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Given a set of points in two dimensional space, statistically significant hotspot detection aims to detect locations where the concentration of points inside the hotspot is much higher than outside. Statistically significant hotspot detection is an important task in application domains such as epidemiology, ecology, criminology, etc. where it may reveal interesting information for domain experts. However, significant hotspot detection is challenging because of a lack of a generic technique for different hotspot patterns (i.e. shapes) and thus a large number of candidate hotspots to be enumerated and tested. Previous hotspot detection techniques focus on specific shapes (e.g. circles, rectangles, ellipses) to identify hotspot areas, but they cannot be used interchangeably which cause a vast variety of complicated and sometimes confusing techniques for each individual hotspot pattern. For example, a circular hotspot detection technique can not be used to discover a rectangular or an elliptical hotspot. In this paper, we propose a generic dual grid based pruning approach for hotspot detection that can be used for different hotspot patterns. We also present a cost analysis, a simplified experiment on the dataset size and a case study on a synthetic dataset to show the applicability of our proposed approach to circular hotspots.

A method is presented to calculate the elastodynamic Green's functions by using the equipartition principle. The imaginary parts are calculated as the average cross correlations of the displacement fields generated by the incidence of body and surface waves with amplitudes weighted by partition factors. The real part is retrieved using the Hilbert transform. The calculation of the partition factors is discussed for several geometrical configurations in two dimensional space: the full-space, a basin in a half-space and for layered media. For the last case, it results in a fast computation of the full Green's functions. Additionally, if the contribution of only selected states is desired, as for instance the surface wave part, the computation is even faster. Its use for full waveform inversion may then be advantageous.

The present work offers the solution for a target speed estimation in two dimensional space by the distributed radar systems. The proposed method supposes initial separated estimation of speeds in all channels (as it is done in conventional systems) and further refined estimation of the target speed by the joined least squares optimization. It was shown that the refined estimation allows obtaining of more precise speed estimate.

In this paper, we propose a closed-form solution for time-difference-of-arrival (TDOA) based joint source and sensor localization in two-dimensional space (2D). This closed-form solution is a combination of two closed-form solutions for time-of-arrival information recovery and time-of-arrival (TOA)-based joint source and sensor localization in 2D. In our previous works, we derived closed-form solutions for TOA-based joint source and sensor localization and near-closed-form solutions for TOA information recovery in three-dimensional space (3D). Since the localization in 2D is simpler than that in 3D, closed-form solutions for both problems in 2D are derived in this paper. The root-mean-square errors (RMSEs) achieved by the proposed closed-form solution are compared with the Cramer-Rao lower bound (CRLB) in synthetic experiments. The results show that the proposed solution works well in both low-noise and noisy cases and with both small and large numbers of sources and sensors.

In this paper, permutation invariant and collision free trajectories for a formation control problem are generated by using the root locus principle. A polynomial based representation space of multiple robots in two dimensional space is proposed, and the invariant properties in this space are analyzed. The formation control problem is solved in the representation space. A set of permutation invariant trajectories is generated by the generalized root locus dynamics. This method can be realized without the knowledge of global coordinates, but only with the local interaction between robots. In addition, the generalized root locus principle gives one degree of freedom to choose a different assignment in the formation. At the end, an example of permutation invariant safe control is provided.

Based on the weighted and shifted Gr\"{u}nwald difference (WSGD) operators [24], we further construct the compact finite difference discretizations for the fractional operators. Then the discretization schemes are used to approximate the one and two dimensional space fractional diffusion equations. The detailed numerical stability and error analysis are theoretically performed. We theoretically prove and numerically verify that the provided numerical schemes have the convergent orders 3 in space and 2 in time.

This paper explores the practical application of a new class of two dimensional arrays, namely, the two dimensional nested arrays, in array processing problems like two dimensional direction of arrival estimation. Nested arrays constitute a class of two dimensional arrays with physical sensors on lattice(s), whose difference co-array gives rise to a virtual two dimensional array with O(MN) elements, although the number of physical sensors used is M + N . The structure of the two dimensional nested array was proposed in a companion paper and several issues related to the geometrical orientation of the difference co-array in the two dimensional space were addressed. In this paper, the practical aspects of the application of the nested array in two dimensional array processing are considered, which can enable us to exploit the increased degrees of freedom offered by the co-array. Under the constraint of a fixed total number of physical sensors, the optimal structure of the 2D nested array is solved which maximizes the number of elements in the virtual co-array. This provides closed form expressions for the sensor locations and the exact degrees of freedom obtainable from the proposed array as a function of the total number of sensors. It is shown that one can obtain O(N2) virtual elements in the co-array using only N physical sensors. To exploit the increased degrees of freedom (large number of virtual sensors) offered by the virtual array for two dimensional DOA estimation of more sources than sensors, a novel algorithm based on the concept of two dimensional spatial smoothing is proposed and several issues related to identifiability in two dimensional DOA estimation problem (which is a fundamental issue in two dimensions), are addressed. The validity of the proposed methods is verified through several numerical examples.

Geometric form perception and its role in reorienting process have been studied extensively in children, but little is known about its early origin in infancy. Here, we present findings of three experiments that used looking-time paradigm to test infants’ sensitivity to geometric and feature information in two-dimensional visual display. One-year-old infants participated in spatial search tasks, which were manipulated regarding the display movement (static, visible rotation and invisible rotation) as a degree of disorientation. The results showed that infants were able to create expectation about a hiding location based on the geometry of a rectangle only in the directionally stable search space, whereas they were capable to use feature cues (color) for reorienting even in that condition when the spatial display was rotated and they were allowed to track the display motion. However, infants did not use either geometry or feature properties of 2-D space in an orientation invariant manner. The findings are discussed within the theory of reorientation with respect to the 2-dimensional space.

Let \( \wp_{1}, \wp_0 \) be two regular polygons of n sides in a space form M 2(κ) of constant curvature κ = 0,1 or − 1 such that \(\wp_0 \subset \wp_1\) and having the same center of mass. Suppose \( \wp_{0} \) is circumscribed by a circle C contained in \( \wp_{1} .\) We fix \(\wp_1\) and vary \(\wp_0\) by rotating it in C about its center of mass. Put \(\Omega=(\wp_{1} \setminus \wp_{0})^{0},\) the interior of \( \wp_{1} \setminus \wp_{0} \) in M 2(κ). It is shown that the first Dirichlet’s eigenvalue λ 1( Ω) attains extremum when the axes of symmetry of \( \wp_{0} \) coincide with those of \( \wp_{1}.\)

The problem of existence of bounded relativistic fermion states in a spherically symmetric well of finite depth in a two-dimensional space is investigated. The well depth critical for the appearance of standard states with energies E = m, 0, and –m is determined; moreover, cases with zero and nonzero fermion momenta are considered. Approximate analytical expressions for the critical depths of narrow and wide wells are derived which are in good agreement with the results of numerical calculations. Approximate energies of levels located on the boundaries of the upper and lower continuums and determined analytically are in good agreement with the results of numerical calculations.

Time intervals are conventionally represented as linear segments in a one-dimensional space. An alternative representation of time intervals is the triangular model (TM), which represents time intervals as points in a two-dimensional space. In this paper, the use of TM in visualising and analysing time intervals is investigated. Not only does this model offer a compact visualisation of the distribution of intervals, it also supports an innovative temporal query mechanism that relies on geometries in the two-dimensional space. This query mechanism has the potential to simplify queries that are difficult to specify using traditional linear temporal query devices. Moreover, a software prototype that implements TM in a geographical information system (GIS) is introduced. This prototype has been applied in a real scenario to analyse time intervals that were detected by a Bluetooth tracking system. This application shows that TM has the potential to support a traditional GIS to analyse interval-based geographical data.

We generalize Scheffers’ method to construct area preserving transformations in the Euclidean plane to Riemannian and Lorentzian two-dimensional space forms in a unified way. We review and extend the classical applications of such transformations in classical differential geometry. We introduce two classes of surfaces in Lorentzian 3-space that admit holomorphic representation and are analogous to the classical Appell and Bonnet surfaces.

The self-consistent field theory (SCFT) is applied to the microphase separation of concentrated solutions of weakly charged polyelectrolytes. The generalized Poisson–Boltzmann equation describing t...

In this paper,a moving mesh BGK scheme (MMBGK) for multi-material flow computa- tions is proposed. The basic idea of cons- tructing the MMBGK is to couple the Lagran- gian method for the material inter- face with the remapping-free ALE-type kinetic method within each single material region. Numerical examples in one and two dimensional space are presented to illustrate the efficiency and accuracy of the scheme.

This paper is concerned with the numerical solutions of a two dimensional space-time fractional differential equation used to model the dynamic properties of complex systems governed by anomalous diffusion. The space-time fractional anomalous diffusion equation is defined by replacing second order space and first order time derivatives with Riesz and Caputo operators, respectively. By using Laplace and Fourier transforms, a general representation of analytical solution is obtained as Mittag-Leffler function. Gr\"{u}nwald-Letnikov (GL) approximation is also used to find numerical solution of the problem. Finally, simulation results for two examples illustrate the comparison of the analytical and numerical solutions and also validity of the GL approach to this problem.

Three simple models estimating the evapotranspiration fraction (EF) were tested, validated and compared with available data from NDVI/albedo and day–night land surface temperature difference (DT). They were analyzed using ground based measurements collected by the energy balance Bowen ratio system at the 11 enhanced facilities located at the Southern Great Planes of the USA between April 2001 and May 2005. One model was superior in predicting the EF. It used an extension of the Priestly–Taylor equation and a relation between the normalized difference vegetation index (NDVI) and DT.

The goal of the article is to prove that four explicitly given transformations, two Heisenberg translations, a rotation and an involution generate the Picard modular group with Gaussian integers acting on the two dimensional complex hyperbolic space. The result answers positively a question raised by A. Kleinschmidt and D. Persson.

An ordering of a two-dimensional matrix assigns consecutive integers to the cells in that matrix. This paper evaluates such orderings by concentrating on the differences between each cell's order key and the keys of its spatial neighbors. In all, ten systematically generated orderings and two hundred random trials from a newly defined class of orderings are compared. The row-by-row (raster) ordering often used in remote sensing and in matrix ordering within computer programs minimizes the mean absolute difference, the root-mean-squared difference (and hence the Geary statistic), and the mean maximum absolute difference for both 8-by-8 and 256-by-256 matrices; of the quadrant-recursive (“quadtree-compatible”) orderings examined, the Morton order had the lowest values for both mean absolute difference measures, whereas the Hilbert order had the lowest root-mean-squared neighbor difference. The Morton order has the overall minimum value for the Moran statistic. Heuristic search procedures applied to the 8-by-8 case found orderings which had considerably “better” values for these statistics (higher for Moran; lower for the others) than did any of the above, suggesting that it will be possible to define new systematic orderings with better scores than any ordering currently in the literature.

This paper suggests an algorithm for optimal positioning individuals(or observations) with p-dimensional measurements into coordinates of a two dimensional space. A criterion for optimizing the rotation is taken as the consistency of the grouping result obtained by the cluster analysis. This paper introduces the criterion and a transformation matrix for the orthogonal rotation. The criterion of the optimal positioning is that standard groups are placed in each quadrant of the positioning. An optimal angle of the orthogonal rotation is investigated and found by this criterions.

This research assessed the relative contribution of 3-D virtual structure that generated the stimulus drawings (scene-based and picture-based theories) and 2-D structure of the drawings (object-based theories). Virtual structures were right-angle convex and concave corners in front of and behind the picture plane, respectively. Virtual corner size was manipulated directly (Experiment 1) and indirectly by manipulating drawing station point distance (Experiments 2 and 3), corner depth (Experiment 4), and corner distance from the picture plane (Experiments 5 and 6). Experiments 2 and 4 held the size of the projected corner edge (interior target line) constant, causing virtual corner size to vary, whereas Experiments 3, 4, 5, and 6 held size of the virtual corners constant, causing size of the projected corner edge or interior target line to vary. Subjects reproduced the length of the projected corner edge (interior target line). The illusions (difference between reproduced size of the projected corner edge and T-junction control) were generally well fit by the weighted sum of virtual corner size and size of the projected corner edge, but the projected distance between boundary line terminations (intertip distance) appeared as an additional contributing factor in Experiments 5 and 6. The implications of this methodological approach are discussed for theories of the illusions.

The purpose of this paper is to provide an exact evaluation of the configurational degeneracy when an arbitrary number (k) of dipoles are placed in a quasi-two-dimensional space (Q2D). This Q2D is made up of three contiguous diagonals 3 × N. Our Q2D space gives to the central sites of the lattice their full coordination number of nearest neighboring compartments. We are going to determine the exact configurational degeneracy W(k, N) when an arbitrary number k of the above mentioned particles are placed in this 3 × NQ2D space. We found that W(k, N) is exactly described by W(k, N) = 8W(k-1, N-1) - 8W(k-2, N-2) + W(k, N-1) W(k, N) is a prerequisite to develop analytical methods to study the interaction between an arbitrary set of dipoles (or spins, magnetic domains, heterogeneous diatomic molecules, etc) placed in a Q2D space., Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas

We consider the Cesaro sequence space ces p as a closed subspace of the infinite l p -sum of finite dimensional spaces. We easily obtain many known results, for example, ces p has property (β) of Rolewicz, uniform Opial property, and weak uniform normal structure. We also consider some generalized Cesaro sequence spaces. Finally, we compute the von Neumann–Jordan and James constants of the two-dimensional Cesaro sequence space ces p ( 2 ) when 1 p ⩽ 2 .

Space-fractional advection–dispersion equation (SFADE) can describe particle transport in a variety of fields more accurately than the classical models of integer-order derivative. Because of nonlocal property of integro-differential operator of space-fractional derivative, it is very challenging to deal with fractional model, and few have been reported in the literature. In this paper, a numerical analysis of the two-dimensional SFADE is carried out by the element-free Galerkin (EFG) method. The trial functions for the SFADE are constructed by the moving least-square (MLS) approximation. By the Galerkin weak form, the energy functional is formulated. Employing the energy functional minimization procedure, the final algebraic equations system is obtained. The Riemann–Liouville operator is discretized by the Grünwald formula. With center difference method, EFG method and Grünwald formula, the fully discrete approximation schemes for SFADE are established. Comparing with exact results and available results by other well-known methods, the computed approximate solutions are presented in the format of tables and graphs. The presented results demonstrate the validity, efficiency and accuracy of the proposed techniques. Furthermore, the error is computed and the proposed method has reasonable convergence rates in spatial and temporal discretizations.

In this study, we obtain some Korovkin type approximation theorems by positive linear operators on the weighted space of all real valued functions defined on the real two-dimensional Euclidean space \({\mathbb{R}^2}\). This paper is mainly consisted of two parts: a Korovkin type approximation theorem via the concept of A-statistical convergence and a Korovkin type approximation theorem via \({\mathcal {A}}\)-summability.

Space-filling curves can be used to organise points in the plane into bounding-box hierarchies (such as R-trees). We develop measures of the bounding-box quality of space-filling curves that express how effective different space-filling curves are for this purpose. We give general lower bounds on the bounding-box quality measures and on locality according to Gotsman and Lindenbaum for a large class of space-filling curves. We describe a generic algorithm to approximate these and similar quality measures for any given curve. Using our algorithm we find good approximations of the locality and the bounding-box quality of several known and new space-filling curves. Surprisingly, some curves with relatively bad locality by Gotsman and Lindenbaum's measure, have good bounding-box quality, while the curve with the best-known locality has relatively bad bounding-box quality., Comment: 24 pages, full version of paper to appear in ESA. Difference with first version: minor editing; Fig. 2(m) corrected

A modified Crank-Nicolson scheme based on one-sided difference approximations is proposed for solving time-dependent convection dominated diffusion equations in two-dimensional space. The modified scheme is consistent and unconditionally stable. A priori L^2 error estimate for the fully discrete modified scheme is derived. With the use of the incremental unknowns preconditioner at each time step, a comparison among several classical numerical schemes has been made and numerical results confirm stability and efficiency of the modified Crank-Nicolson scheme.

In [Y.-F. Jing, T.-Z. Huang, On a new iterative method for solving linear systems and comparison results, J. Comput. Appl. Math. 220 (2008) 74-84], Jing and Huang obtained a new iterative method for solving linear systems. This method can be considered as a projection method which uses a two-dimensional space at each step. In this paper, we generalize this method to a three-dimensional projection process. And a different approach is established, which is both theoretically and numerically proven to be better than (or at least the same as) [Jing and Huang's (2008)].

Low frequency current oscillations have been usually investigated under the influence of the external applied voltage, temperature and illumination. A parallel applied magnetic field has been used in the present work in order to obtain odd periodic windows and bifurcations inside them in a two dimension parameter space for a semi-insulating GaAs sample grown by molecular beam epitaxy. Two kinds of parameter spaces have been used in order to stabilize the odd periodic windows and the bifurcations, namely, the external applied voltage versus the parallel magnetic field and the illumination versus the parallel magnetic field. We report on a successful observation of stable cycles of periodicity 3, 4, 5, 6, 7 and 8 inside a period-3 window. An example of bifurcation route is presented following the sequence from chaos to 4, 3, 6, 3, 5, 7, 5, and back to chaos in the parameter space of voltage versus magnetic field. For this bifurcation route we will show which branch of the cycle is bifurcating and which are coalescing with the control parameters.

A new model for simulating contact line dynamics is proposed. We apply the idea of driving contact-line movement by enforcing the equilibrium contact angle at the boundary, to the conservative level set method for incompressible two-phase flow [E. Olsson, G. Kreiss, A conservative level set method for two phase flow, J. Comput. Phys. 210 (2005) 225-246]. A modified reinitialization procedure provides a diffusive mechanism for contact-line movement, and results in a smooth transition of the interface near the contact line without explicit reconstruction of the interface. We are able to capture contact-line movement without loosing the conservation. Numerical simulations of capillary dominated flows in two space dimensions demonstrate that the model is able to capture contact line dynamics qualitatively correct.

We develop a modulation theory based on a suitably averaged Lagrangian for steady solutions of the Sine–Gordon equation in a two dimensional lattice. These lump solutions are nonzero in circular or polygonal regions and zero elsewhere. The modulation theory gives approximate solutions away from small perturbations of the exact anti-continuum solutions for both radial and polygonal solutions. We show how the Peierls–Nabarro potential determines the shape of the boundary between excited sites and the zero solution. These solutions are compared with the corresponding numerical solutions and significant agreement is found. Moreover, we show that solutions with a large radius (more than sixteen lattice sites) can be explained using a continuous trial function for the averaged Lagrangian, while smaller polygonal solutions can be constructed using a trial function, which takes into account the angular variation of the boundary imposed by the lattice. Finally, the ideas of equivariant bifurcation theory are used to obtain a full numerical description of the solution branches as functions of the coupling parameter between neighboring sites. The results of this work can be used to study steady solutions for other types of lattice equations.

The development of efficient algorithms to analyze complex electromagnetic structures is of topical interest. Application of these algorithms in commercial solvers requires rigorous error controllability. In this paper we focus on the perfectly matched layer based multilevel fast multipole algorithm (PML-MLFMA), a dedicated technique constructed to efficiently analyze large planar structures. More specifically the crux of the algorithm, viz. the pertinent layered medium Green functions, is under investigation. Therefore, particular attention is paid to the plane wave decomposition for 2-D homogeneous space Green functions in very lossy media, as needed in the PML-MLFMA. The result of the investigations is twofold. First, upper bounds expressing the required number of samples in the plane wave decomposition as a function of a preset accuracy are rigorously derived. These formulas can be used in 2-D homogeneous (lossy) media MLFMAs. Second, a more heuristic approach to control the error of the PML-MLFMA's Green functions is presented. The theory is verified by means of several numerical experiments.

What are the constructs that underlie affective experiences? Some authors have suggested Valence and Activation, whereas others have suggested Positive Activation and Negative Activation-both approaches are represented by different axis orientations in traditional two-mode (People x Adjectives) factor analysis. The authors provide new evidence for this debate by using three-mode (People x Adjectives x Occasions) parallel factor (PARAFAC) analysis to determine the appropriate axes (and hence constructs) for representing affective experiences. Unlike traditional factor analysis, with PARAFAC different orientations of the axes fit the data differently so it is possible to determine the best fitting axes. In Study 1, the authors assessed the extent to which the PARAFAC procedure was able recover the axes defining a two-dimensional factor space under different conditions. In both Study 2 (N = 112) and Study 3 (N = 349), undergraduate students rated their emotional states on a variety of occasions. The best fitting axes for two-dimensional affective space were Valence and Activation in both studies. Exploration of higher dimensional solutions in Study 3 revealed a three-factor solution that, in addition to an activation factor, supported the separation of positive and negative emotions.

An approach for analysis of shape of composite dowel shear connector focused on finding a location of the point of maximal principal stress in steel dowel is presented. It is based on analogy between equations of boundary of closed area under plane stress conditions and beam in two dimensional space. Equations are derived from Airy's potential and polar coordinates are used.

We describe the normalized numerical ranges of certain operators. First, the case of a normal operator, acting in a two dimensional space is considered in detail, leading to the general Kantorovich inequality. Then we pass to the finite dimensional case and settle the problem when the Gustafson-Seddighin two component property, failing in general, takes place. In the next part finite and infinite dimensional Jordan cells are investigated.We conclude with the description of the normalized numerical range of a two-dimensional Toeplitz matrix. Mathematics subject classification (2000): 47A12, 47B15, 47N40.

A paradox concerning the flight of insects in two-dimensional space is identified: insects maintaining their bodies in a particular position (hovering) cannot, on average, generate hydrodynamic force if the induced flow is temporally periodic and converges to rest at infinity. This paradox is derived by using the far-field representation of periodic flow and the generalized Blasius formula, an exact formula for a force that acts on a moving body, based on the incompressible Navier–Stokes equations. Using this formula, the time-averaged force can be calculated solely in terms of the time-averaged far-field flow. A straightforward calculation represents the averaged force acting on an insect under a uniform flow, −〈V〉, determined by the balance between the hydrodynamic force and an external force such as gravity. The averaged force converges to zero in the limit 〈V〉 → 0, which implies that insects in two-dimensional space cannot hover under any finite external force if the direction of the uniform flow has a component parallel to the external force. This paradox provides insight into the effect of the singular behaviour of the flow around hovering insects: the far-field wake covers the whole space. On the basis of these assumptions, the relationship between this paradox and real insects that actually achieve hovering is discussed.

This paper describes a new numerical scheme for the approximation of steady state solutions to systems of hyperbolic conservation laws. It generalises the fluctuation distribution framework by allowing the underlying representation of the solution to be discontinuous. This leads to edge-based fluctuations in addition to the standard cell-based fluctuations, which are then distributed to the cell vertices in an upwind manner which retains the properties of the continuous scheme (positivity, linearity preservation, conservation, compactness and continuity). Numerical results are presented on unstructured triangular meshes in two space dimensions for linear and nonlinear scalar equations as well as the Euler equations of gasdynamics. The accuracy of the approximation in smooth regions of the flow is shown to be very similar to the corresponding continuous scheme, but the discontinuous approach improves the sharpness with which discontinuities in the flow can be captured and provides additional flexibility which will allow adaptive techniques to be applied simply to improve efficiency.

We present the geometrical minimum units of fracture patterns in two-dimensional space. For this analysis, a new method is developed from the algebraic approach: the concept of lattice (a type of partially ordered set) is applied to the discrete Walsh functions that have been used to measure symmetropy (an object related to symmetry and entropy) of fracture patterns. We concluded that the minimum units of fracture patterns can be expressed as three kinds of lattice. Our model is applied to the temporal change of the spatial pattern of acoustic-emission events in a rock-fracture experiment. As a result, the symmetropy of lattice decreases with the evolution of fracture process. We find that the pre-nucleation process of fracture corresponds to the subcritical states, and the propagation process to the critical states. Moreover, using a particular mathematical structure called sheaf on a lattice, we suggest the algebraic interpretation of fracture process, and provide justification to regard fracturing as an irreversible process.

This paper introduces a methodology that permits presentation of the results of data envelopment analysis (DEA) graphically. A specialized form of multi-dimensional scaling, Co-Plot, enables presentation of the DEA results in a two-dimensional space, hence in a clear, understandable manner. When plotting ratios rather than original data, DEA efficient units can be visualized clearly, as well as their connections to specific variables and/or ratios. Furthermore, Co-Plot can be used in an exploratory data analysis to identify outliers, whose data require additional scrutiny, and potentially inconsequential variables that could be aggregated or removed from the analysis with little effect on the subsequent DEA results. The Co-Plot diagram of ratios presents super-efficient observations on an outer ring or sector of the plot and all reasonably efficient units on a slightly inner ring/sector, surrounding the remaining inefficient decision-making units. First, the well-known 35 Chinese Cities dataset is provided as an illustration. Second, a simulation study tests the applicability of Co-Plot to present the results of DEA.

A new set of consistent boundary conditions for Yee scheme approximations of wave equations in two space dimensions are developed and analyzed. We show how the classical staircase boundary conditions for hard reflections or, in the electromagnetic case, conducting surfaces in certain cases give O(1) errors. The proposed conditions keep the structure of the Yee scheme and are thus well suited for high performance computing. The higher accuracy is achieved by modifying the coefficients in the difference stencils near the boundary. This generalizes our earlier results with Gustafsson and Wahlund in one space dimension. We study stability and convergence and we present numerical examples.

In this article, we present a general model to deal with the problem of matching multiple objects or configurations of points from a Bayesian point of view. We study both labeled and non labeled cases. Our model generalizes, in terms of non singular affine transformations and multiple configurations, previous two-terms matching models. As a practical application in Bioinformatics, we consider data from a microarray experiment of gorilla, bonobo, and human-cultured fibroblasts. We find out the matchings and the best affine transformation between the projections of genes on a two-dimensional space, obtained by a multidimensional scaling technique.

Objective: The potential advantage of visual momentum in the form of smooth rotation between two-dimensional (2-D) and three-dimensional (3-D) displays of geographic terrain was examined. Background: The relative effectiveness of 2-D and 3-D displays is task dependent, leading to the need for multiple frames of reference as users switch tasks. The use of smooth rotation to provide visual momentum has received little scrutiny in the task-switching context. A cognitive model of the processes involved in switching viewpoints on a set of spatial elements is proposed. Methods: In three experiments, participants judged the properties of two points placed on terrain depicted as 2-D or 3-D displays. Participants indicated whether Point A was higher than Point B, or whether Point B could be seen from Point A. Participants performed the two tasks in pairs of trials, switching tasks and displays within the pair. In the continuous transition condition the display dynamically rotated in depth from one display format to the other. In the discrete condition there was an instantaneous viewpoint shift that varied across experiments (Experiment 1: immediate; Experiment 2: delay; Experiment 3: preview). Results: Performance after continuous transition was superior to that after discrete transition. Conclusion: The visual momentum provided by smooth rotation helped users switch tasks. Application: The use of dynamic transition is recommended when observers examine multiple views of terrain over time. The model may serve as a useful heuristic for designers. The results are pertinent to command and control, geological engineering, urban planning, and imagery analysis domains.

Space-filling curves can be used to organise points in the plane into bounding-box hierarchies (such as R-trees). We develop measures of the bounding-box quality of space-filling curves that express how effective different curves are for this purpose. We give general lower bounds on the bounding-box quality and on locality according to Gotsman and Lindenbaum for a large class of curves. We describe a generic algorithm to approximate these and similar quality measures for any given curve. Using our algorithm we find good approximations of the locality and bounding-box quality of several known and new space-filling curves. Surprisingly, some curves with bad locality by Gotsman and Lindenbaum’s measure, have good bounding-box quality, while the curve with the best-known locality has relatively bad bounding-box quality.

The basic theory on relativistic positioning systems in a two-dimensional space-time and the analysis of the possibility of making relativistic gravimetry with these systems have been presented elsewhere [Phys. Rev. D 73 , 084017 (2006); Phys. Rev. D 74 , 104003 (2006)]. Here we summarize these results and we outline new issues on the relativistic positioning systems in Minkowski plane. We point out that the accelerations of the emitters and of the user along their trajectories are determined by the sole knowledge of the emitter positioning data and of the acceleration of only one of the emitters and only during a light echo interval.

The vacuum structure of N = 2 linear supersymmetry (LSUSY) invariant QED, which is equivalent to N = 2 nonlinear supersymmetry (NLSUSY) model, is studied explicitly in two-dimensional space–time ( d = 2 ). Two different isometries SO ( 1 , 3 ) and SO ( 3 , 1 ) appear for the vacuum field configuration corresponding to the various parameter regions. Two different field configurations of SO ( 3 , 1 ) isometry describe the two different physical vacua, i.e. one breaks spontaneously both U ( 1 ) and SUSY and the other breaks spontaneously SUSY alone.

The derivation of the invariants for a tensor of the third order in a two dimensional space is presented in the paper. The mathematical technique to obtain the expression of the invariants is based upon the so-called polar method, proposed as early as 1979 by G. Verchery as an alternative method to represent a plane tensor by its invariants. The polar components of a third order planar tensor are also introduced. When considered in the framework of piezoelectricity, an energetic interpretation of these components is given.

The objective of this paper is to depict the knowledge array of standards. This is done by identifying and analyzing external effects, specifically spillover effects. The database used is Perinorm. We use a cluster analysis in order to create groups of technology fields for German standards according to the fields of the International Classification of Standards. Methodologically, the distances between these objects or clusters are defined by the chosen distance measure, which in turn is determined by the sum of their cross references. The applied joining clustering method uses these distances between the objects and allows the data to be mapped within a two dimensional space. The results of this mapping show the existence of structures within the standards data fitting to the well-known structure of patent spillovers.

In this paper, the second one in the series beginning with D. Mao, Towards front tracking based on conservation in two space dimensions, SIAM J. Sci. Comput. 22 (1) (2000) 113-151], we study another important feature of our 2D conservative front-tracking method, i.e. discontinuity curves in two space dimensions are tracked in a 1D capturing fashion. The evolution of 2D discontinuity curves are locally described by 1D conservation laws with source terms, which are derived from the governing equations. The front-tracking in our method is then realized by numerically simulating these 1D conservation laws with source terms in a conservative fashion. In this paper, our 2D front-tracking method is described in details, which is Cartesian-grid-based, conservative and much simpler in algorithm than other 2D front-tracking methods. The discussion starts with the 1D case, which facilitates the following 2D discussion. Data structure of the numerical solutions and first- and second-order versions of our 2D front-tracking method are described. Finally, numerical examples for both scalar equations and the Euler system of gas dynamics in 2D are presented to show the efficiency and effectiveness of the method.

We consider the asymptotic behavior of perturbations of planar wave solutions arising in the Cahn–Hilliard equation in space dimensions d ≥ 2 . Such equations are well known to arise in the study of spinodal decomposition, a phenomenon in which rapid cooling of a homogeneously mixed binary alloy causes separation to occur, resolving the mixture into regions in which one component or the other is dominant, with these regions separated by steep transition layers. A critical feature of the Cahn–Hilliard equation in one space dimension is that the linear operator that arises upon linearization of the equation about a standing wave solution has essential spectrum extending onto the imaginary axis, a feature that is known to complicate the step from spectral to nonlinear stability. The analysis of planar waves in multiple space dimensions is further complicated by the fact that the leading eigenvalue for this linearized operator (leading in the case of stability) moves into the negative-real half plane with cubic scaling λ ∼ | ξ | 3 , where ξ ∈ R d − 1 denotes a Fourier variable associated with spatial components transverse to the planar wave. Under the assumption of spectral stability, described in terms of an appropriate Evans function, we develop detailed asymptotics for perturbations from planar wave solutions, establishing asymptotic stability for initial perturbations decaying at an appropriate algebraic rate in an L 1 norm of the transverse variables.