On the effect of topology on cellular automata rule spaces

This thesis presents an empirical study of the effects of topology on cellular automata rule spaces. The classical definition of a cellular automaton is restricted to that of a regular lattice, often with periodic boundary conditions. This definition is extended to allow for arbitrary topologies. The dynamics of cellular automata within the triangular tessellation were analysed when transformed to 2-manifolds of topological genus 0, genus 1 and genus 2. Cellular automata dynamics were analysed from a statistical mechanics perspective. The sample sizes required to obtain accurate entropy calculations were determined by an entropy error analysis which observed the error in the computed entropy against increasing sample sizes. Each cellular automata rule space was sampled repeatedly and the selected cellular automata were simulated over many thousands of trials for each topology. This resulted in an entropy distribution for each rule space. The computed entropy distributions are indicative of the cellular automata dynamical class distribution. Through the comparison of these dynamical class distributions using the E-statistic, it was identified that such topological changes cause these distributions to alter. This is a significant result which implies that both global structure and local dynamics play a important role in defining long term behaviour of cellular automata.

kmth price sealed-bid auctions with general independent values and equilibrium linear mark-ups

A generalised bidding model is developed to calculate a bidder’s expected profit and auctioners expected revenue/payment for both a General Independent Value and Independent Private Value (IPV) kmth price sealed-bid auction (where the mth bidder wins at the kth bid payment) using a linear (affine) mark-up function. The Common Value (CV) assumption, and highbid and lowbid symmetric and asymmetric First Price Auctions and Second Price Auctions are included as special cases. The optimal n bidder symmetric analytical results are then provided for the uniform IPV and CV models in equilibrium. Final comments concern implications, the assumptions involved and prospects for further research.

Exploration of the fundamental equilibrium behaviour of calcium exchange with weak acid cation resins

This study evaluated the complexity of calcium ion exchange with sodium exchanged weak acid cation resin (DOW MAC-3). Exchange equilibria recorded for a range of different solution normalities revealed profiles which were represented by conventional “L” or “H” type isotherms at low values of equilibrium concentration (Ce) of calcium ions, plus a superimposed region of increasing calcium uptake was observed at high Ce values. The loading of calcium ions was determined to be ca. 53.5 to 58.7 g/kg of resin when modelling only the sorption curve created at low Ce values,which exhibited a well-defined plateau. The calculated calcium ion loading capacity for DOWMAC-3 resin appeared to correlate with the manufacturer's recommendation. The phenomenon of super equivalent ion exchange (SEIX) was observed when the “driving force” for the exchange process was increased in excess of 2.25 mmol calcium ions per gram of resin in the starting solution. This latter event was explained in terms of displacement of sodium ions from sodium hydroxide solution which remained in the resin bead following the initial conversion of the as supplied “H+” exchanged resin sites to the “Na+” version required for softening studies. Evidence for hydrolysis of a small fraction of the sites on the sodium exchanged resin surface was noted. The importance of carefully choosing experimental parameters was discussed especially in relation to application of the Langmuir–Vageler expression. This latter model which compared the ratio of the initial calcium ion concentration in solution to resin mass, versus final equilibrium loading of the calcium ions on the resin; was discovered to be an excellent means of identifying the progress of the calcium–sodium ion exchange process. Moreover, the Langmuir–Vageler model facilitated standardization of various calcium–sodium ion exchange experiments which allowed systematic experimental design.

Equilibrium and column studies of iron exchange with strong acid cation resin

The exchange of iron species from iron (III) chloride solutions with a strong acid cation resin has been investigated in relation to a variety of water and wastewater applications. A detailed equilibrium isotherm analysis was conducted wherein models such as Langmuir Vageler, Competitive Langmuir, Freundlich, Temkin, Dubinin Astakhov, Sips and Brouers-Sotolongo were applied to the experimental data. An important conclusion was that both the bottle-point method and solution normality used to generate the ion exchange equilibrium information influenced which sorption model fitted the isotherm profiles optimally. Invariably, the calculated value for the maximum loading of iron on strong acid cation resin was substantially higher than the value of 47.1 g/kg of resin which would occur if one Fe3+ ion exchanged for three “H+” sites on the resin surface. Consequently, it was suggested that above pH 1, various iron complexes sorbed to the resin in a manner which required less than 3 sites per iron moiety. Column trials suggested that the iron loading was 86.6 g/kg of resin when 1342 mg/L Fe (III) ions in water were flowed at 31.7 bed volumes per hour. Regeneration with 5 to 10 % HCl solutions reclaimed approximately 90 % of exchange sites.

Impact of mobility and topology on information diffusion in MANETs

In some delay-tolerant communication systems such as vehicular ad-hoc networks, information flow can be represented as an infectious process, where each entity having already received the information will try to share it with its neighbours. The random walk and random waypoint models are popular analysis tools for these epidemic broadcasts, and represent two types of random mobility. In this paper, we introduce a simulation framework investigating the impact of a gradual increase of bias in path selection (i.e. reduction of randomness), when moving from the former to the latter. Randomness in path selection can significantly alter the system performances, in both regular and irregular network structures. The implications of these results for real systems are discussed in details.

Permanent shift: the topology of Didier Vermeiren's Cariatide à la Pierre

Photographic documentation of sculpture produces significant consequences for the way in which sculptural space is conceived. When viewed as discrete mediums the interaction of the photograph and its sculptural subject is always framed by notions of loss. However, when taken as a composite system, the sculpture-photograph proposes a new ontology of space. In place of the fixity of medium, we can observe a topology at play: a theory drawn from mathematics in which space is understood not as a static field but in terms of properties of connectedness, movement and differentiation. Refracted through the photographic medium, sculpture becomes not a field of fixed points in space, but rather as a fluid set of relations - a continuous sequence of multiple ‘surfaces’, a network of shifting views. This paper will develop a topological account of studio practice through an examination of the work of the contemporary Belgian sculptor Didier Vermeiren (b. 1951). Since the 1980s, Vermeiren has made extensive use of photography in his sculptural practice. By analysing a series of iterations of his work Cariatide à la Pierre (1997-1998), this paper proposes that Vermeiren’s use of photography reveals patterns of connection that expand and complicate the language of sculpture, while also emphasising the broader topology of the artist’s practice as a network of ‘backward glances’ to previous works from the artist’s oeuvre and the art-historical canon. In this context, photography is not simply a method of documentation, but rather a means of revealing the intrinsic condition of sculpture as medium shaped by dynamic patterns of connection and change. In Vermeiren’s work the sculpture-photograph, has a composite identity that exceeds straightforward categories of medium. In their place, we can observe a practice based upon the complex interactions of objects whose ontology is always underpinned by a certain contingency. It is in this fundamental mobility, that the topology of Vermeiren’s practice can be said to rest.

Hierarchical clustering of the genetic connectivity matrix reveals the network topology of gene action on brain microstructure: An N=531 twin study

Genetic correlation (rg) analysis determines how much of the correlation between two measures is due to common genetic influences. In an analysis of 4 Tesla diffusion tensor images (DTI) from 531 healthy young adult twins and their siblings, we generalized the concept of genetic correlation to determine common genetic influences on white matter integrity, measured by fractional anisotropy (FA), at all points of the brain, yielding an NxN genetic correlation matrix rg(x,y) between FA values at all pairs of voxels in the brain. With hierarchical clustering, we identified brain regions with relatively homogeneous genetic determinants, to boost the power to identify causal single nucleotide polymorphisms (SNP). We applied genome-wide association (GWA) to assess associations between 529,497 SNPs and FA in clusters defined by hubs of the clustered genetic correlation matrix. We identified a network of genes, with a scale-free topology, that influences white matter integrity over multiple brain regions.

Brain network efficiency and topology depend on the fiber tracking method: 11 tractography algorithms compared in 536 subjects

As connectivity analyses become more popular, claims are often made about how the brain's anatomical networks depend on age, sex, or disease. It is unclear how results depend on tractography methods used to compute fiber networks. We applied 11 tractography methods to high angular resolution diffusion images of the brain (4-Tesla 105-gradient HARDI) from 536 healthy young adults. We parcellated 70 cortical regions, yielding 70×70 connectivity matrices, encoding fiber density. We computed popular graph theory metrics, including network efficiency, and characteristic path lengths. Both metrics were robust to the number of spherical harmonics used to model diffusion (4th-8th order). Age effects were detected only for networks computed with the probabilistic Hough transform method, which excludes smaller fibers. Sex and total brain volume affected networks measured with deterministic, tensor-based fiber tracking but not with the Hough method. Each tractography method includes different fibers, which affects inferences made about the reconstructed networks.

Biomimicking natural nanopatterned topology by 3D laser lithography

Natural nanopatterned surfaces (nNPS) present on insect wings have demonstrated bactericidal activity [1, 2]. Fabricated nanopatterned surfaces (fNPS) derived by characterization of these wings have also shown superior bactericidal activity [2]. However bactericidal NPS topologies vary in both geometry and chemical characteristics of the individual features in different insects and fabricated surfaces, rendering it difficult to ascertain the optimum geometrical parameters underling bactericidal activity. This situation calls for the adaptation of new and emerging techniques, which are capable of fabricating and characterising comparable structures to nNPS from biocompatible materials. In this research, CAD drawn nNPS representing an area of 10 μm x10 μm was fabricated on a fused silica glass by Nanoscribe photonic professional GT 3D laser lithography system using two photon polymerization lithography. The glass was cleaned with acetone and isopropyl alcohol thrice and a drop of IP-DIP photoresist from Nanoscribe GmbH was cast onto the glass slide prior to patterning. Photosensitive IP-DIP resist was polymerized with high precision to make the surface nanopatterns using a 780 nm wavelength laser. Both moving-beam fixedsample (MBFS) and fixed-beam moving-sample (FBMS) fabrication approaches were tested during the fabrication process to determine the best approach for the precise fabrication of the required nanotopological pattern. Laser power was also optimized to fabricate the required fNPS, where this was changed from 3mW to 10mW to determine the optimum laser power for the polymerization of the photoresist for fabricating FNPS...

The equilibrium geometry and electronic structure of Bi nanolines on clean and hydrogenated Si(001) surfaces

The equilibrium geometry, electronic structure and energetic stability of Bi nanolines on clean and hydrogenated Si(001) surfaces have been examined by means of ab initio total energy calculations and scanning tunnelling microscopy. For the Bi nanolines on a clean Si surface the two most plausible structural models, the Miki or M model (Miki et al 1999 Phys. Rev. B 59 14868) and the Haiku or H model (Owen et al 2002 Phys. Rev. Lett. 88 226104), have been examined in detail. The results of the total energy calculations support the stability of the H model over the M model, in agreement with previous theoretical results. For Bi nanolines on the hydrogenated Si(001) surface, we find that an atomic configuration derived from the H model is also more stable than an atomic configuration derived from the M model. However, the energetically less stable (M) model exhibits better agreement with experimental measurements for equilibrium geometry. The electronic structures of the H and M models are very similar. Both models exhibit a semiconducting character, with the highest occupied Bi-derived bands lying at ~0.5 eV below the valence band maximum. Simulated and experimental STM images confirm that at a low negative bias the Bi lines exhibit an 'antiwire' property for both structural models.

A Global Constraint On Relative Rotation To Avoid Lumped Compliant Mechanisms In Topology Optimization

Some of the well known formulations for topology optimization of compliant mechanisms could lead to lumped compliant mechanisms. In lumped compliance, most of the elastic deformation in a mechanism occurs at few points, while rest of the mechanism remains more or less rigid. Such points are referred to as point-flexures. It has been noted in literature that high relative rotation is associated with point-flexures. In literature we also find a formulation of local constraint on relative rotations to avoid lumped compliance. However it is well known that a global constraint is easier to handle than a local constraint, by a numerical optimization algorithm. The current work presents a way of putting global constraint on relative rotations. This constraint is also simpler to implement since it uses linearized rotation at the center of finite-elements, to compute relative rotations. I show the results obtained by using this constraint oil the following benchmark problems - displacement inverter and gripper.

The nature of non-equilibrium solidification of undercooled Agsingle bondCu alloys in contact with primary copper dendrites

Liquids of silver-copper alloys with near eutectic compositions embedded in a copper matrix were undercooled. The structural and microstructural investigations of these alloys solidified from undercooled temperature indicated the absence of both the eutectic reaction and diffusionless transformation below the equal free energy curve (T0). Instead the liquid maintained local equilibrium with the copper dendrites continuously until it intersected the extended solidus of the silver rich solid solution.

Topology-Guided Tessellation Of Quadratic Elements

Topology-based methods have been successfully used for the analysis and visualization of piecewise-linear functions defined on triangle meshes. This paper describes a mechanism for extending these methods to piecewise-quadratic functions defined on triangulations of surfaces. Each triangular patch is tessellated into monotone regions, so that existing algorithms for computing topological representations of piecewise-linear functions may be applied directly to the piecewise-quadratic function. In particular, the tessellation is used for computing the Reeb graph, a topological data structure that provides a succinct representation of level sets of the function.

On The Topology Of Manifolds With Positive Isotropic Curvature

We show that a closed orientable Riemannian n-manifold, n >= 5, with positive isotropic curvature and free fundamental group is homeomorphic to the connected sum of copies of Sn-1 x S-1.

Equilibrium studies of ammonium exchange with Australian natural zeolites

This paper is concerned with the study of the equilibrium exchange of ammonium ions with two natural zeolite samples sourced in Australia from Castle Mountain Zeolites and Zeolite Australia. A range of sorption models including Langmuir Vageler, Competitive Langmuir, Freundlich, Temkin, Dubinin Astakhov and Brouers–Sotolongo were applied in order to gain an insight as to the exchange process. In contrast to most previous studies, non-linear regression was used in all instances to determine the best fit of the experimental data. Castle Mountain natural zeolite was found to exhibit higher ammonium capacity than Zeolite Australia material when in the freshly received state, and this behavior was related to the greater amount of sodium ions present relative to calcium ions on the zeolite exchange sites. The zeolite capacity for ammonium ions was also found to be dependent on the solution normality, with 35–60% increase inuptake noted when increasing the ammonium concentration from 250 to 1000 mg/L. The optimal fit ofthe equilibrium data was achieved by the Freundlich expression as confirmed by use of Akaikes Information Criteria. It was emphasized that the bottle-point method chosen influenced the isotherm profile in several ways, and could lead to misleading interpretation of experiments, especially if the constant zeolite mass approach was followed. Pre-treatment of natural zeolite with acid and subsequently sodium hydroxide promoted the uptake of ammonium species by at least 90%. This paper highlighted the factors which should be taken into account when investigating ammonium ion exchange with natural zeolites.