Detecting fish in underwater video using the EM algorithm

We consider the problem of detecting fish in underwater video. We adopt a modeling framework, where the shape of each fish is assumed to be multivariate Gaussian. Mixture modeling is used to classify noise and varying numbers of fish. The mixture parameters are estimated using an EM algorithm that incorporates an Akaike information criterion to simultaneously estimate the number of components in the mixture. In addition, the algorithm does not require careful initialization

Phase Transition in a Three-States Reaction-Diffusion System

A one-dimensional reaction-diffusion model consisting of two species of particles and vacancies on a ring is introduced. The number of particles in one species is conserved while in the other species it can fluctuate because of creation and annihilation of particles. It has been shown that the model undergoes a continuous phase transition from a phase where the currents of different species of particles are equal to another phase in which they are different. The total density of particles and also their currents in each phase are calculated exactly.Comment: 6 page

A spatio-temporal modelling framework for assessing the impact of weed management technologies on the spread of herbicide resistance

This paper presents a spatio-temporal modelling framework for predicting the spread of herbicide resistance. It includes a model of the population dynamics of weeds growing in competition with crops, a polygenic model of the development of herbicide resistance, and gene transfer by means of pollen and seed movement. The framework is used to predict the long-term spread of resistant weeds given different integrated weed management choices combining tillage and herbicide treatments, and seed capture at harvest. The model’s predictions will be used to devise management options that minimise the spread of herbicide resistant weeds

Long-term hindcasts of wheat yield in fields using remotely sensed phenology, climate data and machine learning

Satellite remote sensing offers a cost-effective means of generating long-term hindcasts of yield that can be used to understand how yield varies in time and space. This study investigated the use of remotely sensed phenology, climate data and machine learning for estimating yield at a resolution suitable for optimising crop management in fields. We used spatially weighted growth curve estimation to identify the timing of phenological events from sequences of Landsat NDVI and derive phenological and seasonal climate metrics. Using data from a 17,000 ha study area, we investigated the relationships between the metrics and yield over 17 years from 2003 to 2019. We compared six statistical and machine learning models for estimating yield: multiple linear regression, mixed effects models, generalised additive models, random forests, support vector regression using radial basis functions and deep learning neural networks. We used a 50-50 train-test split on paddock-years where 50% of paddock-year combinations were randomly selected and used to train each model and the remaining 50% of paddock-years were used to assess the model accuracy. Using only phenological metrics, accuracy was highest using a linear mixed model with a random effect that allowed the relationship between integrated NDVI and yield to vary by year (R2 = 0.67, MAE = 0.25 t ha−1, RMSE = 0.33 t ha−1, NRMSE = 0.25). We quantified the improvements in accuracy when seasonal climate metrics were also used as predictors. We identified two optimal models using the combined phenological and seasonal climate metrics: support vector regression and deep learning models (R2 = 0.68, MAE = 0.25 t ha−1, RMSE = 0.32 t ha−1, NRMSE = 0.25). While the linear mixed model using only phenological metrics performed similarly to the nonlinear models that are also seasonal climate metrics, the nonlinear models can be more easily generalised to estimate yield in years for which training data are unavailable. We conclude that long-term hindcasts of wheat yield in fields, at 30 m spatial resolution, can be produced using remotely sensed phenology from Landsat NDVI, climate data and machine learning

Fast dispersal simulation using bivariate quantiles

Spatial-temporal models of the spread of invasive species can require dispersal of large numbers of individuals from many locations at recurrent times, making them slow to execute. We present a fast algorithm for simulating dispersal of large numbers of individuals. The algorithm is stochastic and can be applied using any bivariate probability density function as the dispersal kernel. It achieves computational efficiency while still allowing the simulation of rare and important long-distance dispersals by combining different approaches for within and outside the tail of the dispersal kernel. The tail is specified by a given bivariate quantile, where the q-th bivariate quantile is defined to be the contour of equiprobability within which a proportion 0< q <1 of dispersing individuals will settle. We provide a method for finding bivariate quantiles that can be applied to any bivariate dispersal kernel derived from independent densities for distance and direction of dispersal. To illustrate this approach, we show how the Cauchy distribution can be used to produce isotropic and anisotropic bivariate dispersal kernels by assuming that the direction of dispersal is either random or takes a von Mises distribution. We show that the algorithm is considerably faster than generating individual random samples from a bivariate dispersal kernel. It also performs better for larger grid sizes, and when there are larger numbers of individuals to be spread, than an approach that generates samples from a Binomial distribution for each grid cell using the probability of dispersal to that cell. The degree of computational efficiency achieved by the algorithm compared to the Binomial approach depends upon the speed with which random sample scan be generated from the tail of the bivariate dispersal kernel used

Statistical seasonal rainfall forecasts for south west Australia

Climate change projections indicate that south-west Australia (SWWA) will experience a drying climate with declining growing season rainfall and rising temperatures. However, seasonal variability will remain the dominant driver of adaptation at the farm level. Forecasts of seasonal rainfall made at managerially relevant times of year should enable farmers to modify farm management to maximise returns in good seasons and minimise losses in bad seasons. However, current use of seasonal forecasts is limited by perceived low levels of skill and limited availability of long-lead forecasts at appropriate times of year. We present a system for forecasting growing season rainfall in SWWA that uses novel predictors derived from global climate data within sophisticated statistical models. The predictors have been selected based on measurable relationships with SWWA rainfall. The forecasts take the form of probability distributions that describe the most likely rainfall total as well as the predicted variability around it

Modifying agro-economic models to predict effects of spatially varying nitrogen on wheat yields for a farm in Western Australia

Agricultural research in broadacre farming in Western Australiahas a strong history, resulting in a significant public resource of knowledge about biophysical processes affecting crop performance. However, translation of this knowledge into improved on-farm decision making remains a challenge to the industry.Online and mobile decision support tools to assist tactical farm management decisions are not widely adopted, for reasons including: (1) they take too much time and training to learn; and (2) they aren’t integrated with the data they need or with each other, making their use too time-consuming. Meanwhile, as farmers accumulate more data from their machinery, they find themselves unable to use that data to inform decision making.In an ideal future, variable rate technology (VRT) could be programmed to apply optimal rates of fertilisers. However, the existing suite of models and tools are derived from small-scale controlled field experiments and are not suitable forfine-scale paddock management. Using 14 years of data from a farm in the eastern wheatbelt of Western Australia, we investigate the calibration and extension of an agro-economic modelfor spatial prediction of the effects of nitrogen applicationson wheat yield and gross return.We use a simple response curve model, NP-Decide,that was developed in Western Australiaand remains in common use

Landau-De Gennes theory of nematic liquid\ud crystals: the Oseen-Frank limit and beyond

We study global minimizers of a continuum Landau-De Gennes energy functional for nematic liquid crystals, in three-dimensional domains, subject to uniaxial boundary conditions. We analyze the physically relevant limit of small elastic constant and show that global minimizers converge strongly, in W 1,2 , to a global minimizer predicted by the Oseen-Frank theory for uniaxial nematic liquid crystals with constant order parameter. Moreover, the convergence is uniform in the interior of the domain, away from the singularities of the limiting Oseen-Frank global minimizer. We obtain results on the rate of convergence of the eigenvalues and the regularity of the eigenvectors of the Landau-De Gennes global minimizer.\ud \ud \ud We also study the interplay between biaxiality and uniaxiality in Landau-De Gennes global energy minimizers and obtain estimates for various related quantities such as the biaxiality parameter and the size of admissible strongly biaxial regions

Ginzburg-Landau vortex dynamics with pinning and strong applied currents

We study a mixed heat and Schr\"odinger Ginzburg-Landau evolution equation on a bounded two-dimensional domain with an electric current applied on the boundary and a pinning potential term. This is meant to model a superconductor subjected to an applied electric current and electromagnetic field and containing impurities. Such a current is expected to set the vortices in motion, while the pinning term drives them toward minima of the pinning potential and "pins" them there. We derive the limiting dynamics of a finite number of vortices in the limit of a large Ginzburg-Landau parameter, or \ep \to 0, when the intensity of the electric current and applied magnetic field on the boundary scale like \lep. We show that the limiting velocity of the vortices is the sum of a Lorentz force, due to the current, and a pinning force. We state an analogous result for a model Ginzburg-Landau equation without magnetic field but with forcing terms. Our proof provides a unified approach to various proofs of dynamics of Ginzburg-Landau vortices.Comment: 48 pages; v2: minor errors and typos correcte

Critical phenomena in Newtonian gravity

We investigate the stability of self-similar solutions for a gravitationally collapsing isothermal sphere in Newtonian gravity by means of a normal mode analysis. It is found that the Hunter series of solutions are highly unstable, while neither the Larson-Penston solution nor the homogeneous collapse one have an analytic unstable mode. Since the homogeneous collapse solution is known to suffer the kink instability, the present result and recent numerical simulations strongly support a proposition that the Larson-Penston solution will be realized in astrophysical situations. It is also found that the Hunter (A) solution has a single unstable mode, which implies that it is a critical solution associated with some critical phenomena which are analogous to those in general relativity. The critical exponent $\gamma$ is calculated as $\gamma\simeq 0.10567$. In contrast to the general relativistic case, the order parameter will be the collapsed mass. In order to obtain a complete picture of the Newtonian critical phenomena, full numerical simulations will be needed.Comment: 25 pages, 7 figures, accepted for publication in Physical Review