Efficient Batch Update of Unique Identifiers in a Distributed Hash Table for Resources in a Mobile Host

Resources in a distributed system can be identified using identifiers based on random numbers. When using a distributed hash table to resolve such identifiers to network locations, the straightforward approach is to store the network location directly in the hash table entry associated with an identifier. When a mobile host contains a large number of resources, this requires that all of the associated hash table entries must be updated when its network address changes. We propose an alternative approach where we store a host identifier in the entry associated with a resource identifier and the actual network address of the host in a separate host entry. This can drastically reduce the time required for updating the distributed hash table when a mobile host changes its network address. We also investigate under which circumstances our approach should or should not be used. We evaluate and confirm the usefulness of our approach with experiments run on top of OpenDHT.Comment: To be presented at the 2010 International Workshop on Cloud Computing, Applications and Technologie

Rational torsion points on Jacobians of modular curves

Let $p$ be a prime greater than 3. Consider the modular curve $X_0(3p)$ over $\mathbb{Q}$ and its Jacobian variety $J_0(3p)$ over $\mathbb{Q}$. Let $\mathcal{T}(3p)$ and $\mathcal{C}(3p)$ be the group of rational torsion points on $J_0(3p)$ and the cuspidal group of $J_0(3p)$, respectively. We prove that the $3$-primary subgroups of $\mathcal{T}(3p)$ and $\mathcal{C}(3p)$ coincide unless $p\equiv 1 \pmod 9$ and $3^{\frac{p-1}{3}} \equiv 1 \!\pmod {p}$

Precisely Analyzing Loss in Interface Adapter Chains

Interface adaptation allows code written for one interface to be used with a software component with another interface. When multiple adapters are chained together to make certain adaptations possible, we need a way to analyze how well the adaptation is done in case there are more than one chains that can be used. We introduce an approach to precisely analyzing the loss in an interface adapter chain using a simple form of abstract interpretation.Comment: 12 pages, 1 figure. Submitted to IASTED SE 201

Relativistic Effect in Galaxy Clustering

The general relativistic description of galaxy clustering provides a complete and unified treatment of all the effects in galaxy clustering such as the redshift-space distortion, gravitational lensing, Sachs-Wolfe effects, and their relativistic effects. In particular, the relativistic description resolves the gauge issues in the standard Newtonian description of galaxy clustering by providing the gauge-invariant expression for the observed galaxy number density. The relativistic effect in galaxy clustering is significant on large scales, in which dark energy models or alternative theories of modified gravity deviate from general relativity. In this paper, we review the relativistic effect in galaxy clustering by providing a pedagogical derivation of the relativistic formula and by computing the observed galaxy two-point statistics. The relativistic description of galaxy clustering is an essential tool for testing general relativity and probing the early Universe on large scales in the era of precision cosmology.Comment: 21 pages, no figures. Invited review article, accepted for publication in Classical and Quantum Gravity focus issue on "Relativistic Effects in Cosmology", edited by Kazuya Koyam

Determining Rights to Resell: Kirtsaeng v. John Wiley & Sons

This commentary previews an upcoming Supreme Court case, Kirtsaeng v. John Wiley & Sons, in which the Court will decide whether the first sale doctrine applies to foreign-made copies. Broadly, the case will determine the ability of manufacturers to control the distribution of foreign-made copies once they have been sold and asks the Court to resolve a circuit split on the correct interpretation of the relevant provisions of the Copyright Act