, many of the methods that have been proposed for synchronizing chaotic systems do not usually present a satisfactory performance when applied to bandlimited communication channels. Here, the effects of bandwidth limitations imposed by the channel on the synchronous solution of a discrete-time chaotic master-slave network are investigated. The discrete-time system considered in this study is the Henon map. It is analytically shown that synchronism can be achieved in such a network by introducing a digital filter in the feedback loop responsible for generating the chaotic signal that will be sent to the slave node. Numerical simulations relating the filter parameters, such as its order and cut-off frequency, to the maximum Lyapunov exponent of the master node, which determines if the transmitted signal is chaotic or not, are also presented. These results can be useful for practical communication schemes based on chaos.

Multiple synchronous states in static delay-free mutually connected PLL networks

In many engineering applications, the time coordination of geographically separated events is of fundamental importance, as in digital telecommunications and integrated digital circuits. Mutually connected (MC) networks are very good candidates for some new types of application, such as wireless sensor networks. This paper presents a study on the behavior of MC networks of digital phase-locked loops (DPLLs). Analytical results are derived showing that, even for static networks without delays, different synchronous states may exist for the network. An upper bound for the number of such states is also presented. Numerical simulations are used to show the following results: (i) the synchronization precision in MC DPLLs networks; (ii) the existence of synchronous states for the network does not guarantee its achievement and (iii) different synchronous states may be achieved for different initial conditions. These results are important in the neural computation context. as in this case, each synchronous state may be associated to a different analog memory information. (C) 2010 Elsevier B.V. All rights reserved.

Beauty, Class and Discourse: Issues in Debate

In this text we proceed through a brief review of Naomi Lee`s (2009) article, highlighting her significant contributions to social and cultural psychology. In our dialogue with her text we inquire about some arguments and methodological procedures she presents. We raise some specific questions related to how the issue of beauty is framed, and we ponder on how a broadening of the scope to include history-of ideas, of relations-would bring some important elements to her approach. As Lee relates beauty and class, we examine the nuanced meanings of lack and deficiency in her analytical work. We also discuss her assumptions and position concerning discourse and dialogue which mark her ways of proceeding through the analysis of the interviews. We speculate that the depersonalized answer appointed in the interviewees` discourse can be related to a way of considering beauty as disembodied.

Language, discourse and politics

After discussing the meaning of the word politics, this paper shows that there are four possible approaches to the issue of the relationships between language, discourse and politics: a) the intrinsic political nature of language; b) the relations of power between discourses and their political dimension; c) the relations of power between languages and the political dimension of their usage and; d) linguistic policies. This paper addresses only the first two of these items. Languages have an intrinsically political nature because they subject their speakers to their order. The acts of silencing operationalized in discourse manifest a relation of power. The spread of discourses in the social space is also subject to the order of power. The use of language may be the space of pertinence, but is also that of exclusion, separation and even the elimination of the other. Therefore, language is not a neutral communication tool, but it is permeated by politics, by power. Because of the dislocations that it produces, literature is a form of swindling language, unveiling the powers that are imprinted on it.