DSpace Community:
http://hdl.handle.net/2381/445
20150830T13:58:13Z

Time Dependent Diffusion as a Mean Field Counterpart of Levy Type Random Walk
http://hdl.handle.net/2381/32806
Title: Time Dependent Diffusion as a Mean Field Counterpart of Levy Type Random Walk
Authors: Ahmed, D. A.; Petrovskii, S.
Abstract: Insect trapping is commonly used in various pest insect monitoring programs as well as in many ecological field studies. An individual is said to be trapped if it falls within a well defined capturing zone, which it cannot escape. The accumulation of trapped individuals over time forms trap counts or alternatively, the flux of the population density into the trap. In this paper, we study the movement of insects whose dynamics are governed by time dependent diffusion and Lévy walks. We demonstrate that the diffusion model provides an alternative framework for the Cauchy type random walk (Lévy walk with Cauchy distributed steps). Furthermore, by calculating the trap counts using these two conceptually different movement models, we propose that trap counts for pests whose dynamics may be Lévy by nature can effectively be predicted by diffusive flux curves with timedependent diffusivity.
Description: Mathematics Subject Classification: 82B41 / 60K35 / 35Q92
20150722T16:11:10Z

Mathematical Modelling of Spatiotemporal Dynamics of Oxygen in a Plankton System
http://hdl.handle.net/2381/32804
Title: Mathematical Modelling of Spatiotemporal Dynamics of Oxygen in a Plankton System
Authors: Sekerci, Y.; Petrovskii, S.
Abstract: Oxygen production due to phytoplankton photosynthesis is a crucial phenomenon underlying the dynamics of marine ecosystems. However, most of the existing literature focus on other aspects of the plankton community functioning, thus leaving the issue of the coupled oxygenplankton dynamics understudied. In this paper, we consider a generic model of the oxygenphytoplanktonzooplankton dynamics to make an insight into the basic properties of the planktonoxygen interactions. The model is analyzed both analytically and numerically. We first consider the nonspatial model and show that it predicts possible oxygen depletion under certain environmental conditions. We then consider the spatially explicit model and show that it exhibits a rich variety of spatiotemporal patterns including travelling fronts of oxygen depletion, dynamical stabilization of unstable equilibrium and spatiotemporal chaos.
Description: Mathematics Subject Classification: 92D40 / 35B36 / 35Q92 / 37N25
20150722T15:49:51Z

Statistical mechanics of animal movement: Animals's decisionmaking can result in superdiffusive spread
http://hdl.handle.net/2381/32803
Title: Statistical mechanics of animal movement: Animals's decisionmaking can result in superdiffusive spread
Authors: Tilles, Paulo F. C.; Petrovskii, Sergei V.
Abstract: Peculiarities of individual animal movement and dispersal have been a major focus of recent research as they are thought to hold the key to the understanding of many phenomena in spatial ecology. Superdiffusive spread and longdistance dispersal have been observed in different species but the underlying biological mechanisms often remain obscure. In particular, the effect of relevant animal behavior has been largely unaddressed. In this paper, we show that a superdiffusive spread can arise naturally as a result of animal behavioral response to smallscale environmental stochasticity. Surprisingly, the emerging fast spread does not require the standard assumption about the fat tail of the dispersal kernel.
20150722T14:27:23Z

The Role of Host and Microbial Factors in the Pathogenesis of Pneumococcal Bacteraemia Arising from a Single Bacterial Cell Bottleneck
http://hdl.handle.net/2381/32753
Title: The Role of Host and Microbial Factors in the Pathogenesis of Pneumococcal Bacteraemia Arising from a Single Bacterial Cell Bottleneck
Authors: Gerlini, A.; Colomba, L.; Furi, L.; Braccini, T.; Manso, A. S.; Pammolli, A.; Wang, Bo; Vivi, A.; Tassini, M.; van Rooijen, N.; Pozzi, G.; Ricci, S.; Andrew, P. W.; Koedel, U.; Moxon, E. R.; Oggioni, M. R.
Abstract: The pathogenesis of bacteraemia after challenge with one million pneumococci of three isogenic variants was investigated. Sequential analyses of blood samples indicated that most episodes of bacteraemia were monoclonal events providing compelling evidence for a single bacterial cell bottleneck at the origin of invasive disease. With respect to host determinants, results identified novel properties of splenic macrophages and a role for neutrophils in early clearance of pneumococci. Concerning microbial factors, whole genome sequencing provided genetic evidence for the clonal origin of the bacteraemia and identified SNPs in distinct subunits of F0/F1 ATPase in the majority of the ex vivo isolates. When compared to parental organisms of the inoculum, exvivo pneumococci with mutant alleles of the F0/F1 ATPase had acquired the capacity to grow at low pH at the cost of the capacity to grow at high pH. Although founded by a single cell, the genotypes of pneumococci in septicaemic mice indicate strong selective pressure for fitness, emphasising the withinhost complexity of the pathogenesis of invasive disease.
20150720T12:51:16Z

Feeding on Multiple Sources: Towards a Universal Parameterization of the Functional Response of a Generalist Predator Allowing for Switching
http://hdl.handle.net/2381/32698
Title: Feeding on Multiple Sources: Towards a Universal Parameterization of the Functional Response of a Generalist Predator Allowing for Switching
Authors: Morozov, Andrew; Petrovskii, Sergei
Abstract: Understanding of complex trophic interactions in ecosystems requires correct descriptions of the rate at which predators consume a variety of different prey species. Field and laboratory data on multispecies communities are rarely sufficient and usually cannot provide an unambiguous test for the theory. As a result, the conventional way of constructing a multiprey functional response is speculative, and often based on assumptions that are difficult to verify. Predator responses allowing for prey selectivity and active switching are thought to be more biologically relevant compared to the standard proportionbased consumption. However, here we argue that the functional responses with switching may not be applicable to communities with a broad spectrum of resource types. We formulate a set of general rules that a biologically sound parameterization of a predator functional response should satisfy, and show that all existing formulations for the multispecies response with prey selectivity and switching fail to do so. Finally, we propose a universal framework for parameterization of a multiprey functional response by combining patterns of food selectivity and proportionbased feeding.
Description: PMCID: PMC3783441
20150714T14:59:44Z

Revisiting the Role of Individual Variability in Population Persistence and Stability
http://hdl.handle.net/2381/32692
Title: Revisiting the Role of Individual Variability in Population Persistence and Stability
Authors: Morozov, Andrew; Pasternak, A. F.; Arashkevich, E. G.
Abstract: Populations often exhibit a pronounced degree of individual variability and this can be important when constructing ecological models. In this paper, we revisit the role of interindividual variability in population persistence and stability under predation pressure. As a case study, we consider interactions between a structured population of zooplankton grazers and their predators. Unlike previous structured population models, which only consider variability of individuals according to the age or body size, we focus on physiological and behavioural structuring. We first experimentally demonstrate a high degree of variation of individual consumption rates in three dominant species of herbivorous copepods (Calanus finmarchicus, Calanus glacialis, Calanus euxinus) and show that this disparity implies a pronounced variation in the consumption capacities of individuals. Then we construct a parsimonious predatorprey model which takes into account the intrapopulation variability of prey individuals according to behavioural traits: effectively, each organism has a 'personality' of its own. Our modelling results show that structuring of prey according to their growth rate and vulnerability to predation can dampen predatorprey cycles and enhance persistence of a species, even if the resource stock for prey is unlimited. The main mechanism of efficient topdown regulation is shown to work by letting the prey population become dominated by less vulnerable individuals when predator densities are high, while the trait distribution recovers when the predator densities are low.
20150714T14:27:15Z

General Htheorem and Entropies that Violate the Second Law
http://hdl.handle.net/2381/32655
Title: General Htheorem and Entropies that Violate the Second Law
Authors: Gorban, Alexander N.
Abstract: Htheorem states that the entropy production is nonnegative and, therefore, the entropy of a closed system should monotonically change in time. In information processing, the entropy production is positive for random transformation of signals (the information processing lemma). Originally, the Htheorem and the information processing lemma were proved for the classical BoltzmannGibbsShannon entropy and for the correspondent divergence (the relative entropy). Many new entropies and divergences have been proposed during last decades and for all of them the Htheorem is needed. This note proposes a simple and general criterion to check whether the Htheorem is valid for a convex divergence H and demonstrates that some of the popular divergences obey no Htheorem. We consider systems with n states Ai that obey first order kinetics (master equation). A convex function H is a Lyapunov function for all master equations with given equilibrium if and only if its conditional minima properly describe the equilibria of pair transitions A[subscript: i] ⇌ A[subscript: j]. This theorem does not depend on the principle of detailed balance and is valid for general Markov kinetics. Elementary analysis of pair equilibria demonstrate that the popular Bregman divergences like Euclidian distance or ItakuraSaito distance in the space of distribution cannot be the universal Lyapunov functions for the firstorder kinetics and can increase in Markov processes. Therefore, they violate the second law and the information processing lemma. In particular, for these measures of information (divergences) random manipulation with data may add information to data. The main results are extended to nonlinear generalized mass action law kinetic equations.
20150714T09:29:36Z

On Multiple Convolutions and Time Scales
http://hdl.handle.net/2381/32609
Title: On Multiple Convolutions and Time Scales
Authors: Eltayeb, Hassan; Kılıçman, Adem; Fisher, Brian
Abstract: The properties of the multiple Laplace transform and convolutions on a time scale are studied. Further, some related results are also obtained by utilizing the double Laplace transform. We also provide an example in order to illustrate the main result.
20150713T10:41:59Z

Adaptive radial basis functions for option pricing
http://hdl.handle.net/2381/32527
Title: Adaptive radial basis functions for option pricing
Authors: Li, Juxi
Abstract: In this thesis, we have developed meshless adaptive radial basis functions (RBFs)
method for the pricing of financial contracts by solving the BlackScholes partial
differential equation (PDE). In the 1D problem, we priced the financial contracts
of a European call option, Greeks (Delta, Gamma and Vega), an American put
option and a barrier up and out call option with this method. In the BENCHOP
project with Challenge Parameter Set (Parameter Set 2) [97], we have shown
that our adaptive method is highly accurate and with less computational cost in
comparison with the finite difference method for the European call option and
barrier up and out call option. And also we have presented the numerical result of
the equally spaced RBF method for both Parameter Set 1 and 2. In our numerical
simulations with Parameter Set 2, we note that our adaptive method is more
accurate and faster than the equally spaced RBF method. For example for the
barrier up and out call option, the equally spaced method (MQ) with 3000 uniform
nodes has the maximum error of 1.30e02 at three evaluation points, but our
adaptive method (101 nodes) has maximum error of 9.98e05 at the same three
points. This is about 100 times better than the equally spaced method with about
30 times less CPU time. Since our adaptive strategy is accurate and efficient, we
substantially increase the accuracy with fewer number of nodes.
We also developed an adaptive algorithm for the 2 assets BlackScholes problem,
in this algorithm we used the rectangular Voronoi points for the refinement, and
the thin plate spline is used for the local approximation in order to assess the
error. The numerical results of pricing a Margrabe call option are presented for
both adaptive and nonadaptive methods. The adaptive method is more accurate
and requires fewer nodes when compared to the equally spaced RBF method.
20150709T09:26:08Z

Inequalities and eigenvalues of SturmLiouville problems near a singular boundary
http://hdl.handle.net/2381/32450
Title: Inequalities and eigenvalues of SturmLiouville problems near a singular boundary
Authors: Marletta, Marco; Everitt, W. N.; Zettl, A.
Abstract: We study the behavior of eigenvalues of SturmLiouville problems (SLP) when an endpoint of the underlying interval approaches a singularity.
20150630T09:16:49Z

Model Reductions in Biochemical Reaction Networks
http://hdl.handle.net/2381/32442
Title: Model Reductions in Biochemical Reaction Networks
Authors: Khoshnaw, Sarbaz Hamza Abdullah
Abstract: Many complex kinetic models in the field of biochemical reactions
contain a large number of species and reactions. These models often require a
huge array of computational tools to analyse. Techniques of model reduction,
which arise in various theoretical and practical applications in systems biology,
represent key critical elements (variables and parameters) and substructures of
the original system. This thesis aims to study methods of model reduction for
biochemical reaction networks. It has three goals related to techniques of model
reduction. The primary goal provides analytical approximate solutions of such
models. In order to have this set of solutions, we propose an algorithm based on
the Duhamel iterates. This algorithm is an explicit formula that can be studied in
detail for wide regions of concentrations for optimization and parameter identification
purposes. Another goal is to simplify high dimensional models to smaller
sizes in which the dynamics of original models and reduced models should be
similar. Therefore, we have developed some techniques of model reduction such
as geometric singular perturbation method for slow and fast subsystems, and
entropy production analysis for identifying non–important reactions. The suggested
techniques can be applied to some models in systems biology including
enzymatic reactions, elongation factors EF–Tu and EF–Ts signalling pathways,
and nuclear receptor signalling. Calculating the value of deviation at each reduction
stage helps to check that the approximation of concentrations is still within
the allowable limits. The final goal is to identify critical model parameters and
variables for reduced models. We study the methods of local sensitivity in order
to find the critical model elements. The results are obtained in numerical simulations
based on Systems Biology Toolbox (SBToolbox) and SimBiology Toolbox for
Matlab. The simplified models would be accurate, robust, and easily applied by
biologists for various purposes such as reproducing biological data and functions
for the full models.
20150629T14:29:24Z

Approximation with Random Bases: Pro et Contra
http://hdl.handle.net/2381/32428
Title: Approximation with Random Bases: Pro et Contra
Authors: Gorban, Alexander N.; Tyukin, Ivan Yu.; Prokhorov, D. V.; Sofeikov, Konstantin I.
Abstract: In this work we discuss the problem of selecting suitable approximators from families of parameterized elementary functions that are known to be dense in a Hilbert space of functions. We consider and analyze published procedures, both randomized and deterministic, for selecting elements from these families that have been shown to ensure the rate of convergence in $L_2$ norm of order $O(1/N)$, where $N$ is the number of elements. We show that both strategies are successful providing that additional information about the families of functions to be approximated is provided at the stages of learning and practical implementation. In absence of such additional information one may observe exponential growth of the number of terms needed to approximate the function and/or extreme sensitivity of the outcome of the approximation to parameters. Implications of our analysis for applications of neural networks in modeling and control are illustrated with examples.
Description: arXiv admin note: text overlap with arXiv:0905.0677 MSC classes: 41A45, 41A45, 90C59, 92B20, 68W20
20150626T09:00:01Z

Derivative pricing in lévy driven models
http://hdl.handle.net/2381/32222
Title: Derivative pricing in lévy driven models
Authors: Kushpel, Alexander
Abstract: We consider an important class of derivative contracts written on multiple assets
which are traded on a wide range of financial markets. More specifically, we are
interested in developing novel methods for pricing financial derivatives using approximation
theoretic methods which are not wellknown to the financial engineering
community. The problem of pricing of such contracts splits into two parts.
First, we need to approximate the respective density function which depends on the
adapted jumpdiffusion model. Second, we need to construct a sequence of approximation
formulas for the price. These two parts are connected with the problem of
optimal approximation of infinitely differentiable, analytic or entire functions on
noncompact domains. We develop new methods of recovery of density functions
using sksplines (in particular, radial basis functions), Wiener spaces and complex
exponents with frequencies from special domains. The respective lower bounds obtained
show that the methods developed have almost optimal rate of convergence
in the sense of nwidths. On the basis of results obtained we develop a new theory
of pricing of basket options under Lévy processess. In particular, we introduce
and study a class of stochastic systems to model multidimensional return process,
construct a sequence of approximation formulas for the price and establish the
respective rates of convergence.
20150507T13:45:04Z

Leaders do not look back, or do they?
http://hdl.handle.net/2381/32211
Title: Leaders do not look back, or do they?
Authors: Gorban, A. N.; Jarman, N.; Steur, E.; van Leeuwen, C.; Tyukin, I.
Editors: Volpert, V.
Abstract: We study the effect of adding to a directed chain of interconnected systems a
directed feedback from the last element in the chain to the first. The problem is closely related
to the fundamental question of how a change in network topology may influence the behavior of
coupled systems. We begin the analysis by investigating a simple linear system. The matrix that
specifies the system dynamics is the transpose of the network Laplacian matrix, which codes
the connectivity of the network. Our analysis shows that for any nonzero complex eigenvalue λ
of this matrix, the following inequality holds: ℑλ
ℜλ ≤ cot π
n
. This bound is sharp, as it becomes
an equality for an eigenvalue of a simple directed cycle with uniform interaction weights. The
latter has the slowest decay of oscillations among all other network configurations with the same
number of states. The result is generalized to directed rings and chains of identical nonlinear
oscillators. For directed rings, a lower bound σc for the connection strengths that guarantees
asymptotic synchronization is found to follow a similar pattern: σc =
1
1−cos(2π/n)
. Numerical
analysis revealed that, depending on the network size n, multiple dynamic regimes coexist in
the state space of the system. In addition to the fully synchronous state a rotating wave solution
occurs. The effect is observed in networks exceeding a certain critical size. The emergence of a
rotating wave highlights the importance of long chains and loops in networks of oscillators: the
larger the size of chains and loops, the more sensitive the network dynamics becomes to removal
or addition of a single connection.
Description: Mathematics Subject Classification: 34A30, 34D06, 34D45, 92B20, 92B25
20150507T11:08:33Z

Classification of symmetric special biserial algebras with at most one nonuniserial indecomposable projective
http://hdl.handle.net/2381/32158
Title: Classification of symmetric special biserial algebras with at most one nonuniserial indecomposable projective
Authors: Snashall, Nicole; Taillefer, Rachel
Abstract: We consider a natural generalisation of symmetric Nakayama algebras, namely, symmetric special biserial algebras with at most one nonuniserial indecomposable projective module. We describe the basic algebras explicitly by quiver and relations, then classify them up to derived equivalence and up to stable equivalence of Morita type. This includes the algebras of [BocianHolmSkowro\'nski, J. Pure Appl. Algebra 2004], where they study the weakly symmetric algebras of Euclidean type, as well as some algebras of dihedral type.
Description: To appear in the Proceedings of the Edinburgh Mathematical Society. Will appear in 2015  page proofs have been returned to journal. No date/volume/pages are available yet.
20150507T10:12:47Z

The center of a convex set and capital allocation
http://hdl.handle.net/2381/32091
Title: The center of a convex set and capital allocation
Authors: Grechuk, Bogdan
Abstract: A capital allocation scheme for a company that has a random total profit Y and uses a coherent risk measure ρ has been suggested. The scheme returns a unique real number Λρ*(X,Y), which determines the capital that should be allocated to company’s subsidiary with random profit X. The resulting capital allocation is linear and diversifying as defined by Kalkbrener (2005). The problem is reduced to selecting the “center” of a nonempty convex weakly compact subset of a Banach space, and the solution to the latter problem proposed by Lim (1981) has been used. Our scheme can also be applied to selecting the unique Pareto optimal allocation in a wide class of optimal risk sharing problems.
20150430T14:53:03Z

Computational diagnosis of canine lymphoma
http://hdl.handle.net/2381/32072
Title: Computational diagnosis of canine lymphoma
Authors: Mirkes, E. M.; Alexandrakis, I.; Slater, K.; Tuli, R.; Gorban, A. N.
Editors: Vagenas, E. C.; Vlachos, D. S.
Abstract: One out of four dogs will develop cancer in their lifetime and 20% of those will be lymphoma cases. PetScreen developed a lymphoma blood test using serum samples collected from several veterinary practices. The samples were fractionated and analysed by mass spectrometry. Two protein peaks, with the highest diagnostic power, were selected and further identified as acute phase proteins, CReactive Protein and Haptoglobin. Data mining methods were then applied to the collected data for the development of an online computerassisted veterinary diagnostic tool. The generated software can be used as a diagnostic, monitoring and screening tool. Initially, the diagnosis of lymphoma was formulated as a classification problem and then later refined as a lymphoma risk estimation. Three methods, decision trees, kNN and probability density evaluation, were used for classification and risk estimation and several preprocessing approaches were implemented to create the diagnostic system. For the differential diagnosis the best solution gave a sensitivity and specificity of 83.5% and 77%, respectively (using three input features, CRP, Haptoglobin and standard clinical symptom). For the screening task, the decision tree method provided the best result, with sensitivity and specificity of 81.4% and >99%, respectively (using the same input features). Furthermore, the development and application of new techniques for the generation of risk maps allowed their userfriendly visualization.
20150427T14:00:05Z

Adaptive discontinuous Galerkin methods for nonlinear parabolic problems
http://hdl.handle.net/2381/32041
Title: Adaptive discontinuous Galerkin methods for nonlinear parabolic problems
Authors: Metcalfe, Stephen Arthur
Abstract: This work is devoted to the study of a posteriori error estimation and adaptivity
in parabolic problems with a particular focus on spatial discontinuous Galerkin
(dG) discretisations.
We begin by deriving an a posteriori error estimator for a linear nonstationary
convectiondiffusion problem that is discretised with a backward Euler dG method.
An adaptive algorithm is then proposed to utilise the error estimator. The
effectiveness of both the error estimator and the proposed algorithm is shown
through a series of numerical experiments.
Moving on to nonlinear problems, we investigate the numerical approximation
of blowup. To begin this study, we first look at the numerical approximation
of blowup in nonlinear ODEs through standard time stepping schemes. We
then derive an a posteriori error estimator for an implicitexplicit (IMEX) dG
discretisation of a semilinear parabolic PDE with quadratic nonlinearity. An
adaptive algorithm is proposed that uses the error estimator to approach the
blowup time. The adaptive algorithm is then applied in a series of test cases to
gauge the effectiveness of the error estimator.
Finally, we consider the adaptive numerical approximation of a nonlinear
interface problem that is used to model the mass transfer of solutes through
semipermiable membranes. An a posteriori error estimator is proposed for the
IMEX dG discretisation of the model and its effectiveness tested through a series
of numerical experiments.
20150422T14:56:10Z

Is it possible to predict longterm success with kNN? Case study of four market indices (FTSE100, DAX, HANGSENG, NASDAQ)
http://hdl.handle.net/2381/32035
Title: Is it possible to predict longterm success with kNN? Case study of four market indices (FTSE100, DAX, HANGSENG, NASDAQ)
Authors: Shi, Y.; Gorban, A. N.; Yang, T. Y.
Editors: Vagenas, E. C.; Vlachos, D. S.
Abstract: This case study tests the possibility of prediction for 'success' (or 'winner') components of four stock & shares market indices in a time period of three years from 02Jul2009 to 29Jun2012.We compare their performance ain two time frames: initial frame three months at the beginning (02/06/200930/09/2009) and the final three month frame (02/04/201229/06/2012).To label the components, average price ratio between two time frames in descending order is computed. The average price ratio is defined as the ratio between the mean prices of the beginning and final time period. The 'winner' components are referred to the top one third of total components in the same order as average price ratio it means the mean price of final time period is relatively higher than the beginning time period. The 'loser' components are referred to the last one third of total components in the same order as they have higher mean prices of beginning time period. We analyse, is there any information about the winnerlooser separation in the initial fragments of the daily closing prices logreturns time series.The LeaveOneOut CrossValidation with kNN algorithm is applied on the daily logreturn of components using a distance and proximity in the experiment. By looking at the error analysis, it shows that for HANGSENG and DAX index, there are clear signs of possibility to evaluate the probability of longterm success. The correlation distance matrix histograms and 2D/3D elastic maps generated from ViDaExpert show that the 'winner' components are closer to each other and 'winner'/'loser' components are separable on elastic maps for HANGSENG and DAX index while for the negative possibility indices, there is no sign of separation.
20150421T14:32:46Z

Multiscale principal component analysis
http://hdl.handle.net/2381/32009
Title: Multiscale principal component analysis
Authors: Akinduko, A. A.; Gorban, Alexander N.
Editors: Vagenas, E. C.; Vlachos, D. S.
Abstract: Principal component analysis (PCA) is an important tool in exploring data. The conventional approach to PCA leads to a solution which favours the structures with large variances. This is sensitive to outliers and could obfuscate interesting underlying structures. One of the equivalent definitions of PCA is that it seeks the subspaces that maximize the sum of squared pairwise distances between data projections. This definition opens up more flexibility in the analysis of principal components which is useful in enhancing PCA. In this paper we introduce scales into PCA by maximizing only the sum of pairwise distances between projections for pairs of datapoints with distances within a chosen interval of values [l,u]. The resulting principal component decompositions in Multiscale PCA depend on point (l,u) on the plane and for each point we define projectors onto principal components. Cluster analysis of these projectors reveals the structures in the data at various scales. Each structure is described by the eigenvectors at the medoid point of the cluster which represent the structure. We also use the distortion of projections as a criterion for choosing an appropriate scale especially for data with outliers. This method was tested on both artificial distribution of data and real data. For data with multiscale structures, the method was able to reveal the different structures of the data and also to reduce the effect of outliers in the principal component analysis.
20150416T13:57:07Z

Multiscale approach to pest insect monitoring: Random walks, pattern formation, synchronization, and networks
http://hdl.handle.net/2381/31970
Title: Multiscale approach to pest insect monitoring: Random walks, pattern formation, synchronization, and networks
Authors: Petrovskii, Sergei; Petrovskaya, N.; Bearup, Daniel
Abstract: Pest insects pose a significant threat to food production worldwide resulting in annual losses worth hundreds of billions of dollars. Pest control attempts to prevent pest outbreaks that could otherwise destroy a sward. It is good practice in integrated pest management to recommend control actions (usually pesticides application) only when the pest density exceeds a certain threshold. Accurate estimation of pest population density in ecosystems, especially in agroecosystems, is therefore very important, and this is the overall goal of the pest insect monitoring. However, this is a complex and challenging task; providing accurate information about pest abundance is hardly possible without taking into account the complexity of ecosystems' dynamics, in particular, the existence of multiple scales. In the case of pest insects, monitoring has three different spatial scales, each of them having their own scalespecific goal and their own approaches to data collection and interpretation. In this paper, we review recent progress in mathematical models and methods applied at each of these scales and show how it helps to improve the accuracy and robustness of pest population density estimation.
20150410T08:44:10Z

Some analytical and numerical approaches to understanding trap counts resulting from pest insect immigration.
http://hdl.handle.net/2381/31969
Title: Some analytical and numerical approaches to understanding trap counts resulting from pest insect immigration.
Authors: Bearup, D.; Petrovskaya, N.; Petrovskii, Sergei
Abstract: Monitoring of pest insects is an important part of the integrated pest management. It aims to provide information about pest insect abundance at a given location. This includes data collection, usually using traps, and their subsequent analysis and/or interpretation. However, interpretation of trap count (number of insects caught over a fixed time) remains a challenging problem. First, an increase in either the population density or insects activity can result in a similar increase in the number of insects trapped (the so called "activitydensity" problem). Second, a genuine increase of the local population density can be attributed to qualitatively different ecological mechanisms such as multiplication or immigration. Identification of the true factor causing an increase in trap count is important as different mechanisms require different control strategies. In this paper, we consider a meanfield mathematical model of insect trapping based on the diffusion equation. Although the diffusion equation is a wellstudied model, its analytical solution in closed form is actually available only for a few special cases, whilst in a more general case the problem has to be solved numerically. We choose finite differences as the baseline numerical method and show that numerical solution of the problem, especially in the realistic 2D case, is not at all straightforward as it requires a sufficiently accurate approximation of the diffusion fluxes. Once the numerical method is justified and tested, we apply it to the corresponding boundary problem where different types of boundary forcing describe different scenarios of pest insect immigration and reveal the corresponding patterns in the trap count growth.
20150410T08:35:29Z

Are time delays always destabilizing? Revisiting the role of time delays and the Allee effect
http://hdl.handle.net/2381/31968
Title: Are time delays always destabilizing? Revisiting the role of time delays and the Allee effect
Authors: Jankovic, Masha; Petrovskii, Sergei
Abstract: One of the main challenges in ecology is to determine the cause of population fluctuations. Both theoretical and empirical studies suggest that delayed density dependence instigates cyclic behavior in many populations; however, underlying mechanisms through which this occurs are often difficult to determine and may vary within species. In this paper, we consider single species population dynamics affected by the Allee effect coupled with discrete time delay. We use two different mathematical formulations of the Allee effect and analyze (both analytically and numerically) the role of time delay in different feedback mechanisms such as competition and cooperation. The bifurcation value of the delay (that results in the Hopf bifurcation) as a function of the strength of the Allee effect is obtained analytically. Interestingly, depending on the chosen delayed mechanism, even a large time delay may not necessarily lead to instability. We also show that, in case the time delay affects positive feedback (such as cooperation), the population dynamics can lead to selforganized formation of intermediate quasistationary states. Finally, we discuss ecological implications of our findings.
20150410T08:27:00Z

On the composition of the distributions xs+ lnmx+ and xμ+
http://hdl.handle.net/2381/31949
Title: On the composition of the distributions xs+ lnmx+ and xμ+
Authors: Fisher, Brian
Abstract: Let F be a distribution and let f be a locally summable function. The distribution F(f) is defined as the neutrix limit of the sequence {Fn(f)}, where Fn(x) = F(x)*δn(x) and {δn(x)} is a certain sequence of infinitely differentiable functions converging to the Dirac deltafunction δ(x). The composition of the distributions xs + lnm x+ and xμ + is proved to exist and be equal to μmxsμ + lnm x+ for μ > 0 and s,m = 1, 2,....
Description: 2000 Mathematics Subject Classification. 46F10
20150331T10:48:47Z

New Langevin and Gradient Thermostats for Rigid Body Dynamics
http://hdl.handle.net/2381/31940
Title: New Langevin and Gradient Thermostats for Rigid Body Dynamics
Authors: Davidchack, Ruslan L.; Ouldridge, T. E.; Tretyakov, M. V.
Abstract: We introduce two new thermostats, one of Langevin type and one of gradient (Brownian) type, for rigid body dynamics. We formulate rotation using the quaternion representation of angular coordinates; both thermostats preserve the unit length of quaternions. The Langevin thermostat also ensures that the conjugate angular momenta stay within the tangent space of the quaternion coordinates, as required by the Hamiltonian dynamics of rigid bodies. We have constructed three geometric numerical integrators for the Langevin thermostat and one for the gradient thermostat. The numerical integrators reflect key properties of the thermostats themselves. Namely, they all preserve the unit length of quaternions, automatically, without the need of a projection onto the unit sphere. The Langevin integrators also ensure that the angular momenta remain within the tangent space of the quaternion coordinates. The Langevin integrators are quasisymplectic and of weak order two. The numerical method for the gradient thermostat is of weak order one. Its construction exploits ideas of Liegroup type integrators for differential equations on manifolds. We numerically compare the discretization errors of the Langevin integrators, as well as the efficiency of the gradient integrator compared to the Langevin ones when used in the simulation of rigid TIP4P water model with smoothly truncated electrostatic interactions. We observe that the gradient integrator is computationally less efficient than the Langevin integrators. We also compare the relative accuracy of the Langevin integrators in evaluating various static quantities and give recommendations as to the choice of an appropriate integrator.
Description: AMS 2000 subject classification. 65C30, 60H35, 60H10.
20150330T09:07:46Z

Segaltype algebraic models of ntypes
http://hdl.handle.net/2381/31938
Title: Segaltype algebraic models of ntypes
Authors: Blanc, D.; Paoli, Simona
Abstract: For each n ≥ 1, we introduce two new Segaltype models of ntypes of topological
spaces: weakly globular nfold groupoids, and a lax version of these. We show
that any ntype can be represented up to homotopy by such models via an explicit
algebraic fundamental nfold groupoid functor. We compare these models to
Tamsamani’s weak ngroupoids, and extract from them a model for (k − 1)
connected ntypes.
Description: Mathematical Subject Classification 2000
Primary: 55S45
Secondary: 18G50, 18B40
20150330T08:45:24Z

The weakly globular double category of fractions of a category
http://hdl.handle.net/2381/31937
Title: The weakly globular double category of fractions of a category
Authors: Paoli, Simona; Pronk, D.
Abstract: This paper introduces the construction of a weakly globular double category of fractions for a category and studies its universal properties. It shows that this double category is locally small and considers a couple of concrete examples.
Description: 2010 Mathematics Subject Classification: 18D05, 18E35
20150330T08:34:24Z

A circular order on edgecoloured trees and RNA mdiagrams
http://hdl.handle.net/2381/31820
Title: A circular order on edgecoloured trees and RNA mdiagrams
Authors: Marsh, Robert J.; Schroll, Sibylle
Abstract: We study a circular order on labelled, medgecoloured trees with k vertices, and show that the set of such trees with a fixed circular order is in bijection with the set of RNA mdiagrams of degree k, combinatorial objects which can be regarded as RNA secondary structures of a certain kind. We enumerate these sets and show that the set of trees with a fixed circular order can be characterized as an equivalence class for the transitive closure of an operation which, in the case m=3, arises as an induction in the context of interval exchange transformations. © 2013 Elsevier Inc.
Description: 2010 Mathematics Subject Classification: Primary: 05C05, 05A15; Secondary: 37B10
20150309T10:16:25Z

Extensions in Jacobian Algebras and Cluster Categories of Marked Surfaces
http://hdl.handle.net/2381/31819
Title: Extensions in Jacobian Algebras and Cluster Categories of Marked Surfaces
Authors: Canakci, Ilke; Schroll, Sibylle
Abstract: In the context of representation theory of finite dimensional algebras, string algebras have been extensively studied and almost all aspects of their representation theory are wellunderstood. One exception to this is the classification of extensions between indecomposable modules. In this paper we explicitly describe such extensions for a class of string algebras, namely gentle algebras associated to surface triangulations. These algebras arise as Jacobian algebras of unpunctured surfaces. We give bases of their extension spaces and show that the dimensions of these extension spaces are given in terms of crossing arcs in the surface. Our approach is new and consists of interpreting snake graphs as indecomposable modules. To give a complete answer, we need to work in the associated cluster category where we explicitly calculate the middle terms of extensions and give a basis of the extension space. We note that not all extensions in the cluster category give rise to extensions for the Jacobian algebra.
Description: Generalized the results to include selfextensions, Added a new section containing an example, New abstract, Added a new result on snake graphs, Minor corrections, 31 pages, 14 figures. 2000 Mathematics Subject Classification. Primary: 13F60, 16P10, 18G15, 18E30
20150309T10:08:08Z

Trivial Extensions of Gentle Algebras and Brauer Graph Algebras
http://hdl.handle.net/2381/31818
Title: Trivial Extensions of Gentle Algebras and Brauer Graph Algebras
Authors: Schroll, Sibylle
Abstract: We show that two wellstudied classes of tame algebras coincide: namely, the class of symmetric special biserial algebras coincides with the class of Brauer graph algebras. We then explore the connection between gentle algebras and symmetric special biserial algebras by explicitly determining the trivial extension of a gentle algebra by its minimal injective cogenerator. This is a symmetric special biserial algebra and hence a Brauer graph algebra of which we explicitly give the Brauer graph. We further show that a Brauer graph algebra gives rise, via admissible cuts, to many gentle algebras and that the trivial extension of a gentle algebra obtained via an admissible cut is the original Brauer graph algebra. As a consequence we prove that the trivial extension of a Jacobian algebra of an ideal triangulation of a Riemann surface with marked points in the boundary is isomorphic to the Brauer graph algebra with Brauer graph given by the arcs of the triangulation.
Description: Added an example. 2010 Mathematics Subject Classification. Primary 16G10, 16G20; Secondary 16S99, 13F60
20150309T10:05:05Z

The geometry of Brauer graph algebras and cluster mutations
http://hdl.handle.net/2381/31817
Title: The geometry of Brauer graph algebras and cluster mutations
Authors: Marsh, Robert J.; Schroll, Sibylle
Abstract: In this paper we establish a connection between ribbon graphs and Brauer graphs. As
a result, we show that a compact oriented surface with marked points gives rise to a unique Brauer
graph algebra up to derived equivalence. In the case of a disc with marked points we show that a dual
construction in terms of dual graphs exists. The rotation of a diagonal in an mangulation gives rise
to a Whitehead move in the dual graph, and we explicitly construct a tilting complex on the related
Brauer graph algebras reflecting this geometrical move.
Description: MSC
primary, 16G10, 16G20, 16E35; secondary, 13F60, 14J10
20150309T09:51:31Z

A circular order on edgecoloured trees and RNA mdiagrams
http://hdl.handle.net/2381/31816
Title: A circular order on edgecoloured trees and RNA mdiagrams
Authors: Marsh, Robert J.; Schroll, Sibylle
Abstract: We study a circular order on labelled, medgecoloured trees with k vertices, and show that the set of such trees with a fixed circular order is in bijection with the set of RNA mdiagrams of degree k , combinatorial objects which can be regarded as RNA secondary structures of a certain kind. We enumerate these sets and show that the set of trees with a fixed circular order can be characterized as an equivalence class for the transitive closure of an operation which, in the case m=3, arises as an induction in the context of interval exchange transformations.
20150309T09:45:40Z

The Ext algebra of a Brauer graph algebra
http://hdl.handle.net/2381/31815
Title: The Ext algebra of a Brauer graph algebra
Authors: Green, Edward L.; Schroll, Sibylle; Snashall, Nicole; Taillefer, Rachel
Abstract: In this paper we study finite generation of the Ext algebra of a Brauer graph algebra by determining the degrees of the generators. As a consequence we characterize the Brauer graph algebras that are Koszul and those that are K[subscript: 2].
Description: Minor changes only. 2010 Mathematics Subject Classification. 16G20, 16S37, 16E05, 16E30
20150309T09:37:28Z

Group actions and coverings of Brauer graph algebras
http://hdl.handle.net/2381/31808
Title: Group actions and coverings of Brauer graph algebras
Authors: Green, E. L.; Schroll, Sibylle; Snashall, Nicole
Abstract: We develop a theory of group actions and coverings on Brauer graphs that parallels
the theory of group actions and coverings of algebras. In particular, we show that any Brauer
graph can be covered by a tower of coverings of Brauer graphs such that the topmost covering has
multiplicity function identically one, no loops, and no multiple edges. Furthermore, we classify
the coverings of Brauer graph algebras that are again Brauer graph algebras.
Description: 2010 Mathematics Subject Classification. Primary 05E18, 16G20; Secondary 14E20, 16W50, 58E40
20150306T16:08:02Z

Gaussian process regression with multiple response variables
http://hdl.handle.net/2381/31763
Title: Gaussian process regression with multiple response variables
Authors: Wang, Bo; Chen, Tau
Abstract: Gaussian process regression (GPR) is a Bayesian nonparametric technology that has
gained extensive application in databased modelling of various systems, including
those of interest to chemometrics. However, most GPR implementations model only a
single response variable, due to the difficulty in the formulation of covariance function
for correlated multiple response variables, which describes not only the correlation
between data points, but also the correlation between responses. In the paper we
propose a direct formulation of the covariance function for multiresponse GPR, based
on the idea that its covariance function is assumed to be the “nominal” unioutput
covariance multiplied by the covariances between different outputs. The effectiveness
of the proposed multiresponse GPR method is illustrated through numerical examples
and response surface modelling of a catalytic reaction process.
20150304T15:57:18Z

nFold groupoids, ntypes and ntrack categories
http://hdl.handle.net/2381/31752
Title: nFold groupoids, ntypes and ntrack categories
Authors: Blanc, David; Paoli, Simona
Abstract: For each n ≥ 1, we introduce two new Segaltype models of ntypes
of topological spaces: weakly globular nfold groupoids, and a lax version
of these. We show that any ntype can be represented up to homotopy by
such models via an explicit algebraic fundamental nfold groupoid functor.
We compare these models to Tamsamani’s weak ngroupoids, and extract from
them a model for (k − 1)connected ntypes.
Description: 1991 Mathematics Subject Classification. 55S45; 18G50, 18B40
20150304T11:33:24Z

Minimum Distance Estimation of Milky Way Model Parameters and Related Inference
http://hdl.handle.net/2381/31616
Title: Minimum Distance Estimation of Milky Way Model Parameters and Related Inference
Authors: Banerjee, S.; Bhattacharya, S.; Basu, A.; Bose, S.; Chakrabarty, Dalia; Mukherjee, S.
Abstract: We propose a method to estimate the location of the Sun in the disk of the Milky Way using a
method based on the Hellinger distance and construct confidence sets on our estimate of the unknown
location using a bootstrap based method. Assuming the Galactic disk to be twodimensional, the
sought solar location then reduces to the radial distance separating the Sun from the Galactic center
and the angular separation of the Galactic center to Sun line, from a prefixed line on the disk. On
astronomical scales, the unknown solar location is equivalent to the location of us earthlings who
observe the velocities of a sample of stars in the neighborhood of the Sun. This unknown location
is estimated by undertaking pairwise comparisons of the estimated density of the observed set of
velocities of the sampled stars, with the density estimated using synthetic stellar velocity data
sets generated at chosen locations in the Milky Way disk. The synthetic data sets are generated
at a number of locations that we choose from within a constructed grid, at four different base
astrophysical models of the Galaxy. Thus, we work with one observed stellar velocity data and
four distinct sets of simulated data comprising a number of synthetic velocity data vectors, each
generated at a chosen location. For a given base astrophysical model that gives rise to one such
simulated data set, the chosen location within our constructed grid at which the estimated density of
the generated synthetic data best matches the density of the observed data, is used as an estimate
for the location at which the observed data was realized. In other words, the chosen location
corresponding to the highest match offers an estimate of the solar coordinates in the Milky Way
disk. The “match” between the pair of estimated densities is parameterized by the affinity measure
based on the familiar Hellinger distance. We perform a novel crossvalidation procedure to establish
a desirable “consistency” property of the proposed method.
20150205T14:31:58Z

Inverse Bayesian Estimation of Gravitational Mass Density in Galaxies from Missing Kinematic Data
http://hdl.handle.net/2381/31604
Title: Inverse Bayesian Estimation of Gravitational Mass Density in Galaxies from Missing Kinematic Data
Authors: Chakrabarty, Dalia; Saha, P.
Abstract: In this paper, we focus on a type of inverse problem in which the data are expressed as an unknown function of
the sought and unknown model function (or its discretised representation as a model parameter vector). In particular,
we deal with situations in which training data are not available. Then we cannot model the unknown
functional relationship between data and the unknown model function (or parameter vector) with a Gaussian
Process of appropriate dimensionality. A Bayesian method based on state space modelling is advanced instead.
Within this framework, the likelihood is expressed in terms of the probability density function (pdf) of the state
space variable and the sought model parameter vector is embedded within the domain of this pdf. As the measurable
vector lives only inside an identified subvolume of the system state space, the pdf of the state space variable
is projected onto the space of the measurables, and it is in terms of the projected state space density that the
likelihood is written; the final form of the likelihood is achieved after convolution with the distribution of measurement
errors. Application motivated vague priors are invoked and the posterior probability density of the
model parameter vectors, given the data are computed. Inference is performed by taking posterior samples with
adaptive MCMC. The method is illustrated on synthetic as well as real galactic data.
20150204T17:07:47Z

Bayesian Density Estimation via Multiple Sequential Inversions of 2D Images with Application in Electron Microscopy
http://hdl.handle.net/2381/31575
Title: Bayesian Density Estimation via Multiple Sequential Inversions of 2D Images with Application in Electron Microscopy
Authors: Chakrabarty, Dalia; Rigat, F.; Gabrielyan, N.; Beanland, R.; Paul, S.
Abstract: We present a new Bayesian methodology to learn the unknown material density of
a given sample by inverting its twodimensional images that are taken with a Scanning Electron
Microscope. An image results from a sequence of projections of the convolution of the density
function with the unknown microscopy correction function that we also learn from the data;
thus learning of the unknowns demands multiple inversions. We invoke a novel design of experiment,
involving imaging at multiple values of the parameter that controls the subsurface
depth from which information about the density structure is carried, to result in the image.
Reallife material density functions are characterized by high density contrasts and are highly
discontinuous, implying that they exhibit correlation structures that do not vary smoothly. In
the absence of training data, modeling such correlation structures of real material density functions
is not possible. So we discretize the material sample and treat values of the density function
at chosen locations inside it as independent and distributionfree parameters. Resolution
of the available image dictates the discretization length of the model; three models pertaining
to distinct resolution classes (at μm to nano metre scale lengths) are developed. We develop
priors on the material density, such that these priors adapt to the sparsity inherent in the density
function. The likelihood is defined in terms of the distance between the convolution of the unknown
functions and the image data. The posterior probability density of the unknowns given
the data is expressed using the developed priors on the density and priors on the microscopy
correction function as elicited from the Microscopy literature. We achieve posterior samples
using an adaptive MetropoliswithinGibbs inference scheme. The method is applied to learn
the material density of a 3D sample of a nanostructure, using real image data. Illustrations on
simulated image data of alloy samples are also included
20150204T10:02:57Z

Bayesian Learning of Material Density Function by Multiple Sequential Inversions of 2D Images in Electron Microscopy
http://hdl.handle.net/2381/31574
Title: Bayesian Learning of Material Density Function by Multiple Sequential Inversions of 2D Images in Electron Microscopy
Authors: Chakrabarty, Dalia; Paul, S.
Editors: Polpo de Campos, A; Neto,; Ramos Rifo,; Stern,; Lauretto,
Abstract: We discuss a novel inverse problem in which the data is generated by the sequential contractive projections
of the convolution of two unknown functions, both of which we aim to learn. The method is illustrated
using an application that relates to the multiple inversions of image data recorded with a Scanning Electron
Microscope, with the aim of learning the density of a given material sample and the microscopy correction
function. Given the severe logistical difficulties in this application of taking multiple images at different
viewing angles, a novel imaging experiment is undertaken, resulting in expansion of information. In lieu of
training data, it is noted that the highly discontinuous material density function cannot be modelled using a
Gaussian Process (GP) as the parametrisation of the required nonstationary covariance function of such a
GP cannot be achieved without training data. Consequently, we resort to estimating values of the unknown
functions at chosen locations in their domain–locations at which an image data are available. Image data
across a range of resolutions leads to multiscale models which we use to estimate material densities from the
micrometre to nanometre length scales. We discuss applications of the method in nondestructive learning
of material density using simulated metallurgical image data, as well as perform inhomogeneity detection in
multicomponent composite on nano metre scales, by inverting real image data of a brick of nanoparticles.
20150204T09:51:38Z

Simple Locally Finite Lie Algebras of Diagonal Type
http://hdl.handle.net/2381/31502
Title: Simple Locally Finite Lie Algebras of Diagonal Type
Authors: Baranov, Alexander
Abstract: We discuss various characterizations of simple locally finite Lie algebras of diagonal type over an algebraically closed field of characteristic zero.
20150127T14:38:49Z

On time scale invariance of random walks in confined space.
http://hdl.handle.net/2381/31448
Title: On time scale invariance of random walks in confined space.
Authors: Bearup, Daniel; Petrovskii, Sergei
Abstract: Animal movement is often modelled on an individual level using simulated random walks. In such applications it is preferable that the properties of these random walks remain consistent when the choice of time is changed (time scale invariance). While this property is well understood in unbounded space, it has not been studied in detail for random walks in a confined domain. In this work we undertake an investigation of time scale invariance of the drift and diffusion rates of Brownian random walks subject to one of four simple boundary conditions. We find that time scale invariance is lost when the boundary condition is nonconservative, that is when movement (or individuals) is discarded due to boundary encounters. Where possible analytical results are used to describe the limits of the time scaling process, numerical results are then used to characterise the intermediate behaviour.
20150120T14:49:30Z

Modelling biological invasions : population cycles, waves and time delays
http://hdl.handle.net/2381/31392
Title: Modelling biological invasions : population cycles, waves and time delays
Authors: Jankovic, Masha
Abstract: Biological invasions are rapidly gaining importance due to the everincreasing number
of introduced species. Alongside the plenitude of empirical data on invasive
species there exists an equally broad range of mathematical models that might be
of use in understanding biological invasions.
This thesis aims to address several issues related to modelling invasive species
and provide insight into their dynamics. Part I (Chapter 2) documents a case
study of the gypsy moth, Lymantria dispar, invasion in the US. We propose an
alternative hypothesis to explain the patchiness of gypsy moth spread entailing
the interplay between dispersal, predation or a viral infection and the Allee effect.
Using a reactiondiffusion framework we test the two models (preypredator and
susceptibleinfected) and predict qualitatively similar patterns as are observed in
natural populations. As high density gypsy moth populations cause the most
damage, estimating the spread rate would be of help in any suppression strategy.
Correspondingly, using a diffusive SI model we are able to obtain estimates of the
rate of spread comparable to historical data.
Part II (Chapters 3, 4 and 5) is more methodological in nature, and in a single
species context we examine the effect of an ubiquitous phenomenon influencing
population dynamics time delay. In Chapter 3 we show that contrary to the
general opinion, time delays are not always destabilising, using a delay differential
equation with discrete time delay. The concept of distributed delay is introduced
in Chapter 4 and studied through an integrodifferential model. Both Chapters 3
and 4 focus on temporal dynamics of populations, so we further this consideration
to include spatial effects in Chapter 5. Using two different representations of movement,
we show that the onset of spatiotemporal chaos in the wake of population
fronts is possible in a single species model.
20150108T12:53:35Z

Special functions and generalized functions
http://hdl.handle.net/2381/30544
Title: Special functions and generalized functions
Authors: AlSirehy, Fatma.
Abstract: In 1950, Laurent Schwartz marked a convenient starting point for the theory of generalized functions as a subject in its own right. He developed and unified much of the earlier work by Hadamard, Bochner, Sobolev and others. Since then an enormous literature dealing with both theory and applications has grown up, and the subject has undergone extensive further development. The original Schwartz treatment defined a distribution as a linear continuous functional on a space of test functions.;This thesis can be considered a part of the development going in that direction. It is partly an extension of earlier contributions by Fisher, Kuribayashi, Itano and others.;After introducing the background and basic definitions in Chapter One, we developed some basic results concerning the cosine integral Ci(lambda x) and its associated functions Ci+(lambda x) and Ci(lambdax) as well as the neutrix convolution products of the cosine integral.;Chapter Three is devoted to similar results concerning the sine integral Si(lambdax).;In Chapter Four, we generalize some earlier results by Fisher and Kuribayashi concerning the product of the two dimensions xl+ and xlr+ . Moreover, other results are obtained concerning the neutrix product of xlambdar lnp x and sgn x xlambdar. Other theorems are proved about the matrix product of some other distributions such as xl+ ln x+ and xlr .;Chapter Five contains new results about the composition of distributions. It involves the applications of the neutrix limit to establish such relationships between different distributions.
20141215T10:40:16Z

Ancient Egyptian astronomy : timekeeping and cosmography in the New Kingdom
http://hdl.handle.net/2381/30543
Title: Ancient Egyptian astronomy : timekeeping and cosmography in the New Kingdom
Authors: Symons, Sarah.
Abstract: The first part of this study analyses and discusses astronomical timekeeping methods used in the New Kingdom. Diagonal star clocks are examined first, looking at classification of sources, decan lists, and the updating of the tables over time. The date list in the Osireion at Abydos is discussed, and issues concerning its place in the history of astronomical timekeeping are raised. The final stellar timekeeping method, the Ramesside star clock, is then examined. The conventional interpretation of the observational method behind the tables is challenged by a new theory, and a system of analysing the tables is introduced. The conclusions of the previous sections are then gathered together in a discussion of the development of stellar timekeeping methods.;The small instruments known as shadow clocks, and their later relatives the sloping sundials, are also examined. The established hypothesis that the shadow clock was completed by the addition of a crossbar is challenged and refuted.;The second part of this study is based on New Kingdom representations of the sky. Two major texts and several celestial diagrams are discussed in detail, beginning with the Book of Nut, which describes the motions of the sun and stars. New translations of the vignette and dramatic text are presented and discussed. Portions of the Book of the Day describing the behaviour of the sun and circumpolar group of stars are analysed.;Finally, celestial diagrams dating from the New Kingdom are discussed. Their composition and significance is discussed and the conceptual framework behind the diagrams is recreated. By introducing new theories and analysis methods, and using a modern but sympathetic approach to the original sources, this study attempts to update and extend our knowledge of these areas of ancient astronomy..
20141215T10:40:15Z

Data structures and implementation of an adaptive hp finite element method
http://hdl.handle.net/2381/30541
Title: Data structures and implementation of an adaptive hp finite element method
Authors: Senior, Bill.
Abstract: For a fully adaptive hp finite element programme to be implemented it is necessary to implement nirregular meshes efficiently. This requires a sufficiently flexible data structure to be implemented. Because such flexibility is required, the traditional array based approach cannot be used because of its limited applicability. In this thesis this traditional approach has been replaced by an object orientated design and implementation. This leads to an implementation that can be extended easily and safely to include other problems for which it was not originally designed.;The problems with maintaining continuity on such a diverse variety of meshes and how continuity is maintained are discussed. Then the main structure of the mesh is described in the form of domain, subdomains and elements. These are used in conjunction with constraint mappings to give a conforming approximation even with the most irregular of meshes.;There are several varieties of matrix generated by the method each with its own problems of storage. Sparse matrices, with perhaps more than 95% of zero entries, need to be used along side dense matrices. In this thesis an object oriented matrix library is implemented that enables this variety of matrices to be used.;An hp finite element algorithm is then implemented using the data structures, and is tested on a range of test problems. The method is shown to be effective on these problems.
20141215T10:40:15Z

On finite groups of plocal rank one and a conjecture of Robinson
http://hdl.handle.net/2381/30542
Title: On finite groups of plocal rank one and a conjecture of Robinson
Authors: Eaton, Charles.
Abstract: We use the classification of finite simple groups to verify a conjecture of Robinson for finite groups G where G/Op(G) has trivial intersection Sylow psubgroups. Groups of this type are said to have plocal rank one, and it is hoped that this invariant will eventually form the basis for inductive arguments, providing reductions for the conjecture, or even a proof using the results presented here as a base. A positive outcome for Robinson's conjecture would imply Alperin's weight conjecture.;It is shown that in proving Robinson's conjecture it suffices to demonstrate only that it holds for finite groups in which Op(G) is both cyclic and central.;Part of the proof of the former result is used to complete the verification of Dade's inductive conjecture for the Ree groups of type G2.;.
20141215T10:40:15Z

A special numerical method for solving Hamiltonian eigenproblems
http://hdl.handle.net/2381/30540
Title: A special numerical method for solving Hamiltonian eigenproblems
Authors: Maple, Carsten R.
Abstract: In this thesis we develop and implement a new algorithm for finding the solutions of linear Hamiltonian systems arising from ordinary differential equation (ODE) eigenproblems; a large source of these systems is SturmLiouville problems, and these will provide the angle of approach. The convergence properties of the algorithm will be analysed, as will the performance of the algorithm for large values of eigenparameter.;An algorithm is also proposed to find highindex eigenvalues of general SturmLiouville problems.
20141215T10:40:15Z

Multivariate hermite interpolation in euclidean space and its unit sphere by radial basis functions
http://hdl.handle.net/2381/30539
Title: Multivariate hermite interpolation in euclidean space and its unit sphere by radial basis functions
Authors: Luo, Zuhua.
Abstract: In this thesis, we consider radial basis function interpolations in ddimensional Euclidean space Hd and the unit sphere 5d_1, where the data is generated not only by pointevaluations, but also by the derivatives, or differential/pseudodifferential operators. Some sufficient and necessary conditions for the wellposedness of the interpolations are given. The results on sensitivity and sta bility of the interpolation systems are obtained. The optimal properties of the interpolants are analysed through the variational framework and reproducing kernel Hilbert space property, the error bounds and convergence rates of the interpolants are derived. The admissible reproducing kernel Hilbert spaces are also characterised.
20141215T10:40:14Z

On indecomposable modules over clustertilted algebras of type A
http://hdl.handle.net/2381/30538
Title: On indecomposable modules over clustertilted algebras of type A
Authors: Parsons, Mark James
Abstract: Gabriel's Theorem describes the dimension vectors of the finitely generated indecomposable modules over the path algebra of a simplylaced Dynkin quiver. It shows that they can be obtained from the expressions for the positive roots of the corresponding root system in terms of the simple roots. Here, we present a method for finding the dimension vectors of the finitely generated indecomposable modules over a clustertilted algebra of Dynkin type A.;It is known that the quiver of a clustertilted algebra of Dynkin type A is given by an exchange matrix of the corresponding cluster algebra. We define a companion basis for such a quiver to be a Z basis of roots of the integral root lattice of the corresponding root system whose associated matrix of inner products is a positive quasiCartan companion of the corresponding exchange matrix.;Our main result establishes that the dimension vectors of the finitely generated indecomposable modules over a clustertilted algebra of Dynkin type A arise from expressions for the positive roots of the corresponding root system in terms of a companion basis (for the quiver of that algebra). This can be regarded as a generalisation of part of Gabriel's Theorem in the Dynkin type A case. The proof uses the fact that the quivers of the clustertilted algebras of Dynkin type A have a particularly nice description in terms of triangulation of regular polygons.
20141215T10:40:14Z