DSpace Community:
http://hdl.handle.net/2381/445
Mon, 24 Oct 2016 03:29:26 GMT
20161024T03:29:26Z
DSpace Community:
http://lra.le.ac.uk:80/retrieve/2392/mathsequation.jpg
http://hdl.handle.net/2381/445

Longterm transients and complex dynamics of a stagestructured population with time delay and the Allee effect
http://hdl.handle.net/2381/38197
Title: Longterm transients and complex dynamics of a stagestructured 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 longterm transients have been recognized as playing a crucial role in the dynamics of ecosystems. In particular, longterm 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 longterm 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 multiperiodic and chaotic attractors. We then show the existence of longterm 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.
Wed, 12 Oct 2016 10:23:36 GMT
http://hdl.handle.net/2381/38197
20161012T10:23:36Z

Homotopy Types of Topological Groupoids and LusternikSchnirelmann Category of Topological Stacks
http://hdl.handle.net/2381/38094
Title: Homotopy Types of Topological Groupoids and LusternikSchnirelmann 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 LusternikSchnirelmann 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 LScategory 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 LusternikSchnirelmann 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 LusternikSchnirelmann 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.
Mon, 26 Sep 2016 11:04:55 GMT
http://hdl.handle.net/2381/38094
20160926T11:04:55Z

hpVersion discontinuous Galerkin methods for advectiondiffusionreaction problems on polytopic meshes
http://hdl.handle.net/2381/38016
Title: hpVersion discontinuous Galerkin methods for advectiondiffusionreaction problems on polytopic meshes
Authors: Cangiani, Andrea; Dong, Zhaonan; Georgoulis, Emmanuil H.; Houston, Paul
Abstract: We consider the hpversion interior penalty discontinuous Galerkin finite element method (DGFEM) for the numerical approximation of the advectiondiffusionreaction equation on general computational meshes consisting of polygonal/polyhedral (polytopic) elements. In particular, new hpversion a priori error bounds are derived based on a specific choice of the interior penalty parameter which allows for edge/facedegeneration. The proposed method employs elemental polynomial bases of total degree p (𝒫pbasis) 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 pversion DGFEM employing a 𝒫pbasis on both polytopic and tensorproduct elements with a (standard) DGFEM employing a (mapped) 𝒬pbasis. Moreover, a computational example is also presented which demonstrates the performance of the proposed hpversion DGFEM on general agglomerated meshes.
Tue, 30 Aug 2016 15:11:03 GMT
http://hdl.handle.net/2381/38016
20160830T15:11:03Z

The convective instability of the BEK system of rotating boundarylayer flows over rough disks
http://hdl.handle.net/2381/37977
Title: The convective instability of the BEK system of rotating boundarylayer 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 turbomachinery and rotorstator 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 (crossflow) 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 azimuthallyanisotropic 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 radiallyanisotropic roughness (concentric grooves) on all the boundary layers, whereas both azimuthallyanisotropic 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 passivedrag reduction mechanism for the entire BEK system of flows.
Tue, 16 Aug 2016 11:54:44 GMT
http://hdl.handle.net/2381/37977
20160816T11:54:44Z

Mathematical Modelling of Oxygen  Plankton System under the Climate Change
http://hdl.handle.net/2381/37971
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 oxygenplankton dynamics have been overlooked.
This dissertation aims to provide insight into an oxygenplankton system using mathematical modelling. We firstly develop a ‘baseline’ oxygenphytoplankton 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.
Tue, 16 Aug 2016 10:51:51 GMT
http://hdl.handle.net/2381/37971
20160816T10:51:51Z

The Fundamental Groupoid and the Geometry of Monoids
http://hdl.handle.net/2381/37837
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 Katospectrum 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 2category 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.
Wed, 13 Jul 2016 15:42:29 GMT
http://hdl.handle.net/2381/37837
20160713T15:42:29Z

Betting Markets: Defining odds restrictions, exploring market inefficiencies and measuring bookmaker solvency
http://hdl.handle.net/2381/37783
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 setup 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/overreserving 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 quasiarbitrage model.
Fri, 17 Jun 2016 10:02:32 GMT
http://hdl.handle.net/2381/37783
20160617T10:02:32Z

kNN predictability analysis of stock and share closing prices
http://hdl.handle.net/2381/37772
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.
Thu, 16 Jun 2016 09:25:00 GMT
http://hdl.handle.net/2381/37772
20160616T09:25:00Z

Kriging metamodel assisted calibration of computational fluid dynamics models
http://hdl.handle.net/2381/37745
Title: Kriging metamodel 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 metamodelling 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 chisquare distribution and hence existing normal distributionbased 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 singlephase flow in both a straighttype and a convergentdivergenttype annular jet pump, where a single model parameter was calibrated with experimental data.
Description: The file associated with this record is under a 12month embargo from publication in accordance with the publisher's selfarchiving policy. The full text may be available through the publisher links provided above.
Tue, 14 Jun 2016 11:09:22 GMT
http://hdl.handle.net/2381/37745
20160614T11:09:22Z

Delay driven spatiotemporal chaos in single species population dynamics models
http://hdl.handle.net/2381/37594
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 intraspecific 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 integrodifferential 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.
Wed, 18 May 2016 12:05:18 GMT
http://hdl.handle.net/2381/37594
20160518T12:05:18Z

How animals move along? Exactly solvable model of superdiffusive spread resulting from animal's decision making
http://hdl.handle.net/2381/37591
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 superdiffusive, i.e. ballistic. The largetime asymptotic behavior appears to be diffusive in the uncorrelated case but superballistic 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 largetime 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 openaccess article distributed under the terms of the Creative Commons AttributionNon CommercialNo Derivatives License (http://creativecommons.org/licenses/byncnd/4.0/ ), which permits use and distribution in any medium, provided the original work is properly cited, the use is noncommercial and no modifications or adaptations are made.
Wed, 18 May 2016 11:50:36 GMT
http://hdl.handle.net/2381/37591
20160518T11:50:36Z

Towards roughnessbased drag reduction in crossflow dominated flows
http://hdl.handle.net/2381/37570
Title: Towards roughnessbased drag reduction in crossflow 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 boundarylayer flow over rough rotating disks. In this study, radial anisotropic surface roughness (concentric grooves) is modelled using the partialslip approach of Miklavčič & Wang (2004) and the surfacegeometry 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 Reynoldsstress 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 Reynoldsstress energy production increases with roughness under both models. However, the energy dissipation of the Type II mode decreases with the roughness under the surfacegeometry model and increases under the partialslip 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 boundarylayertransition delay and drag reduction in crossflow 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.
Tue, 17 May 2016 09:01:51 GMT
http://hdl.handle.net/2381/37570
20160517T09:01:51Z

An energy analysis of convective instabilities of the Bödewadt and Ekman boundary layers over rough surfaces
http://hdl.handle.net/2381/37569
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 threedimensional Bödewadt and Ekman layers of the so called “BEK family" of rotating boundarylayer 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 (crossflow) instability mode for both flows, with the exception of azimuthallyanisotropic 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 radiallyanisotropic roughness (concentric grooves) on both flows, whereas both azimuthallyanisotropic 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.
Tue, 17 May 2016 08:48:49 GMT
http://hdl.handle.net/2381/37569
20160517T08:48:49Z

On a fixed point theorem of Greguš
http://hdl.handle.net/2381/37550
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 nonexpansive in C and such that IC contains TC, then T and I have a unique common fixed point in C.
Fri, 13 May 2016 14:33:57 GMT
http://hdl.handle.net/2381/37550
20160513T14:33:57Z

On common fixed points of weakly commuting mappings and setvalued mappings
http://hdl.handle.net/2381/37549
Title: On common fixed points of weakly commuting mappings and setvalued mappings
Authors: Sessa, S.; Fisher, B.
Abstract: Our main theorem establishes the uniqueness of the common fixed point of two setvalued mappings and of two singlevalued mappings defined on a complete metric space, under a contractive condition and a weak commutativity concept. This improves a theorem of the second author.
Fri, 13 May 2016 14:30:09 GMT
http://hdl.handle.net/2381/37549
20160513T14:30:09Z

On a fixed point theorem of Pathak
http://hdl.handle.net/2381/37548
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.
Fri, 13 May 2016 14:25:52 GMT
http://hdl.handle.net/2381/37548
20160513T14:25:52Z

Common fixed point theorems for compatible mappings
http://hdl.handle.net/2381/37547
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.
Fri, 13 May 2016 14:22:20 GMT
http://hdl.handle.net/2381/37547
20160513T14:22:20Z

Coincidence theorems for nonlinear hybrid contractions
http://hdl.handle.net/2381/37546
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 singlevalued mappings and multivalued mappings satisfying a rational inequality. Our theorems generalize some results of B. Fisher, M. L. Diviccaro et al. and V. Popa.
Fri, 13 May 2016 14:18:00 GMT
http://hdl.handle.net/2381/37546
20160513T14:18:00Z

Related fixed point theorems on two complete and compact metric spaces
http://hdl.handle.net/2381/37544
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.
Fri, 13 May 2016 14:12:57 GMT
http://hdl.handle.net/2381/37544
20160513T14:12:57Z

A note on commutativity of nonassociative rings
http://hdl.handle.net/2381/37543
Title: A note on commutativity of nonassociative rings
Authors: Khan, M. S. S.
Abstract: A theorem on commutativity of nonassociate ring is given.
Fri, 13 May 2016 14:06:58 GMT
http://hdl.handle.net/2381/37543
20160513T14:06:58Z

A Generalization of Prešić Type Mappings in MetricLike Spaces
http://hdl.handle.net/2381/37541
Title: A Generalization of Prešić Type Mappings in MetricLike Spaces
Authors: Shukla, S.; Fisher, Brian
Abstract: We generalize the result of Prešić in metriclike spaces by proving some common fixed point theorems for Prešić type mappings in metriclike spaces. An example is given which shows that the generalization is proper.
Fri, 13 May 2016 13:19:06 GMT
http://hdl.handle.net/2381/37541
20160513T13:19:06Z

Phacoemulsification Surgery in Eyes with Neovascular AgeRelated Macular Degeneration
http://hdl.handle.net/2381/37538
Title: Phacoemulsification Surgery in Eyes with Neovascular AgeRelated 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 agerelated 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 followup 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 antiVEGF 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 antiVEGF 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 antiVEGF injections to keep the macula dry postoperatively.
Fri, 13 May 2016 11:32:13 GMT
http://hdl.handle.net/2381/37538
20160513T11:32:13Z

Stability modes in vortex structure formation: Canonical examples for rotating components
http://hdl.handle.net/2381/37476
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.
Wed, 04 May 2016 14:50:44 GMT
http://hdl.handle.net/2381/37476
20160504T14:50:44Z

Cohomology of tiling spaces: beyond primitive substitutions
http://hdl.handle.net/2381/37469
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 1dimensional 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 BargeDiamond complex, in the onedimensional 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 nonprimitive substitutions, we naturally divide this set of substitutions
into two cases: the minimal substitutions and the nonminimal substitutions.
We provide a detailed method for replacing any nonprimitive 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 AndersonPutnam 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.
Fri, 29 Apr 2016 13:40:19 GMT
http://hdl.handle.net/2381/37469
20160429T13:40:19Z

Tiling spaces, codimension one attractors and shape
http://hdl.handle.net/2381/37346
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 socalled 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 twotoone covering by such a toruslesspoints. 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 1dimensional tilings is in many cases finer than the cohomological or Ktheoretic invariants studied to date.
Mon, 18 Apr 2016 11:58:33 GMT
http://hdl.handle.net/2381/37346
20160418T11:58:33Z

From Ambiguity Aversion to a Generalized Expected Utility. Modeling Preferences in a Quantum Probabilistic Framework
http://hdl.handle.net/2381/37265
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 Ellsbergtype 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 quantumbased generalization of expected utility theory (QEUT), where subjective probabilities depend on the state of the conceptual entity at play and its interaction with the decisionmaker, while preferences between acts are determined by the maximization of this 'statedependent expected utility'.
Description: The file associated with this record is under a 24month embargo from publication in accordance with the publisher's selfarchiving policy. The full text may be available through the publisher links provided above.
Tue, 12 Apr 2016 11:41:18 GMT
http://hdl.handle.net/2381/37265
20160412T11:41:18Z

A classification of the point spectrum of constant length substitution tiling spaces and general fixed point theorems for tilings
http://hdl.handle.net/2381/37027
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.
Fri, 11 Mar 2016 16:11:58 GMT
http://hdl.handle.net/2381/37027
20160311T16:11:58Z

The centrifugal instability of the boundarylayer flow over a slender rotating cone in an enforced axial free stream
http://hdl.handle.net/2381/36986
Title: The centrifugal instability of the boundarylayer 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 boundarylayer 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 shortwavelength asymptotic approaches, yielding favourable comparisons with existing experiments. Essentially, the boundarylayer 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 Görtlertype counterrotating 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 6month embargo from publication in accordance with the publisher's selfarchiving policy. The full text may be available through the publisher links provided above.
Mon, 07 Mar 2016 11:36:56 GMT
http://hdl.handle.net/2381/36986
20160307T11:36:56Z

The neutral curve for stationary disturbances in rotating disk flow for powerlaw fluids
http://hdl.handle.net/2381/36985
Title: The neutral curve for stationary disturbances in rotating disk flow for powerlaw fluids
Authors: Griffiths, P. T.; Garrett, Stephen John; Stephen, S. O.
Abstract: This paper is concerned with the convective instabilities associated with the boundarylayer flow due to a rotating disk. Shearthinning fluids that adhere to the powerlaw relationship are considered. The neutral curves are computed using a sixthorder system of linear stability equations which include the effects of streamline curvature, Coriolis force and the nonNewtonian 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 upperbranch (crossflow) and type II lowerbranch (streamline curvature) modes. Our results indicate that an increase in shearthinning 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 24month embargo from publication in accordance with the publisher's selfarchiving policy. The full text may be available through the publisher links provided above.
Mon, 07 Mar 2016 11:32:29 GMT
http://hdl.handle.net/2381/36985
20160307T11:32:29Z

Stability of the boundary layer on a rotating disk for powerlaw fluids
http://hdl.handle.net/2381/36963
Title: Stability of the boundary layer on a rotating disk for powerlaw 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 nonNewtonian fluids, specifically shearthinning fluids that satisfy the powerlaw (Ostwaldde 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 threedimensional 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 shearthinning fluids by a linear stability analysis. Predictions for the wavenumber and wave angle of the disturbances suggest that shearthinning fluids may have a stabilising effect on the flow.
Thu, 03 Mar 2016 11:51:44 GMT
http://hdl.handle.net/2381/36963
20160303T11:51:44Z

Global linear stability of the boundarylayer flow over a rotating sphere
http://hdl.handle.net/2381/36889
Title: Global linear stability of the boundarylayer flow over a rotating sphere
Authors: Barrow, A.; Garrett, Stephen J.; Peake, N.
Abstract: We consider the linear global stability of the boundarylayer flow over a rotating sphere. Our results suggest that a selfexcited 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 rotatingsphere flow may be different to that for the rotating disk.
Thu, 25 Feb 2016 13:44:07 GMT
http://hdl.handle.net/2381/36889
20160225T13:44:07Z

The centrifugal instability of the boundarylayer flow over a slender rotating cone in an enforced axial freestream
http://hdl.handle.net/2381/36888
Title: The centrifugal instability of the boundarylayer flow over a slender rotating cone in an enforced axial freestream
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 boundarylayer 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 shortwavelength asymptotic approaches, yielding favourable comparisons with existing experiments. Essentially, the boundarylayer 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 Görtlertype counterrotating 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 6month embargo from publication in accordance with the publisher's selfarchiving policy. The full text may be available through the publisher links provided above.
Thu, 25 Feb 2016 13:41:12 GMT
http://hdl.handle.net/2381/36888
20160225T13:41:12Z

The effect of surface roughness on the convective instability of the BEK family of boundarylayer flows
http://hdl.handle.net/2381/36887
Title: The effect of surface roughness on the convective instability of the BEK family of boundarylayer flows
Authors: Alveroglu, Burhan; Segalini, A.; Garrett, Stephen J.
Abstract: A Chebyshev polynomial discretisation method is used to investigate the effect of both anisotropic (radially and azimuthally) and isotropic surface roughnesses on the convective instability of the BEK family of rotating boundarylayer flows. The meanflow profiles for the velocity components are obtained by modelling surface roughness with a partialslip approach. A linear stability analysis is then performed to investigate the effect of roughness on the convective instability characteristics of the inviscid Type I (crossflow) instability and the viscous Type II instability. It is revealed that all roughness types lead to a stabilisation of the Type I mode in all flows within the BEK family, with the exception of azimuthallyanisotropic roughness (radial grooves) within the Bödewadt layer which causes a mildly destabilising effect. In the case of the Type II mode, the results reveal the destabilising effect of radiallyanisotropic roughness (concentric grooves) on all the boundary layers, whereas both azimuthallyanisotropic and isotropic roughnesses have a stabilising effect on the mode for Ekman and von Kármán layers. Complementary results are also presented by considering the effects of roughness on the growth rates of each instability mode within the Ekman layer.
Description: The file associated with this record is under a 24month embargo from publication in accordance with the publisher's selfarchiving policy. The full text may be available through the publisher links provided above.
Thu, 25 Feb 2016 13:34:13 GMT
http://hdl.handle.net/2381/36887
20160225T13:34:13Z

The effect of anisotropic and isotropic roughness on the convective stability of the rotating disk boundary layer
http://hdl.handle.net/2381/36886
Title: The effect of anisotropic and isotropic roughness on the convective stability of the rotating disk boundary layer
Authors: Cooper, A. J.; Harris, J. H.; Garrett, Stephen John; Oezkan, M.; Thomas, P. J.
Abstract: A theoretical study investigating the effects of both anisotropic and isotropic surface roughness on the convective stability of the boundarylayer flow over a rotating disk is described. Surface roughness is modelled using a partialslip approach, which yields steadyflow profiles for the relevant velocity components of the boundarylayer flow which are a departure from the classic von Kármán solution for a smooth disk. These are then subjected to a linear stability analysis to reveal how roughness affects the stability characteristics of the inviscid Type I (or crossflow) instability and the viscous Type II instability that arise in the rotating disk boundary layer. Stationary modes are studied and both anisotropic (concentric grooves and radial grooves) and isotropic (general) roughness are shown to have a stabilizing effect on the Type I instability. For the viscous Type II instability, it was found that a disk with concentric grooves has a strongly destabilizing effect, whereas a disk with radial grooves or general isotropic roughness has a stabilizing effect on this mode. In order to extract possible underlying physical mechanisms behind the effects of roughness, and in order to reconfirm the results of the linear stability analysis, an integral energy equation for threedimensional disturbances to the undisturbed threedimensional boundarylayer flow is used. For anisotropic roughness, the stabilizing effect on the Type I mode is brought about by reductions in energy production in the boundary layer, whilst the destabilizing effect of concentric grooves on the Type II mode results from a reduction in energy dissipation. For isotropic roughness, both modes are stabilized by combinations of reduced energy production and increased dissipation.
Thu, 25 Feb 2016 13:28:22 GMT
http://hdl.handle.net/2381/36886
20160225T13:28:22Z

On the stability of von Kármán rotatingdisk boundary layers with radial anisotropic surface roughness
http://hdl.handle.net/2381/36885
Title: On the stability of von Kármán rotatingdisk boundary layers with radial anisotropic surface roughness
Authors: Garrett, Stephen J.; Cooper, A. J.; Harris, J. H.; Ozkan, M.; Segalini, A.; Thomas, P. J.
Abstract: We summarise results of a theoretical study investigating the distinct convective instability properties of steady boundarylayer flow over rough rotating disks. A generic roughness pattern of concentric circles with sinusoidal surface undulations in the radial direction is considered. The goal is to compare predictions obtained by means of two alternative, and fundamentally different, modelling approaches for surface roughness for the first time. The motivating rationale is to identify commonalities and isolate results that might potentially represent artefacts associated with the particular methodologies underlying one of the two modelling approaches. The most significant result of practical relevance obtained is that both approaches predict overall stabilising effects on type I instability mode of rotating disk flow. This mode leads to transition of the rotatingdisk boundary layer and, more generally, the transition of boundarylayers with a crossflow profile. Stabilisation of the type 1 mode means that it may be possible to exploit surface roughness for laminarflow control in boundary layers with a crossflow component. However, we also find differences between the two sets of model predictions, some subtle and some substantial. These will represent criteria for establishing which of the two alternative approaches is more suitable to correctly describe experimental data when these become available.
Thu, 25 Feb 2016 13:21:15 GMT
http://hdl.handle.net/2381/36885
20160225T13:21:15Z

Global linear stability of the boundarylayer flow over a rotating sphere
http://hdl.handle.net/2381/36884
Title: Global linear stability of the boundarylayer flow over a rotating sphere
Authors: Barrow, A.; Garrett, Stephen John; Peake, N.
Abstract: We consider the linear global stability of the boundarylayer flow over a rotating sphere. Our results suggest that a selfexcited 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 rotatingsphere flow may be different to that for the rotating disk.
Thu, 25 Feb 2016 13:07:28 GMT
http://hdl.handle.net/2381/36884
20160225T13:07:28Z

On Streamwise Vortices in Large Eddy Simulations of Initially Laminar Plane Mixing Layers
http://hdl.handle.net/2381/36790
Title: On Streamwise Vortices in Large Eddy Simulations of Initially Laminar Plane Mixing Layers
Authors: McMullan, William Andrew; Garrett, Stephen J.
Abstract: x
Description: The file associated with this record is under a 24month embargo from publication in accordance with the publisher's selfarchiving policy. The full text may be available through the publisher links provided above.
Thu, 18 Feb 2016 12:27:41 GMT
http://hdl.handle.net/2381/36790
20160218T12:27:41Z

Multiscale principal component analysis
http://hdl.handle.net/2381/36616
Title: Multiscale principal component analysis
Authors: Akinduko, Ayodeji Akinwumi
Abstract: The problem of approximating multidimensional data with objects of lower dimension is a classical problem in complexity reduction. It is important that data approximation capture the structure(s) and dynamics of the data, however distortion to data by many methods during approximation implies that some geometric structure(s) of the data may not be preserved during data approximation. For methods that model the manifold of the data, the quality of approximation depends crucially on the initialization of the method. The first part of this thesis investigates the effect of initialization on manifold modelling methods. Using Self Organising Maps (SOM) as a case study, we compared the quality of learning of manifold methods for two popular initialization methods; random initialization and principal component initialization. To further understand the dynamics of manifold learning, datasets were further classified into linear, quasilinear and nonlinear.
The second part of this thesis focuses on revealing geometric structure(s) in high dimension data using an extension of Principal Component Analysis (PCA). Feature extraction using (PCA) favours direction with large variance which could obfuscate other interesting geometric structure(s) that could be present in the data. To reveal these intrinsic structures, we analysed the local PCA structures of the dataset. An equivalent definition of PCA is that it seeks subspaces that maximize the sum of pairwise distances of data projection; extending this definition we define localization in term of scale as maximizing the sum of weighted squared pairwise distances between data projections for various distributions of weights (scales). Since for complex data various regions of the dataspace could have different PCA structures, we also define localization with regards to dataspace. The resulting local PCA structures were represented by the projection matrix corresponding to the subspaces and analysed to reveal some structures in the data at various localizations.
Tue, 09 Feb 2016 10:10:00 GMT
http://hdl.handle.net/2381/36616
20160209T10:10:00Z

Outofband and adjacentchannel interference reduction by analog nonlinear filters
http://hdl.handle.net/2381/36471
Title: Outofband and adjacentchannel interference reduction by analog nonlinear filters
Authors: Nikitin, A. V.; Davidchack, Ruslan L.; Smith, J. E.
Abstract: In a perfect world, we would have ‘brick wall’ filters, nodistortion amplifiers and mixers, and wellcoordinated spectrum operations. The real world, however, is prone to various types of unintentional and intentional interference of technogenic (manmade) origin that can disrupt critical communication systems. In this paper, we introduce a methodology for mitigating technogenic interference in communication channels by analog nonlinear filters, with an emphasis on the mitigation of outofband and adjacentchannel interference.
Interference induced in a communications receiver by external transmitters can be viewed as wideband nonGaussian noise affecting a narrowerband signal of interest. This noise may contain a strong component within the receiver passband, which may dominate over the thermal noise. While the total wideband interference seen by the receiver may or may not be impulsive, we demonstrate that the interfering component due to power emitted by the transmitter into the receiver channel is likely to appear impulsive under a wide range of conditions. We give an example of mechanisms of impulsive interference in digital communication systems resulting from the nonsmooth nature of any physically realizable modulation scheme for transmission of a digital (discontinuous) message.
We show that impulsive interference can be effectively mitigated by nonlinear differential limiters (NDLs). An NDL can be configured to behave linearly when the input signal does not contain outliers. When outliers are encountered, the nonlinear response of the NDL limits the magnitude of the respective outliers in the output signal. The signal quality is improved in excess of that achievable by the respective linear filter, increasing the capacity of a communications channel. The behavior of an NDL, and its degree of nonlinearity, is controlled by a single parameter in a manner that enables significantly better overall suppression of the noisecontaining impulsive components compared to the respective linear filter. Adaptive configurations of NDLs are similarly controlled by a single parameter and are suitable for improving quality of nonstationary signals under timevarying noise conditions. NDLs are designed to be fully compatible with existing linear devices and systems and to be used as an enhancement, or as a lowcost alternative, to the stateofart interference mitigation methods.
Mon, 01 Feb 2016 09:58:41 GMT
http://hdl.handle.net/2381/36471
20160201T09:58:41Z

Asymptotic variance of stationary reversible and normal Markov processes
http://hdl.handle.net/2381/36413
Title: Asymptotic variance of stationary reversible and normal Markov processes
Authors: Deligiannidis, G.; Peligrad, M.; Utev, Sergey
Abstract: We obtain necessary and sufficient conditions for the regular variation of the variance of partial sums of functionals of discrete and continuoustime stationary Markov processes with normal transition operators. We also construct a class of MetropolisHastings algorithms which satisfy a central limit theorem and invariance principle when the variance is not linear in n.
Wed, 27 Jan 2016 10:37:50 GMT
http://hdl.handle.net/2381/36413
20160127T10:37:50Z

The HELP inequality for Hamiltonian systems
http://hdl.handle.net/2381/36295
Title: The HELP inequality for Hamiltonian systems
Authors: Brown, B. M.; Evans, W. D.; Marletta, M.
Abstract: We extend the Hardy–Everitt–Littlewood–Polya inequality, hitherto established for 2nth order formally selfadjoint ordinary differential equations, to a wide class of linear Hamiltonian systems. The method follows Dias (Ph.D. thesis, Cardiff: University of Wales, 1994) but without the Hilbert space setting which he uses.
Fri, 15 Jan 2016 15:52:52 GMT
http://hdl.handle.net/2381/36295
20160115T15:52:52Z

Regularized semiclassical limits: linear flows with infinite Lyapunov exponents
http://hdl.handle.net/2381/36266
Title: Regularized semiclassical limits: linear flows with infinite Lyapunov exponents
Authors: Athanassoulis, Agisilaos; Kyza, I.; Katsaounis, T.
Abstract: Semiclassical asymptotics for Schrodinger equations with nonsmooth potentials give rise to illposed formal semiclassical limits. These problems have attracted a lot of attention in the last few years, as a proxy for the treatment of eigenvalue crossings, i.e. general systems. It has recently been shown that the semiclassical limit for conical singularities is in fact wellposed, as long as the Wigner measure (WM) stays away from singular saddle points. In this work we develop a family of refined semiclassical estimates, and use them to derive regularized transport equations for saddle points with infinite Lyapunov exponents, extending the aforementioned recent results. In the process we answer a related question posed by P. L. Lions and T. Paul in 1993. If we consider more singular potentials, our rigorous estimates break down. To investigate whether conical saddle points, such as x, admit a regularized transport asymptotic approximation, we employ a numerical solver based on posterior error controal. Thus rigorous uppen bounds for the asymptotic error on concrete problems are generated. In particular, specific phenomena which render invalid any regularized transport for x are identified and quantified. In that sense our rigorous results are sharp. Finally, we use our findings to formulate a precise conjecture for the condition under which conical saddle points admit a regularized transport solution for the WM.
Description: The file associated with this record is under a permanent embargo while publication is In Press in accordance with the publisher's selfarchiving policy. The full text may be available through the publisher links provided above.
Tue, 12 Jan 2016 12:48:18 GMT
http://hdl.handle.net/2381/36266
20160112T12:48:18Z

On the XFEL Schrödinger Equation: Highly Oscillatory Magnetic Potentials and Time Averaging
http://hdl.handle.net/2381/36247
Title: On the XFEL Schrödinger Equation: Highly Oscillatory Magnetic Potentials and Time Averaging
Authors: Athanassoulis, Agisilaos; Antonelli, P.; Markowich, P. A.; Hajaiej, H.
Abstract: We analyse a nonlinear Schrödinger equation for the timeevolution of the wave function of an electron beam, interacting selfconsistently through a Hartree–Fock nonlinearity and through the repulsive Coulomb interaction of an atomic nucleus. The electrons are supposed to move under the action of a time dependent, rapidly periodically oscillating electromagnetic potential. This can be considered a simplified effective single particle model for an Xray free electron laser. We prove the existence and uniqueness for the Cauchy problem and the convergence of wavefunctions to corresponding solutions of a Schrödinger equation with a timeaveraged Coulomb potential in the high frequency limit for the oscillations of the electromagnetic potential.
Mon, 11 Jan 2016 11:41:27 GMT
http://hdl.handle.net/2381/36247
20160111T11:41:27Z

Numerical Simulations of XRay Free Electron Lasers (XFEL)
http://hdl.handle.net/2381/36243
Title: Numerical Simulations of XRay Free Electron Lasers (XFEL)
Authors: Athanassoulis, Agisilaos; Markowich, P. A.; Antonelli, P.; Huang, Z.
Abstract: We study a nonlinear Schrödinger equation which arises as an effective single particle model in Xray free electron lasers (XFEL). This equation appears as a first principles model for the beammatter interactions that would take place in an XFEL molecular imaging experiment in [A. Fratalocchi and G. Ruocco, Phys. Rev. Lett., 106 (2011), 105504]. Since XFEL are more powerful by several orders of magnitude than more conventional lasers, the systematic investigation of many of the standard assumptions and approximations has attracted increased attention. In this model the electrons move under a rapidly oscillating electromagnetic field, and the convergence of the problem to an effective timeaveraged one is examined. We use an operator splitting pseudospectral method to investigate numerically the behavior of the model versus that of its timeaveraged version in complex situations, namely the energy subcritical/mass supercritical case and in the presence of a periodic lattice. We find the timeaveraged model to be an effective approximation, even close to blowup, for fast enough oscillations of the external field. This work extends previous analytical results for simpler cases [P. Antonelli, A. Athanassoulis, H. Hajaiej, and P. Markowich, Arch. Ration. Mech. Anal., 211 (2014), pp. 711732].
Mon, 11 Jan 2016 10:48:23 GMT
http://hdl.handle.net/2381/36243
20160111T10:48:23Z

Synergy effect of cooperative investment
http://hdl.handle.net/2381/36189
Title: Synergy effect of cooperative investment
Authors: Grechuk, Bogdan; Zabarankin, M.
Abstract: Cooperative investment consists of two problems: finding an optimal cooperative investment strategy and fairly dividing investment outcome among participating agents. In general, the two problems cannot be solved separately. It is known that when agents’ preferences are represented by meandeviation functionals, sharing of optimal portfolio creates instruments that, on the one hand, satisfy individual risk preferences but, on the other hand, are not replicable on an incomplete market, so that each agent is strictly better off in participating in cooperative investment than investing alone. This synergy effect is shown to hold when agents’ acceptance sets are represented by cashinvariant utility functions in the case of multiperiod investment with an arbitrary feasible investment set. In this case, a set of all Paretooptimal allocations is characterized, and an equilibriumbased method for selecting a “fair” Paretooptimal allocation is suggested. It is also shown that if exists, the “fair” allocation belongs to the core of the corresponding cooperative game. The equilibriumbased method is then extended to the case of arbitrary utility functions. The obtained results are demonstrated in a multiperiod cooperative investment problem with investors imposing drawdown constraints on investment strategies.
Description: The file associated with this record is under a 12month embargo from publication in accordance with the publisher's selfarchiving policy, available at http://www.springer.com/gp/openaccess/authorsrights/selfarchivingpolicy/2124. The full text may be available through the publisher links provided above.
Wed, 06 Jan 2016 12:56:39 GMT
http://hdl.handle.net/2381/36189
20160106T12:56:39Z

Related fixed points for setvalued mappings on two uniform spaces
http://hdl.handle.net/2381/36151
Title: Related fixed points for setvalued mappings on two uniform spaces
Authors: Türkoğlu, D.; Fisher, Brian
Abstract: Some related fixed point theorems for setvalued mappings on two complete and compact uniform spaces are proved.
Description: 2000 Mathematics Subject Classification: 54H25, 47H10.
Tue, 05 Jan 2016 10:28:25 GMT
http://hdl.handle.net/2381/36151
20160105T10:28:25Z

On the Fresnel integrals and the convolution
http://hdl.handle.net/2381/36144
Title: On the Fresnel integrals and the convolution
Authors: Kiliçman, A.; Fisher, Brian
Abstract: The Fresnel cosine integral C(x), the Fresnel sine integral S(x), and the associated functions C+(x), C−(x), S+(x), and S−(x) are defined as locally summable functions on the real line. Some convolutions and neutrix convolutions of the Fresnel cosine integral and its associated functions with x+r and xr are evaluated.
Description: 2000 Mathematics Subject Classification: 33B10, 46F10
Mon, 04 Jan 2016 15:10:01 GMT
http://hdl.handle.net/2381/36144
20160104T15:10:01Z

On the sine integral and the convolution
http://hdl.handle.net/2381/36143
Title: On the sine integral and the convolution
Authors: Fisher, Brian; AlSirehy, F.
Abstract: The sine integral Si(λx) and the cosine integral Ci(λx) and their associated functions Si+(λx), Si−(λx), Ci+(λx), Ci−(λx) are defined as locally summable functions on the real line. Some convolutions of these functions and sin(μx), sin+(μx), and sin−(μx) are found.
Description: 2000 Mathematics Subject Classification: 33B10, 46F10.
Mon, 04 Jan 2016 14:57:48 GMT
http://hdl.handle.net/2381/36143
20160104T14:57:48Z

Inverse portfolio problem with coherent risk measures
http://hdl.handle.net/2381/36136
Title: Inverse portfolio problem with coherent risk measures
Authors: Grechuk, Bogdan; Zabarankin, M.
Abstract: In general, a portfolio problem minimizes risk (or negative utility) of a portfolio of financial assets with respect to portfolio weights subject to a budget constraint. The inverse portfolio problem then arises when an investor assumes that his/her risk preferences have a numerical representation in the form of a certain class of functionals, e.g. in the form of expected utility, coherent risk measure or meandeviation functional, and aims to identify such a functional, whose minimization results in a portfolio, e.g. a market index, that he/she is most satisfied with. In this work, the portfolio risk is determined by a coherent risk measure, and the rate of return of investor’s preferred portfolio is assumed to be known. The inverse portfolio problem then recovers investor’s coherent risk measure either through finding a convex set of feasible probability measures (risk envelope) or in the form of either mixed CVaR or negative Yaari’s dual utility. It is solved in singleperiod and multiperiod formulations and is demonstrated in a case study with the FTSE 100 index.
Wed, 23 Dec 2015 13:36:29 GMT
http://hdl.handle.net/2381/36136
20151223T13:36:29Z

Implementing Automotive Telematics for Insurance Covers of Fleets
http://hdl.handle.net/2381/36130
Title: Implementing Automotive Telematics for Insurance Covers of Fleets
Authors: Azzopardi, M.; Cortis, Dominic
Abstract: The advantages of UsageBased Insurance for automotive covers over conventional rating methods have been discussed in literature for over four decades. Notwithstanding their adoption in insurance markets has been slow. This paper seeks to establish the viability of introducing fleet TelematicsBased Insurance by investigating the perceptions of insurance operators, tracking service providers and corporate fleet owners. At its core, the study involves a SWOTanalysis to appraise TelematicsBased Insurance against conventional premium rating systems. Twenty five key stakeholders in Malta, a country with an insurance industry that represents others in microcosm, were interviewed to develop our analysis. We assert that local insurers have interests in such insurance schemes as enhanced fleet management and monitoring translate into an improved insurance risk. The findings presented here have implications for all stakeholders as we argue that telematics enhance fleet management, TBI improves risk management for insurers and adoption of this technology is dependent on telematics providers increasing the perceived control by insurers over managing this technology.
Tue, 22 Dec 2015 16:43:17 GMT
http://hdl.handle.net/2381/36130
20151222T16:43:17Z