DSpace Collection:
http://hdl.handle.net/2381/3823
20150703T22:02:39Z

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

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

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

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

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_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

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

hpVersion discontinuous Galerkin methods on polygonal and polyhedral meshes
http://hdl.handle.net/2381/28886
Title: hpVersion discontinuous Galerkin methods on polygonal and polyhedral meshes
Authors: Cangiani, Andrea; Georgoulis, Emmanuil H.; Houston, Paul
Abstract: An hpversion interior penalty discontinuous Galerkin method (DGFEM) for the numerical solution of secondorder elliptic partial differential equations on general computational meshes consisting of polygonal/polyhedral elements is presented and analyzed. Utilizing a bounding box concept, the method employs elemental polynomial bases of total degree p (P[subscript p]basis) defined on the physical space, without the need to map from a given reference or canonical frame. This, together with a new specific choice of the interior penalty parameter which allows for facedegeneration, ensures that optimal a priori bounds may be established, for general meshes including polygonal elements with degenerating edges in two dimensions and polyhedral elements with degenerating faces and/or edges in three dimensions. Numerical experiments highlighting the performance of the proposed method are presented. Moreover, the competitiveness of the pversion DGFEM employing a P[subscript p]basis in comparison to the conforming pversion finite element method on tensorproduct elements is studied numerically for a simple test problem.
Description: Electronic version of an article published as Mathematical Models and Methods in Applied Sciences, 24 (10), 2014, DOI:10.1142/S0218202514500146 © copyright World Scientific Publishing Company http://www.worldscientific.com/doi/abs/10.1142/S0218202514500146
20140602T12:47:49Z

A statistical model of aggregate fragmentation
http://hdl.handle.net/2381/28811
Title: A statistical model of aggregate fragmentation
Authors: Spahn, F.; Vieira Neto, E.; Guimaraes, A. H. F.; Gorban, Alexander N.; Brilliantov, N. V.
Abstract: A statistical model of fragmentation of aggregates is proposed, based on the stochastic propagation of cracks through the body. The propagation rules are formulated on a lattice and mimic two important features of the process—a crack moves against the stress gradient while dissipating energy during its growth. We perform numerical simulations of the model for twodimensional lattice and reveal that the mass distribution for small and intermediatesize fragments obeys a power law, F(m)∝m[superscript −3/2], in agreement with experimental observations. We develop an analytical theory which explains the detected power law and demonstrate that the overall fragment mass distribution in our model agrees qualitatively with that one observed in experiments.
20140516T13:26:45Z

The inputoutput relationship approach to structural identifiability analysis
http://hdl.handle.net/2381/28585
Title: The inputoutput relationship approach to structural identifiability analysis
Authors: Bearup, Daniel J.; Evans, Neil D.; Chappell, Michael J.
Abstract: Analysis of the identifiability of a given model system is an essential prerequisite to the determination of model parameters from physical data. However, the tools available for the analysis of nonlinear systems can be limited both in applicability and by computational intractability for any but the simplest of models. The inputoutput relation of a model summarises the inputoutput structure of the whole system and as such provides the potential for an alternative approach to this analysis. However for this approach to be valid it is necessary to determine whether the monomials of a differential polynomial are linearly independent. A simple test for this property is presented in this work. The derivation and analysis of this relation can be implemented symbolically within Maple. These techniques are applied to analyse classical models from biomedical systems modelling and those of enzyme catalysed reaction schemes.
20140212T14:16:49Z

Adaptive discontinuous Galerkin methods for nonstationary convection–diffusion problems
http://hdl.handle.net/2381/28539
Title: Adaptive discontinuous Galerkin methods for nonstationary convection–diffusion problems
Authors: Cangiani, Andrea; Georgoulis, Emmanuil H.; Metcalfe, Stephen
Abstract: This work is concerned with the derivation of a robust a posteriori error estimator for a discontinuous Galerkin (dG) method discretization of a linear nonstationary convection–diffusion initial/boundary value problem and with the implementation of a corresponding adaptive algorithm. More specifically, we derive a posteriori bounds for the error in the L[superscript 2](H[superscript 1]) + L∞(L[superscript 2])type norm for an interior penalty dG discretization in space and a backward Euler discretization in time. Finally, an adaptive algorithm is proposed utilizing the error estimator. Optimal rate of convergence of the adaptive algorithm is observed in a number of test problems and for various Pèclet numbers.
20140123T09:55:27Z

On the composition and neutrix composition of the delta function with the hyperbolic tangent and its inverse functions
http://hdl.handle.net/2381/28477
Title: On the composition and neutrix composition of the delta function with the hyperbolic tangent and its inverse functions
Authors: Fisher, Brian; Kılıcman, Adem
Abstract: Let F be a distribution in D[superscript 1] and let f be a locally summable function. The composition F(f(x)) of F and f is said to exist and be equal to the distribution h(x) if the limit of the sequence {F[subscript n](f(x))} is equal to h(x), where F[subscript n](x)= F(x) ∗ δ[subscript n](x) for n = 1, 2, . . . and {δ[subscript n](x)} is a certain regular sequence converging to the Dirac delta function. It is proved that the neutrix composition δ([superscript rs1])((tanh x[subscript +])[superscript 1/r]) exists and δ([superscript rs1])((tanh x[subscript +])[superscript 1/r]) = ∑[superscript s1, subscript k=0] ∑[superscript K[subscript k], subscript i=0] ((1)[superscript k]c[subscript s2i1,k] (rs)!/2sk!)δ([superscript k])(x) for r,s = 1, 2, . . ., where K[subscript k] is the integer part of (sk1)/2 and the constants c[subscript j,k] are defined by the expansion (tanh[superscript 1]x)superscript k = {∑[superscript ∞, subscript i=0] (x[superscript 2i+1]/(2i + 1))}[superscript k] = ∑[superscript ∞, subscript j=k] c[subscript j,k]x[superscript j], for k = 0,1,2,.... Further results also provided.
20131204T15:41:51Z

On the Neutrix Composition of the Delta and Inverse Hyperbolic Sine Functions
http://hdl.handle.net/2381/28476
Title: On the Neutrix Composition of the Delta and Inverse Hyperbolic Sine Functions
Authors: Fisher, Brian; Kılıcman, Adem
Abstract: Let F be a distribution in D[superscript 1] and let f be a locally summable function. The composition F(f(x)) of F and f is said to exist and be equal to the distribution h(x) if the limit of the sequence {F[subscript n](f(x))} is equal to h(x), where F[subscript n](x)= F(x) ∗ δ[subscript n](x) for n = 1, 2, . . . and {δ[subscript n](x)} is a certain regular sequence converging to the Dirac delta function. In the ordinary sense, the composition δ([superscript s])[(sinh[superscript −1]x[subscript +])[superscript r] does not exists. In this study, it is proved that the neutrix composition δ([superscript s])[(sinh[superscript −1]x[subscript +])[superscript r] exists and is given by δ([superscript s])[(sinh[superscript −1]x[subscript +])[superscript r] = ∑[superscript sr+r1, subscript k=0] ∑[superscript k, subscript i=0] ([superscript k, subscript i]) ((1)[superscript k] rc[subscript s,k,i]/2[superscript k+1]k!)δ([superscript k])(x), for s = 0, 1, 2, . . . and r = 1, 2, . . ., where c[subscript s,k,i] = (−1)[superscript s]s![(k − 2i + 1)[superscript rs−1] + (k − 2i − 1)[superscript rs+r−1]/(2(rs + r − 1)!). Further results
are also proved.
20131204T14:56:21Z

Further Results on the Dilogarithm Integral
http://hdl.handle.net/2381/28472
Title: Further Results on the Dilogarithm Integral
Authors: JolevskaTuneska, Biljana; Fisher, Brian
Abstract: The dilogarithm integral Li(x[superscript s]) and its associated functions Li[subscript +](x[superscript s]) and Li[subscript ](x[superscript s]) are defined as locally summable functions on the real line. Some convolutions and neutrix convolutions of these functions and other functions are then found.
20131203T16:35:00Z

Discontinuous Galerkin Methods for Mass Transfer through SemiPermeable Membranes
http://hdl.handle.net/2381/28090
Title: Discontinuous Galerkin Methods for Mass Transfer through SemiPermeable Membranes
Authors: Cangiani, Andrea; Georgoulis, Emmanuil H.; Jensen, Max
Abstract: A discontinuous Galerkin (dG) method for the numerical solution of initial/boundary value multicompartment partial differential equation (PDE) models, interconnected with interface conditions, is presented and analysed. The study of interface problems is motivated by models of mass transfer of solutes through semipermeable membranes. More specifically, a model problem consisting of a system of semilinear parabolic advectiondiffusionreaction partial differential equations in each compartment, equipped with respective initial and boundary conditions, is considered. Nonlinear interface conditions modelling selective permeability, congestion and partial reflection are applied to the compartment interfaces. An interior penalty dG method is presented for this problem and it is analysed in the spacediscrete setting. The a priori analysis shows that the method yields optimal a priori bounds, provided the exact solution is sufficiently smooth. Numerical experiments indicate agreement with the theoretical bounds and highlight the stability of the numerical method in the advectiondominated regime.
20130827T15:28:56Z

Erratum: Collision dynamics of granular particles with adhesion (Physical Review E (2007) 76 (051302))
http://hdl.handle.net/2381/28089
Title: Erratum: Collision dynamics of granular particles with adhesion (Physical Review E (2007) 76 (051302))
Authors: Brilliantov, Nikolai V.; Albers, Nicole; Spahn, Frank; Pöschel, Thorsten
Abstract: An erratum to the article available at http://hdl.handle.net/2381/20218.
20130827T14:59:00Z

The canonical ensemble via symplectic integrators using Nosé and Nosé–Poincaré chains
http://hdl.handle.net/2381/28031
Title: The canonical ensemble via symplectic integrators using Nosé and Nosé–Poincaré chains
Authors: Leimkuhler, Benedict J.; Sweet, Christopher R.
Abstract: Simulations that sample from the canonical ensemble can be generated by the addition of a single degree of freedom, provided that the system is ergodic, as described by Nosé with subsequent modifications by Hoover to allow sampling in real time. Nosé–Hoover dynamics is not ergodic for small or stiff systems and the addition of auxiliary thermostats is needed to overcome this deficiency. Nosé–Hoover dynamics, like its derivatives, does not have a Hamiltonian structure, precluding the use of symplectic integrators which are noted for their long term stability and structure preservation. As an alternative to Nosé–Hoover, the Hamiltonian Nosé–Poincaré method was proposed by Bond, Laird, and Leimkuhler [J. Comput. Phys. 151, 114 (1999)], but the straightforward addition of thermostatting chains does not sample from the canonical ensemble. In this paper a method is proposed whereby additional thermostats can be applied to a Hamiltonian system while retaining sampling from the canonical ensemble. This technique has been used to construct thermostatting chains for the Nosé and Nosé–Poincaré methods.
20130626T15:14:48Z

The anisotropic hardsphere crystalmelt interfacial free energy from fluctuations.
http://hdl.handle.net/2381/28028
Title: The anisotropic hardsphere crystalmelt interfacial free energy from fluctuations.
Authors: Davidchack, Ruslan L.; Morris, James R.; Laird, Brian B.
Abstract: We have calculated the interfacial free energy for the hardsphere system, as a function of crystal interface orientation, using a method that examines the fluctuations in the height of the interface during molecular dynamics simulations. The approach is particularly sensitive for the anisotropy of the interfacial free energy. We find an average interfacial free energy of gamma=0.56+/0.02k(B)Tsigma(2). This value is lower than earlier results based upon direct calculations of the free energy [R. L. Davidchack and B. B. Laird, Phys. Rev. Lett. 85, 4751 (2000)]. However, both the average value and the anisotropy agree with the recent values obtained by extrapolation from direct calculations for a series of the inversepower potentials [R. L. Davidchack and B. B. Laird, Phys. Rev. Lett. 94, 086102 (2005)].
20130626T14:36:42Z

Role of threebody interactions in formation of bulk viscosity in liquid argon
http://hdl.handle.net/2381/27877
Title: Role of threebody interactions in formation of bulk viscosity in liquid argon
Authors: Lishchuk, Sergey V.
Abstract: With the aim of locating the origin of discrepancy between experimental and computer simulation
results on bulk viscosity of liquid argon, a molecular dynamic simulation of argon interacting via
ab initio pair potential and tripledipole threebody potential has been undertaken. Bulk viscosity,
obtained using GreenKubo formula, is different from the values obtained from modeling argon
using LennardJones potential, the former being closer to the experimental data. The conclusion is
made that manybody interatomic interaction plays a significant role in formation of bulk viscosity.
20130424T14:51:14Z

Adaptive Observers and Parameter Estimation for a Class of Systems Nonlinear in the Parameters
http://hdl.handle.net/2381/27849
Title: Adaptive Observers and Parameter Estimation for a Class of Systems Nonlinear in the Parameters
Authors: Tyukin, Ivan Y.; Steur, Erik; Nijmeijer, Henk; Leeuwen, Cees van
Abstract: We consider the problem of asymptotic reconstruction of the state and parameter values in systems of ordinary differential equations. A solution to this problem is proposed for a class of systems of which the unknowns are allowed to be nonlinearly parameterized functions of state and time. Going beyond the concept of asymptotic Lyapunov stability, we provide for this class a reconstruction technique based on the notions of weakly attracting sets and nonuniform convergence. Reconstruction of state and parameter values is subjected to persistency of excitation conditions. In absence of nonlinear parametrization the resulting observers reduce to standard estimation schemes. This allows to view the proposed method as a generalization of the conventional canonical adaptive observer design.
20130409T14:30:08Z

Lyapunovlike Conditions of Forward Invariance and Boundedness for a Class of Unstable Systems
http://hdl.handle.net/2381/27778
Title: Lyapunovlike Conditions of Forward Invariance and Boundedness for a Class of Unstable Systems
Authors: Gorban, Alexander N.; Tyukin, Ivan; Steur, Erik; Nijmeijer, Henk
Abstract: We provide Lyapunovlike characterizations of boundedness and convergence of nontrivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable subsystems with onedimensional unstable dynamics or critically stable dynamics. Systems of this type arise in problems of nonlinear output regulation, parameter estimation and adaptive control. In addition to providing boundedness and convergence criteria the results allow to derive domains of initial conditions corresponding to solutions leaving a given neighborhood of the origin at least once. In contrast to other works addressing convergence issues in unstable systems, our results require neither inputoutput characterizations for the stable part nor estimates of convergence rates. The results are illustrated with examples, including the analysis of phase synchronization of neural oscillators with heterogenous coupling.
Description: Embargo length currently unknown. The article is still in press and full text will be made available once it has been published.
20130306T16:08:28Z

Nonuniform smallgain theorems for systems with unstable invariant sets
http://hdl.handle.net/2381/27777
Title: Nonuniform smallgain theorems for systems with unstable invariant sets
Authors: Tyukin, Ivan; Steur, Erik; Nijmeijer, Henk; Van Leeuwen, Cees
Abstract: We consider the problem of asymptotic convergence to invariant sets in interconnected nonlinear dynamical systems. Standard approaches often require that the invariant sets be uniformly attracting, e. g., stable in the Lyapunov sense. This, however, is neither a necessary requirement nor is always useful. Systems may, for instance, be inherently unstable ( e. g., intermittent, itinerant, metastable) or the problem statement may include requirements that cannot be satisfied with stable solutions. This is often the case in general optimization problems and in nonlinear parameter identification or adaptation. Conventional techniques for these cases either rely on detailed knowledge of the system's vectorfields or require boundedness of its states. The presently proposed method relies only on estimates of the inputoutput maps and steadystate characteristics. The method requires the possibility of representing the system as an interconnection of a stable and contracting part with an unstable and exploratory part. We illustrate with examples how the method can be applied to problems of analyzing the asymptotic behavior of locally unstable systems as well as to problems of parameter identification and adaptation in the presence of nonlinear parametrizations. The relation of our results to conventional smallgain theorems is discussed.
20130306T15:37:09Z

Third Mac Lane cohomology
http://hdl.handle.net/2381/26990
Title: Third Mac Lane cohomology
Authors: Baues, HJ; Jibladze, M; Pirashvili, T
20121024T09:22:48Z

Towards a correct description of zooplankton feeding in models: Taking into account foodmediated unsynchronized vertical migration
http://hdl.handle.net/2381/26992
Title: Towards a correct description of zooplankton feeding in models: Taking into account foodmediated unsynchronized vertical migration
Authors: Morozov, AY; Morozov, AY; Arashkevich, EG
20121024T09:22:48Z

Towards complete detection of unstable periodic orbits in chaotic systems
http://hdl.handle.net/2381/26993
Title: Towards complete detection of unstable periodic orbits in chaotic systems
Authors: Davidchack, RL; Lai, YC; Klebanoff, A; Bollt, EM
20121024T09:22:48Z

Triple cohomology of LieRinehart algebras and the canonical class of associative algebras
http://hdl.handle.net/2381/26994
Title: Triple cohomology of LieRinehart algebras and the canonical class of associative algebras
Authors: Casas, JM; Ladra, M; Pirashvili, T
20121024T09:22:48Z

Vanishing line for the descent spectral sequence
http://hdl.handle.net/2381/26995
Title: Vanishing line for the descent spectral sequence
Authors: Pirashvili, T
20121024T09:22:48Z

Wallinduced prefreezing in hard spheres: A thermodynamic perspective
http://hdl.handle.net/2381/26997
Title: Wallinduced prefreezing in hard spheres: A thermodynamic perspective
Authors: Laird, BB; Davidchack, RL
20121024T09:22:48Z

Variations on the cohomology of loop spaces on generalized homogeneous spaces
http://hdl.handle.net/2381/26996
Title: Variations on the cohomology of loop spaces on generalized homogeneous spaces
Authors: Neumann, F
20121024T09:22:48Z

The hochschild cohomology ring of a class of special biserial algebras
http://hdl.handle.net/2381/26980
Title: The hochschild cohomology ring of a class of special biserial algebras
Authors: Snashall, N; Taillefer, R; Taillefer, R
20121024T09:22:47Z