Quantum Barnes function as the partition function of the resolved conifold

We suggest a new strategy for proving large $N$ duality by interpreting Gromov-Witten, Donaldson-Thomas and Chern-Simons invariants of a Calabi-Yau threefold as different characterizations of the same holomorphic function. For the resolved conifold this function turns out to be the quantum Barnes function, a natural $q$-deformation of the classical one that in its turn generalizes Euler's gamma function. Our reasoning is based on a new formula for this function that expresses it as a graded product of $q$-shifted multifactorials.Comment: 47 pages, 7 figure

Invasion waves in the presence of a mutualist

This paper studies invasion waves in the diffusive Competitor-Competitor-Mutualist model generalizing the 2-species Lotka-Volterra model studied by Weinberger et al. The mutualist may benefit the invading or the resident species producing two different types of invasions. Sufficient conditions for linear determinacy are derived in both cases, and when they hold, explicit formulas for linear spreading speeds of the invasions are obtained by linearizing the model. While in the first case the linear speed is increased by the mutualist, it is unaffected in the second case. Mathematical methods are based on converting the model into a cooperative reaction-diffusion system.Comment: 21 pages, 4 figure

From Golden to Unimodular Cryptography

We introduce a natural generalization of the golden cryptography, which uses general unimodular matrices in place of the traditional Q-matrices, and prove that it preserves the original error correction properties of the encryption. Moreover, the additional parameters involved in generating the coding matrices make this unimodular cryptography resilient to the chosen plaintext attacks that worked against the golden cryptography. Finally, we show that even the golden cryptography is generally unable to correct double errors in the same row of the ciphertext matrix, and offer an additional check number which, if transmitted, allows for the correction.Comment: 20 pages, no figure

Habitat, abundance and productivity of the Asian Houbara Chlamydotis macqueenii in Uzbekistan

For a species threatened with exploitation, before embarking on ex situ measures such as population reinforcement through captive breeding, it is important to explore potential in situ measures that could be used to mitigate species off-take by supporting breeding productivity of wild populations. Asian houbara Chlamydotis macqueenii is a globally threatened bird, with continuing declines across Central Asia, mainly due to unregulated hunting and trapping during migration and in winter. This research aims to improve understanding of the breeding season biology of the Asian houbara migratory populations in Central Asia to inform in-situ conservation of the species. Spring fieldwork during 2012–2015 involved distance sampling, nest monitoring and habitat sampling across 14,500 km2 of the Kyzylkum Desert in Uzbekistan. Contrary to expectations, there appeared to be no negative landscape-scale association between livestock density and the abundance of male houbara, and no grazing effect on desert shrub vegetation. Habitat characteristics selected by males at the landscape scale were more likely to maximise visibility of their displays, with higher male abundance in lower shrub vegetation, on gravelly substrate and flatter terrain. The first robust estimate of local male density stratified by different habitats and an estimate of regional numbers were obtained. Houbara nesting success was unaffected by variation in shrub species composition or livestock density, but nests placed within taller vegetation experienced greater success. Satellite-tracking revealed high site-fidelity of males to their display sites and intra-seasonal fidelity of females to breeding areas. During post-breeding dispersal adult birds were found to be using completely different, more productive in terms of vegetation, areas outside their breeding season range. In conclusion I discuss potential implications of key findings for the conservation and management of the Asian houbara population in the Kyzylkum, and their potential relevance to other houbara populations and study systems, and suggest priorities for further research