Aw A.J.,Raffles Science Institute
Designs, Codes, and Cryptography | Year: 2014
The covering radius problem is a question in coding theory concerned with finding the minimum radius r such that, given a code that is a subset of an underlying metric space, balls of radius r over its code words cover the entire metric space. Klapper (IEEE Trans. Inform. Theory 43:1372-1377, 1997) introduced a code parameter, called the multicovering radius, which is a generalization of the covering radius. In this paper, we introduce an analogue of the multicovering radius for permutation codes (Des. Codes Cryptogr. 41:79-86, cf. 2006) and for codes of perfect matchings (cf. 2012). We apply probabilistic tools to give some lower bounds on the multicovering radii of these codes. In the process of obtaining these results, we also correct an error in the proof of the lower bound of the covering radius that appeared in (Des. Codes Cryptogr. 41:79-86, cf. 2006). We conclude with a discussion of the multicovering radius problem in an even more general context, which offers room for further research. © 2012 Springer Science+Business Media New York.
Chan J.T.,Raffles Science Institute |
Lee J.L.,Princeton University |
Tjeng V.,Massachusetts Institute of Technology |
Yeo Y.,National University of Singapore |
Tan G.,Raffles Science Institute
European Journal of Physics | Year: 2014
The International Young Physicists' Tournament (IYPT) is a worldwide annual competition for high-school students. This paper is adapted from the solution to problem 8, Jet and Film, as presented by the Singapore Team at the 26th IYPT, Taipei, Taiwan. The impact of liquid microjets on stable soap films was investigated. Two steady regimes were observed: refraction (where the microjet penetrates the soap film and is deflected) and absorption (where the microjet merges with the soap film and forms vertical undulating patterns on the soap film surface). This phenomenon has potential applications in controlling the trajectory of a liquid microjet in air. Although Kirstetter et al (2012) investigated this interaction by using the same liquid for both the microjet and the soap film, this paper extends their work by using different liquids for the microjet and the soap film. In addition, the need for a small-angle approximation of Snell's law is removed for the refraction regime, and an alternative expression is proposed for the force exerted by the soap film on the microjet in the absorption regime that accounts for the dependence of the wavelength of the undulating patterns on the angle of incidence of the microjet on the soap film. Empirical data support these improved theoretical predictions. © 2014 IOP Publishing Ltd.
Chan C.S-Y.,Raffles Science Institute |
Cheng J.,Raffles Science Institute |
Loh J.Y.Q.,Raffles Science Institute |
Tan E.,Raffles Science Institute |
And 2 more authors.
Raffles Bulletin of Zoology | Year: 2012
While ants have been commonly associated with rattans, there is no known documentation of this ant-plant interaction on a local context despite the presence of several rattan species in Singapore. With Singapore experiencing rapid urbanisation and inevitable deforestation, and that most of the rattan species are now endangered and the reality of co-extinctions a high possibility, documentation of rattans and related insects is urgently required. In this paper we observed the interactions between ants and the two rattan species, Korthalsia echinometra and Korthalsia rostrata (subfamily Calamoideae, Tribe Calameae, Korthalsiinae) by documenting the ants and other insects that resided within the rattan ocreae. These observations were conducted at Bukit Timah Nature Reserve, MacRitchie Reservoir, and Nee Soon Swamp Forest in Singapore. We identified the ant species that was associated with K. echinometra to be Iridomyrmex sp. (n = 5), while those associated with K. rostrata were Dolichoderus sp. (n = 4) and Philidris sp. (n = 1). This suggests the possibility of a genus-specific relationship between K. echinometra and the ant species Iridomyrmex sp., and a non-specific relationship with ants for K. rostrata within Singapore. Our observations also suggest the possibility of an ant-hemipteran association between Iridomyrmex sp. and the aphid Cerataphis orchidearum aptera that was found in the ocrea of K. echinometra along with a larval brood of Iridomyrmex sp. We suggest that more research is warranted before any postulations can be accurately drawn. © National University of Singapore.