DSpace Collection:http://hdl.handle.net/2381/38232016-05-02T23:19:51Z2016-05-02T23:19:51ZTiling spaces, codimension one attractors and shapeClark, AlexanderHunton, J.http://hdl.handle.net/2381/373462016-04-19T02:15:49Z2016-04-18T11:58:33ZTitle: Tiling spaces, codimension one attractors and shape
Authors: Clark, Alexander; Hunton, J.
Abstract: We establish a close relationship between, on the one hand, expanding, codimension one attractors of diffeomorphisms on closed manifolds (examples of so-called strange attractors), and, on the other, spaces which arise in the study of aperiodic tilings. We show that every such orientable attractor is homeomorphic to a tiling space of either a substitution or a projection tiling, depending on its dimension. We also demonstrate that such an attractor is shape equivalent to a (d+1)-dimensional torus with a finite number of points removed, or, in the nonorientable case, to a space with a two-to-one covering by such a torus-less-points. This puts considerable constraints on the topology of codimension one attractors, and constraints on which manifolds tiling spaces may be embedded in. In the process we develop a new invariant for aperiodic tilings, which, for 1-dimensional tilings is in many cases finer than the cohomological or K-theoretic invariants studied to date.2016-04-18T11:58:33ZFrom Ambiguity Aversion to a Generalized Expected Utility. Modeling Preferences in a Quantum Probabilistic FrameworkAerts, D.Sozzo, Sandrohttp://hdl.handle.net/2381/372652016-04-13T02:22:20Z2016-04-12T11:41:18ZTitle: From Ambiguity Aversion to a Generalized Expected Utility. Modeling Preferences in a Quantum Probabilistic Framework
Authors: Aerts, D.; Sozzo, Sandro
Abstract: Ambiguity and ambiguity aversion have been widely studied in decision theory and economics both at a theoretical and an experimental level. After Ellsberg's seminal studies challenging subjective expected utility theory (SEUT), several (mainly normative) approaches have been put forward to reproduce ambiguity aversion and Ellsberg-type preferences. However, Machina and other authors have pointed out some fundamental difficulties of these generalizations of SEUT to cope with some variants of Ellsberg's thought experiments, which has recently been experimentally confirmed. Starting from our quantum modeling approach to human cognition, we develop here a general probabilistic framework to model human decisions under uncertainty. We show that our quantum theoretical model faithfully represents different sets of data collected on both the Ellsberg and the Machina paradox situations, and is flexible enough to describe different subjective attitudes with respect to ambiguity. Our approach opens the way toward a quantum-based generalization of expected utility theory (QEUT), where subjective probabilities depend on the state of the conceptual entity at play and its interaction with the decision-maker, while preferences between acts are determined by the maximization of this 'state-dependent expected utility'.
Description: The file associated with this record is under a 24-month embargo from publication in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.2016-04-12T11:41:18ZThe centrifugal instability of the boundary-layer flow over a slender rotating cone in an enforced axial free streamHussain, Z.Garrett, Stephen J.Stephen, S. O.Griffiths, Paul Travishttp://hdl.handle.net/2381/369862016-03-08T03:20:27Z2016-03-07T11:36:56ZTitle: The centrifugal instability of the boundary-layer flow over a slender rotating cone in an enforced axial free stream
Authors: Hussain, Z.; Garrett, Stephen J.; Stephen, S. O.; Griffiths, Paul Travis
Abstract: In this study, a new centrifugal instability mode, which dominates within the boundary-layer flow over a slender rotating cone in still fluid, is used for the first time to model the problem within an enforced oncoming axial flow. The resulting problem necessitates an updated similarity solution to represent the basic flow more accurately than previous studies in the literature. The new mean flow field is subsequently perturbed, leading to disturbance equations that are solved via numerical and short-wavelength asymptotic approaches, yielding favourable comparisons with existing experiments. Essentially, the boundary-layer flow undergoes competition between the streamwise flow component, due to the oncoming flow, and the rotational flow component, due to effect of the spinning cone surface, which can be described mathematically in terms of a control parameter, namely the ratio of streamwise to axial flow. For a slender cone rotating in a sufficiently strong axial flow, the instability mode breaks down into Görtler-type counter-rotating spiral vortices, governed by an underlying centrifugal mechanism, which is consistent with experimental and theoretical studies for a slender rotating cone in otherwise still fluid.
Description: The file associated with this record is under a 6-month embargo from publication in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.2016-03-07T11:36:56ZThe neutral curve for stationary disturbances in rotating disk flow for power-law fluidsGriffiths, P. T.Garrett, Stephen JohnStephen, S. O.http://hdl.handle.net/2381/369852016-03-08T03:19:26Z2016-03-07T11:32:29ZTitle: The neutral curve for stationary disturbances in rotating disk flow for power-law fluids
Authors: Griffiths, P. T.; Garrett, Stephen John; Stephen, S. O.
Abstract: This paper is concerned with the convective instabilities associated with the boundary-layer flow due to a rotating disk. Shear-thinning fluids that adhere to the power-law relationship are considered. The neutral curves are computed using a sixth-order system of linear stability equations which include the effects of streamline curvature, Coriolis force and the non-Newtonian viscosity model. Akin to previous Newtonian studies it is found that the neutral curves have two critical values, these are associated with the type I upper-branch (cross-flow) and type II lower-branch (streamline curvature) modes. Our results indicate that an increase in shear-thinning has a stabilising effect on both the type I and II modes, in terms of the critical Reynolds number and growth rate. Favourable agreement is obtained between existing asymptotic predictions and the numerical results presented here.
Description: The file associated with this record is under a 24-month embargo from publication in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.2016-03-07T11:32:29ZStability of the boundary layer on a rotating disk for power-law fluidsGriffiths, P. T.Stephen, S. O.Bassom, A. P.Garrett, Stephen Johnhttp://hdl.handle.net/2381/369632016-03-04T03:22:45Z2016-03-03T11:51:44ZTitle: Stability of the boundary layer on a rotating disk for power-law fluids
Authors: Griffiths, P. T.; Stephen, S. O.; Bassom, A. P.; Garrett, Stephen John
Abstract: The stability of the flow due to a rotating disk is considered for non-Newtonian fluids, specifically shear-thinning fluids that satisfy the power-law (Ostwald-de Waele) relationship. In this case the basic flow is not an exact solution of the Navier–Stokes equations, however, in the limit of large Reynolds number the flow inside the three-dimensional boundary layer can be determined via a similarity solution. An asymptotic analysis is presented in the limit of large Reynolds number. It is shown that the stationary spiral instabilities observed experimentally in the Newtonian case can be described for shear-thinning fluids by a linear stability analysis. Predictions for the wavenumber and wave angle of the disturbances suggest that shear-thinning fluids may have a stabilising effect on the flow.2016-03-03T11:51:44ZGlobal linear stability of the boundary-layer flow over a rotating sphereBarrow, A.Garrett, Stephen J.Peake, N.http://hdl.handle.net/2381/368892016-02-26T03:26:22Z2016-02-25T13:44:07ZTitle: Global linear stability of the boundary-layer flow over a rotating sphere
Authors: Barrow, A.; Garrett, Stephen J.; Peake, N.
Abstract: We consider the linear global stability of the boundary-layer flow over a rotating sphere. Our results suggest that a self-excited linear global mode can exist when the sphere rotates sufficiently fast, with properties fixed by the flow at latitudes between approximately 55°–65° from the pole (depending on the rotation rate). A neutral curve for global linear instabilities is presented with critical Reynolds number consistent with existing experimentally measured values for the appearance of turbulence. The existence of an unstable linear global mode is in contrast to the literature on the rotating disk, where it is expected that nonlinearity is required to prompt the transition to turbulence. Despite both being susceptible to local absolute instabilities, we conclude that the transition mechanism for the rotating-sphere flow may be different to that for the rotating disk.2016-02-25T13:44:07ZThe centrifugal instability of the boundary-layer flow over a slender rotating cone in an enforced axial free-streamHussain, Z.Garrett, Stephen J.Stephen, S. O.Griffiths, Paul T.http://hdl.handle.net/2381/368882016-02-26T03:26:36Z2016-02-25T13:41:12ZTitle: The centrifugal instability of the boundary-layer flow over a slender rotating cone in an enforced axial free-stream
Authors: Hussain, Z.; Garrett, Stephen J.; Stephen, S. O.; Griffiths, Paul T.
Abstract: In this study, a new centrifugal instability mode, which dominates within the boundary-layer flow over a slender rotating cone in still fluid, is used for the first time to model the problem within an enforced oncoming axial flow. The resulting problem necessitates an updated similarity solution to represent the basic flow more accurately than previous studies in the literature. The new mean flow field is subsequently perturbed, leading to disturbance equations that are solved via numerical and short-wavelength asymptotic approaches, yielding favourable comparisons with existing experiments. Essentially, the boundary-layer flow undergoes competition between the streamwise flow component, due to the oncoming flow, and the rotational flow component, due to effect of the spinning cone surface, which can be described mathematically in terms of a control parameter, namely the ratio of streamwise to axial flow. For a slender cone rotating in a sufficiently strong axial flow, the instability mode breaks down into Görtler-type counter-rotating spiral vortices, governed by an underlying centrifugal mechanism, which is consistent with experimental and theoretical studies for a slender rotating cone in otherwise still fluid.
Description: The file associated with this record is under a 6-month embargo from publication in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.2016-02-25T13:41:12ZThe effect of surface roughness on the convective instability of the BEK family of boundary-layer flowsAlveroglu, BurhanSegalini, A.Garrett, Stephen J.http://hdl.handle.net/2381/368872016-02-26T03:26:38Z2016-02-25T13:34:13ZTitle: The effect of surface roughness on the convective instability of the BEK family of boundary-layer flows
Authors: Alveroglu, Burhan; Segalini, A.; Garrett, Stephen J.
Abstract: A Chebyshev polynomial discretisation method is used to investigate the effect of both anisotropic (radially and azimuthally) and isotropic surface roughnesses on the convective instability of the BEK family of rotating boundary-layer flows. The mean-flow profiles for the velocity components are obtained by modelling surface roughness with a partial-slip approach. A linear stability analysis is then performed to investigate the effect of roughness on the convective instability characteristics of the inviscid Type I (cross-flow) instability and the viscous Type II instability. It is revealed that all roughness types lead to a stabilisation of the Type I mode in all flows within the BEK family, with the exception of azimuthally-anisotropic roughness (radial grooves) within the Bödewadt layer which causes a mildly destabilising effect. In the case of the Type II mode, the results reveal the destabilising effect of radially-anisotropic roughness (concentric grooves) on all the boundary layers, whereas both azimuthally-anisotropic and isotropic roughnesses have a stabilising effect on the mode for Ekman and von Kármán layers. Complementary results are also presented by considering the effects of roughness on the growth rates of each instability mode within the Ekman layer.
Description: The file associated with this record is under a 24-month embargo from publication in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.2016-02-25T13:34:13ZThe effect of anisotropic and isotropic roughness on the convective stability of the rotating disk boundary layerCooper, A. J.Harris, J. H.Garrett, Stephen JohnOezkan, M.Thomas, P. J.http://hdl.handle.net/2381/368862016-02-26T03:26:38Z2016-02-25T13:28:22ZTitle: The effect of anisotropic and isotropic roughness on the convective stability of the rotating disk boundary layer
Authors: Cooper, A. J.; Harris, J. H.; Garrett, Stephen John; Oezkan, M.; Thomas, P. J.
Abstract: A theoretical study investigating the effects of both anisotropic and isotropic surface roughness on the convective stability of the boundary-layer flow over a rotating disk is described. Surface roughness is modelled using a partial-slip approach, which yields steady-flow profiles for the relevant velocity components of the boundary-layer flow which are a departure from the classic von Kármán solution for a smooth disk. These are then subjected to a linear stability analysis to reveal how roughness affects the stability characteristics of the inviscid Type I (or cross-flow) instability and the viscous Type II instability that arise in the rotating disk boundary layer. Stationary modes are studied and both anisotropic (concentric grooves and radial grooves) and isotropic (general) roughness are shown to have a stabilizing effect on the Type I instability. For the viscous Type II instability, it was found that a disk with concentric grooves has a strongly destabilizing effect, whereas a disk with radial grooves or general isotropic roughness has a stabilizing effect on this mode. In order to extract possible underlying physical mechanisms behind the effects of roughness, and in order to reconfirm the results of the linear stability analysis, an integral energy equation for three-dimensional disturbances to the undisturbed three-dimensional boundary-layer flow is used. For anisotropic roughness, the stabilizing effect on the Type I mode is brought about by reductions in energy production in the boundary layer, whilst the destabilizing effect of concentric grooves on the Type II mode results from a reduction in energy dissipation. For isotropic roughness, both modes are stabilized by combinations of reduced energy production and increased dissipation.2016-02-25T13:28:22ZOn the stability of von Kármán rotating-disk boundary layers with radial anisotropic surface roughnessGarrett, Stephen J.Cooper, A. J.Harris, J. H.Ozkan, M.Segalini, A.Thomas, P. J.http://hdl.handle.net/2381/368852016-03-02T03:26:01Z2016-02-25T13:21:15ZTitle: On the stability of von Kármán rotating-disk boundary layers with radial anisotropic surface roughness
Authors: Garrett, Stephen J.; Cooper, A. J.; Harris, J. H.; Ozkan, M.; Segalini, A.; Thomas, P. J.
Abstract: We summarise results of a theoretical study investigating the distinct convective instability properties of steady boundary-layer flow over rough rotating disks. A generic roughness pattern of concentric circles with sinusoidal surface undulations in the radial direction is considered. The goal is to compare predictions obtained by means of two alternative, and fundamentally different, modelling approaches for surface roughness for the first time. The motivating rationale is to identify commonalities and isolate results that might potentially represent artefacts associated with the particular methodologies underlying one of the two modelling approaches. The most significant result of practical relevance obtained is that both approaches predict overall stabilising effects on type I instability mode of rotating disk flow. This mode leads to transition of the rotating-disk boundary layer and, more generally, the transition of boundary-layers with a cross-flow profile. Stabilisation of the type 1 mode means that it may be possible to exploit surface roughness for laminar-flow control in boundary layers with a cross-flow component. However, we also find differences between the two sets of model predictions, some subtle and some substantial. These will represent criteria for establishing which of the two alternative approaches is more suitable to correctly describe experimental data when these become available.2016-02-25T13:21:15ZGlobal linear stability of the boundary-layer flow over a rotating sphereBarrow, A.Garrett, Stephen JohnPeake, N.http://hdl.handle.net/2381/368842016-02-26T03:28:14Z2016-02-25T13:07:28ZTitle: Global linear stability of the boundary-layer flow over a rotating sphere
Authors: Barrow, A.; Garrett, Stephen John; Peake, N.
Abstract: We consider the linear global stability of the boundary-layer flow over a rotating sphere. Our results suggest that a self-excited linear global mode can exist when the sphere rotates sufficiently fast, with properties fixed by the flow at latitudes between approximately 55°-65° from the pole (depending on the rotation rate). A neutral curve for global linear instabilities is presented with critical Reynolds number consistent with existing experimentally measured values for the appearance of turbulence. The existence of an unstable linear global mode is in contrast to the literature on the rotating disk, where it is expected that nonlinearity is required to prompt the transition to turbulence. Despite both being susceptible to local absolute instabilities, we conclude that the transition mechanism for the rotating-sphere flow may be different to that for the rotating disk.2016-02-25T13:07:28ZOn Streamwise Vortices in Large Eddy Simulations of Initially Laminar Plane Mixing LayersMcMullan, William AndrewGarrett, Stephen J.http://hdl.handle.net/2381/367902016-02-19T03:24:45Z2016-02-18T12:27:41ZTitle: On Streamwise Vortices in Large Eddy Simulations of Initially Laminar Plane Mixing Layers
Authors: McMullan, William Andrew; Garrett, Stephen J.
Abstract: x
Description: The file associated with this record is under a 24-month embargo from publication in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.2016-02-18T12:27:41ZOut-of-band and adjacent-channel interference reduction by analog nonlinear filtersNikitin, A. V.Davidchack, Ruslan L.Smith, J. E.http://hdl.handle.net/2381/364712016-02-02T03:14:45Z2016-02-01T09:58:41ZTitle: Out-of-band and adjacent-channel interference reduction by analog nonlinear filters
Authors: Nikitin, A. V.; Davidchack, Ruslan L.; Smith, J. E.
Abstract: In a perfect world, we would have ‘brick wall’ filters, no-distortion amplifiers and mixers, and well-coordinated spectrum operations. The real world, however, is prone to various types of unintentional and intentional interference of technogenic (man-made) origin that can disrupt critical communication systems. In this paper, we introduce a methodology for mitigating technogenic interference in communication channels by analog nonlinear filters, with an emphasis on the mitigation of out-of-band and adjacent-channel interference.
Interference induced in a communications receiver by external transmitters can be viewed as wide-band non-Gaussian noise affecting a narrower-band signal of interest. This noise may contain a strong component within the receiver passband, which may dominate over the thermal noise. While the total wide-band interference seen by the receiver may or may not be impulsive, we demonstrate that the interfering component due to power emitted by the transmitter into the receiver channel is likely to appear impulsive under a wide range of conditions. We give an example of mechanisms of impulsive interference in digital communication systems resulting from the nonsmooth nature of any physically realizable modulation scheme for transmission of a digital (discontinuous) message.
We show that impulsive interference can be effectively mitigated by nonlinear differential limiters (NDLs). An NDL can be configured to behave linearly when the input signal does not contain outliers. When outliers are encountered, the nonlinear response of the NDL limits the magnitude of the respective outliers in the output signal. The signal quality is improved in excess of that achievable by the respective linear filter, increasing the capacity of a communications channel. The behavior of an NDL, and its degree of nonlinearity, is controlled by a single parameter in a manner that enables significantly better overall suppression of the noise-containing impulsive components compared to the respective linear filter. Adaptive configurations of NDLs are similarly controlled by a single parameter and are suitable for improving quality of nonstationary signals under time-varying noise conditions. NDLs are designed to be fully compatible with existing linear devices and systems and to be used as an enhancement, or as a low-cost alternative, to the state-of-art interference mitigation methods.2016-02-01T09:58:41ZAsymptotic variance of stationary reversible and normal Markov processesDeligiannidis, G.Peligrad, M.Utev, Sergeyhttp://hdl.handle.net/2381/364132016-01-28T03:09:24Z2016-01-27T10:37:50ZTitle: Asymptotic variance of stationary reversible and normal Markov processes
Authors: Deligiannidis, G.; Peligrad, M.; Utev, Sergey
Abstract: We obtain necessary and sufficient conditions for the regular variation of the variance of partial sums of functionals of discrete and continuous-time stationary Markov processes with normal transition operators. We also construct a class of Metropolis-Hastings algorithms which satisfy a central limit theorem and invariance principle when the variance is not linear in n.2016-01-27T10:37:50ZThe HELP inequality for Hamiltonian systemsBrown, B. M.Evans, W. D.Marletta, M.http://hdl.handle.net/2381/362952016-01-16T03:15:05Z2016-01-15T15:52:52ZTitle: The HELP inequality for Hamiltonian systems
Authors: Brown, B. M.; Evans, W. D.; Marletta, M.
Abstract: We extend the Hardy–Everitt–Littlewood–Polya inequality, hitherto established for 2nth order formally selfadjoint ordinary differential equations, to a wide class of linear Hamiltonian systems. The method follows Dias (Ph.D. thesis, Cardiff: University of Wales, 1994) but without the Hilbert space setting which he uses.2016-01-15T15:52:52ZRegularized semiclassical limits: linear flows with infinite Lyapunov exponentsAthanassoulis, AgisilaosKyza, I.Katsaounis, T.http://hdl.handle.net/2381/362662016-01-13T03:10:37Z2016-01-12T12:48:18ZTitle: Regularized semiclassical limits: linear flows with infinite Lyapunov exponents
Authors: Athanassoulis, Agisilaos; Kyza, I.; Katsaounis, T.
Abstract: Semiclassical asymptotics for Schrodinger equations with non-smooth potentials give rise to ill-posed formal semiclassical limits. These problems have attracted a lot of attention in the last few years, as a proxy for the treatment of eigenvalue crossings, i.e. general systems. It has recently been shown that the semiclassical limit for conical singularities is in fact well-posed, as long as the Wigner measure (WM) stays away from singular saddle points. In this work we develop a family of refined semiclassical estimates, and use them to derive regularized transport equations for saddle points with infinite Lyapunov exponents, extending the aforementioned recent results. In the process we answer a related question posed by P. L. Lions and T. Paul in 1993. If we consider more singular potentials, our rigorous estimates break down. To investigate whether conical saddle points, such as -|x|, admit a regularized transport asymptotic approximation, we employ a numerical solver based on posterior error controal. Thus rigorous uppen bounds for the asymptotic error on concrete problems are generated. In particular, specific phenomena which render invalid any regularized transport for -|x| are identified and quantified. In that sense our rigorous results are sharp. Finally, we use our findings to formulate a precise conjecture for the condition under which conical saddle points admit a regularized transport solution for the WM.
Description: The file associated with this record is under a permanent embargo while publication is In Press in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.2016-01-12T12:48:18ZOn the XFEL Schrödinger Equation: Highly Oscillatory Magnetic Potentials and Time AveragingAthanassoulis, AgisilaosAntonelli, P.Markowich, P. A.Hajaiej, H.http://hdl.handle.net/2381/362472016-01-12T03:09:29Z2016-01-11T11:41:27ZTitle: On the XFEL Schrödinger Equation: Highly Oscillatory Magnetic Potentials and Time Averaging
Authors: Athanassoulis, Agisilaos; Antonelli, P.; Markowich, P. A.; Hajaiej, H.
Abstract: We analyse a nonlinear Schrödinger equation for the time-evolution of the wave function of an electron beam, interacting selfconsistently through a Hartree–Fock nonlinearity and through the repulsive Coulomb interaction of an atomic nucleus. The electrons are supposed to move under the action of a time dependent, rapidly periodically oscillating electromagnetic potential. This can be considered a simplified effective single particle model for an X-ray free electron laser. We prove the existence and uniqueness for the Cauchy problem and the convergence of wave-functions to corresponding solutions of a Schrödinger equation with a time-averaged Coulomb potential in the high frequency limit for the oscillations of the electromagnetic potential.2016-01-11T11:41:27ZNumerical Simulations of X-Ray Free Electron Lasers (XFEL)Athanassoulis, AgisilaosMarkowich, P. A.Antonelli, P.Huang, Z.http://hdl.handle.net/2381/362432016-01-12T03:09:53Z2016-01-11T10:48:23ZTitle: Numerical Simulations of X-Ray Free Electron Lasers (XFEL)
Authors: Athanassoulis, Agisilaos; Markowich, P. A.; Antonelli, P.; Huang, Z.
Abstract: We study a nonlinear Schrödinger equation which arises as an effective single particle model in X-ray free electron lasers (XFEL). This equation appears as a first principles model for the beam-matter interactions that would take place in an XFEL molecular imaging experiment in [A. Fratalocchi and G. Ruocco, Phys. Rev. Lett., 106 (2011), 105504]. Since XFEL are more powerful by several orders of magnitude than more conventional lasers, the systematic investigation of many of the standard assumptions and approximations has attracted increased attention. In this model the electrons move under a rapidly oscillating electromagnetic field, and the convergence of the problem to an effective time-averaged one is examined. We use an operator splitting pseudospectral method to investigate numerically the behavior of the model versus that of its time-averaged version in complex situations, namely the energy subcritical/mass supercritical case and in the presence of a periodic lattice. We find the time-averaged model to be an effective approximation, even close to blowup, for fast enough oscillations of the external field. This work extends previous analytical results for simpler cases [P. Antonelli, A. Athanassoulis, H. Hajaiej, and P. Markowich, Arch. Ration. Mech. Anal., 211 (2014), pp. 711--732].2016-01-11T10:48:23ZSynergy effect of cooperative investmentGrechuk, BogdanZabarankin, M.http://hdl.handle.net/2381/361892016-01-07T03:09:07Z2016-01-06T12:56:39ZTitle: Synergy effect of cooperative investment
Authors: Grechuk, Bogdan; Zabarankin, M.
Abstract: Cooperative investment consists of two problems: finding an optimal cooperative investment strategy and fairly dividing investment outcome among participating agents. In general, the two problems cannot be solved separately. It is known that when agents’ preferences are represented by mean-deviation functionals, sharing of optimal portfolio creates instruments that, on the one hand, satisfy individual risk preferences but, on the other hand, are not replicable on an incomplete market, so that each agent is strictly better off in participating in cooperative investment than investing alone. This synergy effect is shown to hold when agents’ acceptance sets are represented by cash-invariant utility functions in the case of multiperiod investment with an arbitrary feasible investment set. In this case, a set of all Pareto-optimal allocations is characterized, and an equilibrium-based method for selecting a “fair” Pareto-optimal allocation is suggested. It is also shown that if exists, the “fair” allocation belongs to the core of the corresponding cooperative game. The equilibrium-based method is then extended to the case of arbitrary utility functions. The obtained results are demonstrated in a multiperiod cooperative investment problem with investors imposing drawdown constraints on investment strategies.
Description: The file associated with this record is under a 12-month embargo from publication in accordance with the publisher's self-archiving policy, available at http://www.springer.com/gp/open-access/authors-rights/self-archiving-policy/2124. The full text may be available through the publisher links provided above.2016-01-06T12:56:39ZRelated fixed points for set-valued mappings on two uniform spacesTürkoğlu, D.Fisher, Brianhttp://hdl.handle.net/2381/361512016-01-06T03:09:34Z2016-01-05T10:28:25ZTitle: Related fixed points for set-valued mappings on two uniform spaces
Authors: Türkoğlu, D.; Fisher, Brian
Abstract: Some related fixed point theorems for set-valued mappings on two complete and compact uniform spaces are proved.
Description: 2000 Mathematics Subject Classification: 54H25, 47H10.2016-01-05T10:28:25ZOn the Fresnel integrals and the convolutionKiliçman, A.Fisher, Brianhttp://hdl.handle.net/2381/361442016-01-05T03:12:31Z2016-01-04T15:10:01ZTitle: On the Fresnel integrals and the convolution
Authors: Kiliçman, A.; Fisher, Brian
Abstract: The Fresnel cosine integral C(x), the Fresnel sine integral S(x), and the associated functions C+(x), C−(x), S+(x), and S−(x) are defined as locally summable functions on the real line. Some convolutions and neutrix convolutions of the Fresnel cosine integral and its associated functions with x+r and xr are evaluated.
Description: 2000 Mathematics Subject Classification: 33B10, 46F102016-01-04T15:10:01ZOn the sine integral and the convolutionFisher, BrianAl-Sirehy, F.http://hdl.handle.net/2381/361432016-01-05T03:12:29Z2016-01-04T14:57:48ZTitle: On the sine integral and the convolution
Authors: Fisher, Brian; Al-Sirehy, F.
Abstract: The sine integral Si(λx) and the cosine integral Ci(λx) and their associated functions Si+(λx), Si−(λx), Ci+(λx), Ci−(λx) are defined as locally summable functions on the real line. Some convolutions of these functions and sin(μx), sin+(μx), and sin−(μx) are found.
Description: 2000 Mathematics Subject Classification: 33B10, 46F10.2016-01-04T14:57:48ZInverse portfolio problem with coherent risk measuresGrechuk, BogdanZabarankin, M.http://hdl.handle.net/2381/361362015-12-24T03:08:14Z2015-12-23T13:36:29ZTitle: Inverse portfolio problem with coherent risk measures
Authors: Grechuk, Bogdan; Zabarankin, M.
Abstract: In general, a portfolio problem minimizes risk (or negative utility) of a portfolio of financial assets with respect to portfolio weights subject to a budget constraint. The inverse portfolio problem then arises when an investor assumes that his/her risk preferences have a numerical representation in the form of a certain class of functionals, e.g. in the form of expected utility, coherent risk measure or mean-deviation functional, and aims to identify such a functional, whose minimization results in a portfolio, e.g. a market index, that he/she is most satisfied with. In this work, the portfolio risk is determined by a coherent risk measure, and the rate of return of investor’s preferred portfolio is assumed to be known. The inverse portfolio problem then recovers investor’s coherent risk measure either through finding a convex set of feasible probability measures (risk envelope) or in the form of either mixed CVaR or negative Yaari’s dual utility. It is solved in single-period and multi-period formulations and is demonstrated in a case study with the FTSE 100 index.2015-12-23T13:36:29ZImplementing Automotive Telematics for Insurance Covers of FleetsAzzopardi, M.Cortis, Dominichttp://hdl.handle.net/2381/361302015-12-23T03:05:28Z2015-12-22T16:43:17ZTitle: Implementing Automotive Telematics for Insurance Covers of Fleets
Authors: Azzopardi, M.; Cortis, Dominic
Abstract: The advantages of Usage-Based Insurance for automotive covers over conventional rating methods have been discussed in literature for over four decades. Notwithstanding their adoption in insurance markets has been slow. This paper seeks to establish the viability of introducing fleet Telematics-Based Insurance by investigating the perceptions of insurance operators, tracking service providers and corporate fleet owners. At its core, the study involves a SWOT-analysis to appraise Telematics-Based Insurance against conventional premium rating systems. Twenty five key stakeholders in Malta, a country with an insurance industry that represents others in microcosm, were interviewed to develop our analysis. We assert that local insurers have interests in such insurance schemes as enhanced fleet management and monitoring translate into an improved insurance risk. The findings presented here have implications for all stakeholders as we argue that telematics enhance fleet management, TBI improves risk management for insurers and adoption of this technology is dependent on telematics providers increasing the perceived control by insurers over managing this technology.2015-12-22T16:43:17ZPhacoemulsification Surgery in Eyes with Neovascular Age-Related Macular DegenerationGrixti, A.Papavasileiou, E.Cortis, DominicKumar, B. V.Prasad, S.http://hdl.handle.net/2381/361182015-12-23T03:05:25Z2015-12-22T14:47:21ZTitle: Phacoemulsification Surgery in Eyes with Neovascular Age-Related Macular Degeneration
Authors: Grixti, A.; Papavasileiou, E.; Cortis, Dominic; Kumar, B. V.; Prasad, S.
Abstract: Purpose. To evaluate the visual outcomes and effect of phacoemulsification surgery on the progression of neovascular agerelated
macular degeneration (AMD). Methods. Retrospective, noncomparative, and interventional case series. Thirty eyes from 29
subjects with neovascular AMD treated with intravitreal antivascular endothelial growth factor (VEGF) injections who underwent
phacoemulsification and had a postsurgery follow-up of 6 months were included. LogMAR best corrected visual acuity (BCVA)
was assessed preoperatively; 1 month, 3 months, and 6 months postoperatively; and finally at the last visit. The frequency of antiVEGF
therapy, calculated as the number of intravitreal injections per month, and central macular thickness (CMT) before and
after cataract surgery were determined. Results. Median (range) logMAR BCVA was 0.69 (0.16 to 1.32) preoperatively; 0.55 (−0.04
to 1.32) at 1 month, 0.52 (−0.1 to 1.32) at 3 months, and 0.50 (0.0 to 1.32) at 6 months postoperatively; and 0.6 (0.0 to 1.4) at final
visit (𝑃 = 0.0011). There was no difference in the frequency of anti-VEGF injections between the immediate 6 months before
and after phacoemulsification, which was equal to 0.1667 injections per month (𝑃 = 0.6377). Median CMT measured 203 𝜇m
preoperatively, which temporarily increased to 238 𝜇m at 1 month after surgery (𝑃 = 0.0093) and then spontaneously returned
to baseline, measuring 212.5 𝜇m at 3 months postoperatively (𝑃 = 0.3811). Conclusion. Phacoemulsification surgery significantly
improved vision in patients with neovascular AMD, with no increased need for anti-VEGF injections to keep the macula dry
postoperatively2015-12-22T14:47:21ZAtiyah sequences, connections and characteristic forms for principal bundles over groupoids and stacksBiswas, IndranilNeumann, Frankhttp://hdl.handle.net/2381/361022015-12-19T03:18:59Z2015-12-18T12:05:34ZTitle: Atiyah sequences, connections and characteristic forms for principal bundles over groupoids and stacks
Authors: Biswas, Indranil; Neumann, Frank
Abstract: We construct connections and characteristic forms for principal bundles over groupoids and stacks in the differentiable, holomorphic and algebraic category using Atiyah exact sequences associated with transversal tangential distributions.; Nous construisons les connexions et formes caractéristiques pour les fibrés principaux sur
les groupoïdes et les champs dans la catégorie différentiable, holomorphe et algébrique à
l’aide des suites d’Atiyah associées aux distributions transversales tangentielles.2015-12-18T12:05:34ZMathematical Modelling of Plankton-Oxygen Dynamics Under the Climate ChangeSekerci, YadigarPetrovskii, Sergeihttp://hdl.handle.net/2381/360582015-12-12T03:11:55Z2015-12-11T16:00:50ZTitle: Mathematical Modelling of Plankton-Oxygen Dynamics Under the Climate Change
Authors: Sekerci, Yadigar; Petrovskii, Sergei
Abstract: Ocean dynamics is known to have a strong effect on the global climate change and on the composition of the atmosphere. In particular, it is estimated that about 70 % of the atmospheric oxygen is produced in the oceans due to the photosynthetic activity of phytoplankton. However, the rate of oxygen production depends on water temperature and hence can be affected by the global warming. In this paper, we address this issue theoretically by considering a model of a coupled plankton-oxygen dynamics where the rate of oxygen production slowly changes with time to account for the ocean warming. We show that a sustainable oxygen production is only possible in an intermediate range of the production rate. If, in the course of time, the oxygen production rate becomes too low or too high, the system's dynamics changes abruptly, resulting in the oxygen depletion and plankton extinction. Our results indicate that the depletion of atmospheric oxygen on global scale (which, if happens, obviously can kill most of life on Earth) is another possible catastrophic consequence of the global warming, a global ecological disaster that has been overlooked.2015-12-11T16:00:50ZThe centrifugal instability of the boundary-layer flow over slender rotating conesHussain, Z.Garrett, Stephen J.Stephen, S. O.http://hdl.handle.net/2381/360372015-12-11T03:05:26Z2015-12-10T09:45:42ZTitle: The centrifugal instability of the boundary-layer flow over slender rotating cones
Authors: Hussain, Z.; Garrett, Stephen J.; Stephen, S. O.
Abstract: Existing experimental and theoretical studies are discussed which lead to the clear hypothesis of a hitherto unidentified convective instability mode that dominates within the boundary-layer flow over slender rotating cones. The mode manifests as Görtler-type counter-rotating spiral vortices, indicative of a centrifugal mechanism. Although a formulation consistent with the classic rotating-disk problem has been successful in predicting the stability characteristics over broad cones, it is unable to identify such a centrifugal mode as the half-angle is reduced. An alternative formulation is developed and the governing equations solved using both short-wavelength asymptotic and numerical approaches to independently identify the centrifugal mode.2015-12-10T09:45:42ZHard Spheres at a Planar Hard Wall: Simulations and DFTDavidchack, Ruslan L.Laird, Brian B.Roth, Rolandhttp://hdl.handle.net/2381/335602015-12-18T03:08:41Z2015-11-16T10:35:08ZTitle: Hard Spheres at a Planar Hard Wall: Simulations and DFT
Authors: Davidchack, Ruslan L.; Laird, Brian B.; Roth, Roland
Abstract: Hard spheres are a central and important model reference system for both homogeneous and
inhomogeneous fluid systems. In this paper we present new high-precision molecular dynamics computer
simulations for a hard sphere fluid at a planar hard wall. For this system we present
benchmark data for the density profile ρ(z ) at various bulk densities, the wall surface free
energy γ, the excess adsorption Γ, and the excess volume [superscript v]ex , which is closely related to Γ. We
compare all benchmark quantities with predictions from state-of-the-art classical density
functional theory calculations within the framework of fundamental measure theory. While we find
overall good agreement between computer simulations and theory, significant deviations appear at
sufficiently high bulk densities.
Description: Supplementary data for this work can be found at http://hdl.handle.net/2381/335372015-11-16T10:35:08ZNon-Fickian diffusion and the accumulation of methane bubbles in deep-water sedimentsGoldobin, Dennis S.Brilliantov, N. V.Levesley, J.Lovell, M. A.Rochelle, C. A.Jackson, P. D.Haywood, A. M.Hunter, S. J.Rees, J. G.http://hdl.handle.net/2381/333522015-10-23T02:01:05Z2015-10-22T11:42:58ZTitle: Non-Fickian diffusion and the accumulation of methane bubbles in deep-water sediments
Authors: Goldobin, Dennis S.; Brilliantov, N. V.; Levesley, J.; Lovell, M. A.; Rochelle, C. A.; Jackson, P. D.; Haywood, A. M.; Hunter, S. J.; Rees, J. G.
Abstract: In the absence of fractures, methane bubbles in deep-water sediments can be immovably trapped within a porous matrix by surface tension. The dominant mechanism of transfer of gas mass therefore becomes the diffusion of gas molecules through porewater. The accurate description of this process requires non-Fickian diffusion to be accounted for, including both thermal diffusion and gravitational action. We evaluate the diffusive flux of aqueous methane considering non-Fickian diffusion and predict the existence of extensive bubble mass accumulation zones within deep-water sediments. The limitation on the hydrate deposit capacity is revealed; too weak deposits cannot reach the base of the hydrate stability zone and form any bubbly horizon.2015-10-22T11:42:58ZPatchy Invasion of Stage-Structured Alien Species with Short-Distance and Long-Distance Dispersal.Rodrigues, L. A.Mistro, D. C.Cara, E. R.Petrovskaya, N.Petrovskii, Sergeihttp://hdl.handle.net/2381/333072015-10-20T02:00:56Z2015-10-19T11:08:06ZTitle: Patchy Invasion of Stage-Structured Alien Species with Short-Distance and Long-Distance Dispersal.
Authors: Rodrigues, L. A.; Mistro, D. C.; Cara, E. R.; Petrovskaya, N.; Petrovskii, Sergei
Abstract: Understanding of spatiotemporal patterns arising in invasive species spread is necessary for successful management and control of harmful species, and mathematical modeling is widely recognized as a powerful research tool to achieve this goal. The conventional view of the typical invasion pattern as a continuous population traveling front has been recently challenged by both empirical and theoretical results revealing more complicated, alternative scenarios. In particular, the so-called patchy invasion has been a focus of considerable interest; however, its theoretical study was restricted to the case where the invasive species spreads by predominantly short-distance dispersal. Meanwhile, there is considerable evidence that the long-distance dispersal is not an exotic phenomenon but a strategy that is used by many species. In this paper, we consider how the patchy invasion can be modified by the effect of the long-distance dispersal and the effect of the fat tails of the dispersal kernels.
Description: The file associated with this record is under a 12-month embargo from publication in accordance with the publisher's self-archiving policy, available at http://www.springer.com/gp/open-access/authors-rights/self-archiving-policy/2124. The full text may be available in the publisher links provided above.2015-10-19T11:08:06ZApproximation with Random Bases: Pro et ContraGorban, Alexander N.Tyukin, Ivan Yu.Prokhorov, D. V.Sofeikov, Konstantin I.http://hdl.handle.net/2381/331472015-10-02T02:01:11Z2015-10-01T11:29:45ZTitle: 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 L2 norm of order O(1/N), where N is the number of elements. We show that both randomized and deterministic procedures are successful if additional information about the
families of functions to be approximated is provided. In the 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 http://www.sherpa.ac.uk/romeo/issn/0020-0255/2015-10-01T11:29:45ZOn the diagonal subalgebra of an Ext algebraGreen, Edward L.Snashall, NicoleSolberg, Ø.Zacharia, D.http://hdl.handle.net/2381/330852015-09-23T02:00:44Z2015-09-22T11:20:56ZTitle: On the diagonal subalgebra of an Ext algebra
Authors: Green, Edward L.; Snashall, Nicole; Solberg, Ø.; 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 Δ[subscript: M] of the Ext-algebra $\operatorname{Ext}_R^*(M,M)$ 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 Δ[subscript: M] is isomorphic to the graded center of the Koszul dual of R. [abstract with TEX support available at http://arxiv.org/abs/1412.4953]2015-09-22T11:20:56ZTrivial extensions of gentle algebras and Brauer graph algebrasSchroll, Sibyllehttp://hdl.handle.net/2381/330462015-09-21T10:14:05Z2015-09-15T09:03:50ZTitle: Trivial extensions of gentle algebras and Brauer graph algebras
Authors: Schroll, Sibylle
Abstract: We show that two well-studied 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 co-generator. 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.2015-09-15T09:03:50ZTime Dependent Diffusion as a Mean Field Counterpart of Levy Type Random WalkAhmed, D. A.Petrovskii, S.http://hdl.handle.net/2381/328062015-07-23T02:00:41Z2015-07-22T16:11:10ZTitle: Time Dependent Diffusion as a Mean Field Counterpart of Levy Type Random Walk
Authors: Ahmed, D. A.; Petrovskii, S.
Abstract: Insect trapping is commonly used in various pest insect monitoring programs as well as in many ecological field studies. An individual is said to be trapped if it falls within a well defined capturing zone, which it cannot escape. The accumulation of trapped individuals over time forms trap counts or alternatively, the flux of the population density into the trap. In this paper, we study the movement of insects whose dynamics are governed by time dependent diffusion and Lévy walks. We demonstrate that the diffusion model provides an alternative framework for the Cauchy type random walk (Lévy walk with Cauchy distributed steps). Furthermore, by calculating the trap counts using these two conceptually different movement models, we propose that trap counts for pests whose dynamics may be Lévy by nature can effectively be predicted by diffusive flux curves with time-dependent diffusivity.
Description: Mathematics Subject Classification: 82B41 / 60K35 / 35Q922015-07-22T16:11:10ZMathematical Modelling of Spatiotemporal Dynamics of Oxygen in a Plankton SystemSekerci, Y.Petrovskii, S.http://hdl.handle.net/2381/328042015-07-23T02:00:43Z2015-07-22T15:49:51ZTitle: Mathematical Modelling of Spatiotemporal Dynamics of Oxygen in a Plankton System
Authors: Sekerci, Y.; Petrovskii, S.
Abstract: Oxygen production due to phytoplankton photosynthesis is a crucial phenomenon underlying the dynamics of marine ecosystems. However, most of the existing literature focus on other aspects of the plankton community functioning, thus leaving the issue of the coupled oxygen-plankton dynamics understudied. In this paper, we consider a generic model of the oxygen-phytoplankton-zooplankton dynamics to make an insight into the basic properties of the plankton-oxygen interactions. The model is analyzed both analytically and numerically. We first consider the nonspatial model and show that it predicts possible oxygen depletion under certain environmental conditions. We then consider the spatially explicit model and show that it exhibits a rich variety of spatiotemporal patterns including travelling fronts of oxygen depletion, dynamical stabilization of unstable equilibrium and spatiotemporal chaos.
Description: Mathematics Subject Classification: 92D40 / 35B36 / 35Q92 / 37N252015-07-22T15:49:51ZStatistical mechanics of animal movement: Animals's decision-making can result in superdiffusive spreadTilles, Paulo F. C.Petrovskii, Sergei V.http://hdl.handle.net/2381/328032015-07-23T02:00:44Z2015-07-22T14:27:23ZTitle: Statistical mechanics of animal movement: Animals's decision-making can result in superdiffusive spread
Authors: Tilles, Paulo F. C.; Petrovskii, Sergei V.
Abstract: Peculiarities of individual animal movement and dispersal have been a major focus of recent research as they are thought to hold the key to the understanding of many phenomena in spatial ecology. Superdiffusive spread and long-distance dispersal have been observed in different species but the underlying biological mechanisms often remain obscure. In particular, the effect of relevant animal behavior has been largely unaddressed. In this paper, we show that a superdiffusive spread can arise naturally as a result of animal behavioral response to small-scale environmental stochasticity. Surprisingly, the emerging fast spread does not require the standard assumption about the fat tail of the dispersal kernel.2015-07-22T14:27:23ZThe Role of Host and Microbial Factors in the Pathogenesis of Pneumococcal Bacteraemia Arising from a Single Bacterial Cell BottleneckGerlini, A.Colomba, L.Furi, L.Braccini, T.Manso, A. S.Pammolli, A.Wang, BoVivi, A.Tassini, M.van Rooijen, N.Pozzi, G.Ricci, S.Andrew, P. W.Koedel, U.Moxon, E. R.Oggioni, M. R.http://hdl.handle.net/2381/327532015-09-01T09:41:42Z2015-07-20T12:51:16ZTitle: The Role of Host and Microbial Factors in the Pathogenesis of Pneumococcal Bacteraemia Arising from a Single Bacterial Cell Bottleneck
Authors: Gerlini, A.; Colomba, L.; Furi, L.; Braccini, T.; Manso, A. S.; Pammolli, A.; Wang, Bo; Vivi, A.; Tassini, M.; van Rooijen, N.; Pozzi, G.; Ricci, S.; Andrew, P. W.; Koedel, U.; Moxon, E. R.; Oggioni, M. R.
Abstract: The pathogenesis of bacteraemia after challenge with one million pneumococci of three isogenic variants was investigated. Sequential analyses of blood samples indicated that most episodes of bacteraemia were monoclonal events providing compelling evidence for a single bacterial cell bottleneck at the origin of invasive disease. With respect to host determinants, results identified novel properties of splenic macrophages and a role for neutrophils in early clearance of pneumococci. Concerning microbial factors, whole genome sequencing provided genetic evidence for the clonal origin of the bacteraemia and identified SNPs in distinct sub-units of F0/F1 ATPase in the majority of the ex vivo isolates. When compared to parental organisms of the inoculum, ex-vivo pneumococci with mutant alleles of the F0/F1 ATPase had acquired the capacity to grow at low pH at the cost of the capacity to grow at high pH. Although founded by a single cell, the genotypes of pneumococci in septicaemic mice indicate strong selective pressure for fitness, emphasising the within-host complexity of the pathogenesis of invasive disease.2015-07-20T12:51:16ZFeeding on Multiple Sources: Towards a Universal Parameterization of the Functional Response of a Generalist Predator Allowing for SwitchingMorozov, AndrewPetrovskii, Sergeihttp://hdl.handle.net/2381/326982015-07-15T02:00:52Z2015-07-14T14:59:44ZTitle: Feeding on Multiple Sources: Towards a Universal Parameterization of the Functional Response of a Generalist Predator Allowing for Switching
Authors: Morozov, Andrew; Petrovskii, Sergei
Abstract: Understanding of complex trophic interactions in ecosystems requires correct descriptions of the rate at which predators consume a variety of different prey species. Field and laboratory data on multispecies communities are rarely sufficient and usually cannot provide an unambiguous test for the theory. As a result, the conventional way of constructing a multi-prey functional response is speculative, and often based on assumptions that are difficult to verify. Predator responses allowing for prey selectivity and active switching are thought to be more biologically relevant compared to the standard proportion-based consumption. However, here we argue that the functional responses with switching may not be applicable to communities with a broad spectrum of resource types. We formulate a set of general rules that a biologically sound parameterization of a predator functional response should satisfy, and show that all existing formulations for the multispecies response with prey selectivity and switching fail to do so. Finally, we propose a universal framework for parameterization of a multi-prey functional response by combining patterns of food selectivity and proportion-based feeding.
Description: PMCID: PMC37834412015-07-14T14:59:44ZRevisiting the Role of Individual Variability in Population Persistence and StabilityMorozov, AndrewPasternak, A. F.Arashkevich, E. G.http://hdl.handle.net/2381/326922015-07-15T02:00:55Z2015-07-14T14:27:15ZTitle: Revisiting the Role of Individual Variability in Population Persistence and Stability
Authors: Morozov, Andrew; Pasternak, A. F.; Arashkevich, E. G.
Abstract: Populations often exhibit a pronounced degree of individual variability and this can be important when constructing ecological models. In this paper, we revisit the role of inter-individual variability in population persistence and stability under predation pressure. As a case study, we consider interactions between a structured population of zooplankton grazers and their predators. Unlike previous structured population models, which only consider variability of individuals according to the age or body size, we focus on physiological and behavioural structuring. We first experimentally demonstrate a high degree of variation of individual consumption rates in three dominant species of herbivorous copepods (Calanus finmarchicus, Calanus glacialis, Calanus euxinus) and show that this disparity implies a pronounced variation in the consumption capacities of individuals. Then we construct a parsimonious predator-prey model which takes into account the intra-population variability of prey individuals according to behavioural traits: effectively, each organism has a 'personality' of its own. Our modelling results show that structuring of prey according to their growth rate and vulnerability to predation can dampen predator-prey cycles and enhance persistence of a species, even if the resource stock for prey is unlimited. The main mechanism of efficient top-down regulation is shown to work by letting the prey population become dominated by less vulnerable individuals when predator densities are high, while the trait distribution recovers when the predator densities are low.2015-07-14T14:27:15ZGeneral H-theorem and Entropies that Violate the Second LawGorban, Alexander N.http://hdl.handle.net/2381/326552015-07-15T02:00:34Z2015-07-14T09:29:36ZTitle: General H-theorem and Entropies that Violate the Second Law
Authors: Gorban, Alexander N.
Abstract: H-theorem states that the entropy production is nonnegative and, therefore, the entropy of a closed system should monotonically change in time. In information processing, the entropy production is positive for random transformation of signals (the information processing lemma). Originally, the H-theorem and the information processing lemma were proved for the classical Boltzmann-Gibbs-Shannon entropy and for the correspondent divergence (the relative entropy). Many new entropies and divergences have been proposed during last decades and for all of them the H-theorem is needed. This note proposes a simple and general criterion to check whether the H-theorem is valid for a convex divergence H and demonstrates that some of the popular divergences obey no H-theorem. We consider systems with n states Ai that obey first order kinetics (master equation). A convex function H is a Lyapunov function for all master equations with given equilibrium if and only if its conditional minima properly describe the equilibria of pair transitions A[subscript: i] ⇌ A[subscript: j]. This theorem does not depend on the principle of detailed balance and is valid for general Markov kinetics. Elementary analysis of pair equilibria demonstrate that the popular Bregman divergences like Euclidian distance or Itakura-Saito distance in the space of distribution cannot be the universal Lyapunov functions for the first-order kinetics and can increase in Markov processes. Therefore, they violate the second law and the information processing lemma. In particular, for these measures of information (divergences) random manipulation with data may add information to data. The main results are extended to nonlinear generalized mass action law kinetic equations.2015-07-14T09:29:36ZOn Multiple Convolutions and Time ScalesEltayeb, HassanKılıçman, AdemFisher, Brianhttp://hdl.handle.net/2381/326092015-07-14T02:00:29Z2015-07-13T10:41:59ZTitle: On Multiple Convolutions and Time Scales
Authors: Eltayeb, Hassan; Kılıçman, Adem; Fisher, Brian
Abstract: The properties of the multiple Laplace transform and convolutions on a time scale are studied. Further, some related results are also obtained by utilizing the double Laplace transform. We also provide an example in order to illustrate the main result.2015-07-13T10:41:59ZInequalities and eigenvalues of Sturm-Liouville problems near a singular boundaryMarletta, MarcoEveritt, W. N.Zettl, A.http://hdl.handle.net/2381/324502015-07-01T02:00:25Z2015-06-30T09:16:49ZTitle: Inequalities and eigenvalues of Sturm-Liouville problems near a singular boundary
Authors: Marletta, Marco; Everitt, W. N.; Zettl, A.
Abstract: We study the behavior of eigenvalues of Sturm-Liouville problems (SLP) when an endpoint of the underlying interval approaches a singularity.2015-06-30T09:16:49ZApproximation with Random Bases: Pro et ContraGorban, Alexander N.Tyukin, Ivan Yu.Prokhorov, D. V.Sofeikov, Konstantin I.http://hdl.handle.net/2381/324282015-10-01T11:29:46Z2015-06-26T09:00:01ZTitle: 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, 68W202015-06-26T09:00:01ZLeaders do not look back, or do they?Gorban, A. N.Jarman, N.Steur, E.van Leeuwen, C.Tyukin, I.http://hdl.handle.net/2381/322112015-06-30T01:45:08Z2015-05-07T11:08:33ZTitle: 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 co-exist 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, 92B252015-05-07T11:08:33ZClassification of symmetric special biserial algebras with at most one non-uniserial indecomposable projectiveSnashall, NicoleTaillefer, Rachelhttp://hdl.handle.net/2381/321582015-09-22T11:09:21Z2015-05-07T10:12:47ZTitle: Classification of symmetric special biserial algebras with at most one non-uniserial indecomposable projective
Authors: Snashall, Nicole; Taillefer, Rachel
Abstract: We consider a natural generalisation of symmetric Nakayama algebras, namely, symmetric special biserial algebras with at most one non-uniserial indecomposable projective module. We describe the basic algebras explicitly by quiver and relations, then classify them up to derived equivalence and up to stable equivalence of Morita type. This includes the algebras of [Bocian-Holm-Skowro\'nski, J. Pure Appl. Algebra 2004], where they study the weakly symmetric algebras of Euclidean type, as well as some algebras of dihedral type.
Description: To appear in the Proceedings of the Edinburgh Mathematical Society. Will appear in 2015 - page proofs have been returned to journal. No date/volume/pages are available yet.2015-05-07T10:12:47ZThe center of a convex set and capital allocationGrechuk, Bogdanhttp://hdl.handle.net/2381/320912015-05-01T02:00:54Z2015-04-30T14:53:03ZTitle: 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 non-empty 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.2015-04-30T14:53:03ZComputational diagnosis of canine lymphomaMirkes, E. M.Alexandrakis, I.Slater, K.Tuli, R.Gorban, A. N.http://hdl.handle.net/2381/320722015-04-28T02:00:14Z2015-04-27T14:00:05ZTitle: 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, C-Reactive Protein and Haptoglobin. Data mining methods were then applied to the collected data for the development of an online computer-assisted 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 user-friendly visualization.2015-04-27T14:00:05ZIs it possible to predict long-term success with k-NN? Case study of four market indices (FTSE100, DAX, HANGSENG, NASDAQ)Shi, Y.Gorban, A. N.Yang, T. Y.http://hdl.handle.net/2381/320352015-04-22T02:00:17Z2015-04-21T14:32:46ZTitle: Is it possible to predict long-term success with k-NN? 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 02-Jul-2009 to 29-Jun-2012.We compare their performance ain two time frames: initial frame three months at the beginning (02/06/2009-30/09/2009) and the final three month frame (02/04/2012-29/06/2012).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 winner-looser separation in the initial fragments of the daily closing prices log-returns time series.The Leave-One-Out Cross-Validation with k-NN algorithm is applied on the daily log-return 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 long-term success. The correlation distance matrix histograms and 2-D/3-D 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.2015-04-21T14:32:46ZMultiscale principal component analysisAkinduko, A. A.Gorban, Alexander N.http://hdl.handle.net/2381/320092015-04-17T02:00:19Z2015-04-16T13:57:07ZTitle: 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.2015-04-16T13:57:07Z