The Objects of Probabilities. Probabilities impact almost every aspect of our lives. Actuaries calculate probabilities of property loss due to bushfires, while climatologists warn that such probabilities will increase alarmingly. Probabilities abound in engineering, medicine, the law, the sciences and social sciences, and much philosophy. Yet we lack a proper understanding of the kinds of things that receive probabilities: the objects of probabilities. This project will provide such understandin ....The Objects of Probabilities. Probabilities impact almost every aspect of our lives. Actuaries calculate probabilities of property loss due to bushfires, while climatologists warn that such probabilities will increase alarmingly. Probabilities abound in engineering, medicine, the law, the sciences and social sciences, and much philosophy. Yet we lack a proper understanding of the kinds of things that receive probabilities: the objects of probabilities. This project will provide such understanding. It will rethink the foundations of probability and decision theory, with potential ramifications for the philosophy, science, and public policy that are based on these theories. It thus aims to strengthen Australia's research profile and international standing in these areas.Read moreRead less
New frontiers in statistical mechanics. The chiral Potts model has been introduced in 1981 as a model for commensurate-incommensurate phase transitions in a layer of atoms or molecules adsorbed to a solid surface. If the adsorbed atoms all fit to holes between the surface atoms, the added layer is frozen, commensurate with the surface. If the added atoms are unable to fit holes, the added layer is no longer commensurate with the surface and could be in a floating state. A deeper understanding of ....New frontiers in statistical mechanics. The chiral Potts model has been introduced in 1981 as a model for commensurate-incommensurate phase transitions in a layer of atoms or molecules adsorbed to a solid surface. If the adsorbed atoms all fit to holes between the surface atoms, the added layer is frozen, commensurate with the surface. If the added atoms are unable to fit holes, the added layer is no longer commensurate with the surface and could be in a floating state. A deeper understanding of this and similar phenomena in layered systems has nanotechnological implications. This may affect the design of new small electronic devices or could apply to small biological systems and the development of new medicines. The project will surely lead to new applicable mathematics.Read moreRead less
The mathematics and physics of interacting systems. Much of the world around us involves the networked interaction between a large number of components. For example, such complex networks may be physical, biological, social or technical in nature and represent connections between magnetic spins, species, people or computers. This Project will provide a firm theoretical foundation for such complex interacting systems through an investigation of the fascinating mathematics and physics behind them. ....The mathematics and physics of interacting systems. Much of the world around us involves the networked interaction between a large number of components. For example, such complex networks may be physical, biological, social or technical in nature and represent connections between magnetic spins, species, people or computers. This Project will provide a firm theoretical foundation for such complex interacting systems through an investigation of the fascinating mathematics and physics behind them. This perspective from mathematical physics, in particular using the tools of statistical mechanics, will lead to a better understanding of many real-world complex systems.Read moreRead less
Solvable models on regular and random lattices in statistical mechanics and field theory. There are only a few solvable models in statistical mechanics and field theory, but those that are known give deep insights into the cooperative behaviour that characterizes a critical point, as well as
leading to fascinating mathematics. The two chief investigators have been at the forefront of this field for many years. Currently there are many notable exciting challenges they wish to address:
the re ....Solvable models on regular and random lattices in statistical mechanics and field theory. There are only a few solvable models in statistical mechanics and field theory, but those that are known give deep insights into the cooperative behaviour that characterizes a critical point, as well as
leading to fascinating mathematics. The two chief investigators have been at the forefront of this field for many years. Currently there are many notable exciting challenges they wish to address:
the relationship between Tutte's work on dichromatic polynomials and matrix models, the outstanding problem of calculating the order parameters of the chiral Potts model, and the eigenvalue spectra of the transfer matrices that occur in integrable models.
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Solvable models and pattern formation: quantum spin ladders, combinatorics and stromatolite morphogenesis. The aim of this project is to develop new applications of exactly solved models in statistical mechanics. These include the study of quantum spin ladders of great interest in condensed matter physics. The physical properties of new and existing models will be derived to provide valuable benchmarks and predictions for future theoretical and experimental work. We will also undertake the study ....Solvable models and pattern formation: quantum spin ladders, combinatorics and stromatolite morphogenesis. The aim of this project is to develop new applications of exactly solved models in statistical mechanics. These include the study of quantum spin ladders of great interest in condensed matter physics. The physical properties of new and existing models will be derived to provide valuable benchmarks and predictions for future theoretical and experimental work. We will also undertake the study and development of a set of remarkable conjectures relating the properties of a solvable model to an established area of combinatorics. Another aspect of this project involves the investigation of the origins, growth and form of ancient stromatolites.
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Practical and theoretical aspects of structure enumeration. Many areas of study involve processing of large numbers of
objects in some class. These are countless examples in
chemistry, physics, mathematics, and other disciplines.
Structure Enumeration is the study of methods for efficient
generation and analysis of such objects. The project will
involve exploitation and extension of recent advances, many
due to the CI, which have added orders of magnitude to what
was possible only a few ....Practical and theoretical aspects of structure enumeration. Many areas of study involve processing of large numbers of
objects in some class. These are countless examples in
chemistry, physics, mathematics, and other disciplines.
Structure Enumeration is the study of methods for efficient
generation and analysis of such objects. The project will
involve exploitation and extension of recent advances, many
due to the CI, which have added orders of magnitude to what
was possible only a few years ago. The outcome will be a
combination of theoretical results and practical achievements,
whose usefulness will be demonstrated with some serious
applications in physics and mathematics.
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Structure enumeration, applications and analysis. Structure enumeration and analysis is at the heart of finite mathematics and its many fields of application in diverse scientific disciplines. Australia has a substantial status in this field both in mathematics and physics. This project will enhance that status and develop greater ties with the centres of structure research in other parts of the world.
Proof Theoretical Methods for Reasoning about Process Equivalence. The emergence of internet commerce has made the issue of secure computing more urgent than ever. A substantial part of the security issues with today's computer applications are due to design problems.
The principles of secure computation have not been fully understood and adequate tools for the construction of secure applications are still lacking. The understanding of the foundations of secure computation is essential in bu ....Proof Theoretical Methods for Reasoning about Process Equivalence. The emergence of internet commerce has made the issue of secure computing more urgent than ever. A substantial part of the security issues with today's computer applications are due to design problems.
The principles of secure computation have not been fully understood and adequate tools for the construction of secure applications are still lacking. The understanding of the foundations of secure computation is essential in building trusted computer applications. Process calculi and logic represent two promising disciplines in which the principles of analysis and design of secure systems can be studied systematically, out of which formal verification tools can be constructed.Read moreRead less
Expressive power and complexity of temporal logics for model-checking. Hardware verification based upon mathematical logic is now routinely
used in industry to verify the correctness of large digital circuits
using a technique called model-checking. Such discrete systems move
from one state to another according to the regular ticks of a clock.
The challenge now is to find tractable methods for reasoning about
real-time systems and hybrid systems that move in a continuous manner
with respec ....Expressive power and complexity of temporal logics for model-checking. Hardware verification based upon mathematical logic is now routinely
used in industry to verify the correctness of large digital circuits
using a technique called model-checking. Such discrete systems move
from one state to another according to the regular ticks of a clock.
The challenge now is to find tractable methods for reasoning about
real-time systems and hybrid systems that move in a continuous manner
with respect to time: examples include aeroplanes flying according to
the laws of physics and a moving robot arm. We shall invent new logics
which are specifically tailored for tractable reasoning about
real-time and hybrid systems.Read moreRead less