On the Nash-Williams′ Lemma in Graph Reconstruction Theory

A generalization of Nash-Williams′ lemma is proved for the Structure of m-uniform null (m − k)-designs. It is then applied to various graph reconstruction problems. A short combinatorial proof of the edge reconstructibility of digraphs having regular underlying undirected graphs (e.g., tournaments) is given. A type of Nash-Williams′ lemma is conjectured for the vertex reconstruction problem.

Characterization of Birkhoff-James orthogonality

The Birkhoff-James orthogonality is a generalization of Hilbert space orthogonality to Banach spaces. We investigate this notion of orthogonality when the Banach space has more structures. We start by doing so for the Banach space of square matrices moving gradually to all bounded operators on any Hilbert space, then to an arbitrary C*-algebra and finally a Hilbert C*-module.

Community-managed forests and wildlife-friendly agriculture play a subsidiary but not substitutive role to protected areas for the endangered Asian elephant

Global conservation policy is increasingly debating the feasibility of reconciling wildlife conservation and human resource requirements in land uses outside protected areas (PAs). However, there are few quantitative assessments of whether or to what extent these `wildlife-friendly' land uses fulfill a fundamental function of PAs-to separate biodiversity from anthropogenic threats. We distinguish the role of wildlife-friendly land uses as being (a) subsidiary, whereby they augment PAs with secondary habitat, or (b) substitutive, wherein they provide comparable habitat to PAs. We tested our hypotheses by investigating the influence of land use and human presence on space-use intensity of the endangered Asian elephant (Elephas maximus) in a fragmented landscape comprising PAs and wildlife-friendly land uses. We applied multistate occupancy models to spatial data on elephant occurrence to estimate and model the overall probability of elephants using a site, and the conditional probability of high-intensity use given that elephants use a site. The probability of elephants using a site regardless of intensity did not vary between PAs and wildlife-friendly land uses. However, high-intensity use declined with distance to PM, and this effect was accentuated by an increase in village density. Therefore, while wildlife-friendly land uses did play a subsidiary conservation role, their potential to substitute for PAs was offset by a strong human presence. Our findings demonstrate the need to evaluate the role of wildlife-friendly land uses in landscape-scale conservation; for species that have conflicting resource requirements with people, PAs are likely to provide crucial refuge from growing anthropogenic threats. (C) 2014 Elsevier Ltd. All rights reserved.

An estimate of the number of tropical tree species

The high species richness of tropical forests has long been recognized, yet there remains substantial uncertainty regarding the actual number of tropical tree species. Using a pantropical tree inventory database from closed canopy forests, consisting of 657,630 trees belonging to 11,371 species, we use a fitted value of Fisher's alpha and an approximate pantropical stem total to estimate the minimum number of tropical forest tree species to fall between similar to 40,000 and similar to 53,000, i.e., at the high end of previous estimates. Contrary to common assumption, the Indo-Pacific region was found to be as species-rich as the Neotropics, with both regions having a minimum of similar to 19,000-25,000 tree species. Continental Africa is relatively depauperate with a minimum of similar to 4,500-6,000 tree species. Very few species are shared among the African, American, and the Indo-Pacific regions. We provide a methodological framework for estimating species richness in trees that may help refine species richness estimates of tree-dependent taxa.