CamTrapAsia: A dataset of tropical forest vertebrate communities from 239 camera trapping studies.

Information on tropical Asian vertebrates has traditionally been sparse, particularly when it comes to cryptic species inhabiting the dense forests of the region. Vertebrate populations are declining globally due to land-use change and hunting, the latter frequently referred as "defaunation." This is especially true in tropical Asia where there is extensive land-use change and high human densities. Robust monitoring requires that large volumes of vertebrate population data be made available for use by the scientific and applied communities. Camera traps have emerged as an effective, non-invasive, widespread, and common approach to surveying vertebrates in their natural habitats. However, camera-derived datasets remain scattered across a wide array of sources, including published scientific literature, gray literature, and unpublished works, making it challenging for researchers to harness the full potential of cameras for ecology, conservation, and management. In response, we collated and standardized observations from 239 camera trap studies conducted in tropical Asia. There were 278,260 independent records of 371 distinct species, comprising 232 mammals, 132 birds, and seven reptiles. The total trapping effort accumulated in this data paper consisted of 876,606 trap nights, distributed among Indonesia, Singapore, Malaysia, Bhutan, Thailand, Myanmar, Cambodia, Laos, Vietnam, Nepal, and far eastern India. The relatively standardized deployment methods in the region provide a consistent, reliable, and rich count data set relative to other large-scale pressence-only data sets, such as the Global Biodiversity Information Facility (GBIF) or citizen science repositories (e.g., iNaturalist), and is thus most similar to eBird. To facilitate the use of these data, we also provide mammalian species trait information and 13 environmental covariates calculated at three spatial scales around the camera survey centroids (within 10-, 20-, and 30-km buffers). We will update the dataset to include broader coverage of temperate Asia and add newer surveys and covariates as they become available. This dataset unlocks immense opportunities for single-species ecological or conservation studies as well as applied ecology, community ecology, and macroecology investigations. The data are fully available to the public for utilization and research. Please cite this data paper when utilizing the data.

A temporally relaxed theory of physically or chemically non-equilibrium solute transport in heterogeneous porous media.

Groundwater constitutes a critical component in providing fresh water for various human endeavors. Never-theless, its susceptibility to contamination by pollutants represents a significant challenge. A comprehensive understanding of the dynamics of solute transport in groundwater and soils is essential for predicting the spatial and temporal distribution of these contaminants. Presently, conventional models such as the mobile-immobile (MIM) model and the rate-limited sorption (RLS) model are widely employed to describe the non-Fickian behavior of solute transport. In this research, we present a novel approach to solute transport that is founded on the temporally relaxed theory of Fick's Law. Our methodology introduces two relaxation times to account for solute particle collisions and attachment, leading to the derivation of a new advection-dispersion equation. Our findings indicate that the relaxation times possess similar properties to the transport parameters in the MIM and RLS models, and our solution can be applied to accurately predict transport parameters from soil column experiments. Additionally, we discovered that the relaxation times are proportional to the magnitude of Peclet number. This innovative approach provides a deeper insight into solute transport and its impact on groundwater contamination.

Statistical modelling of goalkicking performance in the Australian Football League.

OBJECTIVES: Australian football goal kicking is vital to team success, but its study is limited. Develop and apply Bayesian models incorporating temporal, spatial and situational variables to predict shot outcomes. The models aim to (i) rank players on their goal kicking and (ii) create clusters of statistically similar players and rank these clusters to provide generalised recommendations about player types. DESIGN: Retrospective longitudinal study with goal kicking data from three seasons, 2018-2020, 576 official Australian Football League matches, containing 26,818 attempts at goal from 778 players. METHODS: The Bayesian ordinal regression model enables descriptive analysis of goal kicking performance. The models include spatial variables of distance and kick angle, situational variables of shot type and player or cluster with interaction terms. Alternative models included situational variables of weather and player characteristics, spatial variables of stadium location and temporal variables of time and quarter. Approximate leave-one-out cross validation was used to test the model. RESULTS: Overall goal rate of 47% (12,600), behind rate of 35% (9373) with misses the remaining 18% (4845). Accuracy of both player and cluster model achieved 0.51 against an uninformed (predict goal) model result of 0.47. The models allow for analysis of goal kicking accuracy by distance and angle and analysis of player and player-type performance. CONCLUSIONS: While credible intervals for all players for set shots and general play were relatively large, some 95% credible intervals excluded zero. Therefore, it may be concluded that some players' goal kicking skill can be quantified and differentiated from other players.

A stochastic mathematical model of 4D tumour spheroids with real-time fluorescent cell cycle labelling.

In vitro tumour spheroids have been used to study avascular tumour growth and drug design for over 50 years. Tumour spheroids exhibit heterogeneity within the growing population that is thought to be related to spatial and temporal differences in nutrient availability. The recent development of real-time fluorescent cell cycle imaging allows us to identify the position and cell cycle status of individual cells within the growing spheroid, giving rise to the notion of a four-dimensional (4D) tumour spheroid. We develop the first stochastic individual-based model (IBM) of a 4D tumour spheroid and show that IBM simulation data compares well with experimental data using a primary human melanoma cell line. The IBM provides quantitative information about nutrient availability within the spheroid, which is important because it is difficult to measure these data experimentally.

Profile likelihood analysis for a stochastic model of diffusion in heterogeneous media.

We compute profile likelihoods for a stochastic model of diffusive transport motivated by experimental observations of heat conduction in layered skin tissues. This process is modelled as a random walk in a layered one-dimensional material, where each layer has a distinct particle hopping rate. Particles are released at some location, and the duration of time taken for each particle to reach an absorbing boundary is recorded. To explore whether these data can be used to identify the hopping rates in each layer, we compute various profile likelihoods using two methods: first, an exact likelihood is evaluated using a relatively expensive Markov chain approach; and, second, we form an approximate likelihood by assuming the distribution of exit times is given by a Gamma distribution whose first two moments match the moments from the continuum limit description of the stochastic model. Using the exact and approximate likelihoods, we construct various profile likelihoods for a range of problems. In cases where parameter values are not identifiable, we make progress by re-interpreting those data with a reduced model with a smaller number of layers.

Finite transition times for multispecies diffusion in heterogeneous media coupled via first-order reaction networks.

Calculating how long a coupled multispecies reactive-diffusive transport process in a heterogeneous medium takes to effectively reach steady state is important in many applications. In this paper, we show how the time required for such processes to transition to within a small specified tolerance of steady state can be calculated accurately without having to solve the governing time-dependent model equations. Our approach is valid for general first-order reaction networks and an arbitrary number of species. Three numerical examples are presented to confirm the analysis and investigate the efficacy of the approach. A key finding is that for sequential reactions our approach works better provided the two smallest reaction rates are well separated.

Diffusion in heterogeneous discs and spheres: New closed-form expressions for exit times and homogenization formulas.

Mathematical models of diffusive transport underpin our understanding of chemical, biochemical, and biological transport phenomena. Analysis of such models often focuses on relatively simple geometries and deals with diffusion through highly idealized homogeneous media. In contrast, practical applications of diffusive transport theory inevitably involve dealing with more complicated geometries as well as dealing with heterogeneous media. One of the most fundamental properties of diffusive transport is the concept of mean particle lifetime or mean exit time, which are particular applications of the concept of first passage time and provide the mean time required for a diffusing particle to reach an absorbing boundary. Most formal analysis of mean particle lifetime applies to relatively simple geometries, often with homogeneous (spatially invariant) material properties. In this work, we present a general framework that provides exact mathematical insight into the mean particle lifetime, and higher moments of particle lifetime, for point particles diffusing in heterogeneous discs and spheres with radial symmetry. Our analysis applies to geometries with an arbitrary number and arrangement of distinct layers, where transport in each layer is characterized by a distinct diffusivity. We obtain exact closed-form expressions for the mean particle lifetime for a diffusing particle released at an arbitrary location, and we generalize these results to give exact, closed-form expressions for any higher-order moment of particle lifetime for a range of different boundary conditions. Finally, using these results, we construct new homogenization formulas that provide an accurate simplified description of diffusion through heterogeneous discs and spheres.

Drug delivery from microcapsules: How can we estimate the release time?

Predicting the release performance of a drug delivery device is an important challenge in pharmaceutics and biomedical science. In this paper, we consider a multi-layer diffusion model of drug release from a composite spherical microcapsule into an external surrounding medium. Based on this model, we present two approaches for estimating the release time, i.e. the time required for the drug-filled capsule to be depleted. Both approaches make use of temporal moments of the drug concentration at the centre of the capsule, which provide useful insight into the timescale of the process and can be computed exactly without explicit calculation of the full transient solution of the multi-layer diffusion model. The first approach, which uses the zeroth and first temporal moments only, provides a crude approximation of the release time taking the form of a simple algebraic expression involving the various parameters in the model (e.g. layer diffusivities, mass transfer coefficients, partition coefficients) while the second approach yields an asymptotic estimate of the release time that depends on consecutive higher moments. Through several test cases, we show that both approaches provide a computationally-cheap and useful tool to quantify the release time of composite microcapsule configurations.

New homogenization approaches for stochastic transport through heterogeneous media.

The diffusion of molecules in complex intracellular environments can be strongly influenced by spatial heterogeneity and stochasticity. A key challenge when modelling such processes using stochastic random walk frameworks is that negative jump coefficients can arise when transport operators are discretized on heterogeneous domains. Often this is dealt with through homogenization approximations by replacing the heterogeneous medium with an effective homogeneous medium. In this work, we present a new class of homogenization approximations by considering a stochastic diffusive transport model on a one-dimensional domain containing an arbitrary number of layers with different jump rates. We derive closed form solutions for the kth moment of particle lifetime, carefully explaining how to deal with the internal interfaces between layers. These general tools allow us to derive simple formulae for the effective transport coefficients, leading to significant generalisations of previous homogenization approaches. Here, we find that different jump rates in the layers give rise to a net bias, leading to a non-zero advection, for the entire homogenized system. Example calculations show that our generalized approach can lead to very different outcomes than traditional approaches, thereby having the potential to significantly affect simulation studies that use homogenization approximations.

Advection improves homogenized models of continuum diffusion in one-dimensional heterogeneous media.

We propose an alternative homogenization method for one-dimensional continuum diffusion models with spatially variable (heterogeneous) diffusivity. Our method, which extends recent work on stochastic diffusion, assumes the constant-coefficient homogenized equation takes the form of an advection-diffusion equation with effective (diffusivity and velocity) coefficients. To calculate the effective coefficients, our approach involves solving two uncoupled boundary value problems over the heterogeneous medium and leads to coefficients depending on the spatially varying diffusivity (as usual) as well as the boundary conditions imposed on the heterogeneous model. Computational experiments comparing our advection-diffusion homogenized model to the standard homogenized model demonstrate that including an advection term in the homogenized equation leads to improved approximations of the solution of the original heterogeneous model.

Characteristic time scales for diffusion processes through layers and across interfaces.

This paper presents a simple tool for characterizing the time scale for continuum diffusion processes through layered heterogeneous media. This mathematical problem is motivated by several practical applications such as heat transport in composite materials, flow in layered aquifers, and drug diffusion through the layers of the skin. In such processes, the physical properties of the medium vary across layers and internal boundary conditions apply at the interfaces between adjacent layers. To characterize the time scale, we use the concept of mean action time, which provides the mean time scale at each position in the medium by utilizing the fact that the transition of the transient solution of the underlying partial differential equation model, from initial state to steady state, can be represented as a cumulative distribution function of time. Using this concept, we define the characteristic time scale for a multilayer diffusion process as the maximum value of the mean action time across the layered medium. For given initial conditions and internal and external boundary conditions, this approach leads to simple algebraic expressions for characterizing the time scale that depend on the physical and geometrical properties of the medium, such as the diffusivities and lengths of the layers. Numerical examples demonstrate that these expressions provide useful insight into explaining how the parameters in the model affect the time it takes for a multilayer diffusion process to reach steady state.

Modelling mass diffusion for a multi-layer sphere immersed in a semi-infinite medium: application to drug delivery.

We present a general mechanistic model of mass diffusion for a composite sphere placed in a large ambient medium. The multi-layer problem is described by a system of diffusion equations coupled via interlayer boundary conditions such as those imposing a finite mass resistance at the external surface of the sphere. While the work is applicable to the generic problem of heat or mass transfer in a multi-layer sphere, the analysis and results are presented in the context of drug kinetics for desorbing and absorbing spherical microcapsules. We derive an analytical solution for the concentration in the sphere and in the surrounding medium that avoids any artificial truncation at a finite distance. The closed-form solution in each concentric layer is expressed in terms of a suitably-defined inverse Laplace transform that can be evaluated numerically. Concentration profiles and drug mass curves in the spherical layers and in the external environment are presented and the dependency of the solution on the mass transfer coefficient at the surface of the sphere analyzed.

Quantifying the efficacy of first aid treatments for burn injuries using mathematical modelling and in vivo porcine experiments.

First aid treatment of burns reduces scarring and improves healing. We quantify the efficacy of first aid treatments using a mathematical model to describe data from a series of in vivo porcine experiments. We study burn injuries that are subject to various first aid treatments. The treatments vary in the temperature and duration. Calibrating the mathematical model to the experimental data provides estimates of the thermal diffusivity, the rate at which thermal energy is lost to the blood, and the heat transfer coefficient controlling the loss of thermal energy at the interface of the fat and muscle. A limitation of working with in vivo experiments is the difficulty of measuring variations in temperature across the tissue layers. This limitation motivates us to use a simple, single layer mathematical model. Using the solution of the calibrated mathematical model we visualise the temperature distribution across the thickness of the tissue. With this information we propose a novel measure of the potential for tissue damage. This measure quantifies two important factors: (i) the volume of tissue that rises above the threshold temperature associated with the accumulation of tissue damage; and (ii) the duration of time that the tissue remains above this threshold temperature.

Calculating how long it takes for a diffusion process to effectively reach steady state without computing the transient solution.

Mathematically, it takes an infinite amount of time for the transient solution of a diffusion equation to transition from initial to steady state. Calculating a finite transition time, defined as the time required for the transient solution to transition to within a small prescribed tolerance of the steady-state solution, is much more useful in practice. In this paper, we study estimates of finite transition times that avoid explicit calculation of the transient solution by using the property that the transition to steady state defines a cumulative distribution function when time is treated as a random variable. In total, three approaches are studied: (i) mean action time, (ii) mean plus one standard deviation of action time, and (iii) an approach we derive by approximating the large time asymptotic behavior of the cumulative distribution function. Our approach leads to a simple formula for calculating the finite transition time that depends on the prescribed tolerance δ and the (k-1)th and kth moments (k≥1) of the distribution. Results comparing exact and approximate finite transition times lead to two key findings. First, although the first two approaches are useful at characterizing the time scale of the transition, they do not provide accurate estimates for diffusion processes. Second, the new approach allows one to calculate finite transition times accurate to effectively any number of significant digits using only the moments with the accuracy increasing as the index k is increased.