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In large-scale ad-hoc wireless networks, individual nodes communicate directly and reliably only with their neighbors, namely those nodes within their transmission range. A basic question is to determine the critical transmission range, namely the smallest transmission range value that enables network connectivity amongst participating nodes. On the sensitivity of the critical transmission range: Lessons from the lonely dimension discusses this important resource allocation issue in the context of a simple one-dimensional disk model. It carefully explores how properties of the node distribution affect the critical transmission range, and develop engineering implications for power allocation. Interest in the one-dimensional stems from the fact that a complete set of results is available in that case, suggesting appropriate versions in the less developed higher dimensional situation, possibly by formal transfer.