Computational methods for population-size-dependent branching processes. Branching processes are the primary mathematical tool used to model populations that evolve randomly in time. Most key results in the theory are derived under the simplifying assumption that individuals reproduce and die independently of each other. However, this assumption fails in most real-life situations, in particular when the environment has limited resources or when the habitat has a restricted capacity. This project ....Computational methods for population-size-dependent branching processes. Branching processes are the primary mathematical tool used to model populations that evolve randomly in time. Most key results in the theory are derived under the simplifying assumption that individuals reproduce and die independently of each other. However, this assumption fails in most real-life situations, in particular when the environment has limited resources or when the habitat has a restricted capacity. This project aims to develop novel and effective algorithmic techniques and statistical methods for a class of branching processes with dependences. We will use these results to study significant problems in the conservation of endangered island bird populations in Oceania, and to help inform their conservation management.Read moreRead less
Statistical methods and tools for integrative microarray analysis. Tools used for biological and medical research have been evolving and there has been an increase in high-throughput technologies such as genome sequencing and DNA microarray. The growing number of entries and the increasing availability of public microarray repositories and other sequence databases have generated the new challenge of developing tools to efficiently integrate data by different research groups. This research provi ....Statistical methods and tools for integrative microarray analysis. Tools used for biological and medical research have been evolving and there has been an increase in high-throughput technologies such as genome sequencing and DNA microarray. The growing number of entries and the increasing availability of public microarray repositories and other sequence databases have generated the new challenge of developing tools to efficiently integrate data by different research groups. This research provides new statistical methods to integrate different data sets. Its application in the biomedical field will allow researchers to effectively interpret the myriad of data generated within the community.Read moreRead less
New Approaches to Modelling and Analysing Long-Memory Random Processes. The project aims to develop new approaches using infinite-dimensional Markov processes to solving important long-standing problems from the theory of long memory random processes and their applications. It aims to: construct a class of new representations of random processes; derive inequalities for the key numerical characteristics; and, devise and investigate numerical methods for computing the characteristics and for perf ....New Approaches to Modelling and Analysing Long-Memory Random Processes. The project aims to develop new approaches using infinite-dimensional Markov processes to solving important long-standing problems from the theory of long memory random processes and their applications. It aims to: construct a class of new representations of random processes; derive inequalities for the key numerical characteristics; and, devise and investigate numerical methods for computing the characteristics and for performing statistical inference on the long memory models. The accuracy of numerical approximations will be analysed using simulations on supercomputers. Expected outcomes include models and results of practical importance with applications such as intrusion detection problems, cell motility for biological data and telecommunication.Read moreRead less
New universality in stochastic systems. This project aims to uncover new analyses and effects in the complex behaviour of non-linear systems with random noise. Many systems originate near an unstable equilibrium. This project will develop a new mathematical theory that establishes a universality in the way the long term effect of noise expresses itself as random initial conditions in the dynamics. It will fill gaps in Mathematics and make refinements to existing fundamental scientific laws by in ....New universality in stochastic systems. This project aims to uncover new analyses and effects in the complex behaviour of non-linear systems with random noise. Many systems originate near an unstable equilibrium. This project will develop a new mathematical theory that establishes a universality in the way the long term effect of noise expresses itself as random initial conditions in the dynamics. It will fill gaps in Mathematics and make refinements to existing fundamental scientific laws by including random initial conditions as predicted by our theory. This will advance our understanding of complex systems subjected to noise and will provide significant benefits in the scientific discoveries in Biology, Ecology, Physics and other Sciences where such systems are frequently met.Read moreRead less
Statistical methods for analysing multi-source microarray data and building gene regulatory networks. I will devise a statistical learning technique that does not force a gene to be assigned to exactly one category. This technique reflects the biological reality that a gene can belong to two or more functional categories. Therefore, the new technique will improve a model's ability to identify regulatory genes in different types of cancer; these regulatory genes can be targeted by new anti-cancer ....Statistical methods for analysing multi-source microarray data and building gene regulatory networks. I will devise a statistical learning technique that does not force a gene to be assigned to exactly one category. This technique reflects the biological reality that a gene can belong to two or more functional categories. Therefore, the new technique will improve a model's ability to identify regulatory genes in different types of cancer; these regulatory genes can be targeted by new anti-cancer drugs resulting in a more effective treatment. I will model gene regulatory networks using microarray data from multiple sources. These networks will be used to identify regulatory cliques - a group of genes that are vital for a cellular function. This will improve our understanding of debilitating conditions such as asthma.Read moreRead less