Distributed Decision Through Self-Synchronizing Sensor Networks in the Presence of Propagation Delays and Nonreciprocal Channels

In this paper we propose and analyze a distributed algorithm for achieving globally optimal decisions, either estimation or detection, through a self-synchronization mechanism among linearly coupled integrators initialized with local measurements. We model the interaction among the nodes as a directed graph with weights dependent on the radio interface and we pose special attention to the effect of the propagation delays occurring in the exchange of data among sensors, as a function of the network geometry. We derive necessary and sufficient conditions for the proposed system to reach a consensus on globally optimal decision statistics. One of the major results proved in this work is that a consensus is achieved for any bounded delay condition if and only if the directed graph is quasi-strongly connected. We also provide a closed form expression for the global consensus, showing that the effect of delays is, in general, to introduce a bias in the final decision. The closed form expression is also useful to modify the consensus mechanism in order to get rid of the bias with minimum extra complexity.Comment: Conference paper. Journal version submitted to IEEE Transactions on Signal Processing, January 10, 2007. Paper accepted for the publication on the VIII IEEE Workshop on Signal Processing Advances in Wireless Communications, (SPAWC 2007), January 22, 200

The Computational Cost of Asynchronous Neural Communication

Biological neural computation is inherently asynchronous due to large variations in neuronal spike timing and transmission delays. So-far, most theoretical work on neural networks assumes the synchronous setting where neurons fire simultaneously in discrete rounds. In this work we aim at understanding the barriers of asynchronous neural computation from an algorithmic perspective. We consider an extension of the widely studied model of synchronized spiking neurons [Maass, Neural Networks 97] to the asynchronous setting by taking into account edge and node delays. - Edge Delays: We define an asynchronous model for spiking neurons in which the latency values (i.e., transmission delays) of non self-loop edges vary adversarially over time. This extends the recent work of [Hitron and Parter, ESA\u2719] in which the latency values are restricted to be fixed over time. Our first contribution is an impossibility result that implies that the assumption that self-loop edges have no delays (as assumed in Hitron and Parter) is indeed necessary. Interestingly, in real biological networks self-loop edges (a.k.a. autapse) are indeed free of delays, and the latter has been noted by neuroscientists to be crucial for network synchronization. To capture the computational challenges in this setting, we first consider the implementation of a single NOT gate. This simple function already captures the fundamental difficulties in the asynchronous setting. Our key technical results are space and time upper and lower bounds for the NOT function, our time bounds are tight. In the spirit of the distributed synchronizers [Awerbuch and Peleg, FOCS\u2790] and following [Hitron and Parter, ESA\u2719], we then provide a general synchronizer machinery. Our construction is very modular and it is based on efficient circuit implementation of threshold gates. The complexity of our scheme is measured by the overhead in the number of neurons and the computation time, both are shown to be polynomial in the largest latency value, and the largest incoming degree ? of the original network. - Node Delays: We introduce the study of asynchronous communication due to variations in the response rates of the neurons in the network. In real brain networks, the round duration varies between different neurons in the network. Our key result is a simulation methodology that allows one to transform the above mentioned synchronized solution under edge delays into a synchronized under node delays while incurring a small overhead w.r.t space and time

Fundamentals of Large Sensor Networks: Connectivity, Capacity, Clocks and Computation

Sensor networks potentially feature large numbers of nodes that can sense their environment over time, communicate with each other over a wireless network, and process information. They differ from data networks in that the network as a whole may be designed for a specific application. We study the theoretical foundations of such large scale sensor networks, addressing four fundamental issues- connectivity, capacity, clocks and function computation. To begin with, a sensor network must be connected so that information can indeed be exchanged between nodes. The connectivity graph of an ad-hoc network is modeled as a random graph and the critical range for asymptotic connectivity is determined, as well as the critical number of neighbors that a node needs to connect to. Next, given connectivity, we address the issue of how much data can be transported over the sensor network. We present fundamental bounds on capacity under several models, as well as architectural implications for how wireless communication should be organized. Temporal information is important both for the applications of sensor networks as well as their operation.We present fundamental bounds on the synchronizability of clocks in networks, and also present and analyze algorithms for clock synchronization. Finally we turn to the issue of gathering relevant information, that sensor networks are designed to do. One needs to study optimal strategies for in-network aggregation of data, in order to reliably compute a composite function of sensor measurements, as well as the complexity of doing so. We address the issue of how such computation can be performed efficiently in a sensor network and the algorithms for doing so, for some classes of functions.Comment: 10 pages, 3 figures, Submitted to the Proceedings of the IEE

Distributed Decision Through Self-Synchronizing Sensor Networks in the Presence of Propagation Delays and Asymmetric Channels

In this paper we propose and analyze a distributed algorithm for achieving globally optimal decisions, either estimation or detection, through a self-synchronization mechanism among linearly coupled integrators initialized with local measurements. We model the interaction among the nodes as a directed graph with weights (possibly) dependent on the radio channels and we pose special attention to the effect of the propagation delay occurring in the exchange of data among sensors, as a function of the network geometry. We derive necessary and sufficient conditions for the proposed system to reach a consensus on globally optimal decision statistics. One of the major results proved in this work is that a consensus is reached with exponential convergence speed for any bounded delay condition if and only if the directed graph is quasi-strongly connected. We provide a closed form expression for the global consensus, showing that the effect of delays is, in general, the introduction of a bias in the final decision. Finally, we exploit our closed form expression to devise a double-step consensus mechanism able to provide an unbiased estimate with minimum extra complexity, without the need to know or estimate the channel parameters.Comment: To be published on IEEE Transactions on Signal Processin