3D Structure determination of biomacromolecular assemblies from sparse data. This project has direct impact on pharmaceutical research: Biomacromolecular interactions are key points for pharmaceutical intervention and detailed structural knowledge of dynamic protein interactions can significantly accelerate drug development. Australia has invested in expensive instrumentation that can be used with new laboratory methods to obtain information on delicately balanced biomacromolecular interactions, ....3D Structure determination of biomacromolecular assemblies from sparse data. This project has direct impact on pharmaceutical research: Biomacromolecular interactions are key points for pharmaceutical intervention and detailed structural knowledge of dynamic protein interactions can significantly accelerate drug development. Australia has invested in expensive instrumentation that can be used with new laboratory methods to obtain information on delicately balanced biomacromolecular interactions, and how they malfunction in disease. This project will provide a computational framework to increase the impact of this investment by integrating measurements from a range of novel technologies and developing understanding of changes in structure of large protein complexes in different functional states.Read moreRead less
Structure and informatics of the genetic code. Recent advances in biotechnology have seen its emergence as a highly
quantitative, numerically-based discipline. To exploit the available
data to the full will require, alongside computing power, new
analytical techniques. This project aims to develop such techniques,
by handling the systematics of the genetic code with methods derived
from theoretical physics and chemistry. Expected outcomes include a
dynamical (quantum field theory) model ....Structure and informatics of the genetic code. Recent advances in biotechnology have seen its emergence as a highly
quantitative, numerically-based discipline. To exploit the available
data to the full will require, alongside computing power, new
analytical techniques. This project aims to develop such techniques,
by handling the systematics of the genetic code with methods derived
from theoretical physics and chemistry. Expected outcomes include a
dynamical (quantum field theory) model of phylogenetic branching,
analyses of nucleic acid structure and content (spin chain models of
RNA binding and of DNA open reading frames), and insights into the
origin of the code itself (via numerical codon similarity measures).
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Theoretical Studies on the KcsA Potassium Channel and the L-type Calcium Channel. All electrical activities in the brain are regulated by opening and closing of ion channels. Thus, understanding their mechanisms is a fundamental problem in biology. The project is aimed at developing a theoretical model of two important types of ion channels. Using a supercomputer, we will first deduce the shape of the microstructure formed by a protein wall. Then, using a computer simulation technique, we will c ....Theoretical Studies on the KcsA Potassium Channel and the L-type Calcium Channel. All electrical activities in the brain are regulated by opening and closing of ion channels. Thus, understanding their mechanisms is a fundamental problem in biology. The project is aimed at developing a theoretical model of two important types of ion channels. Using a supercomputer, we will first deduce the shape of the microstructure formed by a protein wall. Then, using a computer simulation technique, we will construct a set of physical models of biological ion channels, which will correctly replicate experimental observations. Such a theory will link the structure and function of an ion channel through the fundamental principles of physics.Read moreRead less
Robust Reformulation Methods. Many decision problems in engineering, business and economics are modeled as nonlinear continuous optimization problems. Often these are made difficult by the existence of constraints. In this project, we reformulate such problems as constrained nonsmooth equations, rather than optimization problems, and develop generalized Newton and quasi-Newton methods for solving them. The expected outcomes of this project include a systematic theory of reformulation methods, ....Robust Reformulation Methods. Many decision problems in engineering, business and economics are modeled as nonlinear continuous optimization problems. Often these are made difficult by the existence of constraints. In this project, we reformulate such problems as constrained nonsmooth equations, rather than optimization problems, and develop generalized Newton and quasi-Newton methods for solving them. The expected outcomes of this project include a systematic theory of reformulation methods, and robust and efficient algorithms for solving some important nonlinear continuous optimization problems. There is high potential for applications in engineering, business and finance.Read moreRead less
Quadratic Support Function Technique to Solving Hard Global Nonconvex Optimization Problems. Optimization techniques are becoming increasingly beneficial to modern Australian society in areas such as manufacturing and commerce by improving technical and management decisions. The proposed research is expected to produce enhanced optimization techniques that can be applied to solve a wider range of important problems too complex to be currently solved. The proposed research also represents an inte ....Quadratic Support Function Technique to Solving Hard Global Nonconvex Optimization Problems. Optimization techniques are becoming increasingly beneficial to modern Australian society in areas such as manufacturing and commerce by improving technical and management decisions. The proposed research is expected to produce enhanced optimization techniques that can be applied to solve a wider range of important problems too complex to be currently solved. The proposed research also represents an international collaboration which will improve Australia's ability to participate effectively in international research and innovation and to produce globally competitive mathematical technologiesRead moreRead less
Continuous Optimization with Linear Matrix Inequality Constraints. The proposed research is expected to lead to new insights and new joint collaborative work for both Autralian and Korean partners. Joining forces of the two teams will ensure that a full range of techniques can be utilized to provide rapid successful research outcomes. The proposed collaboration will give better opportunity to increase the visibility of the work from Korea in Australia, and vice versa. One of the key national be ....Continuous Optimization with Linear Matrix Inequality Constraints. The proposed research is expected to lead to new insights and new joint collaborative work for both Autralian and Korean partners. Joining forces of the two teams will ensure that a full range of techniques can be utilized to provide rapid successful research outcomes. The proposed collaboration will give better opportunity to increase the visibility of the work from Korea in Australia, and vice versa. One of the key national benefits is that the proposed research collaboration will provide extremly fertile ground for training postdoctoral researchers and graduate students in one of the most applicable areas of mathematics.Read moreRead less
Necessary and sufficient conditions for global minimum in multi-extremal global continuous optimization. A basic understanding of the mechanisms for finding local "best" (optimal) solutions has been
achieved through optimization techniques. However, solving global optimization problems, where we may have many local optimal solutions which are not the "absolutely best" (global), is vital for many applications in industry & science, and is intrinsically difficult. The lack of verifiable condition ....Necessary and sufficient conditions for global minimum in multi-extremal global continuous optimization. A basic understanding of the mechanisms for finding local "best" (optimal) solutions has been
achieved through optimization techniques. However, solving global optimization problems, where we may have many local optimal solutions which are not the "absolutely best" (global), is vital for many applications in industry & science, and is intrinsically difficult. The lack of verifiable conditions for a global optimum is a serious limitation. This project will develop verifiable such global optimality conditions for many classes of these problems. A new methodology, functional abstract convexity, developed by CIs and has shown promising results, will be extended and applied for solving these problems.Read moreRead less
A new improved solution to global optimization over multivariate polynomials: Mathematical principles, numerical methods and selected applications. Optimization technology is becoming increasingly beneficial to modern Australian society in areas such as wireless communications and manufacturing by improving performance or reducing costs. Our research will produce enhanced global optimization methodologies, capable of solving a wider range of problems that are currently too complex to be solved. ....A new improved solution to global optimization over multivariate polynomials: Mathematical principles, numerical methods and selected applications. Optimization technology is becoming increasingly beneficial to modern Australian society in areas such as wireless communications and manufacturing by improving performance or reducing costs. Our research will produce enhanced global optimization methodologies, capable of solving a wider range of problems that are currently too complex to be solved. Since global optimization technology is used in many scientific disciplines and modern industrial applications, the research will make many Australian science and industries more competitive. Our research also represents a program of high profile international collaborations that will improve Australia's ability to produce internationally competitive optimization technology.
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Entanglement renormalization: a new route to strongly correlated fermions and novel states of matter in two dimensions. The expected outcome of the research program is a significant boost in our understanding of strongly correlated fermion systems, which will reinforce Australia's competitiveness and international profile in aspects of breakthrough science and frontier technologies. By strengthening both the underpinning theory and innovative computational tools to study fermion systems, and by ....Entanglement renormalization: a new route to strongly correlated fermions and novel states of matter in two dimensions. The expected outcome of the research program is a significant boost in our understanding of strongly correlated fermion systems, which will reinforce Australia's competitiveness and international profile in aspects of breakthrough science and frontier technologies. By strengthening both the underpinning theory and innovative computational tools to study fermion systems, and by applying them to specific problems of recognized importance, this program will have direct implications in condensed matter physics and will exert significant influence in areas such as quantum chemistry, particle, nuclear and atomic physics, quantum computing, quantum atom optics and nanotechnology.Read moreRead less
Advanced computational algorithms for three-dimensional systems. This project deals with the development, analysis and implementation of efficient computer algorithms for a range of complex three dimensional systems. Major areas of focus are forward and inverse acoustic and electromagnetic scattering; dynamical and evolution processes in water waves and tumour growth; and the solution of mathematical models on spheres (earth). Potential application areas of the project include defence science ....Advanced computational algorithms for three-dimensional systems. This project deals with the development, analysis and implementation of efficient computer algorithms for a range of complex three dimensional systems. Major areas of focus are forward and inverse acoustic and electromagnetic scattering; dynamical and evolution processes in water waves and tumour growth; and the solution of mathematical models on spheres (earth). Potential application areas of the project include defence science; ocean engineering; medical research; meteorology and global environmental sciences.Read moreRead less