DSpace Community:
http://hdl.handle.net/2381/445
2016-12-04T20:28:42Z
2016-12-04T20:28:42Z
A New Bayesian Test to test for the Intractability-Countering Hypothesis
Chakrabarty, Dalia
http://hdl.handle.net/2381/38804
2016-12-03T03:57:02Z
2016-12-02T12:24:33Z
Title: A New Bayesian Test to test for the Intractability-Countering Hypothesis
Authors: Chakrabarty, Dalia
Abstract: We present a new test of hypothesis in which we seek the probability of the null conditioned on the data, where the null is a simplification undertaken to counter the intractability of the more complex model, that the simpler null model is nested within. With the more complex model rendered intractable, the null model uses a simplifying assumption that capacitates the learning of an unknown parameter vector given the data. Bayes factors are shown to be known only up to a ratio of unknown data-dependent constants–a problem that cannot be cured using prescriptions similar to those suggested to solve the problem caused to Bayes factor computation, by non-informative priors. Thus, a new test is needed in which we can circumvent Bayes factor computation. In this test, we undertake generation of data from the model in which the null hypothesis is true and can achieve support in the measured data for the null by comparing the marginalised posterior of the model parameter given the measured data, to that given such generated data. However, such a ratio of marginalised posteriors can confound interpretation of comparison of support in one measured data for a null, with that in another data set for a different null. Given an application in which such comparison is undertaken, we alternatively define support in a measured data set for a null by identifying the model parameters that are less consistent with the measured data than is minimally possible given the generated data, and realising that the higher the number of such parameter values, less is the support in the measured data for the null. Then, the probability of the null conditional on the data is given within an MCMC-based scheme, by marginalising the posterior given the measured data, over parameter values that are as, or more consistent with the measured data, than with the generated data. In the aforementioned application, we test the hypothesis that a galactic state space bears an isotropic geometry, where the (missing) data comprising measurements of some components of the state space vector of a sample of observed galactic particles, is implemented to Bayesianly learn the gravitational mass density of all matter in the galaxy. In lieu of an assumption about the state space being isotropic, the likelihood of the sought gravitational mass density given the data, is intractable. For a real example galaxy, we find unequal values of the probability of the null–that the host state space is isotropic–given two different data sets, implying that in this galaxy, the system state space constitutes at least two disjoint sub-volumes that the two data sets respectively live in. Implementation on simulated galactic data is also undertaken, as is an empirical illustration on the well-known O-ring data, to test for the form of the thermal variation of the failure probability of the O-rings.
Description: Details of the Bayesian learning of the gravitational mass density and state spacepd fof the galaxyare provided in SectionS-1of the attached supplementary material. SectionS-2discusses detailsof the Fully Bayesian Significance Test.
2016-12-02T12:24:33Z
Pattern, process, scale, and model's sensitivity: Comment on "Phase separation driven by density-dependent movement: A novel mechanism for ecological patterns" by Quan-Xing Liu et al.
Petrovskii, Sergei
http://hdl.handle.net/2381/38764
2016-11-30T03:21:06Z
2016-11-29T16:09:05Z
Title: Pattern, process, scale, and model's sensitivity: Comment on "Phase separation driven by density-dependent movement: A novel mechanism for ecological patterns" by Quan-Xing Liu et al.
Authors: Petrovskii, Sergei
Abstract: Spatial distribution of ecological populations is rarely homogeneous. Typically, the population density exhibits considerable variability of space, in an extreme yet not uncommon case creating a “patchy” pattern where areas of high population density alternate with areas where the population density is much lower or close to zero [1]. This phenomenon, often generically referred to as ecological patterning or ecological pattern formation, has long been a focus of interest in ecology and a number of theories and models have been developed aiming to explain it under different ecological and/or environmental conditions and on different spatial and temporal scales; see Table 1. A straightforward explanation of the heterogeneous distribution of population density relates it to the heterogeneity of the environment (e.g. to nonuniform distribution of resources) and this is indeed often the case [2]. However, a closer look reveals that this is not enough and in many cases the heterogeneity of population density is only weakly correlated to the heterogeneity of the environment [3] and [19]. Understanding that biological interactions play, on the relevant spatial and temporal scales [20], as important role in shaping the ecological patterns as the physical/chemical forcing resulted in a number of theories. The earliest one that used the idea of Turing's instability [4] was followed by several others [5], [6] and [21] including theories where pattern formation was due to a non-Turing mechanism [8] and [9] and theories where the movement behavior and/or density dependence was an essential factor [12] and [14].
2016-11-29T16:09:05Z
Quantifying uncertainty in partially specified biological models: How can optimal control theory help us?
Adamson, M. W.
Morozov, A. Y.
Kuzenkov, O. A.
http://hdl.handle.net/2381/38719
2016-11-26T04:12:09Z
2016-11-25T09:58:35Z
Title: Quantifying uncertainty in partially specified biological models: How can optimal control theory help us?
Authors: Adamson, M. W.; Morozov, A. Y.; Kuzenkov, O. A.
Abstract: Mathematical models in biology are highly simplified representations of a complex underlying reality and there is always a high degree of uncertainty with regards to model function specification. This uncertainty becomes critical for models in which the use of different functions fitting the same dataset can yield substantially different predictions-a property known as structural sensitivity. Thus, even if the model is purely deterministic, then the uncertainty in the model functions carries through into uncertainty in model predictions, and new frameworks are required to tackle this fundamental problem. Here, we consider a framework that uses partially specified models in which some functions are not represented by a specific form. The main idea is to project infinite dimensional function space into a low-dimensional space taking into account biological constraints. The key question of how to carry out this projection has so far remained a serious mathematical challenge and hindered the use of partially specified models. Here, we propose and demonstrate a potentially powerful technique to perform such a projection by using optimal control theory to construct functions with the specified global properties. This approach opens up the prospect of a flexible and easy to use method to fulfil uncertainty analysis of biological models.
2016-11-25T09:58:35Z
Piece-wise quadratic approximations of arbitrary error functions for fast and robust machine learning
Gorban, A. N.
Mirkes, E. M.
Zinovyev, A.
http://hdl.handle.net/2381/38711
2016-11-24T03:21:35Z
2016-11-23T17:34:11Z
Title: Piece-wise quadratic approximations of arbitrary error functions for fast and robust machine learning
Authors: Gorban, A. N.; Mirkes, E. M.; Zinovyev, A.
Abstract: Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and noisy data, the quadratic error functionals demonstrated many weaknesses including high sensitivity to contaminating factors and dimensionality curse. Therefore, a lot of recent applications in machine learning exploited properties of non-quadratic error functionals based on L1 norm or even sub-linear potentials corresponding to quasinorms Lp (0<p<1). The back side of these approaches is increase in computational cost for optimization. Till so far, no approaches have been suggested to deal with arbitrary error functionals, in a flexible and computationally efficient framework. In this paper, we develop a theory and basic universal data approximation algorithms (k-means, principal components, principal manifolds and graphs, regularized and sparse regression), based on piece-wise quadratic error potentials of subquadratic growth (PQSQ potentials). We develop a new and universal framework to minimize arbitrary sub-quadratic error potentials using an algorithm with guaranteed fast convergence to the local or global error minimum. The theory of PQSQ potentials is based on the notion of the cone of minorant functions, and represents a natural approximation formalism based on the application of min-plus algebra. The approach can be applied in most of existing machine learning methods, including methods of data approximation and regularized and sparse regression, leading to the improvement in the computational cost/accuracy trade-off. We demonstrate that on synthetic and real-life datasets PQSQ-based machine learning methods achieve orders of magnitude faster computational performance than the corresponding state-of-the-art methods, having similar or better approximation accuracy.
2016-11-23T17:34:11Z
R-matrix and inverse Shapovalov form
Mudrov, Andrey
http://hdl.handle.net/2381/38710
2016-11-24T03:21:33Z
2016-11-23T17:26:21Z
Title: R-matrix and inverse Shapovalov form
Authors: Mudrov, Andrey
Abstract: We construct the inverse Shapovalov form of a simple complex quantum group from its universal R-matrix based on a generalized Nagel-Moshinsky approach to lowering operators. We establish a connection between this algorithm and the ABRR equation for dynamical twist.
2016-11-23T17:26:21Z
Evolution of adaptation mechanisms: Adaptation energy, stress, and oscillating death
Gorban, Alexander N.
Tyukina, Tatiana A.
Smirnova, E. V.
Pokidysheva, L. I.
http://hdl.handle.net/2381/38652
2016-11-22T03:23:50Z
2016-11-21T14:29:22Z
Title: Evolution of adaptation mechanisms: Adaptation energy, stress, and oscillating death
Authors: Gorban, Alexander N.; Tyukina, Tatiana A.; Smirnova, E. V.; Pokidysheva, L. I.
Abstract: In 1938, Selye proposed the notion of adaptation energy and published ‘Experimental evidence supporting the conception of adaptation energy.’ Adaptation of an animal to different factors appears as the spending of one resource. Adaptation energy is a hypothetical extensive quantity spent for adaptation. This term causes much debate when one takes it literally, as a physical quantity, i.e. a sort of energy. The controversial points of view impede the systematic use of the notion of adaptation energy despite experimental evidence. Nevertheless, the response to many harmful factors often has general non-specific form and we suggest that the mechanisms of physiological adaptation admit a very general and nonspecific description.
We aim to demonstrate that Selye׳s adaptation energy is the cornerstone of the top-down approach to modelling of non-specific adaptation processes. We analyze Selye׳s axioms of adaptation energy together with Goldstone׳s modifications and propose a series of models for interpretation of these axioms. Adaptation energy is considered as an internal coordinate on the ‘dominant path’ in the model of adaptation. The phenomena of ‘oscillating death’ and ‘oscillating remission’ are predicted on the base of the dynamical models of adaptation. Natural selection plays a key role in the evolution of mechanisms of physiological adaptation. We use the fitness optimization approach to study of the distribution of resources for neutralization of harmful factors, during adaptation to a multifactor environment, and analyze the optimal strategies for different systems of factors.
2016-11-21T14:29:22Z
The Ext algebra and a new generalisation of D-Koszul algebras
Leader, Joanne
Snashall, Nicole
http://hdl.handle.net/2381/38590
2016-11-17T03:21:34Z
2016-11-16T15:48:30Z
Title: The Ext algebra and a new generalisation of D-Koszul algebras
Authors: Leader, Joanne; Snashall, Nicole
Abstract: We generalise Koszul and D-Koszul algebras by introducing a class of graded
algebras called (D, A)-stacked algebras. We give a characterisation of (D, A)-stacked
algebras and show that their Ext algebra is finitely generated as an algebra in degrees
0, 1, 2 and 3. In the monomial case, we give an explicit description of the Ext algebra
by quiver and relations, and show that the ideal of relations has a quadratic Gr¨obner
basis; this enables us to give a regrading of the Ext algebra under which the regraded
Ext algebra is a Koszul algebra.
Description: 2010 Mathematics Subject Classification. 16G20, 16S37, 16E30 12 Month embargo from publication.
2016-11-16T15:48:30Z
Mechanism of chain collapse of strongly charged polyelectrolytes
Tom, A. M.
Vemparala, S.
Rajesh, R.
Brilliantov, Nikolai V.
http://hdl.handle.net/2381/38580
2016-11-17T03:21:31Z
2016-11-16T10:28:02Z
Title: Mechanism of chain collapse of strongly charged polyelectrolytes
Authors: Tom, A. M.; Vemparala, S.; Rajesh, R.; Brilliantov, Nikolai V.
Abstract: We perform extensive molecular dynamics simulations of a charged polymer in a good solvent in the regime where the chain is collapsed. We analyze the dependence of the gyration radius Rg on the reduced Bjerrum length ℓB and find two different regimes. In the first one, called a weak electrostatic regime, Rg∼ℓ−1/2B, which is consistent only with the predictions of the counterion-fluctuation theory. In the second one, called a strong electrostatic regime, we find Rg∼ℓ−1/5B. To explain the novel regime we modify the counterion-fluctuation theory.
Description: The simulations were carried out on the supercomputing
machines Annapurna, Nandadevi, and Satpura at The
Institute of Mathematical Sciences.
2016-11-16T10:28:02Z
On the stability of the BEK family of rotating boundary-layer flows for power-law fluids
Abdulameer, M. A.
Griffiths, P. T.
Alveroğlu, B.
Garrett, Stephen J.
http://hdl.handle.net/2381/38547
2016-11-16T03:20:24Z
2016-11-15T10:42:43Z
Title: On the stability of the BEK family of rotating boundary-layer flows for power-law fluids
Authors: Abdulameer, M. A.; Griffiths, P. T.; Alveroğlu, B.; Garrett, Stephen J.
Abstract: We consider the convective instability of the BEK family of rotating boundary-layer flows for shear-thinning power-law fluids. The Bödewadt, Ekman and von Kármán flows are particular cases within this family. A linear stability analysis is conducted using a Chebyshev polynomial method in order to investigate the effect of shear-thinning fluids on the convective type I (inviscid crossflow) and type II (viscous streamline curvature) modes of instability. The results reveal that an increase in shear-thinning has a universal stabilising effect across the entire BEK family. Our results are presented in terms of neutral curves, growth rates and an analysis of the energy balance. The newly-derived governing equations for both the steady mean flow and unsteady perturbation equations are given in full.
Description: The file associated with this record is under a 24 month embargo from publication in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.
2016-11-15T10:42:43Z
Viscous modes within the compressible boundary-layer flow due to a broad rotating cone
Towers, P. D.
Hussain, Z.
Griffiths, P. T.
Garrett, S. J.
http://hdl.handle.net/2381/38514
2016-11-15T03:21:48Z
2016-11-14T14:26:08Z
Title: Viscous modes within the compressible boundary-layer flow due to a broad rotating cone
Authors: Towers, P. D.; Hussain, Z.; Griffiths, P. T.; Garrett, S. J.
Abstract: We investigate the effects of compressibility and wall cooling on the stationary, viscous (Type II) instability mode within the 3D boundary layer over rotating cones with half-angle greater than 40°. The stationary mode is characterised by zero shear stress at the wall and a triple-deck solution is presented in the isothermal case. Asymptotic solutions are obtained which describe the structure of the wavenumber and the orientation of this mode as a function of local Mach number. It is found that a stationary mode is possible only over a finite range of local Mach number. Our conclusions are entirely consistent with the results of Seddougui 1990, A nonlinear investigation of the stability models of instability of the trhee-dimensional Compresible boundary layer due to a rotating disc Q. J. Mech. Appl. Math., 43, pt. 4. It is suggested that wall cooling has a significant stabilising effect, while reducing the half-angle is marginally destabilising. Solutions are presented for air.
Description: Author confirmed manuscript is post-print.
2016-11-14T14:26:08Z
Equivariant Hochschild Cohomology
Koam, Ali Nasser Ali
http://hdl.handle.net/2381/38502
2016-11-15T03:22:04Z
2016-11-14T11:03:11Z
Title: Equivariant Hochschild Cohomology
Authors: Koam, Ali Nasser Ali
Abstract: In this thesis our goal is to develop the equivariant version of Hochschild cohomology. In the equivariant world there is given a group G which acts on objects. First naive object which can be considered is a G-algebra, that is, an associative algebra A on which G acts via algebra automorphisms. In our work we consider two more general situations. In the first case we develop a cohomology theory for oriented algebras and in the second case we develop a cohomology theory for Green functors.
2016-11-14T11:03:11Z
Discontinuous Galerkin methods for fast reactive mass transfer through semi-permeable membranes
Cangiani, Andrea
Georgoulis, Emmanuil H.
Jensen, M.
http://hdl.handle.net/2381/38467
2016-11-12T04:11:35Z
2016-11-11T15:23:03Z
Title: Discontinuous Galerkin methods for fast reactive mass transfer through semi-permeable membranes
Authors: Cangiani, Andrea; Georgoulis, Emmanuil H.; Jensen, M.
Abstract: A discontinuous Galerkin (dG) method for the numerical solution of initial/boundary value multi-compartment partial differential equation (PDE) models, interconnected with interface conditions, is analysed. The study of interface problems is motivated by models of mass transfer of solutes through semi-permeable membranes. The case of fast reactions is also included. More specifically, a model problem consisting of a system of semilinear parabolic advection–diffusion–reaction partial differential equations in each compartment with only local Lipschitz conditions on the nonlinear reaction terms, equipped with respective initial and boundary conditions, is considered. General nonlinear interface conditions modelling selective permeability, congestion and partial reflection are applied to the compartment interfaces. The interior penalty dG method for this problem, presented recently, is analysed both in the space-discrete and in fully discrete settings for the case of, possibly, fast reactions. The a priori analysis shows that the method yields optimal a priori bounds, provided the exact solution is sufficiently smooth. Numerical experiments indicate agreement with the theoretical bounds.
2016-11-11T15:23:03Z
Conforming and nonconforming virtual element methods for elliptic problems
Cangiani, Andrea
Manzini, G.
Sutton, Oliver J.
http://hdl.handle.net/2381/38460
2016-11-12T04:11:33Z
2016-11-11T14:31:40Z
Title: Conforming and nonconforming virtual element methods for elliptic problems
Authors: Cangiani, Andrea; Manzini, G.; Sutton, Oliver J.
Abstract: We present in a unified framework new conforming and nonconforming Virtual Element Methods (VEM) for general second order elliptic problems in two and three dimensions. The differential operator is split into its symmetric and non-symmetric parts and conditions for stability and accuracy on their discrete counterparts are established. These conditions are shown to lead to optimal $H^1$- and $L^2$-error estimates, confirmed by numerical experiments on a set of polygonal meshes. The accuracy of the numerical approximation provided by the two methods is shown to be comparable.
2016-11-11T14:31:40Z
Optimal Bounds for the Variance of Self-Intersection Local Times
Deligiannidis, G.
Utev, Sergey
http://hdl.handle.net/2381/38406
2016-11-10T03:23:35Z
2016-11-09T10:30:23Z
Title: Optimal Bounds for the Variance of Self-Intersection Local Times
Authors: Deligiannidis, G.; Utev, Sergey
Abstract: For a Zd-valued random walk (Sn)n N0, let l(n,x) be its local time at the site x Zd. For α N, define the α-fold self-intersection local time as Ln(α) xl(n,x)α. Also let LnSRW(α) be the corresponding quantities for the simple random walk in Zd. Without imposing any moment conditions, we show that the variance of the self-intersection local time of any genuinely d-dimensional random walk is bounded above by the corresponding quantity for the simple symmetric random walk; that is, var(Ln(α))=O(var (LnSRW(α))). In particular, for any genuinely d-dimensional random walk, with d≥4, we have var (Ln(α))=O(n). On the other hand, in dimensions d≤3 we show that if the behaviour resembles that of simple random walk, in the sense that lim infn→∞var Lnα/var(LnSRW(α))>0, then the increments of the random walk must have zero mean and finite second moment.
2016-11-09T10:30:23Z
Multiserial and special multiserial algebras and their representations
Green, E. L.
Schroll, Sibylle
http://hdl.handle.net/2381/38391
2016-11-09T03:20:36Z
2016-11-08T12:14:39Z
Title: Multiserial and special multiserial algebras and their representations
Authors: Green, E. L.; Schroll, Sibylle
Abstract: In this paper we study multiserial and special multiserial algebras. These algebras are a natural generalization of biserial and special biserial algebras to algebras of wild representation type. We define a module to be multiserial if its radical is the sum of uniserial modules whose pairwise intersection is either 0 or a simple module. We show that all finitely generated modules over a special multiserial algebra are multiserial. In particular, this implies that, in analogy to special biserial algebras being biserial, special multiserial algebras are multiserial. We then show that the class of symmetric special multiserial algebras coincides with the class of Brauer configuration algebras, where the latter are a generalization of Brauer graph algebras. We end by showing that any symmetric algebra with radical cube zero is special multiserial and so, in particular, it is a Brauer configuration algebra.
Description: MSC 16G20; 16G20; 16D10; 16D50
2016-11-08T12:14:39Z
Revisiting Brownian motion as a description of animal movement: a comparison to experimental movement data
Bearup, Daniel
Benefer, Carly M.
Petrovskii, Sergei V.
Blackshaw, Rod P.
http://hdl.handle.net/2381/38376
2016-11-09T03:20:38Z
2016-11-08T09:51:19Z
Title: Revisiting Brownian motion as a description of animal movement: a comparison to experimental movement data
Authors: Bearup, Daniel; Benefer, Carly M.; Petrovskii, Sergei V.; Blackshaw, Rod P.
Abstract: Summary:
1. Characterization of patterns of animal movement is a major challenge in ecology with applications to conservation, biological invasions and pest monitoring. Brownian random walks, and diffusive flux as their mean field counterpart, provide one framework in which to consider this problem. However, it remains subject to debate and controversy. This study presents a test of the diffusion framework using movement data obtained from controlled experiments.
2. Walking beetles (Tenebrio molitor) were released in an open circular arena with a central hole and the number of individuals falling from the arena edges was monitored over time. These boundary counts were compared, using curve fitting, to the predictions of a diffusion model. The diffusion model is solved precisely, without using numerical simulations.
3. We find that the shape of the curves derived from the diffusion model is a close match to those found experimentally. Furthermore, in general, estimates of the total population obtained from the relevant solution of the diffusion equation are in excellent agreement with the experimental population. Estimates of the dispersal rate of individuals depend on how accurately the initial release distribution is incorporated into the model.
4. We therefore show that diffusive flux is a very good approximation to the movement of a population of Tenebrio molitor beetles. As such, we suggest that it is an adequate theoretical/modelling framework for ecological studies that account for insect movement, although it can be context specific. An immediate practical application of this can be found in the interpretation of trap counts, in particular for the purpose of pest monitoring.
Description: The file associated with this record is under a 12 month embargo from publication in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.
2016-11-08T09:51:19Z
Twisted Hochschild homology and MacLane homology
Pirashvili, Teimuraz
http://hdl.handle.net/2381/38305
2016-11-01T03:19:15Z
2016-10-31T15:53:14Z
Title: Twisted Hochschild homology and MacLane homology
Authors: Pirashvili, Teimuraz
Abstract: We prove that Hi.A; ˆ.A// D 0, i > 0. Here A is a commutative algebra over the
prime field Fp of characteristic p > 0 and ˆ.A/ is A considered as a bimodule,
where the left multiplication is the usual one, while the right multiplication is given
via Frobenius endomorphism and H denotes the Hochschild homology over Fp . This
result has implications in Mac Lane homology theory. Among other results, we prove
that HML .A; T / D 0, provided A is an algebra over a field K of characteristic p >0
and T is a strict homogeneous polynomial functor of degree d with 1<d <Card.K/.
2016-10-31T15:53:14Z
Multilevel Adaptive Radial Basis Function Approximation using Error Indicators
Zhang, Qi
http://hdl.handle.net/2381/38284
2016-11-01T03:23:32Z
2016-10-31T10:53:54Z
Title: Multilevel Adaptive Radial Basis Function Approximation using Error Indicators
Authors: Zhang, Qi
Abstract: In some approximation problems, sampling from the target function can be both expensive and time-consuming. It would be convenient to have a method for indicating where the approximation quality is poor, so that generation of new data provides the user with greater accuracy where needed.
In this thesis, the author describes a new adaptive algorithm for Radial Basis Function (RBF) interpolation which aims to assess the local approximation quality and adds or removes points as required to improve the error in the specified region.
For a multiquadric and Gaussian approximation, one has the flexibility of a shape parameter which one can use to keep the condition number of the interpolation matrix to a moderate size. In this adaptive error indicator (AEI) method, an adaptive shape parameter is applied.
Numerical results for test functions which appear in the literature are given for one, two, and three dimensions, to show that this method performs well. A turbine blade design problem form GE Power (Rugby, UK) is considered and the AEI method is applied to this problem.
Moreover, a new multilevel approximation scheme is introduced in this thesis by coupling it with the adaptive error indicator. Preliminary numerical results from this Multilevel Adaptive Error Indicator (MAEI) approximation method are shown. These indicate that the MAEI is able to express the target function well. Moreover, it provides a highly efficient sampling.
2016-10-31T10:53:54Z
Long-term transients and complex dynamics of a stage-structured population with time delay and the Allee effect
Morozov, A. Y.
Banerjee, M.
Petrovskii, Sergei V.
http://hdl.handle.net/2381/38197
2016-10-13T02:23:54Z
2016-10-12T10:23:36Z
Title: Long-term transients and complex dynamics of a stage-structured population with time delay and the Allee effect
Authors: Morozov, A. Y.; Banerjee, M.; Petrovskii, Sergei V.
Abstract: Traditionally, mathematical modeling in population ecology is mainly focused on asymptotic behavior of the model, i.e. as given by the system attractors. Recently, however, transient regimes and especially long-term transients have been recognized as playing a crucial role in the dynamics of ecosystems. In particular, long-term transients are a potential explanation of ecological regime shifts, when an apparently healthy population suddenly collapses and goes extinct. In this paper, we show that the interplay between delay in maturation and a strong Allee effect can result in long-term transients in a single species system. We first derive a simple ‘conceptual’ model of the population dynamics that incorporates both a strong Allee effect and maturation delay. Unlike much of the previous work, our approach is not empirical since our model is derived from basic principles. We show that the model exhibits a high complexity in its asymptotic dynamics including multi-periodic and chaotic attractors. We then show the existence of long-term transient dynamics in the system, when the population size oscillates for a long time between locally stable stationary states before it eventually settles either at the persistence equilibrium or goes extinct. The parametric space of the model is found to have a complex structure with the basins of attraction corresponding to the persistence and extinction states being of a complicated shape. This impedes the prediction of the eventual fate of the population, as a small variation in the maturation delay or the initial population size can either bring the population to extinction or ensure its persistence.
Description: Following the embargo period the above license applies.
2016-10-12T10:23:36Z
Homotopy Types of Topological Groupoids and Lusternik-Schnirelmann Category of Topological Stacks
Alsulami, Samirah Hameed Break
http://hdl.handle.net/2381/38094
2016-09-27T02:20:49Z
2016-09-26T11:04:55Z
Title: Homotopy Types of Topological Groupoids and Lusternik-Schnirelmann Category of Topological Stacks
Authors: Alsulami, Samirah Hameed Break
Abstract: The concept of a groupoid was first introduced in 1926 by H. Brandt in his fundamental paper [7]. The idea behind it is a small category in which every arrow is invertible. This notion of groupoid can be thought of as a generalisation of the notion of a group. Namely, a group is a groupoid with only one object. After the introduction of topological and differentiable groupoids by Ehresmann in 1950 in his paper on connections [19], the concept has been widely studied by many mathematicians in many areas of topology, geometry and physics. In this thesis, we deal with topological groupoids as the main object of study. We first develop the main concepts of homotopy theory of topological groupoids. Also, we study general versions of Morita equivalence between topological groupoids, which lead us to discuss topological stacks. The main objective of this thesis is then to develop and analyse a notion of Lusternik-Schnirelmann category for general topological groupoids and topological stacks, generalising the classical work by Lusternik and Schnirelmann for topological spaces and manifolds [30] and for orbifolds and Lie groupoids as introduced by Colman [11]. Fundamental in the classical definition of the LS-category of a smooth manifold or topological space is the concept of a categorical set. A subset of a space is said to be categorical if it is contractible in the space. The Lusternik-Schnirelmann category cat(X) of a topological space X is defined to be the least number of categorical open sets required to cover X, if that number is finite. Otherwise the category cat(X) is said to be infinite. Here using a generalised notion of categorical subgroupoid and substack, we generalise the notion of the Lusternik-Schnirelmann category to topological groupoids and topological stacks with the intention of providing a new useful tool and invariant to study homotopy types of topological groupoids and topological stacks, which will be important also to understand the geometry and Morse theory of Lie groupoids and differentiable stacks from a purely homotopical viewpoint.
2016-09-26T11:04:55Z
hp-Version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes
Cangiani, Andrea
Dong, Zhaonan
Georgoulis, Emmanuil H.
Houston, Paul
http://hdl.handle.net/2381/38016
2016-08-31T02:18:46Z
2016-08-30T15:11:03Z
Title: hp-Version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes
Authors: Cangiani, Andrea; Dong, Zhaonan; Georgoulis, Emmanuil H.; Houston, Paul
Abstract: We consider the hp-version interior penalty discontinuous Galerkin finite element method (DGFEM) for the numerical approximation of the advection-diffusion-reaction equation on general computational meshes consisting of polygonal/polyhedral (polytopic) elements. In particular, new hp-version a priori error bounds are derived based on a specific choice of the interior penalty parameter which allows for edge/face-degeneration. The proposed method employs elemental polynomial bases of total degree p (𝒫p-basis) defined in the physical coordinate system, without requiring the mapping from a given reference or canonical frame. Numerical experiments highlighting the performance of the proposed DGFEM are presented. In particular, we study the competitiveness of the p-version DGFEM employing a 𝒫p-basis on both polytopic and tensor-product elements with a (standard) DGFEM employing a (mapped) 𝒬p-basis. Moreover, a computational example is also presented which demonstrates the performance of the proposed hp-version DGFEM on general agglomerated meshes.
2016-08-30T15:11:03Z
The convective instability of the BEK system of rotating boundary-layer flows over rough disks
Alveroğlu, Burhan
http://hdl.handle.net/2381/37977
2016-08-17T02:26:40Z
2016-08-16T11:54:44Z
Title: The convective instability of the BEK system of rotating boundary-layer flows over rough disks
Authors: Alveroğlu, Burhan
Abstract: A numerical study investigating the effects of surface roughness on the stability properties of the BEK system of flows is introduced. The BEK system of flows occur in many engineering applications such as turbo-machinery and rotor-stator devices, therefore they have great practical importance. Recent studies have been concerned with the effects of surface roughness on the von Kármán flow. The aim of this thesis is to investigate whether distributed surface roughness could be used as a passive drag reduction technique for the broader BEK system of flows. If it can, what is “the right sort of roughness?" To answer these questions, a linear stability analysis is performed using the Chebyshev collocation method to investigate the effect of particular types of distributed surface roughness, both anisotropic and isotropic, on the convective instability characteristics of the inviscid Type I (cross-flow) instability and the viscous Type II instability. The results reveal that all roughness types lead to a stabilisation of the Type I mode in all flows within the BEK family, with the exception of azimuthally-anisotropic roughness (radial grooves) within the Bődewadt flow which causes a mildly destabilising effect. In the case of the Type II mode, the results reveal the destabilising effect of radially-anisotropic roughness (concentric grooves) on all the boundary layers, whereas both azimuthally-anisotropic and isotropic roughness have a stabilising effect on the mode for Ekman and von Kármán flows. Moreover, an energy analysis is performed to investigate the underlying physical mechanisms behind the effects of rough surfaces on the BEK system. The conclusion is that isotropic surface roughness is the most effective type of the distributed surface roughness and can be recommended as a passive-drag reduction mechanism for the entire BEK system of flows.
2016-08-16T11:54:44Z
Mathematical Modelling of Oxygen - Plankton System under the Climate Change
Sekerci Firat, Yadigar
http://hdl.handle.net/2381/37971
2016-08-17T02:26:05Z
2016-08-16T10:51:51Z
Title: Mathematical Modelling of Oxygen - Plankton System under the Climate Change
Authors: Sekerci Firat, Yadigar
Abstract: Oxygen production due to phytoplankton photosynthesis is an important phenomenon keeping in mind the underlying dynamics of marine ecosystems. However, despite its crucial importance, not only for marine but also for terrestrial ecosystems, the coupled oxygen-plankton dynamics have been overlooked.
This dissertation aims to provide insight into an oxygen-plankton system using mathematical modelling. We firstly develop a ‘baseline’ oxygen-phytoplankton model which is then further developed through the addition of biologically relevant factors such as plankton respiration and the predator effect of zooplankton. The properties of the model have been studied both in the nonspatial case, which corresponds to a well mixed system with a spatially uniform distribution of species, and in the spatially explicit extension, by taking into account the transport of oxygen and movement of plankton by turbulent diffusion.
Since the purpose of this work is to reveal the oxygen dynamics, the effect of global warming is considered taken into consideration and modelled by various oxygen production rates and phytoplankton growth functions in Chapters 5 and 6. It is shown that sustainable oxygen production is only possible in an intermediate range of the production rate. If the oxygen production rate becomes sufficiently low or high, in the course of time, the system’s dynamics shows abrupt changes resulting in plankton extinction and oxygen depletion. We show that the spatial system’s sustainability range is larger that of the corresponding nonspatial system. We show that oxygen production by phytoplankton can stop suddenly if the water temperature exceeds a certain critical threshold. Correspondingly, this dissertation reveals the scenarios of extinction which can potentially lead to an ecological disaster.
2016-08-16T10:51:51Z
The Fundamental Groupoid and the Geometry of Monoids
Pirashvili, Ilia
http://hdl.handle.net/2381/37837
2016-07-14T02:19:15Z
2016-07-13T15:42:29Z
Title: The Fundamental Groupoid and the Geometry of Monoids
Authors: Pirashvili, Ilia
Abstract: This thesis is divided in two equal parts. We start the first part by studying the Kato-spectrum of a commutative monoid M, denoted by KSpec(M). We show that the functor M → KSpec(M) is representable and discuss a few consequences of this fact. In particular, when M is additionally finitely generated, we give an efficient way of calculating it explicitly.
We then move on to study the cohomology theory of monoid schemes in general and apply it to vector- and particularly, line bundles. The isomorphism class of the latter is the Picard group. We show that under some assumptions on our monoid scheme X, if k is an integral domain (resp. PID), then the induced map Pic(X) → Pic(Xk) from X to its realisation is a monomorphism (resp. isomorphism).
We then focus on the Pic functor and show that it respects finite products. Finally, we generalise several important constructions and notions such as cancellative monoids, smoothness and Cartier divisors, and prove important results for them.
The main results of the second part can be summed up in fewer words. We prove that for good topological spaces X the assignment U → II₁(U) is the terminal object of the 2-category of costacks. Here U is an open subset of X and II₁(U) denotes the fundamental groupoid of U. This result translates to the étale fundamental groupoid as well, though the proof there is completely different and involves studying and generalising Galois categories.
2016-07-13T15:42:29Z
Betting Markets: Defining odds restrictions, exploring market inefficiencies and measuring bookmaker solvency
Cortis, Dominic
http://hdl.handle.net/2381/37783
2016-06-18T03:13:56Z
2016-06-17T10:02:32Z
Title: Betting Markets: Defining odds restrictions, exploring market inefficiencies and measuring bookmaker solvency
Authors: Cortis, Dominic
Abstract: Betting markets have been of great interest to researchers as they represent a simpler set-up of financial markets. With an estimated Gross Gambling Revenue of 45bn yearly on betting on outcomes alone (excluding other gambling markets such as Casino, Poker and Lottery), these markets deserve attention on their own merit.
This thesis provides simple mathematical derivation of a number of key statements in setting odds. It estimates the expected bookmaker profit as a function of wagers placed and bookmaker margin. Moreover it shows that odds set by bookmakers should have implied probabilities that add up to at least one. Bookmakers do not require the exact probability of an outcome to have positive expected profits. They can increase profitability by having more accurate odds and offering more multiples/accumulators. Bookmakers can lower variation in payouts by maintaining the ratio of wagers and implied probability per outcome.
While bookmakers face significant regulatory pressures as well as increased taxes and levies, there is no standard industry model that can be applied to evaluate the minimum reserves for a bookmaker. Hence a bookmaker may be under/over-reserving funds required to conduct business. A solvency regime for bookmakers is presented in this work.
Furthermore a model is proposed to forecast soccer results – this focuses on goal differences in contrast to traditional models that predict outcome or goals scored per team.
Significant investigations are made on the inefficiencies of betting markets. The likelihood of Brazil reaching different stages of the 2014 World Cup, as perceived by odds, is compared to events on and outside the pitch to imply bias. An analysis of over 136,000 odds for European soccer matches shows evidence of the longshot bias. Finally this work investigates how it is possible to profit from market inefficiencies on betting exchanges during short tournaments by using a Monte Carlo simulation method as a quasi-arbitrage model.
2016-06-17T10:02:32Z
kNN predictability analysis of stock and share closing prices
Shi, Yanshan
http://hdl.handle.net/2381/37772
2016-06-17T02:17:44Z
2016-06-16T09:25:00Z
Title: kNN predictability analysis of stock and share closing prices
Authors: Shi, Yanshan
Abstract: The k nearest neighbor rule or the kNN rule is a nonparametric algorithm that search for the k nearest neighbors of a query set in another set of points. In this thesis, application of the kNN rule in predictability analysis of stock and share returns is proposed. The first experiment tests the possibility of prediction for ‘success’ (or ‘winner’) components of four stock and shares market indices in a selected time period [1]. We have developed a method of labeling the component with either ‘winner’ or ‘loser’. We analyze the existence of information on the winner–loser separation in the initial fragments of the daily closing prices log–returns time series. The Leave–One–Out Cross–Validation with the kNN algorithm is applied on the daily log–returns of components. Two distance measurements are used in our experiment, a correlation distance, and its proximity. By analyzing the error, for the HANGSENG and the DAX index, there are clear signs of possibility to evaluate the probability of long–term success. The correlation distance matrix histograms and 2–D/3–D elastic maps generated from the ViDaExpert show that the ‘winner’ components are closer to each other and ‘winner’/‘loser’ components are separable on elastic maps for the HANGSENG and the DAX index while for the negative possibility indices, there is no sign of separation.
In the second experiment, for a selected time interval, daily log–return time series is split into “history”, “present” and “future” parts. The kNN rule is used to search for nearest neighbors of “present” from a set. This set is created by using the sliding window strategy. The nearest neighbors are considered as the predicted “future” part. We then use ideas from dynamical systems and to regenerate “future” part closing prices from nearest neighbors log–returns. Different sub–experiments are created in terms of the difference in generation of “history” part, different market indices, and different distance measurements. This approach of modeling or forecasting works for both the ergodic dynamic systems and the random processes.
The Lorenz attractor with noise is used to generate data and the data are used in the kNN experiment with the Euclidean distance. The sliding window strategy is applied in both test and training set. The kNN rule is used to find the k nearest neighbors and the next ‘window’ is used as the prediction. The error analysis of the relative mean squared error RMSE shows that k = 1 can give the best prediction and when k → 100, the average RMSE values converge. The average standard deviation values converge when k → 100. The solution Z(t) is predicted quite accurate using the kNN experiment.
2016-06-16T09:25:00Z
Kriging meta-model assisted calibration of computational fluid dynamics models
Kajero, Olumayowa T.
Thorpe, Rex B.
Chen, Tao
Wang, Bo
Yao, Yuan
http://hdl.handle.net/2381/37745
2016-12-02T11:50:01Z
2016-06-14T11:09:22Z
Title: Kriging meta-model assisted calibration of computational fluid dynamics models
Authors: Kajero, Olumayowa T.; Thorpe, Rex B.; Chen, Tao; Wang, Bo; Yao, Yuan
Abstract: Computational fluid dynamics (CFD) is a simulation technique widely used in chemical and process engineering applications. However, computation has become a bottleneck when calibration of CFD models with experimental data (also known as model parameter estimation) is needed. In this research, the kriging meta-modelling approach (also termed Gaussian process) was coupled with expected improvement (EI) to address this challenge. A new EI measure was developed for the sum of squared errors (SSE) which conforms to a generalised chi-square distribution and hence existing normal distribution-based EI measures are not applicable. The new EI measure is to suggest the CFD model parameter to simulate with, hence minimising SSE and improving match between simulation and experiments. The usefulness of the developed method was demonstrated through a case study of a single-phase flow in both a straight-type and a convergent-divergent-type annular jet pump, where a single model parameter was calibrated with experimental data.
Description: The file associated with this record is under a 12-month embargo from publication in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.
2016-06-14T11:09:22Z
Delay driven spatiotemporal chaos in single species population dynamics models
Petrovskiy, Sergei
Jankovic, Masha
Banerjee, Malay
http://hdl.handle.net/2381/37594
2016-10-12T10:16:33Z
2016-05-18T12:05:18Z
Title: Delay driven spatiotemporal chaos in single species population dynamics models
Authors: Petrovskiy, Sergei; Jankovic, Masha; Banerjee, Malay
Abstract: Questions surrounding the prevalence of complex population dynamics form one of the central themes in ecology. Limit cycles and spatiotemporal chaos are examples that have been widely recognised theoretically, although their importance and applicability to natural populations remains debatable. The ecological processes underlying such dynamics are thought to be numerous, though there seems to be consent as to delayed density dependence being one of the main driving forces. Indeed, time delay is a common feature of many ecological systems and can significantly influence population dynamics. In general, time delays may arise from inter- and intra-specific trophic interactions or population structure, however in the context of single species populations they are linked to more intrinsic biological phenomena such as gestation or resource regeneration. In this paper, we consider theoretically the spatiotemporal dynamics of a single species population using two different mathematical formulations. Firstly, we revisit the diffusive logistic equation in which the per capita growth is a function of some specified delayed argument. We then modify the model by incorporating a spatial convolution which results in a biologically more viable integro-differential model. Using the combination of analytical and numerical techniques, we investigate the effect of time delay on pattern formation. In particular, we show that for sufficiently large values of time delay the system’s dynamics are indicative to spatiotemporal chaos. The chaotic dynamics arising in the wake of a travelling population front can be preceded by either a plateau corresponding to dynamical stabilisation of the unstable equilibrium or by periodic oscillations.
2016-05-18T12:05:18Z
How animals move along? Exactly solvable model of superdiffusive spread resulting from animal's decision making
Petrovskiy, Sergei V.
Tilles, Paulo F. C.
http://hdl.handle.net/2381/37591
2016-05-19T02:07:45Z
2016-05-18T11:50:36Z
Title: How animals move along? Exactly solvable model of superdiffusive spread resulting from animal's decision making
Authors: Petrovskiy, Sergei V.; Tilles, Paulo F. C.
Abstract: Patterns of individual animal movement have been a focus of considerable attention recently. Of particular interest is a question how different macroscopic properties of animal dispersal result from the stochastic processes occurring on the microscale of the individual behavior. In this paper, we perform a comprehensive analytical study of a model where the animal changes the movement velocity as a result of its behavioral response to environmental stochasticity. The stochasticity is assumed to manifest itself through certain signals, and the animal modifies its velocity as a response to the signals. We consider two different cases, i.e. where the change in the velocity is or is not correlated to its current value. We show that in both cases the early, transient stage of the animal movement is super-diffusive, i.e. ballistic. The large-time asymptotic behavior appears to be diffusive in the uncorrelated case but super-ballistic in the correlated case. We also calculate analytically the dispersal kernel of the movement and show that, whilst it converge to a normal distribution in the large-time limit, it possesses a fatter tail during the transient stage, i.e. at early and intermediate time. Since the transients are known to be highly relevant in ecology, our findings may indicate that the fat tails and superdiffusive spread that are sometimes observed in the movement data may be a feature of the transitional dynamics rather than an inherent property of the animal movement.
Description: Copyright © the authors, 2015. After embargo this version will be an open-access article distributed under the terms of the Creative Commons Attribution-Non Commercial-No Derivatives License (http://creativecommons.org/licenses/by-nc-nd/4.0/ ), which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.
2016-05-18T11:50:36Z
Towards roughness-based drag reduction in cross-flow dominated flows
Garrett, Sephen J.
Cooper, A. J.
Ozkan, M.
Thomas, P. J.
http://hdl.handle.net/2381/37570
2016-05-18T02:08:20Z
2016-05-17T09:01:51Z
Title: Towards roughness-based drag reduction in cross-flow dominated flows
Authors: Garrett, Sephen J.; Cooper, A. J.; Ozkan, M.; Thomas, P. J.
Abstract: Recent theoretical results are presented from our ongoing study investigating the distinct convective instability properties of the boundary-layer flow over rough rotating disks. In this study, radial anisotropic surface roughness (concentric grooves) is modelled using the partial-slip approach of Miklavčič & Wang (2004) and the surface-geometry approach of Yoon et. Al (2007). An energy analysis reveals that for both instability modes, the main contributors to the energy balance are the energy production by the Reynolds stresses and conventional viscous dissipation. For the Type I mode, energy dissipation increases and the Reynolds-stress energy production decreases with roughness under both models. This suggests a clear stabilising effect of the anisotropic roughness on the Type I mode. For the Type II mode, the Reynolds-stress energy production increases with roughness under both models. However, the energy dissipation of the Type II mode decreases with the roughness under the surface-geometry model and increases under the partial-slip model. This sensitivity to the precise form of the anisotropic roughness suggests that maximising dissipation by an appropriately designed roughness can theoretically lead to an overall beneficial stabilisation of both the Type I and Type II modes. This is a potential route to overall boundary-layer-transition delay and drag reduction in cross-flow dominated flows.
Description: This paper is under embargo as it has been submitted for publication to European Journal of Mechanics - B/Fluids. If accepted the file associated with this record is embargoed until 24 months after the date of publication.
2016-05-17T09:01:51Z
An energy analysis of convective instabilities of the Bödewadt and Ekman boundary layers over rough surfaces
Alveroglu, B.
Segalini, A.
Garrett, Stephen J.
http://hdl.handle.net/2381/37569
2016-05-18T02:08:13Z
2016-05-17T08:48:49Z
Title: An energy analysis of convective instabilities of the Bödewadt and Ekman boundary layers over rough surfaces
Authors: Alveroglu, B.; Segalini, A.; Garrett, Stephen J.
Abstract: An energy balance equation for the three-dimensional Bödewadt and Ekman layers of the so called “BEK family" of rotating boundary-layer flows is derived. A Chebyshev discretisation method is used to solve the equations and investigate the effect of surface roughness on the physical mechanisms of transition. All roughness types lead to a stabilization of the Type I (cross-flow) instability mode for both flows, with the exception of azimuthally-anisotropic roughness (radial grooves) within the Bödewadt layer which is destabilising. In the case of the viscous Type II instability mode, the results predict a destabilisation effect of radially-anisotropic roughness (concentric grooves) on both flows, whereas both azimuthally-anisotropic roughness and isotropic roughness have a stabilisation effect. The results presented here confirm the results of our prior linear stability analyses.
Description: This paper is under embargo as it has been submitted for publication to European Journal of Mechanics - B/Fluids. If accepted the file associated with this record is embargoed until 24 months after the date of publication.
2016-05-17T08:48:49Z
On a fixed point theorem of Greguš
Fisher, Brian
Sessa, S.
http://hdl.handle.net/2381/37550
2016-05-14T03:33:26Z
2016-05-13T14:33:57Z
Title: On a fixed point theorem of Greguš
Authors: Fisher, Brian; Sessa, S.
Abstract: We consider two selfmaps T and I of a closed convex subset C of a Banach space X which are weakly commuting in X, i.e.
‖TIx−ITx‖≤‖Ix−Tx‖ for any x in X,
and satisfy the inequality
‖Tx−Ty‖≤a‖Ix−Iy‖+(1−a)max{‖Tx−Ix‖,‖Ty−Iy‖}
for all x, y in C, where 0<a<1. It is proved that if I is linear and non-expansive in C and such that IC contains TC, then T and I have a unique common fixed point in C.
2016-05-13T14:33:57Z
On common fixed points of weakly commuting mappings and set-valued mappings
Sessa, S.
Fisher, B.
http://hdl.handle.net/2381/37549
2016-05-14T03:29:59Z
2016-05-13T14:30:09Z
Title: On common fixed points of weakly commuting mappings and set-valued mappings
Authors: Sessa, S.; Fisher, B.
Abstract: Our main theorem establishes the uniqueness of the common fixed point of two set-valued mappings and of two single-valued mappings defined on a complete metric space, under a contractive condition and a weak commutativity concept. This improves a theorem of the second author.
2016-05-13T14:30:09Z
On a fixed point theorem of Pathak
Fisher, Brian
http://hdl.handle.net/2381/37548
2016-05-14T03:30:41Z
2016-05-13T14:25:52Z
Title: On a fixed point theorem of Pathak
Authors: Fisher, Brian
Abstract: It is shown that the continuity of the mapping in Pathak's fixed point theorem for normed spaces is not necessary.
2016-05-13T14:25:52Z
Common fixed point theorems for compatible mappings
Taş, K.
Telci, M.
Fisher, Brian
http://hdl.handle.net/2381/37547
2016-05-14T03:35:55Z
2016-05-13T14:22:20Z
Title: Common fixed point theorems for compatible mappings
Authors: Taş, K.; Telci, M.; Fisher, Brian
Abstract: By using a compatibility condition due to Jungck we establish some common fixed point theorems for four mappings on complete and compact metric spaces These results also generalize a theorem of Sharma and Sahu.
2016-05-13T14:22:20Z
Coincidence theorems for nonlinear hybrid contractions
Cho, Y. J.
Fisher, B.
Genga, G. S.
http://hdl.handle.net/2381/37546
2016-05-14T03:32:25Z
2016-05-13T14:18:00Z
Title: Coincidence theorems for nonlinear hybrid contractions
Authors: Cho, Y. J.; Fisher, B.; Genga, G. S.
Abstract: In this paper, we give some common fixed point theorems for single-valued mappings and multi-valued mappings satisfying a rational inequality. Our theorems generalize some results of B. Fisher, M. L. Diviccaro et al. and V. Popa.
2016-05-13T14:18:00Z
Related fixed point theorems on two complete and compact metric spaces
Namdeo, R. K.
Tiwari, N. K.
Fisher, B.
Taş, K.
http://hdl.handle.net/2381/37544
2016-05-14T03:31:08Z
2016-05-13T14:12:57Z
Title: Related fixed point theorems on two complete and compact metric spaces
Authors: Namdeo, R. K.; Tiwari, N. K.; Fisher, B.; Taş, K.
Abstract: A new related fixed point theorem on two complete metric spaces is obtained. A generalization is given for two compact metric spaces.
2016-05-13T14:12:57Z
A note on commutativity of nonassociative rings
Khan, M. S. S.
http://hdl.handle.net/2381/37543
2016-05-14T03:35:09Z
2016-05-13T14:06:58Z
Title: A note on commutativity of nonassociative rings
Authors: Khan, M. S. S.
Abstract: A theorem on commutativity of nonassociate ring is given.
2016-05-13T14:06:58Z
A Generalization of Prešić Type Mappings in Metric-Like Spaces
Shukla, S.
Fisher, Brian
http://hdl.handle.net/2381/37541
2016-05-14T03:34:31Z
2016-05-13T13:19:06Z
Title: A Generalization of Prešić Type Mappings in Metric-Like Spaces
Authors: Shukla, S.; Fisher, Brian
Abstract: We generalize the result of Prešić in metric-like spaces by proving some common fixed point theorems for Prešić type mappings in metric-like spaces. An example is given which shows that the generalization is proper.
2016-05-13T13:19:06Z
Phacoemulsification Surgery in Eyes with Neovascular Age-Related Macular Degeneration
Grixti, A.
Papavasileiou, E.
Cortis, Dominic
Kumar, B. V.
Prasad, S.
http://hdl.handle.net/2381/37538
2016-05-14T03:27:38Z
2016-05-13T11:32:13Z
Title: Phacoemulsification Surgery in Eyes with Neovascular Age-Related Macular Degeneration
Authors: Grixti, A.; Papavasileiou, E.; Cortis, Dominic; Kumar, B. V.; Prasad, S.
Abstract: Purpose. To evaluate the visual outcomes and effect of phacoemulsification surgery on the progression of neovascular age-related macular degeneration (AMD). Methods. Retrospective, noncomparative, and interventional case series. Thirty eyes from 29 subjects with neovascular AMD treated with intravitreal antivascular endothelial growth factor (VEGF) injections who underwent phacoemulsification and had a postsurgery follow-up of 6 months were included. LogMAR best corrected visual acuity (BCVA) was assessed preoperatively; 1 month, 3 months, and 6 months postoperatively; and finally at the last visit. The frequency of anti-VEGF therapy, calculated as the number of intravitreal injections per month, and central macular thickness (CMT) before and after cataract surgery were determined. Results. Median (range) logMAR BCVA was 0.69 (0.16 to 1.32) preoperatively; 0.55 (−0.04 to 1.32) at 1 month, 0.52 (−0.1 to 1.32) at 3 months, and 0.50 (0.0 to 1.32) at 6 months postoperatively; and 0.6 (0.0 to 1.4) at final visit (P=0.0011). There was no difference in the frequency of anti-VEGF injections between the immediate 6 months before and after phacoemulsification, which was equal to 0.1667 injections per month (P=0.6377). Median CMT measured 203 μm preoperatively, which temporarily increased to 238 μm at 1 month after surgery (P=0.0093) and then spontaneously returned to baseline, measuring 212.5 μm at 3 months postoperatively (P=0.3811). Conclusion. Phacoemulsification surgery significantly improved vision in patients with neovascular AMD, with no increased need for anti-VEGF injections to keep the macula dry postoperatively.
2016-05-13T11:32:13Z
Stability modes in vortex structure formation: Canonical examples for rotating components
Gostelow, J. Paul
Garrett, Stephen J.
Rona, Aldo
Adebayo, David S.
http://hdl.handle.net/2381/37476
2016-05-05T02:09:18Z
2016-05-04T14:50:44Z
Title: Stability modes in vortex structure formation: Canonical examples for rotating components
Authors: Gostelow, J. Paul; Garrett, Stephen J.; Rona, Aldo; Adebayo, David S.
Abstract: Three rather different physical cases have been studied. All represent very practical geometries for which the modal behavior of vortex structures is not completely understood. The work on these problems is ongoing with the objective of obtaining physical confirmation, enhanced understanding and predictive capability for the vortex structures encountered in rotating machines.
2016-05-04T14:50:44Z
Cohomology of tiling spaces: beyond primitive substitutions
Rust, Daniel George
http://hdl.handle.net/2381/37469
2016-04-30T02:28:11Z
2016-04-29T13:40:19Z
Title: Cohomology of tiling spaces: beyond primitive substitutions
Authors: Rust, Daniel George
Abstract: This thesis explores the combinatorial and topological properties of tiling spaces
associated to 1-dimensional symbolic systems of aperiodic type and their associated
algebraic invariants. We develop a framework for studying systems which are more
general than primitive substitutions, naturally partitioned into two instances: in the
first instance we allow systems associated to sequences of substitutions of primitive
type from a finite family of substitutions (called mixed substitutions); in the second
instance we concentrate on systems associated to a single substitution, but where
we entirely remove the condition of primitivity.
We generalise the notion of a Barge-Diamond complex, in the one-dimensional case,
to any mixed system of symbolic substitutions. This gives a way of describing
the associated tiling space as an inverse limit of complexes. We give an effective
method for calculating the Cech cohomology of the tiling space via an exact sequence
relating the associated sequence of substitution matrices and certain subcomplexes
appearing in the approximants. As an application, we show that there exists a
system of substitutions on two letters which exhibit an uncountable collection of
minimal tiling spaces with distinct isomorphism classes of Cech cohomology.
In considering non-primitive substitutions, we naturally divide this set of substitutions
into two cases: the minimal substitutions and the non-minimal substitutions.
We provide a detailed method for replacing any non-primitive but minimal substitution
with a topologically conjugate primitive substitution, and a more simple
method for replacing the substitution with a primitive substitution whose tiling
space is orbit equivalent. We show that an Anderson-Putnam complex with a collaring
of some appropriately large radius suffices to provide a model of the tiling
space as an inverse limit with a single map. We apply these methods to effectively
calculate the Cech cohomology of any substitution which does not admit a periodic
point in its subshift. Using its set of closed invariant subspaces, we provide a pair
of invariants which are each strictly finer than the usual Cech cohomology for a
substitution tiling space.
2016-04-29T13:40:19Z
Tiling spaces, codimension one attractors and shape
Clark, Alexander
Hunton, J.
http://hdl.handle.net/2381/37346
2016-04-19T02:15:49Z
2016-04-18T11:58:33Z
Title: Tiling spaces, codimension one attractors and shape
Authors: Clark, Alexander; Hunton, J.
Abstract: We establish a close relationship between, on the one hand, expanding, codimension one attractors of diffeomorphisms on closed manifolds (examples of so-called strange attractors), and, on the other, spaces which arise in the study of aperiodic tilings. We show that every such orientable attractor is homeomorphic to a tiling space of either a substitution or a projection tiling, depending on its dimension. We also demonstrate that such an attractor is shape equivalent to a (d+1)-dimensional torus with a finite number of points removed, or, in the nonorientable case, to a space with a two-to-one covering by such a torus-less-points. This puts considerable constraints on the topology of codimension one attractors, and constraints on which manifolds tiling spaces may be embedded in. In the process we develop a new invariant for aperiodic tilings, which, for 1-dimensional tilings is in many cases finer than the cohomological or K-theoretic invariants studied to date.
2016-04-18T11:58:33Z
From Ambiguity Aversion to a Generalized Expected Utility. Modeling Preferences in a Quantum Probabilistic Framework
Aerts, D.
Sozzo, Sandro
http://hdl.handle.net/2381/37265
2016-04-13T02:22:20Z
2016-04-12T11:41:18Z
Title: From Ambiguity Aversion to a Generalized Expected Utility. Modeling Preferences in a Quantum Probabilistic Framework
Authors: Aerts, D.; Sozzo, Sandro
Abstract: Ambiguity and ambiguity aversion have been widely studied in decision theory and economics both at a theoretical and an experimental level. After Ellsberg's seminal studies challenging subjective expected utility theory (SEUT), several (mainly normative) approaches have been put forward to reproduce ambiguity aversion and Ellsberg-type preferences. However, Machina and other authors have pointed out some fundamental difficulties of these generalizations of SEUT to cope with some variants of Ellsberg's thought experiments, which has recently been experimentally confirmed. Starting from our quantum modeling approach to human cognition, we develop here a general probabilistic framework to model human decisions under uncertainty. We show that our quantum theoretical model faithfully represents different sets of data collected on both the Ellsberg and the Machina paradox situations, and is flexible enough to describe different subjective attitudes with respect to ambiguity. Our approach opens the way toward a quantum-based generalization of expected utility theory (QEUT), where subjective probabilities depend on the state of the conceptual entity at play and its interaction with the decision-maker, while preferences between acts are determined by the maximization of this 'state-dependent expected utility'.
Description: The file associated with this record is under a 24-month embargo from publication in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.
2016-04-12T11:41:18Z
A classification of the point spectrum of constant length substitution tiling spaces and general fixed point theorems for tilings
Abuzaid, Dina Asaad
http://hdl.handle.net/2381/37027
2016-03-12T04:27:12Z
2016-03-11T16:11:58Z
Title: A classification of the point spectrum of constant length substitution tiling spaces and general fixed point theorems for tilings
Authors: Abuzaid, Dina Asaad
Abstract: We examine the point spectrum of the various tiling spaces that result from
different choices of tile lengths for substitution of constant length on a two or a three letter
alphabet. In some cases we establish insensitivity to changes in length. In a wide range
of cases, we establish that the typical choice of length leads to trivial point spectrum.
We also consider a problem related to tilings of the integers and their connection to fixed
point theorems. Using this connection, we prove a generalization of the Banach Contraction
Principle.
2016-03-11T16:11:58Z
The centrifugal instability of the boundary-layer flow over a slender rotating cone in an enforced axial free stream
Hussain, Z.
Garrett, Stephen J.
Stephen, S. O.
Griffiths, Paul Travis
http://hdl.handle.net/2381/36986
2016-06-22T01:45:07Z
2016-03-07T11:36:56Z
Title: The centrifugal instability of the boundary-layer flow over a slender rotating cone in an enforced axial free stream
Authors: Hussain, Z.; Garrett, Stephen J.; Stephen, S. O.; Griffiths, Paul Travis
Abstract: In this study, a new centrifugal instability mode, which dominates within the boundary-layer flow over a slender rotating cone in still fluid, is used for the first time to model the problem within an enforced oncoming axial flow. The resulting problem necessitates an updated similarity solution to represent the basic flow more accurately than previous studies in the literature. The new mean flow field is subsequently perturbed, leading to disturbance equations that are solved via numerical and short-wavelength asymptotic approaches, yielding favourable comparisons with existing experiments. Essentially, the boundary-layer flow undergoes competition between the streamwise flow component, due to the oncoming flow, and the rotational flow component, due to effect of the spinning cone surface, which can be described mathematically in terms of a control parameter, namely the ratio of streamwise to axial flow. For a slender cone rotating in a sufficiently strong axial flow, the instability mode breaks down into Görtler-type counter-rotating spiral vortices, governed by an underlying centrifugal mechanism, which is consistent with experimental and theoretical studies for a slender rotating cone in otherwise still fluid.
Description: The file associated with this record is under a 6-month embargo from publication in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.
2016-03-07T11:36:56Z
The neutral curve for stationary disturbances in rotating disk flow for power-law fluids
Griffiths, P. T.
Garrett, Stephen John
Stephen, S. O.
http://hdl.handle.net/2381/36985
2016-09-28T01:45:10Z
2016-03-07T11:32:29Z
Title: The neutral curve for stationary disturbances in rotating disk flow for power-law fluids
Authors: Griffiths, P. T.; Garrett, Stephen John; Stephen, S. O.
Abstract: This paper is concerned with the convective instabilities associated with the boundary-layer flow due to a rotating disk. Shear-thinning fluids that adhere to the power-law relationship are considered. The neutral curves are computed using a sixth-order system of linear stability equations which include the effects of streamline curvature, Coriolis force and the non-Newtonian viscosity model. Akin to previous Newtonian studies it is found that the neutral curves have two critical values, these are associated with the type I upper-branch (cross-flow) and type II lower-branch (streamline curvature) modes. Our results indicate that an increase in shear-thinning has a stabilising effect on both the type I and II modes, in terms of the critical Reynolds number and growth rate. Favourable agreement is obtained between existing asymptotic predictions and the numerical results presented here.
Description: The file associated with this record is under a 24-month embargo from publication in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.
2016-03-07T11:32:29Z
Stability of the boundary layer on a rotating disk for power-law fluids
Griffiths, P. T.
Stephen, S. O.
Bassom, A. P.
Garrett, Stephen John
http://hdl.handle.net/2381/36963
2016-03-04T03:22:45Z
2016-03-03T11:51:44Z
Title: Stability of the boundary layer on a rotating disk for power-law fluids
Authors: Griffiths, P. T.; Stephen, S. O.; Bassom, A. P.; Garrett, Stephen John
Abstract: The stability of the flow due to a rotating disk is considered for non-Newtonian fluids, specifically shear-thinning fluids that satisfy the power-law (Ostwald-de Waele) relationship. In this case the basic flow is not an exact solution of the Navier–Stokes equations, however, in the limit of large Reynolds number the flow inside the three-dimensional boundary layer can be determined via a similarity solution. An asymptotic analysis is presented in the limit of large Reynolds number. It is shown that the stationary spiral instabilities observed experimentally in the Newtonian case can be described for shear-thinning fluids by a linear stability analysis. Predictions for the wavenumber and wave angle of the disturbances suggest that shear-thinning fluids may have a stabilising effect on the flow.
2016-03-03T11:51:44Z
Global linear stability of the boundary-layer flow over a rotating sphere
Barrow, A.
Garrett, Stephen J.
Peake, N.
http://hdl.handle.net/2381/36889
2016-02-26T03:26:22Z
2016-02-25T13:44:07Z
Title: Global linear stability of the boundary-layer flow over a rotating sphere
Authors: Barrow, A.; Garrett, Stephen J.; Peake, N.
Abstract: We consider the linear global stability of the boundary-layer flow over a rotating sphere. Our results suggest that a self-excited linear global mode can exist when the sphere rotates sufficiently fast, with properties fixed by the flow at latitudes between approximately 55°–65° from the pole (depending on the rotation rate). A neutral curve for global linear instabilities is presented with critical Reynolds number consistent with existing experimentally measured values for the appearance of turbulence. The existence of an unstable linear global mode is in contrast to the literature on the rotating disk, where it is expected that nonlinearity is required to prompt the transition to turbulence. Despite both being susceptible to local absolute instabilities, we conclude that the transition mechanism for the rotating-sphere flow may be different to that for the rotating disk.
2016-02-25T13:44:07Z
The centrifugal instability of the boundary-layer flow over a slender rotating cone in an enforced axial free-stream
Hussain, Z.
Garrett, Stephen J.
Stephen, S. O.
Griffiths, Paul T.
http://hdl.handle.net/2381/36888
2016-06-26T01:45:07Z
2016-02-25T13:41:12Z
Title: The centrifugal instability of the boundary-layer flow over a slender rotating cone in an enforced axial free-stream
Authors: Hussain, Z.; Garrett, Stephen J.; Stephen, S. O.; Griffiths, Paul T.
Abstract: In this study, a new centrifugal instability mode, which dominates within the boundary-layer flow over a slender rotating cone in still fluid, is used for the first time to model the problem within an enforced oncoming axial flow. The resulting problem necessitates an updated similarity solution to represent the basic flow more accurately than previous studies in the literature. The new mean flow field is subsequently perturbed, leading to disturbance equations that are solved via numerical and short-wavelength asymptotic approaches, yielding favourable comparisons with existing experiments. Essentially, the boundary-layer flow undergoes competition between the streamwise flow component, due to the oncoming flow, and the rotational flow component, due to effect of the spinning cone surface, which can be described mathematically in terms of a control parameter, namely the ratio of streamwise to axial flow. For a slender cone rotating in a sufficiently strong axial flow, the instability mode breaks down into Görtler-type counter-rotating spiral vortices, governed by an underlying centrifugal mechanism, which is consistent with experimental and theoretical studies for a slender rotating cone in otherwise still fluid.
Description: The file associated with this record is under a 6-month embargo from publication in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.
2016-02-25T13:41:12Z