DSpace Collection:http://hdl.handle.net/2381/38232017-06-23T03:24:13Z2017-06-23T03:24:13ZDynamics of a Two Subpopulations System Including ImmigrationZincenko, A.Petrovskii, Sergeihttp://hdl.handle.net/2381/399422017-06-23T02:20:27Z2017-06-22T14:22:55ZTitle: Dynamics of a Two Subpopulations System Including Immigration
Authors: Zincenko, A.; Petrovskii, Sergei
Abstract: The phenomenon of replacement migration into declining population prompts development of multicomponent models in population dynamics. We propose a simple model of population including resident and migrant components with migration flow as an external input. The main assumption is that offspring that are born to migrants will have the same vital rates as the resident population. The proposed model is based on partial differential equation to take into account the age structure of the population. The formulae for exact solutions are derived. We focus on the case when native population declines in the absence of migration. Assuming a sufficiently large constant growth rate of migration we obtain asymptotic solutions as t → â. Using the asymptotic solutions, we have calculated "critical" value of growth rate of migrant inflow that is the value that provides, as time tends to infinity, the equal number of residents and migrants in the population. We provide numerical illustrations using demographic data for Germany in 2010.2017-06-22T14:22:55ZWhich Random Walk is Faster? Methods to Compare Different Step Length Distributions in Individual Animal MovementChoules, J. D.Petrovskii, Sergeihttp://hdl.handle.net/2381/399402017-06-23T02:20:22Z2017-06-22T14:04:28ZTitle: Which Random Walk is Faster? Methods to Compare Different Step Length Distributions in Individual Animal Movement
Authors: Choules, J. D.; Petrovskii, Sergei
Abstract: Good understanding of individual animal movement is needed in the context of epidemiology in order to predict the rate of spread of infectious diseases. It is also required for problems arising in nature conservation, biological invasion, pest monitoring, etc. A question that often appears in the centre of the movement studies is which movement pattern is 'faster' or more efficient. For instance, it is widely believed that the pattern quantified by a power law distribution of movement steps is faster than the Brownian motion. Here we show that the answer to this question may be not so straightforward and depends on the way how different step length distributions are compared.2017-06-22T14:04:28ZSpectral Sequences for Hochschild cohomology and graded centers of derived categoriesNeumann, FrankSzymik, Markushttp://hdl.handle.net/2381/399082017-06-15T02:22:10Z2017-06-14T15:08:22ZTitle: Spectral Sequences for Hochschild cohomology and graded centers of derived categories
Authors: Neumann, Frank; Szymik, Markus
Abstract: The Hochschild cohomology of a differential graded algebra, or a differential graded category, admits a natural map to the graded center of its homology category: the characteristic homomorphism. We interpret it as an edge homomorphism in a spectral sequence. This gives a conceptual explanation of the failure of the characteristic homomorphism to be injective or surjective, in general. To illustrate this, we discuss modules over the dual numbers, coherent sheaves over algebraic curves, as well as examples related to free loop spaces and string topology.
Description: The file associated with this record is embargoed until 12 months after the date of publication. The final published version may be available through the links above.2017-06-14T15:08:22ZAdaptive radial basis function interpolation using an error indicatorZhang, QiZhao, YangzhangLevesley, Jeremyhttp://hdl.handle.net/2381/398102017-05-18T02:21:52Z2017-05-17T15:34:19ZTitle: Adaptive radial basis function interpolation using an error indicator
Authors: Zhang, Qi; Zhao, Yangzhang; Levesley, Jeremy
Abstract: In some approximation problems, sampling from the target function can be both expensive and time-consuming. It would be convenient to have a method for indicating where approximation quality is poor, so that generation of new data provides the user with greater accuracy where needed. In this paper, we propose a new adaptive algorithm for radial basis function (RBF) interpolation which aims to assess the local approximation quality, and add or remove points as required to improve the error in the specified region. For Gaussian and multiquadric approximation, we have the flexibility of a shape parameter which we can use to keep the condition number of interpolation matrix at a moderate size. Numerical results for test functions which appear in the literature are given for dimensions 1 and 2, to show that our method performs well. We also give a three-dimensional example from the finance world, since we would like to advertise RBF techniques as useful tools for approximation in the high-dimensional settings one often meets in finance.2017-05-17T15:34:19ZA Trefftz polynomial space-time discontinuous Galerkin method for the second order wave equationBanjai, LehelGeorgoulis, Emmanuil H.Lijoka, Oluwaseunhttp://hdl.handle.net/2381/397852017-05-16T02:22:27Z2017-05-15T13:54:03ZTitle: A Trefftz polynomial space-time discontinuous Galerkin method for the second order wave equation
Authors: Banjai, Lehel; Georgoulis, Emmanuil H.; Lijoka, Oluwaseun
Abstract: A new space-time discontinuous Galerkin (dG) method utilizing special Trefftz polynomial basis functions is proposed and fully analyzed for the scalar wave equation in a second order formulation. The dG method considered is motivated by the class of interior penalty dG methods, as well as by the classical work of Hughes and Hulbert [Comput. Methods Appl. Mech. Engrg., 66 (1988), pp. 339-363; Comput. Methods Appl. Mech. Engrg., 84 (1990), pp. 327-348]. The choice of the penalty terms included in the bilinear form is essential for both the theoretical analysis and for the practical behavior of the method for the case of lowest order basis functions. A best approximation result is proven for this new space-time dG method with Trefftz-type basis functions. Rates of convergence are proved in any dimension and verified numerically in spatial dimensions d = 1 and d = 2. Numerical experiments highlight the effectivness of the Trefftz method in problems with energy at high frequencies.2017-05-15T13:54:03ZOn the non-parallel instability of the rotating-sphere boundary layerSegalini, AntonioGarrett, Stephen J.http://hdl.handle.net/2381/397782017-05-16T02:22:21Z2017-05-15T10:38:27ZTitle: On the non-parallel instability of the rotating-sphere boundary layer
Authors: Segalini, Antonio; Garrett, Stephen J.
Abstract: We present a new solution for the steady boundary-layer flow over the rotating sphere that also accounts for the eruption of the boundary layer at the equator and other higher-order viscous effects. Non-parallel corrections to the local type I and type II convective instability modes of this flow are also computed as a function of spin rate. Our instability results are associated with the previously observed spiral vortices and remarkable agreement between our predictions of the number of vortices and experimental observations is found. Vortices travelling at 70 %–80 % of the local surface speed are found to be the most amplified for sufficient spin rates, also consistent with prior experimental observations.2017-05-15T10:38:27ZApplications of Quaternionic Holomorphic Geometry to minimal surfacesLeschke, K.Moriya, K.http://hdl.handle.net/2381/397752017-05-13T03:13:53Z2017-05-12T15:29:05ZTitle: Applications of Quaternionic Holomorphic Geometry to minimal surfaces
Authors: Leschke, K.; Moriya, K.
Abstract: In this paper we give a survey of methods of Quaternionic Holomorphic Geometry and of applications of the theory to minimal surfaces. We discuss recent developments in minimal surface theory using integrable systems. In particular, we give the Lopez–Ros deformation and the simple factor dressing in terms of the Gauss map and the Hopf differential of the minimal surface. We illustrate the results for well–known examples of minimal surfaces, namely the Riemann minimal surfaces and the Costa surface.2017-05-12T15:29:05ZInteraction of human migration and wealth distributionVolpert, V.Petrovskii, SergeiZincenko, A.http://hdl.handle.net/2381/397602017-05-11T02:22:46Z2017-05-10T15:05:00ZTitle: Interaction of human migration and wealth distribution
Authors: Volpert, V.; Petrovskii, Sergei; Zincenko, A.
Abstract: Dynamics of human populations depends on various economical and social factors. Their migration is partially determined by the economical conditions and it can also influence these conditions. This work is devoted to the analysis of the interaction of human migration and wealth distribution. The model consists of a system of equations for the population density and for the wealth distribution with conventional diffusion terms and with cross diffusion terms describing human migration determined by the wealth gradient and wealth flux determined by human migration. Wealth production and consumption depend on the population density while the natality and mortality rates depend on the level of wealth. In the absence of cross diffusion terms, dynamics of solutions is described by travelling wave solutions of the corresponding reaction-diffusion systems of equations. We show persistence of such solutions for sufficiently small cross diffusion coefficients. This result is based on the perturbation methods and on the spectral properties of the linearized operators.
Description: The file associated with this record is embargoed until 12 months after the date of publication. The final published version may be available through the links above. Following the embargo period the above license will apply.2017-05-10T15:05:00ZFortune favours the brave: Movement responses shape demographic dynamics in strongly competing populationsPotts, Jonathan R.Petrovskii, Sergei V.http://hdl.handle.net/2381/397592017-05-11T02:22:45Z2017-05-10T14:56:57ZTitle: Fortune favours the brave: Movement responses shape demographic dynamics in strongly competing populations
Authors: Potts, Jonathan R.; Petrovskii, Sergei V.
Abstract: Animal movement is a key mechanism for shaping population dynamics. The effect of interactions between competing animals on a population's survival has been studied for many decades. However, interactions also affect an animal's subsequent movement decisions. Despite this, the indirect effect of these decisions on animal survival is much less well-understood. Here, we incorporate movement responses to foreign animals into a model of two competing populations, where inter-specific competition is greater than intra-specific competition. When movement is diffusive, the travelling wave moves from the stronger population to the weaker. However, by incorporating behaviourally induced directed movement towards the stronger population, the weaker one can slow the travelling wave down, even reversing its direction. Hence movement responses can switch the predictions of traditional mechanistic models. Furthermore, when environmental heterogeneity is combined with aggressive movement strategies, it is possible for spatially segregated co-existence to emerge. In this situation, the spatial patterns of the competing populations have the unusual feature that they are slightly out-of-phase with the environmental patterns. Finally, incorporating dynamic movement responses can also enable stable co-existence in a homogeneous environment, giving a new mechanism for spatially segregated co-existence.
Description: The file associated with this record is embargoed until 12 months after the date of publication. The final published version may be available through the links above. Following the embargo period the above license applies.2017-05-10T14:56:57ZBabuška-Osborn techniques in discontinuous Galerkin methods: $L^2$-norm error estimates for unstructured meshesGeorgoulis, EmmanuilMakridakis, CharalambosPryer, Tristanhttp://hdl.handle.net/2381/397082017-04-28T02:21:13Z2017-04-27T14:22:23ZTitle: Babuška-Osborn techniques in discontinuous Galerkin methods: $L^2$-norm error estimates for unstructured meshes
Authors: Georgoulis, Emmanuil; Makridakis, Charalambos; Pryer, Tristan
Abstract: We prove the inf-sup stability of the interior penalty class of discontinuous Galerkin schemes in unbalanced mesh-dependent norms, under a mesh condition allowing for a general class of meshes, which includes many examples of geometrically graded element neighbourhoods. The inf-sup condition results in the stability of the interior penalty Ritz projection in $L^2$ as well as, for the first time, quasi-best approximations in the $L^2$-norm which in turn imply a priori error estimates that do not depend on the global maximum meshsize in that norm. Some numerical experiments are also given.2017-04-27T14:22:23ZSmall Cocycles, Fine Torus Fibrations, and a Z^2 Subshift with NeitherClark, AlexSadun, Lorenzohttp://hdl.handle.net/2381/396732017-04-20T02:18:01Z2017-04-19T15:45:19ZTitle: Small Cocycles, Fine Torus Fibrations, and a Z^2 Subshift with Neither
Authors: Clark, Alex; Sadun, Lorenzo
Abstract: Following an earlier similar conjecture of Kellendonk and Putnam, Giordano, Putnam, and Skau conjectured that all minimal, free ZdZd actions on Cantor sets admit “small cocycles.” These represent classes in H1H1 that are mapped to small vectors in RdRd by the Ruelle–Sullivan (RS) map. We show that there exist Z2Z2 actions where no such small cocycles exist, and where the image of H1H1 under RS is Z2Z2 . Our methods involve tiling spaces and shape deformations, and along the way we prove a relation between the image of RS and the set of “virtual eigenvalues,” i.e., elements of RdRd that become topological eigenvalues of the tiling flow after an arbitrarily small change in the shapes and sizes of the tiles.2017-04-19T15:45:19ZCalculating Exceedance Probabilities Using a Distributionally Robust MethodFaridafshin, FarzadGrechuk, BogdanNaess, Arvidhttp://hdl.handle.net/2381/396692017-06-14T13:18:30Z2017-04-19T14:49:39ZTitle: Calculating Exceedance Probabilities Using a Distributionally Robust Method
Authors: Faridafshin, Farzad; Grechuk, Bogdan; Naess, Arvid
Abstract: Calculation of exceedance probabilities or the inverse problem of finding the level corresponding to a given exceedance probability occurs in many practical applications. For instance, it is often of interest in offshore engineering to evaluate the wind, wave, current, and sea ice properties with annual exceedance probabilities of, e.g., 10−1, 10−2, and 10−3, or so-called 10-year, 100-year, and 1000-year values. A methodology is provided in this article to calculate a tight upper bound of the exceedance probability, given any probability distribution from a wide range of commonly used distributions. The approach is based on a generalization of the Chebyshev inequality for the class of distributions with a logarithmically concave cumulative distribution function, and has the potential to relieve the often-debated exercise of determining an appropriate probability distribution function based on limited data, particularly in terms of tail behavior. Two numerical examples are provided for illustration.
Description: The file associated with this record is embargoed until 12 months after the date of publication. The final published version may be available through the links above.2017-04-19T14:49:39ZRegimes of electrostatic collapse of a highly charged polyelectrolyte in a poor solventTom, Anvy MolyVemparala, SatyavaniRajesh, R.Brilliantov, Nikolai V.http://hdl.handle.net/2381/396512017-04-12T02:22:08Z2017-04-11T11:12:38ZTitle: Regimes of electrostatic collapse of a highly charged polyelectrolyte in a poor solvent
Authors: Tom, Anvy Moly; Vemparala, Satyavani; Rajesh, R.; Brilliantov, Nikolai V.
Abstract: We perform extensive molecular dynamics simulations of a highly charged, collapsed, flexible polyelectrolyte chain in a poor solvent for the case when the electrostatic interactions, characterized by the reduced Bjerrum length ℲB, are strong. We find the existence of several sub-regimes in the dependence of the gyration radius of the chain Rg on ℲB characterized by Rg ∼ Ⅎ−γB. In contrast to a good solvent, the exponent γ for a poor solvent crucially depends on the size and valency of the counterions. To explain the different sub-regimes, we generalize the existing counterion fluctuation theory by including a more complete account of all possible volume interactions in the free energy of the polyelectrolyte chain. We also show that the presence of condensed counterions modifies the effective attraction among the chain monomers and modulates the sign of the second virial coefficient under poor solvent conditions.
Description: The file associated with this record is embargoed until 12 months after the date of publication. The final published version may be available through the links above.2017-04-11T11:12:38ZBeyond Navier–Stokes equations: capillarity of ideal gasGorban, Alexander N.Karlin, I. V.http://hdl.handle.net/2381/396502017-04-12T02:22:08Z2017-04-11T11:06:09ZTitle: Beyond Navier–Stokes equations: capillarity of ideal gas
Authors: Gorban, Alexander N.; Karlin, I. V.
Abstract: The system of Navier–Stokes–Fourier equations is one of the most celebrated systems of equations in modern science. It describes dynamics of fluids in the limit when gradients of density, velocity and temperature are sufficiently small, and loses its applicability when the flux becomes so non-equilibrium that the changes of velocity, density or temperature on the length compatible with the mean free path are non-negligible. The question is: how to model such fluxes? This problem is still open. (Despite the fact that the first ‘final equations of motion’ modified for analysis of thermal creep in rarefied gas were proposed by Maxwell in 1879.) There are, at least, three possible answers: (i) use molecular dynamics with individual particles, (ii) use kinetic equations, like Boltzmann’s equation or (iii) find a new system of equations for description of fluid dynamics with better accounting of non-equilibrium effects. These three approaches work at different scales. We explore the third possibility using the recent findings of capillarity of internal layers in ideal gases and of saturation effect in dissipation (there is a limiting attenuation rate for very short waves in ideal gas and it cannot increase infinitely). One candidate equation is discussed in more detail, the Korteweg system proposed in 1901. The main ideas and approaches are illustrated by a kinetic system for which the problem of reduction of kinetics to fluid dynamics is analytically solvable.
Description: The file associated with this record is embargoed until 12 months after the date of publication. The final published version may be available through the links above.2017-04-11T11:06:09ZA dissipative force between colliding viscoelastic bodies: Rigorous approachBrilliantov, Nikolay V.Pimenova, Anastasiya V.Goldobin, Denis S.http://hdl.handle.net/2381/395442017-03-23T03:21:13Z2017-03-22T13:48:38ZTitle: A dissipative force between colliding viscoelastic bodies: Rigorous approach
Authors: Brilliantov, Nikolay V.; Pimenova, Anastasiya V.; Goldobin, Denis S.
Abstract: A collision of viscoelastic bodies is analysed within a mathematically rigorous approach. We develop a perturbation scheme to solve continuum mechanics equation, which deals simultaneously with strain and strain rate in the bulk of the bodies' material. We derive dissipative force that acts between particles and express it in terms of particles' deformation, deformation rate and material parameters. It differs noticeably from the currently used dissipative force, found within the quasi-static approximation and does not suffer from inconsistencies of this approximation. The proposed approach may be used for other continuum mechanics problems where the bulk dissipation is addressed.2017-03-22T13:48:38ZA Generalist Predator Regulating Spread of a Wildlife Disease: Exploring Two Infection Transmission ScenariosSen, M.Banerjee, M.Morozov, A.http://hdl.handle.net/2381/395432017-03-23T03:21:13Z2017-03-22T13:39:47ZTitle: A Generalist Predator Regulating Spread of a Wildlife Disease: Exploring Two Infection Transmission Scenarios
Authors: Sen, M.; Banerjee, M.; Morozov, A.
Abstract: Ecoepidemiology is a well-developed branch of theoretical ecology, which explores interplay between the trophic interactions and the disease spread. In most ecoepidemiological models, however, the authors assume the predator to be a specialist, which consumes only a single prey species. In few existing papers, in which the predator was suggested to be a generalist, the alternative food supply was always considered to be constant. This is obviously a simplification of reality, since predators can often choose between a number of different prey. Consumption of these alternative prey can dramatically change their densities and strongly influence the model predictions. In this paper, we try to bridge the gap and explore a generic eco-epidemiological system with a generalist predator, where the densities of all prey are dynamical variables. The model consists of two prey species, one of which is subject to an infectious disease, and a predator, which consumes both prey species. We investigate two main scenarios of infection transmission mode: (i) the disease transmission rate is predator independent and (ii) the transmission rate is a function of predator density. For both scenarios we fulfil an extensive bifurcation analysis. We show that including a second dynamical prey in the system can drastically change the dynamics of the single prey case. In particular, the presence of a second prey impedes disease spread by decreasing the basic reproduction number and can result in a substantial drop of the disease prevalence. We demonstrate that with efficient consumption of the second prey species by the predator, the predator-dependent disease transmission can not destabilize interactions, as in the case with a specialist predator. Interestingly, even if the population of the second prey eventually vanishes and only one prey species finally remains, the system with two prey species may exhibit different properties to those of the single prey system.2017-03-22T13:39:47ZModelling in Ecology, Epidemiology and Ecoepidemiology: Introduction to the Special IssueMorozov, A.http://hdl.handle.net/2381/395422017-03-23T03:21:13Z2017-03-22T10:03:33ZTitle: Modelling in Ecology, Epidemiology and Ecoepidemiology: Introduction to the Special Issue
Authors: Morozov, A.2017-03-22T10:03:33ZNoise-Produced Patterns in Images Constructed from Magnetic Flux Leakage DataGoldobin, D. S.Pimenova, A. V.Levesley, J.Elkington, P.Bacciarelli, M.http://hdl.handle.net/2381/395412017-03-23T03:21:12Z2017-03-22T09:58:52ZTitle: Noise-Produced Patterns in Images Constructed from Magnetic Flux Leakage Data
Authors: Goldobin, D. S.; Pimenova, A. V.; Levesley, J.; Elkington, P.; Bacciarelli, M.
Abstract: Magnetic flux leakage measurements help identify the position, size and shape of corrosion-related defects in steel casings used to protect boreholes drilled into oil and gas reservoirs. Images constructed from magnetic flux leakage data contain patterns related to noise inherent in the method. We investigate the patterns and their scaling properties for the case of delta-correlated input noise, and consider the implications for the method’s ability to resolve defects. The analytical evaluation of the noise-produced patterns is made possible by model reduction facilitated by large-scale approximation. With appropriate modification, the approach can be employed to analyze noise-produced patterns in other situations where the data of interest are not measured directly, but are related to the measured data by a complex linear transform involving integrations with respect to spatial coordinates.
Description: Mathematics Subject Classification: 78A30 / 78M34 / 60G602017-03-22T09:58:52ZMagnetic Flux Leakage Method: Large-Scale ApproximationPimenova, A. V.Goldobin, D. S.Levesley, J.Ivantsov, A. O.Elkington, P.Bacciarelli, M.http://hdl.handle.net/2381/395402017-03-23T03:21:12Z2017-03-22T09:55:42ZTitle: Magnetic Flux Leakage Method: Large-Scale Approximation
Authors: Pimenova, A. V.; Goldobin, D. S.; Levesley, J.; Ivantsov, A. O.; Elkington, P.; Bacciarelli, M.
Abstract: We consider the application of the magnetic flux leakage (MFL) method to the detection of defects in ferromagnetic (steel) tubulars. The problem setup corresponds to the cases where the distance from the casing and the point where the magnetic field is measured is small compared to the curvature radius of the undamaged casing and the scale of inhomogeneity of the magnetic field in the defect-free case. Mathematically this corresponds to the planar ferromagnetic layer in a uniform magnetic field oriented along this layer. Defects in the layer surface result in a strong deformation of the magnetic field, which provides opportunities for the reconstruction of the surface profile from measurements of the magnetic field. We deal with large-scale defects whose depth is small compared to their longitudinal sizes—these being typical of corrosive damage. Within the framework of large-scale approximation, analytical relations between the casing thickness profile and the measured magnetic field can be derived.
Description: Mathematics Subject Classification: 78A30 / 78M34 / 78A552017-03-22T09:55:42ZThree Waves of Chemical DynamicsGorban, A. N.Yablonsky, G. S.http://hdl.handle.net/2381/395392017-03-23T03:21:10Z2017-03-22T09:46:50ZTitle: Three Waves of Chemical Dynamics
Authors: Gorban, A. N.; Yablonsky, G. S.
Abstract: Three epochs in development of chemical dynamics are presented. We try to understand the modern research programs in the light of classical works.2017-03-22T09:46:50ZGeneration of mechanical force by grafted polyelectrolytes in an electric fieldBrilliantov, N. V.Budkov, Yu. A.Seidel, C.http://hdl.handle.net/2381/395302017-03-22T03:22:09Z2017-03-21T10:25:12ZTitle: Generation of mechanical force by grafted polyelectrolytes in an electric field
Authors: Brilliantov, N. V.; Budkov, Yu. A.; Seidel, C.
Abstract: We study theoretically and by means of molecular dynamics (MD) simulations the generation of mechanical force by grafted polyelectrolytes in an external electric field, which favors its adsorption on the grafting plane. The force arises in deformable bodies linked to the free end of the chain. Varying the field, one controls the length of the nonadsorbed part of the chain and hence the deformation of the target body, i.e., the arising force too. We consider target bodies with a linear force-deformation relation and with a Hertzian one. While the first relation models a coiled Gaussian chain, the second one describes the force response of a squeezed colloidal particle. The theoretical dependences of generated force and compression of the target body on an applied field agree very well with the results of MD simulations. The analyzed phenomenon may play an important role in future nanomachinery, e.g., it may be used to design nanovices to fix nanosized objects.2017-03-21T10:25:12ZForward-Invariant Peeling in Chemical Dynamics: a Simple Case StudyGorban, A. N.http://hdl.handle.net/2381/395282017-03-22T03:22:08Z2017-03-21T10:12:37ZTitle: Forward-Invariant Peeling in Chemical Dynamics: a Simple Case Study
Authors: Gorban, A. N.
Abstract: Forward-invariant peeling aims to produce forward-invariant subset from a given set in phase space. The structure of chemical kinetic equations allows us to describe the general operations of the forward-invariant peeling. For example, we study a simple reaction network with three components A1,A2,A3 and reactions A1 → A2 → A3 → A1, 2A1 ⇌ 3A2 (without any stoichiometric conservation law). We assume that kinetics obey the classical mass action law and reaction rate constants are positive intervals 0 <ki min ≤ ki ≤ ki max< ∞. Kinetics of this system is described by a system of differential inclusions. We produce forward-invariant sets for these kinetic inclusions from the sets { c | ci ≥ 0, ∑ ci ≥ ε } by the forward-invariant peeling (for sufficiently small ε> 0). In particular, this construction proves persistence of this kinetic system (a positive solution cannot approach the origin even asymptotically, as t → ∞).
Description: Mathematics Subject Classification: 37C10, 34D20, 93D052017-03-21T10:12:37ZGeneralized Mass Action Law and Thermodynamics of Nonlinear Markov ProcessesGorban, A. N.Kolokoltsov, V. N.http://hdl.handle.net/2381/395272017-03-22T03:22:08Z2017-03-21T09:59:51ZTitle: Generalized Mass Action Law and Thermodynamics of Nonlinear Markov Processes
Authors: Gorban, A. N.; Kolokoltsov, V. N.
Abstract: The nonlinear Markov processes are measure-valued dynamical systems which preserve positivity. They can be represented as the law of large numbers limits of general Markov models of interacting particles. In physics, the kinetic equations allow Lyapunov functionals (entropy, free energy, etc.). This may be considered as a sort of inheritance of the Lyapunov functionals from the microscopic master equations. We study nonlinear Markov processes that inherit thermodynamic properties from the microscopic linear Markov processes. We develop the thermodynamics of nonlinear Markov processes and analyze the asymptotic assumption, which are sufficient for this inheritance.
Description: Mathematics Subject Classification: 80A30 / 60J25 / 60J60 / 60J75 / 82B402017-03-21T09:59:51ZThe Impact of Fragmented Habitat's Size and Shape on Populations with Allee EffectAlharbi, W. G.Petrovskii, S. V.http://hdl.handle.net/2381/395242017-03-22T03:22:05Z2017-03-21T09:34:56ZTitle: The Impact of Fragmented Habitat's Size and Shape on Populations with Allee Effect
Authors: Alharbi, W. G.; Petrovskii, S. V.
Abstract: This study aims to explore the ways in which population dynamics are affected by the shape and size of fragmented habitats. Habitat fragmentation has become a key concern in ecology over the past 20 years as it is thought to increase the threat of extinction for a number of plant and animal species; particularly those close to the fragment edge. In this study, we consider this issue using mathematical modelling and computer simulations in several domains of various shape and with different strength of the Allee effect. A two-dimensional reaction-diffusion equation (taking the Allee effect into account) is used as a model. Extensive simulations are performed in order to determine how the boundaries impact the population persistence. Our results indicate the following: (i) for domains of simple shape (e.g. rectangle), the effect of the critical patch size (amplified by the Allee effect) is similar to what is observed in 1D space, in particular, the likelihood of population survival is determined by the interplay between the domain size and thee strength of the Allee effect; (ii) in domains of complicated shape, for the population to survive, the domain area needs to be larger than the area of the corresponding rectangle. Hence, it can be concluded that domain size and shape both have crucial effect on population survival.
Description: Mathematics Subject Classification: 92D40 / 35B36 / 35Q92 / 37N252017-03-21T09:34:56ZModelling in Ecology, Epidemiology and Ecoepidemiology: Introduction to the Special IssueMorozov, A.Petrovskii, S.http://hdl.handle.net/2381/395232017-03-21T03:21:58Z2017-03-20T17:05:07ZTitle: Modelling in Ecology, Epidemiology and Ecoepidemiology: Introduction to the Special Issue
Authors: Morozov, A.; Petrovskii, S.2017-03-20T17:05:07ZFast Sampling of Evolving Systems with Periodic TrajectoriesTyukin, I. Yu.Gorban, A. N.Tyukina, T. A.Al-Ameri, J. M.Korablev, Yu. A.http://hdl.handle.net/2381/395222017-03-21T03:21:57Z2017-03-20T16:55:54ZTitle: Fast Sampling of Evolving Systems with Periodic Trajectories
Authors: Tyukin, I. Yu.; Gorban, A. N.; Tyukina, T. A.; Al-Ameri, J. M.; Korablev, Yu. A.
Abstract: We propose a novel method for fast and scalable evaluation of periodic solutions of systems of ordinary differential equations for a given set of parameter values and initial conditions. The equations governing the system dynamics are supposed to be of a special class, albeit admitting nonlinear parametrization and nonlinearities. The method enables to represent a given periodic solution as sums of computable integrals and functions that are explicitly dependent on parameters of interest and initial conditions. This allows invoking parallel computational streams in order to increase speed of calculations. Performance and practical implications of the method are illustrated with examples including classical predator-prey system and models of neuronal cells.
Description: Mathematics Subject Classification: 93B30 / 34A05 / 92B99 / 93B152017-03-20T16:55:54ZTri-trophic Plankton Models Revised: Importance of Space, Food Web Structure and Functional Response ParametrisationEgilmez, H. I.Morozov, A. Yu.http://hdl.handle.net/2381/395192017-03-21T03:21:56Z2017-03-20T16:19:32ZTitle: Tri-trophic Plankton Models Revised: Importance of Space, Food Web Structure and Functional Response Parametrisation
Authors: Egilmez, H. I.; Morozov, A. Yu.
Abstract: Revealing mechanisms of efficient top-down control in eutrophic ecosystems remains a long term challenge in theoretical ecology. In this paper, we revisit the role of environmental heterogeneity, food web structure and shape of the predator functional response in persistence and stabilization of a planktonic system with high nutrient supply. We consider a 1D vertically resolved tri-trophic planktonic food web composed of a primary producer, an intermediate predator and a highly mobile top predator, such as a system of phytoplankton, microzooplankton and copepods. We explore the realistic scenario in which the top predator is omnivorous, i.e. when copepods can feed both on phytoplankton and microzooplankton. We show that the interplay between heterogeneity of the environment due to for instance, a light gradient in the water column, and trophic interaction between species can result in an efficient top-down control which would otherwise be impossible in the corresponding well-mixed system. We also find that allowing the top predator to feed on the primary producer may dramatically impede the coexistence of the three trophic levels, with only two levels generally surviving. The coexistence of all three trophic levels within a wide range of parameters becomes possible only when the top predator exhibits active food source switching behaviour. We also show the phenomenon of bistability in the considered tri-trophic food web: a small initial amount of the top predator should lead to its extinction whereas introduction of a supercritical initial amount will eventually result in establishment of the population. The demonstrated mechanism of top-down control seems to be rather generic and might be a good candidate to explain stability in some other non-planktonic tri-trophic ecosystems.
Description: Mathematics Subject Classification: 47A75 / 45K05 / 92D402017-03-20T16:19:32ZPreface. Bifurcations and Pattern Formation in Biological ApplicationsMorozov, A.Ptashnyk, M.Volpert, V.http://hdl.handle.net/2381/395172017-03-21T03:21:55Z2017-03-20T16:05:40ZTitle: Preface. Bifurcations and Pattern Formation in Biological Applications
Authors: Morozov, A.; Ptashnyk, M.; Volpert, V.
Abstract: In the preface we present a short overview of articles included in the issue "Bifurcations and pattern formation in biological applications" of the journal Mathematical Modelling of Natural Phenomena.2017-03-20T16:05:40ZA random walk description of individual animal movement accounting for periods of restTilles, Paulo F. C.Petrovskii, Sergei V.Natti, Paulo L.http://hdl.handle.net/2381/395162017-03-21T03:21:54Z2017-03-20T14:54:02ZTitle: A random walk description of individual animal movement accounting for periods of rest
Authors: Tilles, Paulo F. C.; Petrovskii, Sergei V.; Natti, Paulo L.
Abstract: Animals do not move all the time but alternate the period of actual movement (foraging) with periods of rest (e.g. eating or sleeping). Although the existence of rest times is widely acknowledged in the literature and has even become a focus of increased attention recently, the theoretical approaches to describe animal movement by calculating the dispersal kernel and/or the mean squared displacement (MSD) rarely take rests into account. In this study, we aim to bridge this gap. We consider a composite stochastic process where the periods of active dispersal or ‘bouts’ (described by a certain baseline probability density function (pdf) of animal dispersal) alternate with periods of immobility. For this process, we derive a general equation that determines the pdf of this composite movement. The equation is analysed in detail in two special but important cases such as the standard Brownian motion described by a Gaussian kernel and the Levy flight described by a Cauchy distribution. For the Brownian motion, we show that in the large-time asymptotics the effect of rests results in a rescaling of the diffusion coefficient. The movement occurs as a subdiffusive transition between the two diffusive asymptotics. Interestingly, the Levy flight case shows similar properties, which indicates a certain universality of our findings.2017-03-20T14:54:02ZCatching ghosts with a coarse net: use and abuse of spatial sampling data in detecting synchronization.Petrovskaya, NataliaPetrovskii, Sergeihttp://hdl.handle.net/2381/395152017-03-21T03:21:54Z2017-03-20T14:47:07ZTitle: Catching ghosts with a coarse net: use and abuse of spatial sampling data in detecting synchronization.
Authors: Petrovskaya, Natalia; Petrovskii, Sergei
Abstract: Synchronization of population dynamics in different habitats is a frequently observed phenomenon. A common mathematical tool to reveal synchronization is the (cross)correlation coefficient between time courses of values of the population size of a given species where the population size is evaluated from spatial sampling data. The corresponding sampling net or grid is often coarse, i.e. it does not resolve all details of the spatial configuration, and the evaluation error-i.e. the difference between the true value of the population size and its estimated value-can be considerable. We show that this estimation error can make the value of the correlation coefficient very inaccurate or even irrelevant. We consider several population models to show that the value of the correlation coefficient calculated on a coarse sampling grid rarely exceeds 0.5, even if the true value is close to 1, so that the synchronization is effectively lost. We also observe 'ghost synchronization' when the correlation coefficient calculated on a coarse sampling grid is close to 1 but in reality the dynamics are not correlated. Finally, we suggest a simple test to check the sampling grid coarseness and hence to distinguish between the true and artifactual values of the correlation coefficient.
Description: The file associated with this record is under embargo until 12 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.2017-03-20T14:47:07Z$hp$-Version space-time discontinuous Galerkin methods for parabolic problems on prismatic meshesCangiani, AndreaDong, ZhaonanGeorgoulis, Emmanuil H.http://hdl.handle.net/2381/394732017-03-16T03:21:58Z2017-03-15T16:01:58ZTitle: $hp$-Version space-time discontinuous Galerkin methods for parabolic problems on prismatic meshes
Authors: Cangiani, Andrea; Dong, Zhaonan; Georgoulis, Emmanuil H.
Abstract: We present a new $hp$-version space-time discontinuous Galerkin (dG) finite element method for the numerical approximation of parabolic evolution equations on general spatial meshes consisting of polygonal/polyhedral (polytopic) elements, giving rise to prismatic space-time elements. A key feature of the proposed method is the use of space-time elemental polynomial bases of \emph{total} degree, say $p$, defined in the physical coordinate system, as opposed to standard dG-time-stepping methods whereby spatial elemental bases are tensorized with temporal basis functions. This approach leads to a fully discrete $hp$-dG scheme using less degrees of freedom for each time step, compared to standard dG time-stepping schemes employing tensorized space-time, with acceptable deterioration of the approximation properties. A second key feature of the new space-time dG method is the incorporation of very general spatial meshes consisting of possibly polygonal/polyhedral elements with \emph{arbitrary} number of faces. A priori error bounds are shown for the proposed method in various norms. An extensive comparison among the new space-time dG method, the (standard) tensorized space-time dG methods, the classical dG-time-stepping, and conforming finite element method in space, is presented in a series of numerical experiments.
Description: AMS subject classifications. 65N30, 65M60, 65J102017-03-15T16:01:58ZThe non-conforming virtual element method for the Stokes equationsCangiani, AndreaGyrya, VitaliyManzini, Gianmarcohttp://hdl.handle.net/2381/394722017-03-16T03:21:58Z2017-03-15T15:51:49ZTitle: The non-conforming virtual element method for the Stokes equations
Authors: Cangiani, Andrea; Gyrya, Vitaliy; Manzini, Gianmarco
Abstract: We present the non-conforming Virtual Element Method (VEM) for the numerical approximation of velocity and pressure in the steady Stokes problem. The pressure is approximated using discontinuous piecewise polynomials, while each component of the velocity is approximated using the nonconforming virtual element space. On each mesh element the local virtual space contains the space of polynomials of up to a given degree, plus suitable non-polynomial functions. The virtual element functions are implicitly defined as the solution of local Poisson problems with polynomial Neumann boundary conditions. As typical in VEM approaches, the explicit evaluation of the non-polynomial functions is not required. This approach makes it possible to construct nonconforming (virtual) spaces for any polynomial degree regardless of the parity, for two-and three-dimensional problems, and for meshes with very general polygonal and polyhedral elements. We show that the non-conforming VEM is inf-sup stable and establish optimal a priori error estimates for the velocity and pressure approximations. Numerical examples confirm the convergence analysis and the effectiveness of the method in providing high-order accurate approximations.
Description: AMS subject classifications. 65N30, 65N12, 65G99, 76R992017-03-15T15:51:49ZMapping cones in the bounded derived category of a gentle algebraCanakci, IlkePauksztello, DavidSchroll, Sibyllehttp://hdl.handle.net/2381/394632017-03-15T03:21:29Z2017-03-14T16:07:26ZTitle: Mapping cones in the bounded derived category of a gentle algebra
Authors: Canakci, Ilke; Pauksztello, David; Schroll, Sibylle
Abstract: Gentle algebras are a class of algebras that are derived tame. They therefore provide a concrete setting to study the structure of the (bounded) derived category in detail. In this article we explicitly describe the triangulated structure of the bounded derived category of a gentle algebra by describing its triangles. In particular, we develop a graphical calculus which gives the indecomposable summands of the mapping cones of morphisms in a canonical basis of the Hom-space between any two indecomposable complexes.
Description: 34 pages, many figures2017-03-14T16:07:26ZRepresentation theory of the Drinfeld doubles of a family of Hopf algebras II: corrections and new resultsErdmann, KarinGreen, Edward L.Snashall, NicoleTaillefer, Rachelhttp://hdl.handle.net/2381/393702017-02-25T04:03:47Z2017-02-24T14:45:11ZTitle: Representation theory of the Drinfeld doubles of a family of Hopf algebras II: corrections and new results
Authors: Erdmann, Karin; Green, Edward L.; Snashall, Nicole; Taillefer, Rachel
Abstract: We return to the fusion rules for the Drinfeld double of the duals of the generalised Taft algebras that we studied in [Erdmann et al., J. Pure Appl. Algebra 2006]. We first correct some proofs and statements in [Erdmann et al., J. Pure Appl. Algebra 2006] that were incorrect, using stable homomorphisms. We then complete this with new results on fusion rules for the modules we had not studied in [Erdmann et al., J. Pure Appl. Algebra 2006] and a classification of endotrivial and algebraic modules.2017-02-24T14:45:11ZGaussian process regression with functional covariates and multivariate responseWang, BoChen, TaoXu, Aipinghttp://hdl.handle.net/2381/393242017-03-06T16:41:08Z2017-02-03T15:36:06ZTitle: Gaussian process regression with functional covariates and multivariate response
Authors: Wang, Bo; Chen, Tao; Xu, Aiping
Abstract: Gaussian process regression (GPR) has been shown to be a powerful and effective nonparametric method for regression, classification and interpolation, due to many of its desirable properties. However, most GPR models consider univariate or multivariate covariates only. In this paper we extend the GPR models to cases where the covariates include both functional and multivariate variables and the response is multidimensional. The model naturally incorporates two different types of covariates: multivariate and functional, and the principal component analysis is used to de-correlate the multivariate response which avoids the widely recognised difficulty in the multi-output GPR models of formulating covariance functions which have to describe the correlations not only between data points but also between responses. The usefulness of the proposed method is demonstrated through a simulated example and two real data sets in chemometrics.
Description: The file associated with this record is embargoed until 12 months after the date of publication. The final published version may be available through the links above. Following the embargo period the above license applies.2017-02-03T15:36:06ZOn the effects of changing mortality patterns on investment, labour and consumption under uncertaintyEwald, Christian-OliverZhang, Aihuahttp://hdl.handle.net/2381/393202017-04-12T14:09:25Z2017-02-02T09:56:40ZTitle: On the effects of changing mortality patterns on investment, labour and consumption under uncertainty
Authors: Ewald, Christian-Oliver; Zhang, Aihua
Abstract: In this paper we extend the consumption-investment life cycle model for an
uncertain-lived agent, proposed by Richard (1974), to allow for
flexible labor supply. We further study the consumption, labor supply and portfolio
decisions of an agent facing age-dependent mortality risk, as presented by
UK actuarial life tables spanning the time period from 1951-2060 (including
mortality forecasts). We find that historical changes in mortality produces
significant changes in portfolio investment (more risk taking), labour (de- crease of hours) and consumption level (shift to higher level) contributing
up to 5% to GDP growth during the period from 1980 until 2010.
Description: JEL Subject Classi cation: G11; J11; J22; C61; 18 months embargo from publication; The file associated with this record is under embargo until 18 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.2017-02-02T09:56:40ZDetailed balance in micro- and macrokinetics and micro-distinguishability of macro-processesGorban, A. N.http://hdl.handle.net/2381/392172017-01-19T03:16:37Z2017-01-18T16:43:31ZTitle: Detailed balance in micro- and macrokinetics and micro-distinguishability of macro-processes
Authors: Gorban, A. N.
Abstract: We develop a general framework for the discussion of detailed balance and analyse its microscopic background. We find that there should be two additions to the well-known T- or PT-invariance of the microscopic laws of motion:
1. Equilibrium should not spontaneously break the relevant T- or PT-symmetry.
2. The macroscopic processes should be microscopically distinguishable to guarantee persistence of detailed balance in the model reduction from micro- to macrokinetics.
We briefly discuss examples of the violation of these rules and the corresponding violation of detailed balance.2017-01-18T16:43:31ZEfficient Option Pricing under Levy Processes, with CVA and FVAShek, C. K.Law, J.Levendorskiĭ, Sergeihttp://hdl.handle.net/2381/391102017-01-11T03:20:36Z2017-01-10T10:09:37ZTitle: Efficient Option Pricing under Levy Processes, with CVA and FVA
Authors: Shek, C. K.; Law, J.; Levendorskiĭ, Sergei
Abstract: We generalize the Piterbarg [1] model to include (1) bilateral default risk as in Burgard and Kjaer [2], and (2) jumps in the dynamics of the underlying asset using general classes of Lévy processes of exponential type. We develop an efficient explicit-implicit scheme for European options and barrier options taking CVA-FVA into account. We highlight the importance of this work in the context of trading, pricing and management a derivative portfolio given the trajectory of regulations.2017-01-10T10:09:37ZQuantifying non-Newtonian effects in rotating boundary-layer flowsGriffiths, P. T.Garrett, S. J.Stephen, S. O.Hussain, Z.http://hdl.handle.net/2381/390892017-01-10T03:20:43Z2017-01-09T14:39:47ZTitle: Quantifying non-Newtonian effects in rotating boundary-layer flows
Authors: Griffiths, P. T.; Garrett, S. J.; Stephen, S. O.; Hussain, Z.
Abstract: The stability of the boundary-layer on a rotating disk is considered for fluids that adhere to a non-Newtonian governing viscosity relationship. For fluids with shear-rate dependent viscosity the base flow is no longer an exact solution of the Navier–Stokes equations, however, in the limit of large Reynolds number the flow inside the three-dimensional boundary-layer can be determined via a similarity solution. The convective instabilities associated with flows of this nature are described both asymptotically and numerically via separate linear stability analyses. Akin to previous Newtonian studies it is found that there exists two primary modes of instability; the upper-branch type I modes, and the lower-branch type II modes. Results show that both these modes can be stabilised or destabilised depending on the choice of non-Newtonian viscosity model. A number of comments are made regarding the suitability of some of the more well-known non-Newtonian constitutive relationships within the context of the rotating disk model. Such a study is presented with a view to suggesting potential control mechanisms for flows that are practically relevant to the turbo-machinery industry.
Description: 12 month embargo2017-01-09T14:39:47ZComparison of the effects of surface roughness and confinement on rotor–stator cavity flowÖzkan, M.Thomas, P. J.Cooper, A. J.Garrett, Stephen Johnhttp://hdl.handle.net/2381/390232016-12-21T03:31:56Z2016-12-20T16:51:40ZTitle: Comparison of the effects of surface roughness and confinement on rotor–stator cavity flow
Authors: Özkan, M.; Thomas, P. J.; Cooper, A. J.; Garrett, Stephen John
Abstract: Results of a computational study are discussed which investigate roughness-induced and geometry-induced (confinement) effects on the steady-state velocity components in 3-D boundary-layer flow over the rotor disc in a rotor–stator flow configuration. It is found that, for the rotor–stator flow investigated, the roughness-induced effects are very similar to geometry-induced effects, both in nature and magnitude. The overall aim was to compare these two types of effects with corresponding roughness-induced effects in the von Kármán boundary-layer flow over a disc spinning freely in an unrestricted fluid environment. The research was conducted in the context of a programme investigating surface roughness as a means of laminar flow control for the development of new passive drag-reduction techniques. The goal was to establish whether it was possible unequivocally to distinguish between roughness-induced and geometry-induced effects on the boundary-layer flow above the rotor disc. The results obtained suggest that, for the type of system discussed here, it must be expected to be difficult to distinguish between these effects in experiments. The similarities regarding the nature and magnitude of results obtained from comparing predictions for three different computational modelling approaches indicate the required sensitivity of measurement technologies aiming to resolve the investigated effects in experimental studies.2016-12-20T16:51:40ZOn the diagonal subalgebra of an Ext algebraGreen, E. L.Snashall, Nicole JaneSolberg, O.Zacharia, D.http://hdl.handle.net/2381/389662016-12-16T03:19:18Z2016-12-15T15:05:06ZTitle: On the diagonal subalgebra of an Ext algebra
Authors: Green, E. L.; Snashall, Nicole Jane; Solberg, O.; Zacharia, D.
Abstract: Let R be a Koszul algebra over a field k and M be a linear R-module. We study a graded subalgebra ΔM of the Ext-algebra ExtR⁎(M,M) called the diagonal subalgebra and its properties. Applications to the Hochschild cohomology ring of R and to periodicity of linear modules are given. Viewing R as a linear module over its enveloping algebra, we also show that ΔR is isomorphic to the graded center of the Koszul dual of R. When R is selfinjective and not necessarily graded, we study connections between periodic modules M, complexity of M and existence of non-nilpotent elements of positive degree in the Ext-algebra of M. Characterizations of periodic algebras are given.2016-12-15T15:05:06ZSpecial multiserial algebras are quotients of symmetric special multiserial algebrasGreen, E. L.Schroll, Sibyllehttp://hdl.handle.net/2381/388942016-12-13T03:20:03Z2016-12-12T14:48:22ZTitle: Special multiserial algebras are quotients of symmetric special multiserial algebras
Authors: Green, E. L.; Schroll, Sibylle
Abstract: In this paper we give a new definition of symmetric special multiserial algebras in terms of defining cycles. As a consequence, we show that every special multiserial algebra is a quotient of a symmetric special multiserial algebra.
Description: MSC 16G202016-12-12T14:48:22ZHourglass stabilization and the virtual element methodCangiani, A.Manzini, G.Russo, A.Sukumar, N.http://hdl.handle.net/2381/388482016-12-07T03:23:09Z2016-12-06T15:38:40ZTitle: Hourglass stabilization and the virtual element method
Authors: Cangiani, A.; Manzini, G.; Russo, A.; Sukumar, N.
Abstract: In this paper, we establish the connections between the virtual element method (VEM) and the hourglass control techniques that have been developed since the early 1980s to stabilize underintegrated C0 Lagrange finite element methods. In the VEM, the bilinear form is decomposed into two parts: a consistent term that reproduces a given polynomial space and a correction term that provides stability. The essential ingredients of inline image-continuous VEMs on polygonal and polyhedral meshes are described, which reveals that the variational approach adopted in the VEM affords a generalized and robust means to stabilize underintegrated finite elements. We focus on the heat conduction (Poisson) equation and present a virtual element approach for the isoparametric four-node quadrilateral and eight-node hexahedral elements. In addition, we show quantitative comparisons of the consistency and stabilization matrices in the VEM with those in the hourglass control method of Belytschko and coworkers. Numerical examples in two and three dimensions are presented for different stabilization parameters, which reveals that the method satisfies the patch test and delivers optimal rates of convergence in the L2 norm and the H1 seminorm for Poisson problems on quadrilateral, hexahedral, and arbitrary polygonal meshes.2016-12-06T15:38:40ZOn the stability of continuous-discontinuous Galerkin methods for advection-diffusion-reaction problemsCangiani, AndreaChapman, J.Georgoulis, EmmanuilJensen, M.http://hdl.handle.net/2381/388472016-12-07T03:23:06Z2016-12-06T15:29:49ZTitle: On the stability of continuous-discontinuous Galerkin methods for advection-diffusion-reaction problems
Authors: Cangiani, Andrea; Chapman, J.; Georgoulis, Emmanuil; Jensen, M.
Abstract: We consider a finite element method which couples the continuous Galerkin method away from internal and boundary layers with a discontinuous Galerkin method in the vicinity of layers. We prove that this consistent method is stable in the streamline diffusion norm if the convection field flows non-characteristically from the region of the continuous Galerkin to the region of the discontinuous Galerkin method. The stability properties of the coupled method are illustrated with a numerical experiment.2016-12-06T15:29:49ZÉtale homotopy types of moduli stacks of polarised abelian schemesFrediani, P.Neumann, Frankhttp://hdl.handle.net/2381/388282016-12-06T03:22:15Z2016-12-05T16:29:23ZTitle: Étale homotopy types of moduli stacks of polarised abelian schemes
Authors: Frediani, P.; Neumann, Frank
Abstract: We determine the Artin–Mazur étale homotopy types of moduli stacks of polarised abelian schemes using transcendental methods and derive some arithmetic properties of the étale fundamental groups of these moduli stacks. Finally we analyse the Torelli morphism between the moduli stacks of algebraic curves and principally polarised abelian schemes from an étale homotopy point of view.
Description: Mathematics Subject Classification
14F35 14K10 14H10 14C342016-12-05T16:29:23ZGeometry of moduli stacks of (k, l)-stable vector bundles over algebraic curvesMata-Gutiérrez, O.Neumann, Frankhttp://hdl.handle.net/2381/388272016-12-06T03:22:07Z2016-12-05T16:22:03ZTitle: Geometry of moduli stacks of (k, l)-stable vector bundles over algebraic curves
Authors: Mata-Gutiérrez, O.; Neumann, Frank
Abstract: We study the geometry of the moduli stack of vector bundles of fixed rank and degree over an algebraic curve by introducing a filtration made of open substacks build from (k,l)-stable vector bundles. The concept of (k,l)-stability was introduced by Narasimhan and Ramanan to study the geometry of the coarse moduli space of stable bundles. We will exhibit the stacky picture and analyse the geometric and cohomological properties of the moduli stacks of (k,l)-stable vector bundles. For particular pairs (k,l) of integers we also show that these moduli stacks admit coarse moduli spaces and we discuss their interplay.
Description: MSC
primary, 14H60, 14D23; secondary, 14D202016-12-05T16:22:03ZA New Bayesian Test to test for the Intractability-Countering HypothesisChakrabarty, Daliahttp://hdl.handle.net/2381/388042016-12-03T03:57:02Z2016-12-02T12:24:33ZTitle: A New Bayesian Test to test for the Intractability-Countering Hypothesis
Authors: Chakrabarty, Dalia
Abstract: We present a new test of hypothesis in which we seek the probability of the null conditioned on the data, where the null is a simplification undertaken to counter the intractability of the more complex model, that the simpler null model is nested within. With the more complex model rendered intractable, the null model uses a simplifying assumption that capacitates the learning of an unknown parameter vector given the data. Bayes factors are shown to be known only up to a ratio of unknown data-dependent constants–a problem that cannot be cured using prescriptions similar to those suggested to solve the problem caused to Bayes factor computation, by non-informative priors. Thus, a new test is needed in which we can circumvent Bayes factor computation. In this test, we undertake generation of data from the model in which the null hypothesis is true and can achieve support in the measured data for the null by comparing the marginalised posterior of the model parameter given the measured data, to that given such generated data. However, such a ratio of marginalised posteriors can confound interpretation of comparison of support in one measured data for a null, with that in another data set for a different null. Given an application in which such comparison is undertaken, we alternatively define support in a measured data set for a null by identifying the model parameters that are less consistent with the measured data than is minimally possible given the generated data, and realising that the higher the number of such parameter values, less is the support in the measured data for the null. Then, the probability of the null conditional on the data is given within an MCMC-based scheme, by marginalising the posterior given the measured data, over parameter values that are as, or more consistent with the measured data, than with the generated data. In the aforementioned application, we test the hypothesis that a galactic state space bears an isotropic geometry, where the (missing) data comprising measurements of some components of the state space vector of a sample of observed galactic particles, is implemented to Bayesianly learn the gravitational mass density of all matter in the galaxy. In lieu of an assumption about the state space being isotropic, the likelihood of the sought gravitational mass density given the data, is intractable. For a real example galaxy, we find unequal values of the probability of the null–that the host state space is isotropic–given two different data sets, implying that in this galaxy, the system state space constitutes at least two disjoint sub-volumes that the two data sets respectively live in. Implementation on simulated galactic data is also undertaken, as is an empirical illustration on the well-known O-ring data, to test for the form of the thermal variation of the failure probability of the O-rings.
Description: Details of the Bayesian learning of the gravitational mass density and state spacepd fof the galaxyare provided in SectionS-1of the attached supplementary material. SectionS-2discusses detailsof the Fully Bayesian Significance Test.2016-12-02T12:24:33ZPattern, process, scale, and model's sensitivity: Comment on "Phase separation driven by density-dependent movement: A novel mechanism for ecological patterns" by Quan-Xing Liu et al.Petrovskii, Sergeihttp://hdl.handle.net/2381/387642016-11-30T03:21:06Z2016-11-29T16:09:05ZTitle: Pattern, process, scale, and model's sensitivity: Comment on "Phase separation driven by density-dependent movement: A novel mechanism for ecological patterns" by Quan-Xing Liu et al.
Authors: Petrovskii, Sergei
Abstract: Spatial distribution of ecological populations is rarely homogeneous. Typically, the population density exhibits considerable variability of space, in an extreme yet not uncommon case creating a “patchy” pattern where areas of high population density alternate with areas where the population density is much lower or close to zero [1]. This phenomenon, often generically referred to as ecological patterning or ecological pattern formation, has long been a focus of interest in ecology and a number of theories and models have been developed aiming to explain it under different ecological and/or environmental conditions and on different spatial and temporal scales; see Table 1. A straightforward explanation of the heterogeneous distribution of population density relates it to the heterogeneity of the environment (e.g. to nonuniform distribution of resources) and this is indeed often the case [2]. However, a closer look reveals that this is not enough and in many cases the heterogeneity of population density is only weakly correlated to the heterogeneity of the environment [3] and [19]. Understanding that biological interactions play, on the relevant spatial and temporal scales [20], as important role in shaping the ecological patterns as the physical/chemical forcing resulted in a number of theories. The earliest one that used the idea of Turing's instability [4] was followed by several others [5], [6] and [21] including theories where pattern formation was due to a non-Turing mechanism [8] and [9] and theories where the movement behavior and/or density dependence was an essential factor [12] and [14].2016-11-29T16:09:05ZQuantifying uncertainty in partially specified biological models: How can optimal control theory help us?Adamson, M. W.Morozov, A. Y.Kuzenkov, O. A.http://hdl.handle.net/2381/387192016-11-26T04:12:09Z2016-11-25T09:58:35ZTitle: Quantifying uncertainty in partially specified biological models: How can optimal control theory help us?
Authors: Adamson, M. W.; Morozov, A. Y.; Kuzenkov, O. A.
Abstract: Mathematical models in biology are highly simplified representations of a complex underlying reality and there is always a high degree of uncertainty with regards to model function specification. This uncertainty becomes critical for models in which the use of different functions fitting the same dataset can yield substantially different predictions-a property known as structural sensitivity. Thus, even if the model is purely deterministic, then the uncertainty in the model functions carries through into uncertainty in model predictions, and new frameworks are required to tackle this fundamental problem. Here, we consider a framework that uses partially specified models in which some functions are not represented by a specific form. The main idea is to project infinite dimensional function space into a low-dimensional space taking into account biological constraints. The key question of how to carry out this projection has so far remained a serious mathematical challenge and hindered the use of partially specified models. Here, we propose and demonstrate a potentially powerful technique to perform such a projection by using optimal control theory to construct functions with the specified global properties. This approach opens up the prospect of a flexible and easy to use method to fulfil uncertainty analysis of biological models.2016-11-25T09:58:35ZPiece-wise quadratic approximations of arbitrary error functions for fast and robust machine learningGorban, A. N.Mirkes, E. M.Zinovyev, A.http://hdl.handle.net/2381/387112016-11-24T03:21:35Z2016-11-23T17:34:11ZTitle: Piece-wise quadratic approximations of arbitrary error functions for fast and robust machine learning
Authors: Gorban, A. N.; Mirkes, E. M.; Zinovyev, A.
Abstract: Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and noisy data, the quadratic error functionals demonstrated many weaknesses including high sensitivity to contaminating factors and dimensionality curse. Therefore, a lot of recent applications in machine learning exploited properties of non-quadratic error functionals based on L1 norm or even sub-linear potentials corresponding to quasinorms Lp (0<p<1). The back side of these approaches is increase in computational cost for optimization. Till so far, no approaches have been suggested to deal with arbitrary error functionals, in a flexible and computationally efficient framework. In this paper, we develop a theory and basic universal data approximation algorithms (k-means, principal components, principal manifolds and graphs, regularized and sparse regression), based on piece-wise quadratic error potentials of subquadratic growth (PQSQ potentials). We develop a new and universal framework to minimize arbitrary sub-quadratic error potentials using an algorithm with guaranteed fast convergence to the local or global error minimum. The theory of PQSQ potentials is based on the notion of the cone of minorant functions, and represents a natural approximation formalism based on the application of min-plus algebra. The approach can be applied in most of existing machine learning methods, including methods of data approximation and regularized and sparse regression, leading to the improvement in the computational cost/accuracy trade-off. We demonstrate that on synthetic and real-life datasets PQSQ-based machine learning methods achieve orders of magnitude faster computational performance than the corresponding state-of-the-art methods, having similar or better approximation accuracy.2016-11-23T17:34:11Z