On WZ-pairs which prove Ramanujan series

The known WZ-proofs for Ramanujan-type series related to $1/\pi$ gave us the insight to develop a new proof strategy based on the WZ-method. Using this approach we are able to find more generalizations and discover first WZ-proofs for certain series of this type.Comment: 12 pages (preprint) + 1 page (addendum). The addendum (A Maple program) is not in the Journal referenc

Optical Absorption by Indirect Excitons in a Transition Metal Dichalcogenide Double Layer

We calculate the binding energy, transition energies, oscillator strength, and absorption coefficient of indirect excitons in transition metal dichalcogenide (TMDC) double layers separated by an integer number of hexagonal boron nitride (h-BN) monolayers. The absorption factor, a dimensionless quantity which gives the fraction of incoming photons absorbed by the indirect excitons in the double layer, is evaluated. The aforementioned optical quantities are obtained for transitions from the ground state to the first two excited states. All quantities are studied as a function of the interlayer separation, which may be experimentally controlled by varying the number of h-BN monolayers between the TMDC layers. Calculations are performed by using the exciton wave function and eigenenergies obtained for the Keldysh potential. For each material, we choose a combination of the exciton reduced mass and the dielectric screening length from the existing literature which give the largest and the smallest indirect exciton binding energy. These combinations of material parameters provide upper and lower bounds on all quantities presented. Our findings can be examined experimentally via two-photon spectroscopy.Comment: 13 pages, 3 figure

Monitoring and conservation of the critically endangered Alaotran gentle lemur Hapalemur alaotrensis

The Alaotran gentle lemur Hapalemur alaotrensis is a Critically Endangered lemur, which exclusively inhabits the marshes around Lac Alaotra in northeast Madagascar. In the past decades the population of H. alaotrensis has experienced a dramatic decline due to poaching, habitat destruction and degradation. Surveys have been carried out periodically to follow the status of the population. Here we present the results of a survey carried out between May and June 2008 in the southwestern part of the marshes around Alaotra and discuss the key findings derived from the analysis of the data collected. Our study indicates that the probability of detecting the species in an area where it is present is very low and depends on factors that vary in space and time. These results stress the need to account for imperfect detection when monitoring this species, an issue especially relevant when reporting population trends. Our analyses also show that habitat fragmentation is a key determinant of habitat suitability for H. alaotrensis, with fragmented areas of marsh showing low suitability. Finally, our observations and analysis suggest that the protection provided by the local community to H. alaotrensis in Andreba is contributing to the conservation of this Critically Endangered species. This highlights the need to continue working on engaging the local communities in the conservation of the marshes at Lac Alaotra as a critical element to secure the future of H. alaotrensis

How to generate all possible rational Wilf-Zeilberger pairs?

A Wilf--Zeilberger pair $(F, G)$ in the discrete case satisfies the equation $F(n+1, k) - F(n, k) = G(n, k+1) - G(n, k)$. We present a structural description of all possible rational Wilf--Zeilberger pairs and their continuous and mixed analogues.Comment: 17 pages, add the notion of pseudo residues in the differential case, and some related papers in the reference, ACMES special volume in the Fields Institute Communications series, 201

Cost-efficient effort allocation for camera-trap occupancy surveys of mammals

Camera-traps are increasingly used to survey threatened mammal species and are an important tool for estimating habitat occupancy. To date, cost-efficient occupancy survey effort allocation studies have focused on trade-offs between number of sample units (SUs) and sampling occasions, with simplistic accounts of associated costs which do not reflect camera-trap survey realities. Here we examine camera-trap survey costs as a function of the number of SUs, survey duration and camera-traps per SU, linking costs to precision in occupancy estimation. We evaluate survey effort trade-offs for hypothetical species representing different levels of occupancy (?) and detection (p) probability to identify optimal design strategies. We apply our cost function to three threatened species as worked examples. Additionally, we use an extensive camera-trap data set to evaluate independence between multiple camera traps per SU. The optimal number of sampling occasions that result in minimum cost decrease as detection probability increases, irrespective of whether the species is rare (? 0.5). The most expensive survey scenarios occur for elusive (p 10 km2), where the survey is conducted on foot. Minimum survey costs for elusive species can be achieved with fewer sampling occasions and multiple cameras per SU. Multiple camera-traps set within a single SU can yield independent species detections. We provide managers and researchers with guidance for conducting cost-efficient camera-trap occupancy surveys. Efficient use of survey budgets will ultimately contribute to the conservation of threatened and data deficient mammals

The Borwein brothers, Pi and the AGM

We consider some of Jonathan and Peter Borweins' contributions to the high-precision computation of $\pi$ and the elementary functions, with particular reference to their book "Pi and the AGM" (Wiley, 1987). Here "AGM" is the arithmetic-geometric mean of Gauss and Legendre. Because the AGM converges quadratically, it can be combined with fast multiplication algorithms to give fast algorithms for the $n$-bit computation of $\pi$, and more generally the elementary functions. These algorithms run in almost linear time $O(M(n)\log n)$, where $M(n)$ is the time for $n$-bit multiplication. We outline some of the results and algorithms given in Pi and the AGM, and present some related (but new) results. In particular, we improve the published error bounds for some quadratically and quartically convergent algorithms for $\pi$, such as the Gauss-Legendre algorithm. We show that an iteration of the Borwein-Borwein quartic algorithm for $\pi$ is equivalent to two iterations of the Gauss-Legendre quadratic algorithm for $\pi$, in the sense that they produce exactly the same sequence of approximations to $\pi$ if performed using exact arithmetic.Comment: 24 pages, 6 tables. Changed style file and reformatted algorithms in v

Implications of zero-deforestation commitments: forest quality and hunting pressure limit mammal persistence in fragmented tropical landscapes

Zero-deforestation commitments seek to decouple agricultural production and forest loss to improve prospects for biodiversity. However, the effectiveness of methods designed to meet these commitments is poorly understood. In a highly-fragmented tropical landscape dominated by oil palm, we tested the capacity for the High Carbon Stock (HCS) Approach to prioritise forest remnants that sustain mammal diversity. Patches afforded High Priority by HCS protocols (100 ha core area) provided important refuges for IUCN-threatened species and megafauna. However, patch-scale HCS area recommendations conserved only 35% of the mammal community. At least 3,000 ha would be required to retain intact mammal assemblages, with nearly ten times this area needed if hunting pressure was high. While current HCS protocols will safeguard patches capable of sustaining biodiversity, highly-fragmented tropical landscapes typical of zero-deforestation pledges will require thinking beyond the patch, towards strategically configured forest remnants at the landscape-level and enforcing strict controls on hunting

High carbon stock forests provide co-benefits for tropical biodiversity

1. Carbon-based policies provide powerful opportunities to unite tropical forest conservation with climate change mitigation. However, their effectiveness in delivering biodiversity co-benefits is dependent on high levels of biodiversity being found in high carbon areas. Previous studies have focussed solely on the co-benefits associated with Reducing Emissions from Deforestation and forest Degradation (REDD+) over large spatial scales, with few empirically testing carbon-biodiversity correlations at management unit scales appropriate to decision-makers. Yet, in development frontiers, where most biodiversity and carbon loss occurs, carbon-based policies are increasingly driven by commodity certification schemes, which are applied at the concession-level. 2. Working in a typical human-modified landscape in Southeast Asia, we examined the biodiversity value of land prioritised via application of REDD+ or the High Carbon Stock (HCS) Approach, the emerging land-use planning tool for oil palm certification. Carbon stocks were estimated via low- and high-resolution datasets derived from global or local level biomass. Mammalian species richness was predicted using hierarchical Bayesian multi-species occupancy models of camera-trap data from forest and oil palm habitats. 3. At the community level, HCS forest supported comparable mammal diversity to control sites in continuous forest, while lower carbon strata exhibited reduced species occupancy. 4. No association was found between species richness and carbon when the latter was estimated using coarse-resolution data. However, when using high-resolution, field validated biomass data, diversity demonstrated positive relationships with carbon for threatened and disturbance-sensitive species, suggesting sensitivity of co-benefits to carbon data sources and the species considered. 5. Policy implications. Our work confirms the potential for environmental certification and REDD+ to work in tandem with conservation to mitigate agricultural impacts on tropical forest carbon stocks and biodiversity, especially if this directs development to low carbon, low biodiversity areas

Monotone and fast computation of Euler’s constant

Abstract We construct sequences of finite sums ( l ˜ n ) n ≥ 0 $(\tilde{l}_{n})_{n\geq 0}$ and ( u ˜ n ) n ≥ 0 $(\tilde{u}_{n})_{n\geq 0}$ converging increasingly and decreasingly, respectively, to the Euler-Mascheroni constant γ at the geometric rate 1/2. Such sequences are easy to compute and satisfy complete monotonicity-type properties. As a consequence, we obtain an infinite product representation for 2 γ $2^{\gamma }$ converging in a monotone and fast way at the same time. We use a probabilistic approach based on a differentiation formula for the gamma process