How long is enough to detect terrestrial animals? Estimating the minimum trapping effort on camera traps

Camera traps is an important wildlife inventory tool for estimating species diversity at a site. Knowing what minimum trapping effort is needed to detect target species is also important to designing efficient studies, considering both the number of camera locations, and survey length. Here, we take advantage of a two-year camera trapping dataset from a small (24-ha) study plot in Gutianshan National Nature Reserve, eastern China to estimate the minimum trapping effort actually needed to sample the wildlife community. We also evaluated the relative value of adding new camera sites or running cameras for a longer period at one site. The full dataset includes 1727 independent photographs captured during 13,824 camera days, documenting 10 resident terrestrial species of birds and mammals. Our rarefaction analysis shows that a minimum of 931 camera days would be needed to detect the resident species sufficiently in the plot, and c. 8700 camera days to detect all 10 resident species. In terms of detecting a diversity of species, the optimal sampling period for one camera site was c. 40, or long enough to record about 20 independent photographs. Our analysis of evaluating the increasing number of additional camera sites shows that rotating cameras to new sites would be more efficient for measuring species richness than leaving cameras at fewer sites for a longer period

Smooth Solutions of a Nonhomogeneous Iterative Functional Differential Equation with Variable Coefficients

AbstractUsing the fixed point theorems of Banach and Schauder, in this paper we discuss the existence, uniqueness, and stability of smooth solutions of a nonhomogeneous iterative functional differential equation with variable coefficients

Thermal Decomposition of Condensed-Phase Nitromethane from Molecular Dynamics from ReaxFF Reactive Dynamics

We studied the thermal decomposition and subsequent reaction of the energetic material nitromethane (CH_3NO_2) using molecular dynamics with ReaxFF, a first principles-based reactive force field. We characterize the chemistry of liquid and solid nitromethane at high temperatures (2000−3000 K) and density 1.97 g/cm^3 for times up to 200 ps. At T = 3000 K the first reaction in the decomposition of nitromethane is an intermolecular proton transfer leading to CH_3NOOH and CH_2NO_2. For lower temperatures (T = 2500 and 2000 K) the first reaction during decomposition is often an isomerization reaction involving the scission of the C−N bond the formation of a C−O bond to form methyl nitrate (CH_3ONO). Also at very early times we observe intramolecular proton transfer events. The main product of these reactions is H_2O which starts forming following those initiation steps. The appearance of H_2O marks the beginning of the exothermic chemistry. Recent quantum-mechanics-based molecular dynamics simulations on the chemical reactions and time scales for decomposition of a crystalline sample heated to T = 3000 K for a few picoseconds are in excellent agreement with our results, providing an important, direct validation of ReaxFF

Analytic Solutions of an Iterative Functional Differential Equation

AbstractThis paper is concerned with an iterative functional differential equation x′(x[r](z))=c0z+c1x(z)+c2x(x(z))+⋯+cmx[m](z), where r and m are nonnegative integers, x[0](z)=z,x[1](z)=x(z),x[3](z)=x(x(x(z))), etc. are the iterates of the function x(z), and ∑j=0mcj≠0. By constructing a convergent power series solution y(z) of a companion equation of the form αy′(αr+1z)=y′(αrz)∑j=0mcjy(αjz), analytic solutions of the form y(αy−1(z)) for the original differential equation are obtained

Overarching framework between Gaussian quantum discord and Gaussian quantum illumination

We cast the problem of illuminating an object in a noisy environment into a communication protocol. A probe is sent into the environment, and the presence or absence of the object constitutes a signal encoded on the probe. The probe is then measured to decode the signal. We calculate the Holevo information and bounds to the accessible information between the encoded and received signal with two different Gaussian probes---an Einstein-Podolsky-Rosen (EPR) state and a coherent state. We also evaluate the Gaussian discord consumed during the encoding process with the EPR probe. We find that the Holevo quantum advantage, defined as the difference between the Holevo information obtained from the EPR and coherent state probes, is approximately equal to the discord consumed. These quantities become exact in the typical illumination regime of low object reflectivity and low probe energy. Hence we show that discord is the resource responsible for the quantum advantage in Gaussian quantum illumination.Comment: 12 pages, 8 figure