A Message-Passing Algorithm for Counting Short Cycles in a Graph

A message-passing algorithm for counting short cycles in a graph is presented. For bipartite graphs, which are of particular interest in coding, the algorithm is capable of counting cycles of length g, g +2,..., 2g - 2, where g is the girth of the graph. For a general (non-bipartite) graph, cycles of length g; g + 1, ..., 2g - 1 can be counted. The algorithm is based on performing integer additions and subtractions in the nodes of the graph and passing extrinsic messages to adjacent nodes. The complexity of the proposed algorithm grows as $O(g|E|^2)$, where $|E|$ is the number of edges in the graph. For sparse graphs, the proposed algorithm significantly outperforms the existing algorithms in terms of computational complexity and memory requirements.Comment: Submitted to IEEE Trans. Inform. Theory, April 21, 2010

Quantum clocks observe classical and quantum time dilation

At the intersection of quantum theory and relativity lies the possibility of a clock experiencing a superposition of proper times. We consider quantum clocks constructed from the internal degrees of relativistic particles that move through curved spacetime. The probability that one clock reads a given proper time conditioned on another clock reading a different proper time is derived. From this conditional probability distribution, it is shown that when the center-of-mass of these clocks move in localized momentum wave packets they observe classical time dilation. We then illustrate a quantum correction to the time dilation observed by a clock moving in a superposition of localized momentum wave packets that has the potential to be observed in experiment. The Helstrom-Holevo lower bound is used to derive a proper time-energy/mass uncertainty relation.Comment: Updated to match published versio

Photonic Crystal Laser Accelerator Structures

Photonic crystals have great potential for use as laser-driven accelerator structures. A photonic crystal is a dielectric structure arranged in a periodic geometry. Like a crystalline solid with its electronic band structure, the modes of a photonic crystal lie in a set of allowed photonic bands. Similarly, it is possible for a photonic crystal to exhibit one or more photonic band gaps, with frequencies in the gap unable to propagate in the crystal. Thus photonic crystals can confine an optical mode in an all-dielectric structure, eliminating the need for metals and their characteristic losses at optical frequencies. We discuss several geometries of photonic crystal accelerator structures. Photonic crystal fibers (PCFs) are optical fibers which can confine a speed-of-light optical mode in vacuum. Planar structures, both two- and three-dimensional, can also confine such a mode, and have the additional advantage that they can be manufactured using common microfabrication techniques such as those used for integrated circuits. This allows for a variety of possible materials, so that dielectrics with desirable optical and radiation-hardness properties can be chosen. We discuss examples of simulated photonic crystal structures to demonstrate the scaling laws and trade-offs involved, and touch on potential fabrication processes.Comment: 3 pages, 3 figures; Submitted to Particale Accelerator Conference (PAC 2003), May 12-16, 2003, Portland, Oregon (IEEE

Communication between inertial observers with partially correlated reference frames

In quantum communication protocols the existence of a shared reference frame between two spatially separated parties is normally presumed. However, in many practical situations we are faced with the problem of misaligned reference frames. In this paper, we study communication between two inertial observers who have partial knowledge about the Lorentz transformation that relates their frames of reference. Since every Lorentz transformation can be decomposed into a pure boost followed by a rotation, we begin by analysing the effects on communication when the parties have partial knowledge about the transformation relating their frames, when the transformation is either a rotation or pure boost. This then enables us to investigate how the efficiency of communication is affected due to partially correlated inertial reference frames related by an arbitrary Lorentz transformation. Furthermore, we show how the results of previous studies where reference frames are completely uncorrelated are recovered from our results in appropriate limits.Comment: 9 pages, 3 figures, typos corrected, figures update

All photonic analogue to digital and digital to analogue conversion techniques for digital radio over fibre system applications

Copyright @ 2011 IEEEWideband electronic analogue to digital conversion (ADC) systems have critical problems encountered in high-frequency broadband communication systems that the recent electronic ADCs (EADC) have experienced those such as uncertainty of sampling time. In this paper, an all photonic sampling and quantization ADC and photonic digital to analogue conversion system with six effective number of bits (ENOB) is designed. By using this photonic ADC (PADC), a novel digital radio over fibre link for wireless radio frequency (RF) signal transportation over 20 Km single mode fibre has been designed whose performance is investigated in this paper. In the digital radio over fibre, the dynamic range is independent of the fibre length