On Many-to-Many Communication in Packet Radio Networks

Radio networks model wireless data communication when bandwidth is limited to one wave frequency. The key restriction of such networks is mutual interference of packets arriving simultaneously to a node. The many-to-many (m2m) communication primitive involves p participant nodes of a distance at most d between any pair of them, from among n nodes in the network, and the task is to have all participants get to know all input messages. We consider three cases of the m2m communication problem. In the ad-hoc case, each participant knows only its name and the values of n, p and d. In the partially centralized case, each participant knows the topology of the network and the values of p and d, but does not know the names of other participants. In the centralized case each participant knows the topology of the network and the names of all the participants. For the centralized m2m problem, we give deterministic protocols, for both undirected and directed networks, working in O(d + p) time, which is provably optimal. For the partially centralized m2m problem, we give a randomized protocol for undirected networks working in O((d + p + log2 n)log p) time with high probability (whp), and we show that any deterministic protocol requires Ω(plogn/p n + d) time. For the ad-hoc m2m problem, we develop a randomized protocol for undirected networks that works in O((d + log p)log2 n + plog p) time whp. We show two lower bounds for the ad-hoc m2m problem. One states that any m2m deterministic protocol requires Ω(nlogn/d+1 n) time when n − p = Ω(n) and d> 1; Ω(n) time when n − p = o(n); and Ω(plogn/p n) time when d = 1. The other lower bound states that any m2m randomized protocol requires Ω(p + d log(n/d + 1)+log2 n) expected time

Monitoring Hippocampus Electrical Activity In Vitro on an Elastically Deformable Microelectrode Array

Interfacing electronics and recording electrophysiological activity in mechanically active biological tissues is challenging. This challenge extends to recording neural function of brain tissue in the setting of traumatic brain injury (TBI), which is caused by rapid (within hundreds of milliseconds) and large (greater than 5% strain) brain deformation. Interfacing electrodes must be biocompatible on multiple levels and should deform with the tissue to prevent additional mechanical damage. We describe an elastically stretchable microelectrode array (SMEA) that is capable of undergoing large, biaxial, 2-D stretch while remaining functional. The new SMEA consists of elastically stretchable thin metal films on a silicone membrane. It can stimulate and detect electrical activity from cultured brain tissue (hippocampal slices), before, during, and after large biaxial deformation. We have incorporated the SMEA into a well-characterized in vitro TBI research platform, which reproduces the biomechanics of TBI by stretching the SMEA and the adherent brain slice culture. Mechanical injury parameters, such as strain and strain rate, can be precisely controlled to generate specific levels of damage. The SMEA allowed for quantification of neuronal function both before and after injury, without breaking culture sterility or repositioning the electrodes for the injury event, thus enabling serial and long-term measurements. We report tests of the SMEA and an initial application to study the effect of mechanical stimuli on neuron function, which could be employed as a high-content, drug-screening platform for TBI