DSpace Collection:
http://hdl.handle.net/2381/3823
20160213T15:08:56Z

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

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

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

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

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

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

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

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

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

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

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

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

Phacoemulsification Surgery in Eyes with Neovascular AgeRelated Macular Degeneration
http://hdl.handle.net/2381/36118
Title: Phacoemulsification Surgery in Eyes with Neovascular AgeRelated Macular Degeneration
Authors: Grixti, A.; Papavasileiou, E.; Cortis, Dominic; Kumar, B. V.; Prasad, S.
Abstract: Purpose. To evaluate the visual outcomes and effect of phacoemulsification surgery on the progression of neovascular agerelated
macular degeneration (AMD). Methods. Retrospective, noncomparative, and interventional case series. Thirty eyes from 29
subjects with neovascular AMD treated with intravitreal antivascular endothelial growth factor (VEGF) injections who underwent
phacoemulsification and had a postsurgery followup of 6 months were included. LogMAR best corrected visual acuity (BCVA)
was assessed preoperatively; 1 month, 3 months, and 6 months postoperatively; and finally at the last visit. The frequency of antiVEGF
therapy, calculated as the number of intravitreal injections per month, and central macular thickness (CMT) before and
after cataract surgery were determined. Results. Median (range) logMAR BCVA was 0.69 (0.16 to 1.32) preoperatively; 0.55 (−0.04
to 1.32) at 1 month, 0.52 (−0.1 to 1.32) at 3 months, and 0.50 (0.0 to 1.32) at 6 months postoperatively; and 0.6 (0.0 to 1.4) at final
visit (𝑃 = 0.0011). There was no difference in the frequency of antiVEGF injections between the immediate 6 months before
and after phacoemulsification, which was equal to 0.1667 injections per month (𝑃 = 0.6377). Median CMT measured 203 𝜇m
preoperatively, which temporarily increased to 238 𝜇m at 1 month after surgery (𝑃 = 0.0093) and then spontaneously returned
to baseline, measuring 212.5 𝜇m at 3 months postoperatively (𝑃 = 0.3811). Conclusion. Phacoemulsification surgery significantly
improved vision in patients with neovascular AMD, with no increased need for antiVEGF injections to keep the macula dry
postoperatively
20151222T14:47:21Z

Atiyah sequences, connections and characteristic forms for principal bundles over groupoids and stacks
http://hdl.handle.net/2381/36102
Title: 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.
20151218T12:05:34Z

Mathematical Modelling of PlanktonOxygen Dynamics Under the Climate Change
http://hdl.handle.net/2381/36058
Title: Mathematical Modelling of PlanktonOxygen 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 planktonoxygen 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.
20151211T16:00:50Z

The centrifugal instability of the boundarylayer flow over slender rotating cones
http://hdl.handle.net/2381/36037
Title: The centrifugal instability of the boundarylayer 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 boundarylayer flow over slender rotating cones. The mode manifests as Görtlertype counterrotating spiral vortices, indicative of a centrifugal mechanism. Although a formulation consistent with the classic rotatingdisk problem has been successful in predicting the stability characteristics over broad cones, it is unable to identify such a centrifugal mode as the halfangle is reduced. An alternative formulation is developed and the governing equations solved using both shortwavelength asymptotic and numerical approaches to independently identify the centrifugal mode.
20151210T09:45:42Z

Hard Spheres at a Planar Hard Wall: Simulations and DFT
http://hdl.handle.net/2381/33560
Title: 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 highprecision 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 stateoftheart 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/2381/33537
20151116T10:35:08Z

NonFickian diffusion and the accumulation of methane bubbles in deepwater sediments
http://hdl.handle.net/2381/33352
Title: NonFickian diffusion and the accumulation of methane bubbles in deepwater 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 deepwater 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 nonFickian diffusion to be accounted for, including both thermal diffusion and gravitational action. We evaluate the diffusive flux of aqueous methane considering nonFickian diffusion and predict the existence of extensive bubble mass accumulation zones within deepwater 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.
20151022T11:42:58Z

Patchy Invasion of StageStructured Alien Species with ShortDistance and LongDistance Dispersal.
http://hdl.handle.net/2381/33307
Title: Patchy Invasion of StageStructured Alien Species with ShortDistance and LongDistance 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 socalled 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 shortdistance dispersal. Meanwhile, there is considerable evidence that the longdistance 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 longdistance dispersal and the effect of the fat tails of the dispersal kernels.
Description: The file associated with this record is under a 12month embargo from publication in accordance with the publisher's selfarchiving policy, available at http://www.springer.com/gp/openaccess/authorsrights/selfarchivingpolicy/2124. The full text may be available in the publisher links provided above.
20151019T11:08:06Z

Approximation with Random Bases: Pro et Contra
http://hdl.handle.net/2381/33147
Title: Approximation with Random Bases: Pro et Contra
Authors: Gorban, Alexander N.; Tyukin, Ivan Yu.; Prokhorov, D. V.; Sofeikov, Konstantin I.
Abstract: In this work we discuss the problem of selecting suitable approximators from families of parameterized elementary functions that are known to be dense in a Hilbert space of functions. We consider and analyze published procedures, both randomized and deterministic, for selecting elements from these families that have been shown to ensure the rate of convergence in 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/00200255/
20151001T11:29:45Z

On the diagonal subalgebra of an Ext algebra
http://hdl.handle.net/2381/33085
Title: 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 Rmodule. We study a graded subalgebra Δ[subscript: M] of the Extalgebra $\operatorname{Ext}_R^*(M,M)$ 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]
20150922T11:20:56Z

Trivial extensions of gentle algebras and Brauer graph algebras
http://hdl.handle.net/2381/33046
Title: Trivial extensions of gentle algebras and Brauer graph algebras
Authors: Schroll, Sibylle
Abstract: We show that two wellstudied classes of tame algebras coincide: namely, the class of symmetric special biserial algebras coincides with the class of Brauer graph algebras. We then explore the connection between gentle algebras and symmetric special biserial algebras by explicitly determining the trivial extension of a gentle algebra by its minimal injective cogenerator. This is a symmetric special biserial algebra and hence a Brauer graph algebra of which we explicitly give the Brauer graph. We further show that a Brauer graph algebra gives rise, via admissible cuts, to many gentle algebras and that the trivial extension of a gentle algebra obtained via an admissible cut is the original Brauer graph algebra.As a consequence we prove that the trivial extension of a Jacobian algebra of an ideal triangulation of a Riemann surface with marked points in the boundary is isomorphic to the Brauer graph algebra with Brauer graph given by the arcs of the triangulation.
20150915T09:03:50Z

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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