@article{Reich2012, author = {Reich, Sebastian}, title = {A Gaussian-mixture ensemble transform filter}, series = {Quarterly journal of the Royal Meteorological Society}, volume = {138}, journal = {Quarterly journal of the Royal Meteorological Society}, number = {662}, publisher = {Wiley-Blackwell}, address = {Malden}, issn = {0035-9009}, doi = {10.1002/qj.898}, pages = {222 -- 233}, year = {2012}, abstract = {We generalize the popular ensemble Kalman filter to an ensemble transform filter, in which the prior distribution can take the form of a Gaussian mixture or a Gaussian kernel density estimator. The design of the filter is based on a continuous formulation of the Bayesian filter analysis step. We call the new filter algorithm the ensemble Gaussian-mixture filter (EGMF). The EGMF is implemented for three simple test problems (Brownian dynamics in one dimension, Langevin dynamics in two dimensions and the three-dimensional Lorenz-63 model). It is demonstrated that the EGMF is capable of tracking systems with non-Gaussian uni- and multimodal ensemble distributions.}, language = {en} } @article{NehringZessin2012, author = {Nehring, Benjamin and Zessin, Hans}, title = {A representation of the moment measures of the general ideal Boe gas}, series = {Mathematische Nachrichten}, volume = {285}, journal = {Mathematische Nachrichten}, number = {7}, publisher = {Wiley-VCH}, address = {Weinheim}, issn = {0025-584X}, doi = {10.1002/mana.201000111}, pages = {878 -- 888}, year = {2012}, abstract = {We reconsider the fundamental work of Fichtner 2 and exhibit the permanental structure of the ideal Bose gas again, using a new approach which combines a characterization of infinitely divisible random measures (due to Kerstan, Kummer and Matthes 4, 6 and Mecke 9, 10) with a decomposition of the moment measures into its factorial measures due to Krickeberg 5. To be more precise, we exhibit the moment measures of all orders of the general ideal Bose gas in terms of certain loop integrals. This representation can be considered as a point process analogue of the old idea of Symanzik 15 that local times and self-crossings of the Brownian motion can be used as a tool in quantum field theory. Behind the notion of a general ideal Bose gas there is a class of infinitely divisible point processes of all orders with a Levy-measure belonging to some large class of measures containing that of the classical ideal Bose gas considered by Fichtner. It is well-known that the calculation of moments of higher order of point processes is notoriously complicated. See for instance Krickebergs calculations for the Poisson or the Cox process in 5. Relations to the work of Shirai, Takahashi 12 and Soshnikov 14 on permanental and determinantal processes are outlined.}, language = {en} } @article{BergemannReich2012, author = {Bergemann, Kay and Reich, Sebastian}, title = {An ensemble Kalman-Bucy filter for continuous data assimilation}, series = {Meteorologische Zeitschrift}, volume = {21}, journal = {Meteorologische Zeitschrift}, number = {3}, publisher = {Schweizerbart}, address = {Stuttgart}, issn = {0941-2948}, doi = {10.1127/0941-2948/2012/0307}, pages = {213 -- 219}, year = {2012}, abstract = {The ensemble Kalman filter has emerged as a promising filter algorithm for nonlinear differential equations subject to intermittent observations. In this paper, we extend the well-known Kalman-Bucy filter for linear differential equations subject to continous observations to the ensemble setting and nonlinear differential equations. The proposed filter is called the ensemble Kalman-Bucy filter and its performance is demonstrated for a simple mechanical model (Langevin dynamics) subject to incremental observations of its velocity.}, language = {en} } @article{HolschneiderNarteauShebalinetal.2012, author = {Holschneider, Matthias and Narteau, C. and Shebalin, P. and Peng, Z. and Schorlemmer, Danijel}, title = {Bayesian analysis of the modified Omori law}, series = {Journal of geophysical research : Solid earth}, volume = {117}, journal = {Journal of geophysical research : Solid earth}, number = {6089}, publisher = {American Geophysical Union}, address = {Washington}, issn = {2169-9313}, doi = {10.1029/2011JB009054}, pages = {12}, year = {2012}, abstract = {In order to examine variations in aftershock decay rate, we propose a Bayesian framework to estimate the {K, c, p}-values of the modified Omori law (MOL), lambda(t) = K(c + t)(-p). The Bayesian setting allows not only to produce a point estimator of these three parameters but also to assess their uncertainties and posterior dependencies with respect to the observed aftershock sequences. Using a new parametrization of the MOL, we identify the trade-off between the c and p-value estimates and discuss its dependence on the number of aftershocks. Then, we analyze the influence of the catalog completeness interval [t(start), t(stop)] on the various estimates. To test this Bayesian approach on natural aftershock sequences, we use two independent and non-overlapping aftershock catalogs of the same earthquakes in Japan. Taking into account the posterior uncertainties, we show that both the handpicked (short times) and the instrumental (long times) catalogs predict the same ranges of parameter values. We therefore conclude that the same MOL may be valid over short and long times.}, language = {en} } @article{BettenbuehlRusconiEngbertetal.2012, author = {Bettenb{\"u}hl, Mario and Rusconi, Marco and Engbert, Ralf and Holschneider, Matthias}, title = {Bayesian selection of Markov Models for symbol sequences application to microsaccadic eye movements}, series = {PLoS one}, volume = {7}, journal = {PLoS one}, number = {9}, publisher = {PLoS}, address = {San Fransisco}, issn = {1932-6203}, doi = {10.1371/journal.pone.0043388}, pages = {10}, year = {2012}, abstract = {Complex biological dynamics often generate sequences of discrete events which can be described as a Markov process. The order of the underlying Markovian stochastic process is fundamental for characterizing statistical dependencies within sequences. As an example for this class of biological systems, we investigate the Markov order of sequences of microsaccadic eye movements from human observers. We calculate the integrated likelihood of a given sequence for various orders of the Markov process and use this in a Bayesian framework for statistical inference on the Markov order. Our analysis shows that data from most participants are best explained by a first-order Markov process. This is compatible with recent findings of a statistical coupling of subsequent microsaccade orientations. Our method might prove to be useful for a broad class of biological systems.}, language = {en} } @article{BlanchardMathe2012, author = {Blanchard, Gilles and Mathe, Peter}, title = {Discrepancy principle for statistical inverse problems with application to conjugate gradient iteration}, series = {Inverse problems : an international journal of inverse problems, inverse methods and computerised inversion of data}, volume = {28}, journal = {Inverse problems : an international journal of inverse problems, inverse methods and computerised inversion of data}, number = {11}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {0266-5611}, doi = {10.1088/0266-5611/28/11/115011}, pages = {23}, year = {2012}, abstract = {The authors discuss the use of the discrepancy principle for statistical inverse problems, when the underlying operator is of trace class. Under this assumption the discrepancy principle is well defined, however a plain use of it may occasionally fail and it will yield sub-optimal rates. Therefore, a modification of the discrepancy is introduced, which corrects both of the above deficiencies. For a variety of linear regularization schemes as well as for conjugate gradient iteration it is shown to yield order optimal a priori error bounds under general smoothness assumptions. A posteriori error control is also possible, however at a sub-optimal rate, in general. This study uses and complements previous results for bounded deterministic noise.}, language = {en} } @article{Wallenta2012, author = {Wallenta, D.}, title = {Elliptic quasicomplexes on compact closed manifolds}, series = {Integral equations and operator theor}, volume = {73}, journal = {Integral equations and operator theor}, number = {4}, publisher = {Springer}, address = {Basel}, issn = {0378-620X}, doi = {10.1007/s00020-012-1983-7}, pages = {517 -- 536}, year = {2012}, abstract = {We consider quasicomplexes of pseudodifferential operators on a smooth compact manifold without boundary. To each quasicomplex we associate a complex of symbols. The quasicomplex is elliptic if this symbol complex is exact away from the zero section. We prove that elliptic quasicomplexes are Fredholm. Moreover, we introduce the Euler characteristic for elliptic quasicomplexes and prove a generalisation of the Atiyah-Singer index theorem.}, language = {en} } @article{SchachtschneiderHolschneiderMandea2012, author = {Schachtschneider, R. and Holschneider, Matthias and Mandea, M.}, title = {Error distribution in regional modelling of the geomagnetic field}, series = {Geophysical journal international}, volume = {191}, journal = {Geophysical journal international}, number = {3}, publisher = {Wiley-Blackwell}, address = {Hoboken}, issn = {0956-540X}, doi = {10.1111/j.1365-246X.2012.05675.x}, pages = {1015 -- 1024}, year = {2012}, abstract = {In this study we analyse the error distribution in regional models of the geomagnetic field. Our main focus is to investigate the distribution of errors when combining two regional patches to obtain a global field from regional ones. To simulate errors in overlapping patches we choose two different data region shapes that resemble that scenario. First, we investigate the errors in elliptical regions and secondly we choose a region obtained from two overlapping circular spherical caps. We conduct a Monte-Carlo simulation using synthetic data to obtain the expected mean errors. For the elliptical regions the results are similar to the ones obtained for circular spherical caps: the maximum error at the boundary decreases towards the centre of the region. A new result emerges as errors at the boundary vary with azimuth, being largest in the major axis direction and minimal in the minor axis direction. Inside the region there is an error decay towards a minimum at the centre at a rate similar to the one in circular regions. In the case of two combined circular regions there is also an error decay from the boundary towards the centre. The minimum error occurs at the centre of the combined regions. The maximum error at the boundary occurs on the line containing the two cap centres, the minimum in the perpendicular direction where the two circular cap boundaries meet. The large errors at the boundary are eliminated by combining regional patches. We propose an algorithm for finding the boundary region that is applicable to irregularly shaped model regions.}, language = {en} } @article{FeherWhelanMueller2012, author = {Feher, Kristen and Whelan, James and M{\"u}ller, Samuel}, title = {Exploring multicollinearity using a random matrix theory approach}, series = {Statistical applications in genetics and molecular biology}, volume = {11}, journal = {Statistical applications in genetics and molecular biology}, number = {3}, publisher = {De Gruyter}, address = {Berlin}, issn = {1544-6115}, doi = {10.1515/1544-6115.1668}, pages = {35}, year = {2012}, abstract = {Clustering of gene expression data is often done with the latent aim of dimension reduction, by finding groups of genes that have a common response to potentially unknown stimuli. However, what is poorly understood to date is the behaviour of a low dimensional signal embedded in high dimensions. This paper introduces a multicollinear model which is based on random matrix theory results, and shows potential for the characterisation of a gene cluster's correlation matrix. This model projects a one dimensional signal into many dimensions and is based on the spiked covariance model, but rather characterises the behaviour of the corresponding correlation matrix. The eigenspectrum of the correlation matrix is empirically examined by simulation, under the addition of noise to the original signal. The simulation results are then used to propose a dimension estimation procedure of clusters from data. Moreover, the simulation results warn against considering pairwise correlations in isolation, as the model provides a mechanism whereby a pair of genes with 'low' correlation may simply be due to the interaction of high dimension and noise. Instead, collective information about all the variables is given by the eigenspectrum.}, language = {en} } @article{ShebalinNarteauHolschneider2012, author = {Shebalin, Peter and Narteau, Clement and Holschneider, Matthias}, title = {From alarm-based to rate-based earthquake forecast models}, series = {Bulletin of the Seismological Society of America}, volume = {102}, journal = {Bulletin of the Seismological Society of America}, number = {1}, publisher = {Seismological Society of America}, address = {Albany}, issn = {0037-1106}, doi = {10.1785/0120110126}, pages = {64 -- 72}, year = {2012}, abstract = {We propose a conversion method from alarm-based to rate-based earthquake forecast models. A differential probability gain g(alarm)(ref) is the absolute value of the local slope of the Molchan trajectory that evaluates the performance of the alarm-based model with respect to the chosen reference model. We consider that this differential probability gain is constant over time. Its value at each point of the testing region depends only on the alarm function value. The rate-based model is the product of the event rate of the reference model at this point multiplied by the corresponding differential probability gain. Thus, we increase or decrease the initial rates of the reference model according to the additional amount of information contained in the alarm-based model. Here, we apply this method to the Early Aftershock STatistics (EAST) model, an alarm-based model in which early aftershocks are used to identify space-time regions with a higher level of stress and, consequently, a higher seismogenic potential. The resulting rate-based model shows similar performance to the original alarm-based model for all ranges of earthquake magnitude in both retrospective and prospective tests. This conversion method offers the opportunity to perform all the standard evaluation tests of the earthquake testing centers on alarm-based models. In addition, we infer that it can also be used to consecutively combine independent forecast models and, with small modifications, seismic hazard maps with short- and medium-term forecasts.}, language = {en} } @article{IochumLevyVassilevich2012, author = {Iochum, B. and Levy, C. and Vassilevich, D. V.}, title = {Global and local aspects of spectral actions}, series = {Journal of physics : A, Mathematical and theoretical}, volume = {45}, journal = {Journal of physics : A, Mathematical and theoretical}, number = {37}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1751-8113}, doi = {10.1088/1751-8113/45/37/374020}, pages = {19}, year = {2012}, abstract = {The principal object in noncommutative geometry is the spectral triple consisting of an algebra A, a Hilbert space H and a Dirac operator D. Field theories are incorporated in this approach by the spectral action principle, which sets the field theory action to Tr f (D-2/Lambda(2)), where f is a real function such that the trace exists and Lambda is a cutoff scale. In the low-energy (weak-field) limit, the spectral action reproduces reasonably well the known physics including the standard model. However, not much is known about the spectral action beyond the low-energy approximation. In this paper, after an extensive introduction to spectral triples and spectral actions, we study various expansions of the spectral actions (exemplified by the heat kernel). We derive the convergence criteria. For a commutative spectral triple, we compute the heat kernel on the torus up to the second order in gauge connection and consider limiting cases. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker's 75th birthday devoted to 'Applications of zeta functions and other spectral functions in mathematics and physics'.}, language = {en} } @article{ChengLenkoshi2012, author = {Cheng, Yuan and Lenkoshi, Alex}, title = {Hierarchical gaussian graphical models beyond reversible jump}, series = {Electronic journal of statistics}, volume = {6}, journal = {Electronic journal of statistics}, publisher = {Institute of Mathematical Statistics}, address = {Cleveland}, issn = {1935-7524}, doi = {10.1214/12-EJS746}, pages = {2309 -- 2331}, year = {2012}, abstract = {The Gaussian Graphical Model (GGM) is a popular tool for incorporating sparsity into joint multivariate distributions. The G-Wishart distribution, a conjugate prior for precision matrices satisfying general GGM constraints, has now been in existence for over a decade. However, due to the lack of a direct sampler, its use has been limited in hierarchical Bayesian contexts, relegating mixing over the class of GGMs mostly to situations involving standard Gaussian likelihoods. Recent work has developed methods that couple model and parameter moves, first through reversible jump methods and later by direct evaluation of conditional Bayes factors and subsequent resampling. Further, methods for avoiding prior normalizing constant calculations-a serious bottleneck and source of numerical instability-have been proposed. We review and clarify these developments and then propose a new methodology for GGM comparison that blends many recent themes. Theoretical developments and computational timing experiments reveal an algorithm that has limited computational demands and dramatically improves on computing times of existing methods. We conclude by developing a parsimonious multivariate stochastic volatility model that embeds GGM uncertainty in a larger hierarchical framework. The method is shown to be capable of adapting to swings in market volatility, offering improved calibration of predictive distributions.}, language = {en} } @article{MenzLatorreSchuetteetal.2012, author = {Menz, Stephan and Latorre, Juan C. and Sch{\"u}tte, Christof and Huisinga, Wilhelm}, title = {Hybrid stochastic-deterministic solution of the chemical master equation}, series = {Multiscale modeling \& simulation : a SIAM interdisciplinary journal}, volume = {10}, journal = {Multiscale modeling \& simulation : a SIAM interdisciplinary journal}, number = {4}, publisher = {Society for Industrial and Applied Mathematics}, address = {Philadelphia}, issn = {1540-3459}, doi = {10.1137/110825716}, pages = {1232 -- 1262}, year = {2012}, abstract = {The chemical master equation (CME) is the fundamental evolution equation of the stochastic description of biochemical reaction kinetics. In most applications it is impossible to solve the CME directly due to its high dimensionality. Instead, indirect approaches based on realizations of the underlying Markov jump process are used, such as the stochastic simulation algorithm (SSA). In the SSA, however, every reaction event has to be resolved explicitly such that it becomes numerically inefficient when the system's dynamics include fast reaction processes or species with high population levels. In many hybrid approaches, such fast reactions are approximated as continuous processes or replaced by quasi-stationary distributions in either a stochastic or a deterministic context. Current hybrid approaches, however, almost exclusively rely on the computation of ensembles of stochastic realizations. We present a novel hybrid stochastic-deterministic approach to solve the CME directly. Our starting point is a partitioning of the molecular species into discrete and continuous species that induces a partitioning of the reactions into discrete-stochastic and continuous-deterministic processes. The approach is based on a WKB (Wentzel-Kramers-Brillouin) ansatz for the conditional probability distribution function (PDF) of the continuous species (given a discrete state) in combination with Laplace's method of integral approximation. The resulting hybrid stochastic-deterministic evolution equations comprise a CME with averaged propensities for the PDF of the discrete species that is coupled to an evolution equation of the related expected levels of the continuous species for each discrete state. In contrast to indirect hybrid methods, the impact of the evolution of discrete species on the dynamics of the continuous species has to be taken into account explicitly. The proposed approach is efficient whenever the number of discrete molecular species is small. We illustrate the performance of the new hybrid stochastic-deterministic approach in an application to model systems of biological interest.}, language = {en} } @article{ShinReichFrank2012, author = {Shin, Seoleun and Reich, Sebastian and Frank, Jason}, title = {Hydrostatic Hamiltonian particle-mesh (HPM) methods for atmospheric modelling}, series = {Quarterly journal of the Royal Meteorological Society}, volume = {138}, journal = {Quarterly journal of the Royal Meteorological Society}, number = {666}, publisher = {Wiley-Blackwell}, address = {Hoboken}, issn = {0035-9009}, doi = {10.1002/qj.982}, pages = {1388 -- 1399}, year = {2012}, abstract = {We develop a hydrostatic Hamiltonian particle-mesh (HPM) method for efficient long-term numerical integration of the atmosphere. In the HPM method, the hydrostatic approximation is interpreted as a holonomic constraint for the vertical position of particles. This can be viewed as defining a set of vertically buoyant horizontal meshes, with the altitude of each mesh point determined so as to satisfy the hydrostatic balance condition and with particles modelling horizontal advection between the moving meshes. We implement the method in a vertical-slice model and evaluate its performance for the simulation of idealized linear and nonlinear orographic flow in both dry and moist environments. The HPM method is able to capture the basic features of the gravity wave to a degree of accuracy comparable with that reported in the literature. The numerical solution in the moist experiment indicates that the influence of moisture on wave characteristics is represented reasonably well and the reduction of momentum flux is in good agreement with theoretical analysis.}, language = {en} } @article{KurtenbachEickerMayerGuerretal.2012, author = {Kurtenbach, E. and Eicker, A. and Mayer-Guerr, T. and Holschneider, Matthias and Hayn, M. and Fuhrmann, M. and Kusche, J.}, title = {Improved daily GRACE gravity field solutions using a Kalman smoother}, series = {Journal of geodynamics}, volume = {59}, journal = {Journal of geodynamics}, number = {3}, publisher = {Elsevier}, address = {Oxford}, issn = {0264-3707}, doi = {10.1016/j.jog.2012.02.006}, pages = {39 -- 48}, year = {2012}, abstract = {Different GRACE data analysis centers provide temporal variations of the Earth's gravity field as monthly, 10-daily or weekly solutions. These temporal mean fields cannot model the variations occurring during the respective time span. The aim of our approach is to extract as much temporal information as possible out of the given GRACE data. Therefore the temporal resolution shall be increased with the goal to derive daily snapshots. Yet, such an increase in temporal resolution is accompanied by a loss of redundancy and therefore in a reduced accuracy if the daily solutions are calculated individually. The approach presented here therefore introduces spatial and temporal correlations of the expected gravity field signal derived from geophysical models in addition to the daily observations, thus effectively constraining the spatial and temporal evolution of the GRACE solution. The GRACE data processing is then performed within the framework of a Kalman filter and smoother estimation procedure. The approach is at first investigated in a closed-loop simulation scenario and then applied to the original GRACE observations (level-1B data) to calculate daily solutions as part of the gravity field model ITG-Grace2010. Finally, the daily models are compared to vertical GPS station displacements and ocean bottom pressure observations. From these comparisons it can be concluded that particular in higher latitudes the daily solutions contain high-frequent temporal gravity field information and represent an improvement to existing geophysical models.}, language = {en} } @article{Baumgaertel2012, author = {Baumg{\"a}rtel, Hellmut}, title = {On a critical radiation density in the Friedmann equation}, series = {Journal of mathematical physics}, volume = {53}, journal = {Journal of mathematical physics}, number = {12}, publisher = {American Institute of Physics}, address = {Melville}, issn = {0022-2488}, doi = {10.1063/1.4771668}, pages = {9}, year = {2012}, abstract = {The paper presents a classification of the basic types of admissible solutions of the general Friedmann equation with non-vanishing cosmological constant and for the case that radiation and matter do not couple. There are four distinct types. The classification uses first the discriminant of a polynomial of the third degree, closely related to the right hand side of the Friedmann equation. The decisive term is then a critical radiation density which can be calculated explicitly.}, language = {en} } @article{PfaeffleStephan2012, author = {Pf{\"a}ffle, Frank and Stephan, Christoph A.}, title = {On gravity, torsion and the spectral action principle}, series = {Journal of functional analysis}, volume = {262}, journal = {Journal of functional analysis}, number = {4}, publisher = {Elsevier}, address = {San Diego}, issn = {0022-1236}, doi = {10.1016/j.jfa.2011.11.013}, pages = {1529 -- 1565}, year = {2012}, abstract = {We consider compact Riemannian spin manifolds without boundary equipped with orthogonal connections. We investigate the induced Dirac operators and the associated commutative spectral triples. In case of dimension four and totally anti-symmetric torsion we compute the Chamseddine-Connes spectral action, deduce the equations of motions and discuss critical points.}, language = {en} } @article{EichmairMetzger2012, author = {Eichmair, Michael and Metzger, Jan}, title = {On large volume preserving stable CMC surfaces in initial data sets}, series = {Journal of differential geometry}, volume = {91}, journal = {Journal of differential geometry}, number = {1}, publisher = {International Press of Boston}, address = {Somerville}, issn = {0022-040X}, pages = {81 -- 102}, year = {2012}, abstract = {Let (M, g) be a complete 3-dimensional asymptotically flat manifold with everywhere positive scalar curvature. We prove that, given a compact subset K subset of M, all volume preserving stable constant mean curvature surfaces of sufficiently large area will avoid K. This complements the results of G. Huisken and S.-T. Yau [17] and of J. Qing and G. Tian [26] on the uniqueness of large volume preserving stable constant mean curvature spheres in initial data sets that are asymptotically close to Schwarzschild with mass m > 0. The analysis in [17] and [26] takes place in the asymptotic regime of M. Here we adapt ideas from the minimal surface proof of the positive mass theorem [32] by R. Schoen and S.-T. Yau and develop geometric properties of volume preserving stable constant mean curvature surfaces to handle surfaces that run through the part of M that is far from Euclidean.}, language = {en} } @article{GauthierTarkhanov2012, author = {Gauthier, P. M. and Tarkhanov, Nikolai Nikolaevich}, title = {On the instability of the Riemann hypothesis for curves over finite fields}, series = {Journal of approximation theory}, volume = {164}, journal = {Journal of approximation theory}, number = {4}, publisher = {Elsevier}, address = {San Diego}, issn = {0021-9045}, doi = {10.1016/j.jat.2011.12.002}, pages = {504 -- 515}, year = {2012}, abstract = {We show that it is possible to approximate the zeta-function of a curve over a finite field by meromorphic functions which satisfy the same functional equation and moreover satisfy (respectively do not satisfy) an analog of the Riemann hypothesis. In the other direction, it is possible to approximate holomorphic functions by simple manipulations of such a zeta-function. No number theory is required to understand the theorems and their proofs, for it is known that the zeta-functions of curves over finite fields are very explicit meromorphic functions. We study the approximation properties of these meromorphic functions.}, language = {en} } @article{DimitrovaKoppitz2012, author = {Dimitrova, Ilinka and Koppitz, J{\"o}rg}, title = {On the monoid of all partial order-preserving extensive transformations}, series = {Communications in algebra}, volume = {40}, journal = {Communications in algebra}, number = {5}, publisher = {Taylor \& Francis Group}, address = {Philadelphia}, issn = {0092-7872}, doi = {10.1080/00927872.2011.557813}, pages = {1821 -- 1826}, year = {2012}, abstract = {A partial transformation alpha on an n-element chain X-n is called order-preserving if x <= y implies x alpha <= y alpha for all x, y in the domain of alpha and it is called extensive if x <= x alpha for all x in the domain of alpha. The set of all partial order-preserving extensive transformations on X-n forms a semiband POEn. We determine the maximal subsemigroups as well as the maximal subsemibands of POEn.}, language = {en} }