Applications and Modelling Research Projects
Project title: Analysis and Modelling of Collective Animal Motion Project participants: Dr Timothy Schaerf (University of New England), Professor Ashley Ward (University of Sydney) Project description: Related publications: Project Title: Convexification of bilinear functions Project Participants: Natashia Boland (Georgia Tech), Akshay Gupte (University of Edinburgh) Thomas Kalinowski (UNE), Hamish Waterer (University of Newcastle) Project Description: Relevant Publications Project Title: Integration of network design and scheduling Project Participants: Natashia Boland (Georgia Tech), Konrad Engel (University of Rostock), Thomas Kalinowski (UNE), Dmytro Matsypura (University of Sydney), Martin Savelsbergh (Georgia Tech), Hamish Waterer (University of Newcastle) Project Description: Related Publications Project title: Mathematics in Sport Science. Project participants: Matthew Cooper (mathematics), Adam Harris (mathematics), Aron Murphy (sport science), David Paul (computer science), Kathleen Shorter (sport science), Jelena Schmalz (mathematics) Project Desription: This is an interdisciplinary project in mathematics, computer science, and sport science. We investigate and model the human gait, based on the analysis of one of the three dimensional components of the movement of the centre of mass during walking or running. Data collected by sport scientists is numerically approximated by the best fitting curve in a truncated jet space. Our approach allows us to relate the best fitting curves to differential equation of second order. The model that we suggest is a Duffing equation with coefficients that depend on body measurements of a walker or runner and on the angular frequency of the oscillation. One of our practical aims of this project is to compare and classify the curves for different participants. We intend to answer some questions from sport scientists, for example, to describe the transition between standing and walking, and between walking and running, mathematically. Related publications: Project title: Modelling the effects of climate change on dung beetle populations Project participants: Associate Professor Nigel Andrew (University of New England), Dr Timothy Schaerf (University of New England) Project description: As part of their life-cycle, dung beetles actively remove dung from the environment, either for use as food or breeding chambers for their offspring. The removal of dung by these beetles is also an important ecosystem service, with impact that extends to human agriculture. For example, in Australia dung beetles remove pasture dung, and as a consequence: enhance soil nutrient cycling, water penetration and soil aeration; destroy pest-fly breeding sites; and reduce the impacts of livestock gastro-intestinal parasites. Available evidence suggests that climate change will have a substantial impact on dung beetles. At the individual level, warming advances egg laying and hatching rates, decreases egg and larval size, and decreases dung beetle survival. At population levels, warmer conditions have been linked to altitudinal shifts in the ranges of dung beetle species, and to changes in habitat selection by dung beetles. There is also evidence that warming substantially reduces dung breakdown by beetles, with an associated reduction in growth of plants surrounding dung patches. Logically, the impacts on beetles are likely to effect the services that they provide to their ecosystems. This project will involve the development of individual based models that model dung beetle growth, development and reproductive output using dynamic energy budget theory (systems of ordinary differential equations that model how organisms allocate available energy resources in order to grow and reproduce). These models will be informed by experimental and observational work performed by Associate Professor Nigel Andrew and members of the Insect Ecology Laboratory at the University of New England. Observational data from multiple species present in Australia will include the effects of variable climate on beetle growth, maturation and reproductive output, competition within and between species for available dung resources, movements of beetles through their environment, and the general availability of dung. The models can be developed to examine possible climate effects on dung beetle populations at varying spatial scales, and to examine possible adaptation of beetles across multiple generations subject to changing climatic conditions. Related publications: 1. X Wu and S Sun, Artificial warming advances egg-laying and decreases larval size in the dung beetle Aphodius erraticus (Coleoptera: Scarabaeidae) in a Tibetan alpine meadow, Annales Zoologci Fennici, 49:174-180, (2012). 2. T H Larsen, Upslope range shifts of Andean dung beetles in response to deforestation: compounding and confounding effects of microclimatic change, Biotropica, 44:82-89, (2012). 3. R Menéndez and D Gutiérrez, Shifts in habitat associations of dung beetles in northern Spain: climate change implications, Écoscience, 11:329-337, (2004). 4. X Wu, J E Duffy, P B Reich and S Sun, A brown-world cascade in the dung decomposer food web of an alpine meadow: effects of predator interactions and warming, Ecological Monographs, 81: 313-328, (2011). 5. S A L M Kooijman, Dynamic Energy Budget Theory for Metabolic Organisation, Cambridge University Press, (2010). 6. B T Martin, E I Zimmer, V Grimm and T Jager, Dynamic energy budget theory meets individual-based modelling: a generic and accessible implementation, Methods in Ecology and Evolution, 3:445-449, (2012). 7. B T Martin, T Jager, R M Nisbet, T G Preuss and V Grimm, Predicting population dynamics from the properties of individuals: a cross-level test of dynamic energy budget theory, American Naturalist, 181:506-519, (2013). 8. M Renton, Aristotle and adding an evolutionary perspective to models of plant architecture in changing environments, Frontiers in Plant Science, 4:284, (2013). 9. M C Welch, P W Kwan and A S M Sajeev, Applying GIS and high performance agent-based simulation for managing old world screwworm fly invasion of Australia, Acta Tropica, 138S:S82-S93, (2014). Project title: Models of the honeybee nest-site selection process Project participants: Dr Timothy Schaerf (University of New England), Professor Mary Myerscough (University of Sydney), Professor Madeleine Beekman (University of Sydney) Project description: As part of their reproductive cycle, colonies of honeybees issue swarms. These swarms must then find a site to establish a new colony quickly, as a swarm is unable to store food without established combs, and is often vulnerable to the elements. Aspects of the complex process used by the cavity nesting honeybee Apis mellifera to select a new nest-site are relatively well understood due to a century of scientific research founded on the works of Karl von Frisch and Martin Lindauer (A. mellifera is the species of honeybee used by the honey industry). It is only in the last decade that detailed scientific investigations of the nest-site selection process of other species, of which there are at least six, have been undertaken. Common to each of the species studied with some detail (the cavity nesting A. mellifera, the red dwarf honeybee, A. florea, and the giant honeybee, A. dorsata) swarms release scouts to investigate the surrounding landscape for potential nest-sites. Upon their return to the swarm, scouts that have found a suitable target then perform a waggle dance, a stylised behaviour first recognised by Karl von Frisch as encoding the distance and direction to a resource of interest in the environment (in the context of nest-site selection, this resource is a potential new home). Other bees on the swarm follow such waggle dances, and then use the encoded information to help them find and assess the advertised site themselves. If these recruited bees also think that the advertised site is suitable, then they will return to the swarm, and advertise the location of the site to other bees with their own waggle dances. Over time, if enough bees are recruited to a particular specific site (in the case of A. mellifera) or a general direction (as seems to be the case for A. florea and perhaps A. dorsata), then the swarm chooses that site as a collective, and then flies to the new site to start building their new colony. A number of mathematical models have been developed to better understand the honeybee nest-site selection process, including systems of ordinary and stochastic differential equations, matrix models and individual-based simulation models. Most of these models have been developed specifically to examine nest-site selection by A. mellifera, and take into account a number of known species specific behaviours. Participants in this project will build on existing models, and develop new models, to best reflect current knowledge of the overall nest-site selection processes of A. mellifera, A. florea and A. dorsata. These models will then be used to examine effects of swarm size (and hence the number of active participants in nest-site selection), noisy communication, and the number and relative positions of viable nesting sites on the decision-making ability of swarms of each species. Further work could then include developing a multi-generational nest-site selection model to examine how quickly species can adjust their nest-site selection process, if at all, when changing environmental conditions force a change in the type of nest-site sought. Related publications: 1. T D Seeley and S C Buhrman, Group decision making in swarms of honey bees, Behavioral Ecology and Sociobiology, 45:19-31, (1999). 2. T D Seeley and S C Buhrman, Nest-site selection in honey bees: how well do swarms implement the “best-of-N” rule?, Behavioral Ecology and Sociobiology, 49:416-427, (2001). 3. N F Britton, N R Franks, S C Pratt and T D Seeley, Deciding on a new home: how do honeybees agree?, Proceedings of the Royal Society of London B, 269:1383-1388, (2002). 4. M R Myerscough, Dancing for a decision: a matrix model for nest-site choice by honeybees, Proceedings of the Royal Society of London B, 270:577-582, (2003). 5. K M Passino and T D Seeley, Modeling and analysis of nest-site selection by honeybee swarms: the speed and accuracy trade-off, 59:427-442, (2006). 6. B P Oldroyd, R S Gloag, N Even, W Wattanachaiyingcharoen and M Beekman, Nest site selection in the open-nesting honeybee Apis florea, Behavioral Ecology and Sociobiology, 62:1643-1653, (2008). 7. C List, C Elshotlz and T D Seeley, Independence and interdependence in collective decision making: an agent-based model of nest-site choice by honeybee swarms, Philosophical Transactions of the Royal Society Bm 364:755-762, (2009). 8. J C Makinson, B P Oldroyd, T M Schaerf, W Wattanachaiyingcharoen and M Beekman, Moving home: nest-site selection in the Red Dwarf honeybee (Apis florea), Behavioral Ecology and Sociobiology, 65:945-958, (2011). 9. K Diwold, T M Schaerf, M R Myerscough, M Middendorf and M Beekman, Deciding on the wing: in-flight decision making and search space sampling in the red dwarf honeybee Apis florea, Swarm Intelligence, 5:121-141, (2011). 10. T M Schaerf, M R Myerscough, J C Makinson and M Beekman, Inaccurate and unverified information in decision making: a model for the nest site selection process of Apis florea, Animal Behaviour, 82:995-1013, (2011). 12. T D Seeley, P K Visscher, T Schlegel, P M Hogan, N R Franks and J A R Marshall, Stop signals provide cross inhibition in collective decision-making by honeybee swarms, Science, 335:108-111, (2012). 13. T M Schaerf, J C Makinson, M R Myerscough and M Beekman, Do small swarms have an advantage when house hunting? The effect of swarm size on nest-site selection by Apis mellifera, Journal of the Royal Society Interface, 10:20130533, (2013). 14. J C Makinson, T M Schaerf, A Rattanawannee, B P Oldroyd and M Beekman, Consensus building in giant Asian honeybee, Apis dorsata, swarms on the move, Animal Behaviour, 93:191-199, (2014). 15. M Beekman, J C Makinson, M J Couvillon, K Preece and T M Schaerf, Honeybee linguistics – a comparative analysis of the waggle dance among species of Apis, Frontiers in Ecology and Evolution, 3:11, (2015). 16. J C Makinson, T M Schaerf, A Rattanawannee, B P Oldroyd and M Beekman, How does a swarm of the giant Asian honeybee Apis dorsata reach consensus? A study of the individual behaviour of scout bees, Insectes Sociaux, 63:395-406, (2016). 17. J C Makinson, T M Schaerf, N Wagner, B P Oldroyd and M Beekman, Collective decision making in the red dwarf honeybee Apis florea: do the bees simply follow the flowers?, Insectes Sociaux, 64:557-566, (2017). Project Title: Propagation via nonlinear partial differential equations Principal investigator: Prof. Yihong Du (UNE) Other participants: Funding body: Australian Research Council (DP190103757, 2019-2021) Project description: The goal of this project is to develop new mathematics to better understand these propagation phenomena. Although the sources of propagation are diverse, the basic phenomena have been observed to follow certain rules that can be captured by mathematical models of nonlinear partial differential equations (PDEs) or systems of such equations. Thus it is possible for a mathematical theory based on a set of such equations to provide vital insights and useful predictions for the spreading of a variety of subjects, such as the propagation of nerve impulses, and the spreading of invasive species or cancerous cells. This topic has attracted the efforts of numerous first rate mathematicians in the past several decades, and extensive research in this area is currently conducted by several top tier research groups around the world. Yet, with the advances of the relevant sciences, more and more demanding questions arise in this area, with many important and basic ones waiting to be answered. The specific aims of this proposal focus on the following three tasks: This project is a continuation of the ARC funded project (DP150101867, 2015-2018). Related publications: Project title: Using Persistent Homology To Analyse Digital Images Image Resolution: Persistent homology data from micro-CT images of porous materials provide a useful summary of the geometrical and topological structure of the material correlated with physical properties such as permeability and trapping capacity. As the cost of acquiring a micro-CT image is proportional to the imaging resolution it is essential to understand how persistent homology changes with resolution, and what minimum resolution is required for extracting useable data. Duality: Images are represented as arrays of numbers and there are two ways to obtain a cubical complex modelling a given image: The T-construction treats pixels as top dimensional cells (squares in 2D, cubes in 3D) and corresponds to the indirect adjacency (or closed topology) of classical digital topology. The V-construction considers pixels as vertices and corresponds to direct adjacency (or open topology). In both cases, the function values from the original array are extended to all cells of the cubical complex to obtain filtered complexes IT and IV, respectively. Persistent homology is described by persistence diagrams or barcodes which encode the structure of the indecomposable summands of the homology of these filtered complexes. Some of the packages developed for computing barcodes for digital images use the V-construction while others use the T-construction. We investigate the relationship between the barcodes of IT and IV to allow flexible choice of package as well as comparison between these. These questions are investigated with sample micro-CT images of porous materials provided by the ANU CTLab for context. Related Publications: Publications A. Garin, T. Heiss, K. Maggs, B. Bleile and V. Robins, Duality in Persistent Homology of Images, Extended abstract for SoCG YRF 2020 URL: https://arxiv.org/abs/2005.04597 Funding: This project was initiated at the Second Workshop for Women in Computational Topology hosted by the Mathematical Sciences Institute at ANU, Canberra, in July 2019. It also received funding from AWM, NSF, and AMSI.
The spectacular patterns of collective movement have been, and remain, a long standing and major interest in many branches of science, including biology, mathematics, physics and computational science. From the early 1980s until the late 2000s computational self-propelled particle models were the dominant methods for examining how, and what type of, individual-level interactions could result in the amazing emergent patterns formed by groups such as flocking birds, shoaling fish and even crowds of humans. The influence of these models on the study of collective motion has been immense, with multiple model-based studies led by contemporary researchers cited thousands of times each. It is only in the last decade that advances in automated tracking methods have led to the exciting development of techniques for estimating the local rules of interaction used by real animals to coordinate collective motion directly from observational data (as opposed to inferring possible rules using models). In spite of these advances, many of the techniques for analysis are still in their infancy. This project will focus on refining existing techniques and developing new techniques for quantifying individual-interactions from automated tracking data. The more accurate analysis of experimental data will then be used to help refine and build on simulation models for collective animal movement.
Optimisation problems with bilinear functions in the constraints or the objective functions are important in applications, for instance in the petrochemical industry, since they appear naturally in the description of blending processes. Due to the non-convexity of these functions and the problem sizes appearing in practice, it is very challenging to solve such problems. An important ingredient in all state-of-the-art solvers is the approximation of the non-convex functions by convex ones, and the quality of this approximation is crucial for the performance of the algorithm. Certain properties of such a function are captured by a graph whose vertices are the decision variables, and two variables are joined by an edge if their product appears in the function. We study the relation between the combinatorics of this graph and the convex hull of the graph of the function. Methods from the theory of random graphs and linear programming duality can be used to characterise the worst case gap between the convex hull and the McCormick hull, which is a standard convexification used in most software packages. In this project we apply geometric methods to characterise the convex hulls for some special classes of functions.
We study optimisation problems in which a network is used over a certain time horizon, and at the same time the network is modified using limited resources. Applications arise in the optimal reconstruction planning for infrastructure networks (transportation, water, electricity) after natural disasters like earthquakes or hurricanes, and in planning maintenance or capacity expansions in transportation networks. The class of incremental network design problems has been introduced to study essential features of these complex optimisation problems in a simplified context. Every classical network optimisation problem (shortest path, maximum flow,...) yields an incremental variant. In general, these problems are NP-complete, and this motivates the following questions: Can the problem be solved in polynomial time under additional assumptions which might be satisfied in some application contexts? Can we find approximation algorithms, that is, algorithms with polynomial run-time and a guarantee for the quality of the solution? Or is the problem even hard to approximate? How can we understand the combinatorial and polyhedral structure of the problem better, and then use this understanding for the development of practical algorithms?
Dr Maolin Zhou (UNE), Prof. Bendong Lou (Shanghai Normal Univ), Prof Xing Liang (Univ of Sci and Tech of China), Prof Mingxin Wang (Harbin Inst. Tech.), Dr Wenjie Ni (UNE), Dr Ting-Ying Chang (UNE), Prof Fang Li (Zhong Shan Univ), Prof Rui Peng (Jiangsu Normal Univ.).
Propagation occurs in various forms, such as the spreading of invasive species, infectious diseases or cancer cells, or the progression of the healing front of a wound.
Project participants: Dr Vanessa Robins (Australian National University), Dr Bea Bleile (University of New England), Hoa Bui (Curtin University), Brittany Carr (Colorado State University), Adélie Garin (École PFL), Teresa Heiss (Institute of Science and Technology Austria), Kelly Maggs (Australian National University), Kritika Singhal (Ohio State University), Sarah Tymochko (Michigan State University)
Description: This project considers questions of image resolution and the duality between two methods for building a cell complex from a digital grid.
