Subtropical futures : Victoria Park re-imagined

Brisbane, the capital of Queensland, in South-East Queensland is situated on the Brisbane River, one of the largest rivers (and floodplains) on the east coast of Australia. The river defines the city and gives it its name. The river has been a natural place to accommodate some population growth for the city with high-density development that capitalises on the natural amenity, cycleways and a string of parks and the flatter land. The major floods of 2011 and the scare of 2013, has seen a more malevolent quality of the river and shift of thinking on its role within the city. The floods have made council, for the first time, acquire prime development sites near the river, with proposals for high density development and made them parks, at great cost. The pressure for population growth in Brisbane remains. 140,000 new dwellings are required by 2031. Brownfield sites are less plentiful and there is interest to rethink of some of the other strategic locations in the city away from the river on higher ground and steeper slopes. Some of these places are currently open spaces. Victoria Park Golf Course sits on a high ridge line and a very strategic part of the city just north of the city centre is one of the few remaining golf courses close to the centre of an Australian capital city. While it is a public course and a valuable community asset, it has been compromised by the recently completed northern busway with two bus stations constructed on its edges. It is bounded on the west and north-east by two major community facilities, the Queensland University of Technology (QUT) to the west and RBW Hospital at its northern end. In a city in need of urban consolidation, perhaps it is time to review the future of the golf course. This question has been investigated as a conjecture in the Master of Architecture program at the QUT. The project has been to re-imagine Victoria Park as a new city parkland and a place that makes an urban connection from the QUT to the hospital. This new urban precinct is be a medium to high-density transit oriented development that capitalises on the bus way stations and the proximity of the university and hospital. The precinct will frame/define/interact with the new major urban park for the city. A key question being addressed is how the design can embody and define principles of a subtropical urbanism. Students are identifying the appropriate street and block structure, density and built form to be accommodated on blocks that define and activate a rich sequence of streets and public spaces. The paper will present a critical overview of the project work that provides a lens to how future professionals may respond to these issue that will be the focus of their professional lives.

Populations of models, experimental designs and coverage of parameter space by Latin Hypercube and Orthogonal Sampling

In this paper we have used simulations to make a conjecture about the coverage of a t-dimensional subspace of a d-dimensional parameter space of size n when performing k trials of Latin Hypercube sampling. This takes the form P(k,n,d,t) = 1 - e^(-k/n^(t-1)). We suggest that this coverage formula is independent of d and this allows us to make connections between building Populations of Models and Experimental Designs. We also show that Orthogonal sampling is superior to Latin Hypercube sampling in terms of allowing a more uniform coverage of the t-dimensional subspace at the sub-block size level. These ideas have particular relevance when attempting to perform uncertainty quantification and sensitivity analyses.

Two linear beetle-type scanning tunneling microscopes

Two beetle-type scanning tunneling microscopes are described. Both designs have the thermal stability of the Besocke beetle and the simplicity of the Wilms beetle. Moreover, sample holders were designed that also allow both semiconductor wafers and metal single crystals to be studied. The coarse approach is a linear motion of the beetle towards the sample using inertial slip–stick motion. Ten wires are required to control the position of the beetle and scanner and measure the tunneling current. The two beetles were built with different sized piezolegs, and the vibrational properties of both beetles were studied in detail. It was found, in agreement with previous work, that the beetle bending mode is the lowest principal eigenmode. However, in contrast to previous vibrational studies of beetle-type scanning tunneling microscopes, we found that the beetles did not have the “rattling” modes that are thought to arise from the beetle sliding or rocking between surface asperities on the raceway. The mass of our beetles is 3–4 times larger than the mass of beetles where rattling modes have been observed. We conjecture that the mass of our beetles is above a “critical beetle mass.” This is defined to be the beetle mass that attenuates the rattling modes by elastically deforming the contact region to the extent that the rattling modes cannot be identified as distinct modes in cross-coupling measurements.

On optimum stratification with proportional allocation for a class of pareto distributions

Cum ./LSTA_A_8828879_O_XML_IMAGES/LSTA_A_8828879_O_ILM0001.gif rule [Singh (1975)] has been suggested in the literature for finding approximately optimum strata boundaries for proportional allocation, when the stratification is done on the study variable. This paper shows that for the class of density functions arising from the Wang and Aggarwal (1984) representation of the Lorenz Curve (or DBV curves in case of inventory theory), the cum ./LSTA_A_8828879_O_XML_IMAGES/LSTA_A_8828879_O_ILM0002.gif rule in place of giving approximately optimum strata boundaries, yields exactly optimum boundaries. It is also shown that the conjecture of Mahalanobis (1952) “. . .an optimum or nearly optimum solutions will be obtained when the expected contribution of each stratum to the total aggregate value of Y is made equal for all strata” yields exactly optimum strata boundaries for the case considered in the paper.

Limitations of the manual supination resistance test

The aim of this study was to asses results obtained from a range of commonly performed lower extremity “open and closed” chain kinetic tests used for predicting foot function and correlate these test findings to data obtained from the Zebris WinFDM-T system®. When performed correctly these tests are thought to be indicators of lower extremity function. Podiatrists frequently perform examinations of joint and muscle structures to understand biomechanical function; however the relationship between these routine tests and forces generated during the gait cycle are not always well understood. This can introduce a degree of variability in clinical interpretation which creates conjecture regarding the value of these tests.

Acyclic Edge Coloring of Graphs with Maximum Degree 4

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by a'(G). It was conjectured by Alon, Sudakov, and Zaks that for any simple and finite graph G, a'(G) <= Delta+2, where Delta=Delta(G) denotes the maximum degree of G. We prove the conjecture for connected graphs with Delta(G)<= 4, with the additional restriction that m <= 2n-1, where n is the number of vertices and m is the number of edges in G. Note that for any graph G, m <= 2n, when Delta(G)<= 4. It follows that for any graph G if Delta(G)<= 4, then a'(G) <= 7.

Generalized Burgers equations and Euler-Painleve transcendents. II

It was proposed earlier [P. L. Sachdev, K. R. C. Nair, and V. G. Tikekar, J. Math. Phys. 27, 1506 (1986)] that the Euler Painlevé equation yy[script `]+ay[script ']2+ f(x)yy[script ']+g(x) y2+by[script ']+c=0 represents the generalized Burgers equations (GBE's) in the same manner as Painlevé equations do the KdV type. The GBE was treated with a damping term in some detail. In this paper another GBE ut+uaux+Ju/2t =(gd/2)uxx (the nonplanar Burgers equation) is considered. It is found that its self-similar form is again governed by the Euler Painlevé equation. The ranges of the parameter alpha for which solutions of the connection problem to the self-similar equation exist are obtained numerically and confirmed via some integral relations derived from the ODE's. Special exact analytic solutions for the nonplanar Burgers equation are also obtained. These generalize the well-known single hump solutions for the Burgers equation to other geometries J=1,2; the nonlinear convection term, however, is not quadratic in these cases. This study fortifies the conjecture regarding the importance of the Euler Painlevé equation with respect to GBE's. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Improvement On Brooks Chromatic Bound For A Class Of Graphs

Brooks' Theorem says that if for a graph G,Δ(G)=n, then G is n-colourable, unless (1) n=2 and G has an odd cycle as a component, or (2) n>2 and Kn+1 is a component of G. In this paper we prove that if a graph G has none of some three graphs (K1,3;K5−e and H) as an induced subgraph and if Δ(G)greater-or-equal, slanted6 and d(G)<Δ(G), then χ(G)<Δ(G). Also we give examples to show that the hypothesis Δ(G)greater-or-equal, slanted6 can not be non-trivially relaxed and the graph K5−e can not be removed from the hypothesis. Moreover, for a graph G with none of K1,3;K5−e and H as an induced subgraph, we verify Borodin and Kostochka's conjecture that if for a graph G,Δ(G)greater-or-equal, slanted9 and d(G)<Δ(G), then χ(G)<Δ(G).

Ultrasound of paediatric appendicitis and its secondary sonographic signs: Providing a more meaningful finding

Sonography is an important clinical tool in diagnosing appendicitis in children as it can obviate both exposure to potentially harmful ionising radiation from computed tomography scans and the need for unnecessary appendicectomies. This review examines the diagnostic accuracy of ultrasound in the identification of acute appendicitis, with a particular focus on the the utility of secondary sonographic signs as an adjunct or corollary to traditionally examined criteria. These secondary signs can be important in cases where the appendix cannot be identified with ultrasound and a more meaningful finding may be made by incorporating the presence or absence of secondary sonographic signs. There is evidence that integrating these secondary signs into the final ultrasound diagnosis can improve the utility of ultrasound in cases where appendicitis is expected, though there remains some conjecture about whether they play a more important role in negative or positive prediction in the absence of an identifiable appendix.

Conformal Field Theory Methods for Variants of Schramm-Loewner Evolutions

This thesis consists of an introduction, four research articles and an appendix. The thesis studies relations between two different approaches to continuum limit of models of two dimensional statistical mechanics at criticality. The approach of conformal field theory (CFT) could be thought of as the algebraic classification of some basic objects in these models. It has been succesfully used by physicists since 1980's. The other approach, Schramm-Loewner evolutions (SLEs), is a recently introduced set of mathematical methods to study random curves or interfaces occurring in the continuum limit of the models. The first and second included articles argue on basis of statistical mechanics what would be a plausible relation between SLEs and conformal field theory. The first article studies multiple SLEs, several random curves simultaneously in a domain. The proposed definition is compatible with a natural commutation requirement suggested by Dubédat. The curves of multiple SLE may form different topological configurations, ``pure geometries''. We conjecture a relation between the topological configurations and CFT concepts of conformal blocks and operator product expansions. Example applications of multiple SLEs include crossing probabilities for percolation and Ising model. The second article studies SLE variants that represent models with boundary conditions implemented by primary fields. The most well known of these, SLE(kappa, rho), is shown to be simple in terms of the Coulomb gas formalism of CFT. In the third article the space of local martingales for variants of SLE is shown to carry a representation of Virasoro algebra. Finding this structure is guided by the relation of SLEs and CFTs in general, but the result is established in a straightforward fashion. This article, too, emphasizes multiple SLEs and proposes a possible way of treating pure geometries in terms of Coulomb gas. The fourth article states results of applications of the Virasoro structure to the open questions of SLE reversibility and duality. Proofs of the stated results are provided in the appendix. The objective is an indirect computation of certain polynomial expected values. Provided that these expected values exist, in generic cases they are shown to possess the desired properties, thus giving support for both reversibility and duality.

Distortion of Dimension under Quasiconformal Mappings

Quasiconformal mappings are natural generalizations of conformal mappings. They are homeomorphisms with 'bounded distortion' of which there exist several approaches. In this work we study dimension distortion properties of quasiconformal mappings both in the plane and in higher dimensional Euclidean setting. The thesis consists of a summary and three research articles. A basic property of quasiconformal mappings is the local Hölder continuity. It has long been conjectured that this regularity holds at the Sobolev level (Gehring's higher integrabilty conjecture). Optimal regularity would also provide sharp bounds for the distortion of Hausdorff dimension. The higher integrability conjecture was solved in the plane by Astala in 1994 and it is still open in higher dimensions. Thus in the plane we have a precise description how Hausdorff dimension changes under quasiconformal deformations for general sets. The first two articles contribute to two remaining issues in the planar theory. The first one concerns distortion of more special sets, for rectifiable sets we expect improved bounds to hold. The second issue consists of understanding distortion of dimension on a finer level, namely on the level of Hausdorff measures. In the third article we study flatness properties of quasiconformal images of spheres in a quantitative way. These also lead to nontrivial bounds for their Hausdorff dimension even in the n-dimensional case.

Semi-Classical Mechanics in Phase Space: A Study of Wigner's Function

We explore the semi-classical structure of the Wigner functions ($\Psi $(q, p)) representing bound energy eigenstates $|\psi \rangle $ for systems with f degrees of freedom. If the classical motion is integrable, the classical limit of $\Psi $ is a delta function on the f-dimensional torus to which classical trajectories corresponding to ($|\psi \rangle $) are confined in the 2f-dimensional phase space. In the semi-classical limit of ($\Psi $ ($\hslash $) small but not zero) the delta function softens to a peak of order ($\hslash ^{-\frac{2}{3}f}$) and the torus develops fringes of a characteristic 'Airy' form. Away from the torus, $\Psi $ can have semi-classical singularities that are not delta functions; these are discussed (in full detail when f = 1) using Thom's theory of catastrophes. Brief consideration is given to problems raised when ($\Psi $) is calculated in a representation based on operators derived from angle coordinates and their conjugate momenta. When the classical motion is non-integrable, the phase space is not filled with tori and existing semi-classical methods fail. We conjecture that (a) For a given value of non-integrability parameter ($\epsilon $), the system passes through three semi-classical regimes as ($\hslash $) diminishes. (b) For states ($|\psi \rangle $) associated with regions in phase space filled with irregular trajectories, ($\Psi $) will be a random function confined near that region of the 'energy shell' explored by these trajectories (this region has more than f dimensions). (c) For ($\epsilon \neq $0, $\hslash $) blurs the infinitely fine classical path structure, in contrast to the integrable case ($\epsilon $ = 0, where $\hslash $ )imposes oscillatory quantum detail on a smooth classical path structure.

Strategic Information Acquisition: Applications to Herding and Auctions

The information that the economic agents have and regard relevant to their decision making is often assumed to be exogenous in economics. It is assumed that the agents either poses or can observe the payoff relevant information without having to exert any effort to acquire it. In this thesis we relax the assumption of ex-ante fixed information structure and study what happens to the equilibrium behavior when the agents must also decide what information to acquire and when to acquire it. This thesis addresses this question in the two essays on herding and two essays on auction theory. In the first two essays, that are joint work with Klaus Kultti, we study herding models where it is costly to acquire information on the actions that the preceding agents have taken. In our model the agents have to decide both the action that they take and additionally the information that they want to acquire by observing their predecessors. We characterize the equilibrium behavior when the decision to observe preceding agents' actions is endogenous and show how the equilibrium outcome may differ from the standard model, where all preceding agents actions are assumed to be observable. In the latter part of this thesis we study two dynamic auctions: the English and the Dutch auction. We consider a situation where bidder(s) are uninformed about their valuations for the object that is put up for sale and they may acquire this information for a small cost at any point during the auction. We study the case of independent private valuations. In the third essay of the thesis we characterize the equilibrium behavior in an English auction when there are informed and uninformed bidders. We show that the informed bidder may jump bid and signal to the uninformed that he has a high valuation, thus deterring the uninformed from acquiring information and staying in the auction. The uninformed optimally acquires information once the price has passed a particular threshold and the informed has not signalled that his valuation is high. In addition, we provide an example of an information structure where the informed bidder initially waits and then makes multiple jumps. In the fourth essay of this thesis we study the Dutch auction. We consider two cases where all bidders are all initially uninformed. In the first case the information acquisition cost is the same across all bidders and in the second also the cost of information acquisition is independently distributed and private information to the bidders. We characterize a mixed strategy equilibrium in the first and a pure strategy equilibrium in the second case. In addition we provide a conjecture of an equilibrium in an asymmetric situation where there is one informed and one uninformed bidder. We compare the revenues that the first price auction and the Dutch auction generate and we find that under some circumstances the Dutch auction outperforms the first price sealed bid auction. The usual first price sealed bid auction and the Dutch auction are strategically equivalent. However, this equivalence breaks down in case information is acquired during the auction.

Phylogeography and Population Genetics of the Moor frog (Rana arvalis Nilsson) in Northern Europe

The ongoing climate change along with increasing levels of pollutants, diseases, habitat loss and fragmentation constitute global threats to the persistence of many populations, species and ecosystems. However, for the long-term persistence of local populations, one of the biggest threats is the intrinsic loss of genetic variation. In order to adapt to changes in the environment, organisms must have a sufficient supply of heritable variation in traits important for their fitness. With a loss of genetic variation, the risk of extinction will increase. For conservational practices, one should therefore understand the processes that shape the genetic population structure and also the broader (historical) phylogenetic patterning of the species in focus. In this thesis, microsatellite markers were applied to study genetic diversity and population differentiation of the protected moor frog (Rana arvalis) in Fennoscandia from both historical (evolutionary) and applied (conservation) perspectives. The results demonstrate that R. arvalis populations are highly structured over rather short geographic distances. Moreover, the results suggest that R. arvalis recolonized Fennoscandia from two directions after the last ice age. This has had implications for the genetic structuring and population differentiation, especially in the northernmost parts where the two lineages have met. Compared to more southern populations, the genetic variation decreases and the interpopulation differentiation increases dramatically towards north. This could be an outcome of serial population bottlenecking along the recolonization route. Also, current isolation and small population sizes increase the effect of drift, thus reinforcing the observed pattern. The same pattern can also be seen in island populations. However, though R. arvalis on the island of Gotland has lost most of its neutral genetic variability, our results indicate that the levels of additive genetic variation have remained high. This conforms to the conjecture that though neutral markers are widely used in conservation purposes, they may be quite uninformative about the levels of genetic variation in ecologically important traits. Finally, the evolutionary impact of the typical amphibian mating behaviour on genetic diversity was investigated. Given the short time available for larval development, it is important that mating takes place as early as possible. The genetic data and earlier capture-recapture data suggest that R. arvalis gather at mating grounds they are familiar with. However, by forming leks in random to relatedness, and having multiple paternities in single clutches, the risk of inbreeding may be minimized in this otherwise highly philopatric species.

The Consequences of Phenotypic Plasticity in Cyclically Varying Environments: A Genetic Algorithm Study

By “phenotypic plasticity” we refer to the capacity of a genotype to exhibit different phenotypes, whether in the same or in different environments. We have previously demonstrated that phenotypic plasticity can improve the degree of adaptation achieved via natural selection (Behera & Nanjundiah, 1995). That result was obtained from a genetic algorithm model of haploid genotypes (idealized as one-dimensional strings of genes) evolving in a fixed environment. Here, the dynamics of evolution is examined under conditions of a cyclically varying environment. We find that the rate of evolution, as well as the extent of adaptation (as measured by mean population fitness) is lowered because of environmental cycling. The decrease is adaptation caused by a varying environment can, however, be partly or wholly compensated by an increase in the degree of plasticity that a genotype is capable of. Also, the reduction of population fitness caused by a variable environment can be partially offset by decreasing the total number of genetic loci. We conjecture that an increase in genome size may have been among the factors responsible for the evolution of phenotypic plasticity.