arXiv subjects

David Phillips

Publications and source records attributed to David Phillips.

22 records · Page 2Linked to original sources

arXiv2015

Orbital Angular Momentum (OAM) Vertical-Cavity Surface-Emitting Lasers

Harnessing the Orbital Angular Momentum (OAM) of light is an appealing approach to developing photonic technologies for future applications in optical communications and high- dimensional Quantum Key Distributions (QKD). An outstanding challenge to the widespread uptake of the OAM resource is its efficient generation. We design a new device which can directly emit an OAM-carrying light beam. By fabricating micro-scale Spiral Phase Plates (SPPs) within the aperture of a Vertical-Cavity Surface-Emitting Laser (VCSELs), the linearly polarized Gaussian beam emitted by the VCSEL is converted into a beam carrying specific OAM modes and their superposition states with high efficiency and high beam quality. The innovative OAM emitter opens a new horizon in the field of OAM-based optical and quantum communications, especially for short reach data interconnects and Quantum Key Distribution (QKD).

physics.optics↗

arXiv2014

Algorithm and Complexity for a Network Assortativity Measure

We show that finding a graph realization with the minimum Randić index for a given degree sequence is solvable in polynomial time by formulating the problem as a minimum weight perfect b-matching problem. However, the realization found via this reduction is not guaranteed to be connected. Approximating the minimum weight b-matching problem subject to a connectivity constraint is shown to be NP-Hard. For instances in which the optimal solution to the minimum Randić index problem is not connected, we describe a heuristic to connect the graph using pairwise edge exchanges that preserves the degree sequence. In our computational experiments, the heuristic performs well and the Randić index of the realization after our heuristic is within 3% of the unconstrained optimal value on average. Although we focus on minimizing the Randić index, our results extend to maximizing the Randić index as well. Applications of the Randić index to synchronization of neuronal networks controlling respiration in mammals and to normalizing cortical thickness networks in diagnosing individuals with dementia are provided.

math.CO↗

arXiv2014

Explorations of edge-weighted Cayley graphs and p-ary bent functions

Let f be a function mapping an n dimensional vector space over GF(p) to GF(p). When p is 2, Bernasconi et al. have shown that there is a correspondence between certain properties of f (e.g., if it is bent) and properties of its associated Cayley graph. Analogously, but much earlier, Dillon showed that f is bent if and only if the "level curves" of f had certain combinatorial properties (again, only when p is 2). The attempt is to investigate an analogous theory when p is greater than 2 using the (apparently new) combinatorial concept of a weighted partial difference set. More precisely, we try to investigate which properties of the Cayley graph of f can be characterized in terms of function-theoretic properties of f, and which function-theoretic properties of f correspond to combinatorial properties of the set of "level curves", i.e., the inverse map of f. While the natural generalizations of the Bernasconi correspondence and Dillon correspondence are not true in general, using extensive computations, we are able to determine a classification in some small cases. Our main conjecture is Conjecture 67.

math.CO↗

arXiv2013

An Earth-sized planet with an Earth-like density

Kepler-78 (KIC 8435766) was identified by Sanchis-Ojeda et al. (2013) as harbouring a transiting planet of 1.16 times the size of the Earth and an orbital period of only 8.5 hours. While the exquisite Kepler photometry was able to determine its radius and period, the mass of the planet (and thus its mean density) remained unconstrained in the absence of precise radial-velocity measurements. Here we present an accurate mass measurement of Kepler-78b using the HARPS-N spectrograph, recently installed on the Telescopio Nazionale Galileo (INAF) at the Roque de los Muchachos Observatory, La Palma, Spain. These new data yield a mass of 1.86 Earth masses. The resulting mean density of the planet is 5.57 grams per cubic centimetre, which is similar to that of the Earth and implies a composition of iron and rock. Kepler-78b, which orbits a Sun-like star called Kepler 78 located in the Cygnus constellation at a distance of about 400 light years from us, is now the smallest exoplanet for which both the mass and radius are known accurately.

astro-ph.EP↗