A Combined Renormalization Group-Multiple Scale Method for Singularly Perturbed Problems

This paper introduces a straightforward method to asymptotically solve a variety of initial and boundary value problems for singularly perturbed ordinary differential equations whose solution structure can be anticipated. The approach is simpler than conventional methods, including those based on asymptotic matching or on eliminating secular terms. © 2010 by the Massachusetts Institute of Technology.

Reduction of amplitude equations by the renormalization group approach

This article elucidates and analyzes the fundamental underlying structure of the renormalization group (RG) approach as it applies to the solution of any differential equation involving multiple scales. The amplitude equation derived through the elimination of secular terms arising from a naive perturbation expansion of the solution to these equations by the RG approach is reduced to an algebraic equation which is expressed in terms of the Thiele semi-invariants or cumulants of the eliminant sequence { Zi } i=1 . Its use is illustrated through the solution of both linear and nonlinear perturbation problems and certain results from the literature are recovered as special cases. The fundamental structure that emerges from the application of the RG approach is not the amplitude equation but the aforementioned algebraic equation. © 2008 The American Physical Society.

The renormalization group and the implicit function theorem for amplitude equations

This article lays down the foundations of the renormalization group (RG) approach for differential equations characterized by multiple scales. The renormalization of constants through an elimination process and the subsequent derivation of the amplitude equation [Chen, Phys. Rev. E 54, 376 (1996)] are given a rigorous but not abstract mathematical form whose justification is based on the implicit function theorem. Developing the theoretical framework that underlies the RG approach leads to a systematization of the renormalization process and to the derivation of explicit closed-form expressions for the amplitude equations that can be carried out with symbolic computation for both linear and nonlinear scalar differential equations and first order systems but independently of their particular forms. Certain nonlinear singular perturbation problems are considered that illustrate the formalism and recover well-known results from the literature as special cases. © 2008 American Institute of Physics.

Secular series and renormalization group for amplitude equations

We have developed a technique that circumvents the process of elimination of secular terms and reproduces the uniformly valid approximations, amplitude equations, and first integrals. The technique is based on a rearrangement of secular terms and their grouping into the secular series that multiplies the constants of the asymptotic expansion. We illustrate the technique by deriving amplitude equations for standard nonlinear oscillator and boundary-layer problems. © 2008 The American Physical Society.

Renormalization group interpretation of the Born and Rytov approximations

In this paper the method of renormalization group (RG) [Phys. Rev. E 54, 376 (1996)] is related to the well-known approximations of Rytov and Born used in wave propagation in deterministic and random media. Certain problems in linear and nonlinear media are examined from the viewpoint of RG and compared with the literature on Born and Rytov approximations. It is found that the Rytov approximation forms a special case of the asymptotic expansion generated by the RG, and as such it gives a superior approximation to the exact solution compared with its Born counterpart. Analogous conclusions are reached for nonlinear equations with an intensity-dependent index of refraction where the RG recovers the exact solution. © 2008 Optical Society of America.

A non-malleable group key exchange protocol robust against active insiders

In this paper we make progress towards solving an open problem posed by Katz and Yung at CRYPTO 2003. We propose the first protocol for key exchange among n ≥2k+1 parties which simultaneously achieves all of the following properties: 1. Key Privacy (including forward security) against active attacks by group outsiders, 2. Non-malleability — meaning in particular that no subset of up to k corrupted group insiders can ‘fix’ the agreed key to a desired value, and 3. Robustness against denial of service attacks by up to k corrupted group insiders. Our insider security properties above are achieved assuming the availability of a reliable broadcast channel.

An adaptive spherical view representation for navigation in changing environments

Real-world environments such as houses and offices change over time, meaning that a mobile robot’s map will become out of date. In previous work we introduced a method to update the reference views in a topological map so that a mobile robot could continue to localize itself in a changing environment using omni-directional vision. In this work we extend this longterm updating mechanism to incorporate a spherical metric representation of the observed visual features for each node in the topological map. Using multi-view geometry we are then able to estimate the heading of the robot, in order to enable navigation between the nodes of the map, and to simultaneously adapt the spherical view representation in response to environmental changes. The results demonstrate the persistent performance of the proposed system in a long-term experiment.

Long-term experiments with an adaptive spherical view representation for navigation in changing environments

Real-world environments such as houses and offices change over time, meaning that a mobile robot’s map will become out of date. In this work, we introduce a method to update the reference views in a hybrid metrictopological map so that a mobile robot can continue to localize itself in a changing environment. The updating mechanism, based on the multi-store model of human memory, incorporates a spherical metric representation of the observed visual features for each node in the map, which enables the robot to estimate its heading and navigate using multi-view geometry, as well as representing the local 3D geometry of the environment. A series of experiments demonstrate the persistence performance of the proposed system in real changing environments, including analysis of the long-term stability.

Predicting sense convergence with distributional semantics : an application to the CogALex-IV 2014 shared task

This paper presents our system to address the CogALex-IV 2014 shared task of identifying a single word most semantically related to a group of 5 words (queries). Our system uses an implementation of a neural language model and identifies the answer word by finding the most semantically similar word representation to the sum of the query representations. It is a fully unsupervised system which learns on around 20% of the UkWaC corpus. It correctly identifies 85 exact correct targets out of 2,000 queries, 285 approximate targets in lists of 5 suggestions.

Testing the international linkage in the platinum-group metal futures markets

This study tests whether an international market exists in the platinum-group metal (PGM) futures markets. For this purpose, we tested the law of one price (LOP) and the causality between the U.S. and Japanese platinum and palladium futures markets. We also performed the test when structural breaks are considered. Long-run price relationships were found in both platinum and palladium markets but the LOP only sustained in the palladium market. The causality test revealed that it is the U.S. market that leads the price to transmit information between the U.S. and Japanese markets. Structural breaks had large impacts on the test results, suggesting that incorporating breaks is important when investigating the international price linkage in the PGM futures markets.

Sentencing and public confidence in Australia: The dynamics and foci of small group deliberations

This study is the first of its kind in Australia to use the deliberative small group methodology to explore participants’ deeper, nuanced thoughts on specific criminal justice issues in order to gain insight into the underlying beliefs that influence people’s opinions on sentencing. The use of small group discussions allows an analysis of the dynamics of people’s interactions and the potential of these to elicit deeper, more thoughtful deliberation. Participants’ comments around two policy areas – mandatory sentencing and the use of alternatives to imprisonment – were founded on concerns about the need for judges to tailor the sentence to fit the specific circumstances of each case. The methodology itself has shown that people may change their initial opinions on complex issues when given the opportunity to discuss and reflect on their beliefs.

‘It's all scientific to me’ : focus group insights into why young people do not apply safe-sex knowledge

Despite rising levels of safe-sex knowledge in Australia, sexually transmitted infection notifications continue to increase. A culture-centred approach suggests it is useful in attempting to reach a target population first to understand their perspective on the issues. Twenty focus groups were conducted with 89 young people between the ages of 14 and 16 years. Key findings suggest that scientific information does not articulate closely with everyday practice, that young people get the message that sex is bad and they should not be preparing for it and that it is not appropriate to talk about sex. Understanding how young people think about these issues is particularly important because the focus groups also found that young people disengage from sources of information that do not match their own experiences.

Graph theory based representation of building information models for access control applications

Building information models are increasingly being utilised for facility management of large facilities such as critical infrastructures. In such environments, it is valuable to utilise the vast amount of data contained within the building information models to improve access control administration. The use of building information models in access control scenarios can provide 3D visualisation of buildings as well as many other advantages such as automation of essential tasks including path finding, consistency detection, and accessibility verification. However, there is no mathematical model for building information models that can be used to describe and compute these functions. In this paper, we show how graph theory can be utilised as a representation language of building information models and the proposed security related functions. This graph-theoretic representation allows for mathematically representing building information models and performing computations using these functions.