Supplementary Tables for “Numerical Results on Class Groups of Imaginary Quadratic Fields”

We present supplemental tables and additional data that extend that presented in [7]. Data corresponding to all the conjectures mentioned in [7] are included, and all tables are complete, including previously published results. In addition, two corrections to the data in [7] are included: – Originally, we only listed first occurrences of p-Sylow subgroups for primes p ≤ 173. In this paper, we present the entire list, for primes p ≤ 389. See Table 7. – When listing the first ∆ needing prime ideals of norm up to p, we pointed out an anomaly in the data at p = 181. Subsequent analysis has shown this to be a bug in our statistics gathering program. The data no longer contains any anomalies of this sort. See Table 15. Bounds on L(1, χ) There has been significant interest [2, 3, 6, 11] in the extreme values of L(1, χ∆) due to the relationship between it and the class number h∆. This can be seen in the analytic class number formula, L(1, χ∆) = h∆π where extreme values of L(1, χ∆) correspond to extreme values of h∆. In [10], Littlewood developed bounds on L(1, χ∆), namely that under the ERH, {1 + o(1)}(c1 log log ∆) −1 < L(1, χ∆) < {1 + o(1)}c2 log log(∆) , (0.1) where c1 and c2 are defined as follows: c1 = 12e γ /π 2 and c2 = 2e γ when 2 ∤ ∆ c1 = 8e γ /π 2 and c2 = e γ when 2 | ∆. ⋆ All three authors are supported in part by NSERC of Canada. In [11], Shanks investigated Littlewood’s bounds, and defined two values he termed the upper and lower Littlewood indices ULI = L(1, χ∆)/(c2 log log ∆) LLI = L(1, χ∆)c1 log log ∆. These indices effectively ignore the o(1) given in Littlewood’s bounds. We would expect extreme values of the LLI and the ULI to approach 1. Finally, as in [11], we define the functio

A Framework for the Management of Large-Scale Wireless Network Testbeds

Abstract — Wireless testbeds are typically distributed over large physical areas. There are often many nodes, some of which are difficult to reach on-site or via remote access. As a result, such nodes may be manageable using only in-band management techniques making the task of testbed management challenging. As a remedy, we propose the ATMA framework, a framework which enables out-of-band management by deploying a multihop mesh network alongside a testbed to manage the latter. The ATMA mesh network is designed to be self-configuring and therefore can be installed with minimal effort. As an extension of the ATMA framework to multi-hop wireless testbeds, we have designed and developed a suite of tools for the management and monitoring of multi-hop wireless testbeds. This paper presents the design of the ATMA framework, its extensions, and describes our implementation of the framework using low-cost, commodity wireless devices. I

Damon: A distributed architecture for monitoring multi-hop mobile networks

Abstract — With the advent of small form-factor devices, protocol standardization, and robust protocol implementations, multihop mobile networks are witnessing widespread deployment. The monitoring of such networks is crucial for their robust operation. To this end, this paper presents DAMON, a distributed system for monitoring multi-hop mobile networks. DAMON uses agents within the network to monitor network behavior and send collected measurements to data repositories. DAMON's generic architecture supports the monitoring of a wide range of protocol, device, and network parameters. Other key features of DAMON include seamless support for multiple repositories, auto-discovery of sinks by the agents, and resiliency of agents to repository failures. We have implemented DAMON agents that collect statistics on data traffic and the Ad hoc On-demand Distance Vector (AODV) routing protocol. We have used our implementation to monitor an ad hoc network at the 58th Internet Engineering Task Force (IETF) meeting held November 2003 in Minneapolis, MN. In this paper, we describe the architecture of DAMON and report on the performance of the IETF network using monitoring information collected by DAMON. Our network monitoring system is available online for use by other researchers. I

Interference-Aware Channel Assignment in Multi-Radio Wireless Mesh Networks

Abstract — The capacity problem in wireless mesh networks can be alleviated by equipping the mesh routers with multiple radios tuned to non-overlapping channels. However, channel assignment presents a challenge because co-located wireless networks are likely to be tuned to the same channels. The resulting increase in interference can adversely affect performance. This paper presents an interference-aware channel assignment algorithm and protocol for multi-radio wireless mesh networks that address this interference problem. The proposed solution intelligently assigns channels to radios to minimize interference within the mesh network and between the mesh network and co-located wireless networks. It utilizes a novel interference estimation technique implemented at each mesh router. An extension to the conflict graph model, the multi-radio conflict graph, is used to model the interference between the routers. We demonstrate our solution’s practicality through the evaluation of a prototype implementation in a IEEE 802.11 testbed. We also report on an extensive evaluation via simulations. In a sample multi-radio scenario, our solution yields performance gains in excess of 40% compared to a static assignment of channels. I

Rapid Mixing Methods for Exploring the Kinetics of Protein Folding

Information on the time-dependence of molecular species is critical for elucidating reaction mechanisms in chemistry and biology. Rapid flow experiments involving turbulent mixing of two or more solutions continue to be the main source of kinetic information on protein folding and other biochemical processes, such as ligand binding and enzymatic reactions. Recent advances in mixer design and detection methods have opened a new window for exploring conformational changes in proteins on the microsecond time scale. These developments have been especially important for exploring early stages of protein folding