The Lagrange-Galerkin method for the two-dimensional shallow water equations on adaptive grids The weak Lagrange-Galerkin finite element method for the two-dimensional shallow water equations on adaptive unstructured grids is presented. The equations are written in conservation form and the domains are discretized using triangular elements. Lagrangian methods integrate the governing equations along the characteristic curves, thus being well suited for resolving the non-linearities introduced by the advection operator of the fluid dynamics equations. An additional fortuitous consequence of using Lagrangian methods is that the resulting spatial operator is self-adjoint, thereby justifying the use of a Galerkin formulation; this formulation has been proven to be optimal for such differential operators. The weak Lagrange-Galerkin method automatically takes into account the dilation of the control volume, thereby resulting in a conservative scheme. The use of linear triangular elements permits the construction of accurate (by virtue of the second-order spatial and temporal accuracies of the scheme) and efficient (by virtue of the less stringent Courant-Friedrich-Lewy (CFL) condition of Lagrangian methods) schemes on adaptive unstructured triangular grids. Lagrangian methods are natural candidates for use with adaptive unstructured grids because the resolution of the grid can be increased without having to decrease the time step in order to satisfy stability. An advancing front adaptive unstructured triangular mesh generator is presented. The highlight of this algorithm is that the weak Lagrange -Galerkin method is used to project the conservation variables from the old mesh onto the newly adapted mesh. In addition, two new schemes for computing the characteristic curves are presented: a composite mid-point rule and a general family of Runge-Kutta schemes. Results for the two-dimensional advection equation with and without time-dependent velocity fields are illustrated to confirm the accuracy of the particle trajectories. Results for the two-dimensional shallow water equations on a non-linear soliton wave are presented to illustrate the power and flexibility of this strategy. The advection terms in the governing equations of fluid motion present formidable challenges to many spatial discretization methods, including Galerkin methods. These terms prevent the operator from being self-adjoint and as a result, Galerkin methods are no longer optimal for the spatial discretization. Researchers have tried circumventing this problem by using highorder Eulerian methods and characteristic-based Lagrangian methods. In this section a brief overview of some of the more interesting methods is given, identifying their weaknesses and assessing their strengths.. A limited number of new Eulerian methods have been introduced in recent years for solving hyperbolic partial differential equations (PDEs) (such as the shallow water equations), perhaps the best being the spectral element method [1 -3] . This method offers high accuracy solutions and spectral convergence (provided the solution is smooth) but at the price of having to use small time steps (due to the explicit solvers typically used) and structured grids (due to the restriction that the elements be quadrilaterals). Recently, Giraldo [4] showed how to increase the time step by combining the Lagrange -Galerkin method with the spectral element method, while Taylor and Wingate [5] have been working on developing a triangular spectral element method.. In contrast, there exists a multitude of characteristic-based methods. Eulerian-Lagrangian methods combine the standard finite element procedure with the method of characteristics. By integrating the equation in time along the characteristics the resulting spatial operator becomes self-adjoint, which then justifies the use of Galerkin spatial discretizations. These methods can be classified into the following three groups: the direct (or strong) Lagrange-Galerkin method, the weak Lagrange -Galerkin method, and the Eulerian-Lagrangian localized adjoint method. In the strong Lagrange -Galerkin method, the time derivative and the advection terms are combined into the Lagrangian derivative and the resulting operator is then discretized using the standard finite element method. This is the approach used by, for example, Bercovier and Pironneau [6] , Bermejo [7] , Douglas and Russell [8] , and Priestley [9] . In this method the basis functions are the typical Lagrange polynomials used in the standard finite element method, which are only dependent on the spatial co-ordinates. The success of this method hinges on determining the values at the feet of the characteristics. Related to this method are the semi-Lagrangian [10] and characteristic-Galerkin [11] methods (see also the Taylor-Galerkin method [12] ). The semi-Lagrangian method is essentially the strong Lagrange-Galerkin method with the exception that the spatial discretization is achieved through finite differencing; this method is quite ubiquitous in the meteorology community. In this method, the values of the variables at the feet of the characteristics are obtained through interpolation. The characteristic-Galerkin method avoids interpolations by using approximations obtained from Taylor series expansions. Therefore, the computations all take place in terms of the Eulerian grid, which eliminates the difficulties of the Lagrangian grid but at the expense of having to use smaller time steps due to the stricter stability restrictions that govern all Eulerian methods.. In contrast, the weak Lagrange -Galerkin method uses basis functions that are dependent on both space and time by forcing the basis functions to disappear along the adjoint of the transport operator (the transport operator referring to a homogeneous conservation law); this results in the basis functions vanishing along the characteristics. Using the conservation form of the governing equations simplifies the resulting discretization by introducing the Reynolds' transport theorem [13] , which then eliminates the boundary terms arising from the integration by parts used to obtain the adjoint of the transport operator. This is the method introduced by Benque et al. [14, 15] and the approach used in this paper.. Finally, the Eulerian -Lagrangian localized adjoint method forces the basis functions to disappear along the adjoint of the entire differential operator (not just the transport operator). Since the Reynolds' transport theorem is not used in this formulation, all of the boundary terms remain, which makes it rather easy to enforce any type of boundary conditions. This is the method introduced by Celia et al. [16] and used in References [17] [18] [19] [20] . Thus, for applications where the boundaries play an important role it would seem prudent to use this method. However, since the final objective of our work is to develop a shallow water model on the sphere, where there are no boundary conditions, the weak Lagrange-Galerkin method appears to be the perfect candidate for such a model.. Lagrange-Galerkin methods have increased in popularity in the last 10 years because they offer increased accuracy and efficiency by virtue of their independence on the CourantFriedrich-Lewy (CFL) condition; however, almost all research has involved the strong method as opposed to the weak method presented here. Currently the only applications (of which this author is aware) using the weak method or variations thereof are the following: twodimensional advection [14, 21] , two-dimensional shallow water on the plane [22] , twodimensional Navier -Stokes [15] , and two-dimensional shallow water on the sphere [23] .. There have been few attempts at using the weak Lagrange-Galerkin method for the shallow water equations. In Reference [22] , the weak Lagrange-Galerkin method of Benque [15] is presented for estuary flows on structured quadrilateral grids. In their paper, the interpolations for the departure point values at the vertices of the elements are bilinear and the variables inside their respective Lagrangian element are then assumed continuous and linearly varying throughout the element. Assuming a linear variation within the Lagrangian element results in a highly stable scheme but a strongly diffusive one as well. In our paper, triangular grids are used and the integration can either be done piecewise exactly or numerically. Neither approach assumes a linear variation within the element but rather takes into consideration the gradient across the different Eulerian element that the Lagrangian element spans.. In Reference [23] an exactly integrated weak Lagrange-Galerkin method on the spherical shallow water equations is presented. The basis functions used are not the natural co-ordinates derived for linear triangles. In our paper, the natural co-ordinates are used. This means that we can not only derive explicit basis function formulas that can be used for computing derivatives or searching for inclusion of departure points, but also they can be used to construct exact integration formulas for all of the finite element integrals including those occurring at the Lagrangian elements. In addition, the use of the explicit natural co-ordinates has ramifications for higher-dimensional models. All of the algorithms presented in this paper are directly generalizable to a two-dimensional spherical or three-dimensional Cartesian shallow water model. This has been the focus of our previous [21] and future work. Therefore, the idea of using the natural co-ordinates on the triangle in two-dimensional space is directly applicable to a spherical model. For a full three-dimensional model, rather than using the linear triangular natural co-ordinates, the linear tetrahedral natural co-ordinates are used with little change to the algorithms presented in this paper.. The method presented in Reference [22] uses quadrilaterals instead of triangles, which are used in this paper. There are many advantages in using triangles over quadrilaterals. Since the triangle is the two-simplex, any two-dimensional domain can be discretized with triangles no matter how multiply-connected (i.e., non-convex) it is. In addition, it is irrelevant to the scheme whether the flow has strong shears or is highly rotational. If quadrilaterals are used, the Lagrangian elements may become highly skewed or completely distorted, whereas this is of no concern with triangles. Using quadrilateral elements also requires a non-linear iterative solver in order to compute the local element co-ordinates from the global co-ordinates obtained from the trajectory equation. This is required because the interpolations within an element must be carried out using the local co-ordinates because the local basis functions are defined only in terms of these co-ordinates and not in terms of the global co-ordinates. On triangles, because the basis functions are defined in terms of the global co-ordinate, this procedure is not required. Furthermore, in this paper we show how to apply the weak method with adaptive unstructured grids, which can only be accomplished with triangles. The idea of using adaptive unstructured grids with Lagrange-Galerkin methods is attractive because the resolution of the grid can be increased without the need to decrease the time step. In Eulerian methods, the time step must be decreased in order to satisfy the CFL condition; violating the CFL condition results in instabilities and inaccuracies. In Lagrangian methods, on the other hand, the CFL condition is less stringent and typically the time step need not be decreased. Numerical tests are presented that show the effects of increasing the time step on the accuracy of the scheme. The weak Lagrange -Galerkin finite element method on adaptive unstructured grids is presented. In order to apply the weak Lagrange-Galerkin method to the shallow water equations they must first be written in conservation form. The combination of the conservative weak Lagrange-Galerkin method along with the governing equations having been written in conservation form results in a highly conservative scheme. In fact, the mass and energy were exactly conserved (up to 99.8 percent) for all the grids and for all of the test cases regardless of the size of the time step. The weak Lagrange-Galerkin method produces a very efficient scheme for solving the shallow water equations that are not just applicable to the two-dimensional planar shallow water equations but are also directly extendible to the two-dimensional spherical and three-dimensional Cartesian shallow water equations. This generalization is possible through the use of the natural co-ordinates as the finite element basis functions. Although the shallow water equations are a coupled system of non-linear first-order PDEs, after discretizing by the weak Lagrange -Galerkin method they yield a decoupled system of linear first-order equations. The decoupling occurs between the mass and the momentum equations; the n momentum equations (for R n space) remain weakly coupled through the Coriolis term. In this paper we have described in detail the application of the weak Lagrange-Galerkin method to the shallow water equations. In additions, we have shown how to integrate all of the equations exactly, not just those at the arrival points (the Eulerian elements at time t n + 1 ) but also the departure points (the Lagrangian elements at time t n ). However, it was found that the numerical integration approach yielded results equal or close to the exact integration approach while costing a factor of two less. But since this is such and elegant method, further work to increase its efficiency needs to be explored.. Perhaps one of the most important aspects of a Lagrangian method is the correct capturing of the fluid particle trajectories. In this paper, we have introduced two new methods for calculating these trajectories: the Runge -Kutta (RK) and the composite mid-point rule (CM). Both methods are shown to be extremely accurate not just for steady state velocity fields but for transient ones as well. The RK method performed better than the CM method but further improvements can always be made.. Linear triangular elements are used in this study, which give three advantages over quadrilaterals: exact or numerical integration can be used to integrate all of the finite element integrals; regardless of shear or rotational aspects of the flow, triangles will not become non-convex polygons whereas this danger exists and is very probable with quadrilaterals; and finally adaptive unstructured grids can be used. The adaptive unstructured grid generator presented is an advancing front method, which uses the idea of the weak Lagrange-Galerkin method to project the values at the grid points from the old mesh onto the newly adapted mesh. This idea results in a difference in conservation of mass and energy from one mesh to the other on the order of 1× 10 − 8 percent. Three test cases were run in order to validate the algorithms: a solid body rotation of a Gaussian with a steady state velocity field, a solid body rotation of a Gaussian with a transient velocity field, and a westward traveling soliton wave. The first two test cases are given primarily to show that the convergence rate of the weak Lagrange-Galerkin method is quadratic (second-order) and to compare the two methods for calculating the fluid particle trajectories. The soliton case tests the ability of the scheme to handle a non-linear phenomenon and it performed extremely well, not only for the structured and unstructured grids but also for the adaptive unstructured grids.. The results obtained for the three problems demonstrate that the weak Lagrange-Galerkin finite element method with adaptive unstructured triangles offer a viable method for solving the shallow water equations on the plane. This paper describes the approach in detail while future papers will focus on the application of this method for various types of problem. The development of a three-dimensional weak Lagrange-Galerkin shallow water model is currently underway.

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The discrete strategy improvement algorithm for parity games and complexity measures for directed graphs For some time the discrete strategy improvement algorithm due to Jurdziński and Vöge had been considered as a candidate for solving parity games in polynomial time. However, it has recently been proved by Oliver Friedmann that the strategy improvement algorithm requires super-polynomially many iteration steps, for all popular local improvements rules, including switch-all (also with Fearnley's snare memorisation), switch-best, random-facet, random-edge, switch-half, least-recently-considered, and Zadeh's Pivoting rule.We analyse the examples provided by Friedmann in terms of complexity measures for directed graphs such as treewidth, DAG-width, Kelly-width, entanglement, directed pathwidth, and cliquewidth. It is known that for every class of parity games on which one of these parameters is bounded, the winning regions can be efficiently computed. It turns out that with respect to almost all of these measures, the complexity of Friedmann's counterexamples is bounded, and indeed in most cases by very small numbers. This analysis strengthens in some sense Friedmann's results and shows that the discrete strategy improvement algorithm is even more limited than one might have thought. Not only does it require super-polynomial running time in the general case, where the problem of polynomialtime solvability is open, it even has super-polynomial lower time bounds on natural classes of parity games on which efficient algorithms are known. Parity games are a family of infinite two-player games on directed graphs. They are important for several reasons. Many classes of games arising in practical applications admit reductions to parity games (over larger game graphs). This is the case for games modelling reactive systems, with winning conditions specified in some temporal logic or in monadic second-order logic over infinite paths (S1S), for Muller games, but also for games with partial information appearing in the synthesis of distributed controllers. Further, parity games arise as the model-checking games for fixed-point logics such as the modal µ-calculus or LFP, the extension of first-order logic by least and greatest fixed-points. Conversely, winning regions of parity games (with a bounded number of priorities) are definable in both LFP and the µ-calculus. Parity games are also of crucial importance in the analysis of structural properties of fixed-point logics.. From an algorithmic point of view parity games are highly intriguing as well. It is an immediate consequence of the positional determinacy of parity games, that their winning regions can be decided in NP ∩ Co-NP. In fact, it was proved in [11] that the problem is in UP ∩ Co-UP, where UP denotes the class of NP-problems with unique witnesses. The best known deterministic algorithm has complexity n O( combined to achieve a worst-case running time of O(n d/3+O (1) ) for solving parity games with d priorities, with d = √ n (see [1, Chapter 3] . Although the question whether parity games are in general solvable in Ptime is still open, there are efficient algorithms that solve parity games in special cases, where the structural complexity of the underlying directed graphs, measured by numerical graph parameters, is low. These include parity games of bounded treewidth [15] , bounded entanglement [3, 4] , bounded DAG-width [2] , bounded Kelly-width [10] , or bounded cliquewidth [16] .. One algorithm that, for a long time, had been considered as a candidate for solving parity games in polynomial time is the discrete strategy improvement algorithm by Jurdziński and Vöge [14] . The basic idea behind the algorithm is to take an arbitrary initial strategy for Player 0 and improve it step by step until an optimal strategy is found. The algorithm is parametrized by an improvement rule. Indeed, there are many possibilities to improve the current strategy at any iteration step, and the improvement rule determines the choice that is made. Popular improvement rules are switch-all, switch-best, randomfacet, random-edge, switch-half and Zadeh's Pivoting rule. Although it is open whether there is an improvement rule that results in a polynomial worst-case runtime of the strategy improvement algorithm, Friedmann [9] was able to show that there are super-polynomial lower bounds for all popular improvement rules mentioned above. For each of these rules, Friedmann constructed a family of parity games on which the strategy improvement algorithm requires super-polynomial running time.. In this paper we analyse the examples provided by Friedmann in terms of complexity measures for directed graphs. It turns out that with respect to most of these measures, the complexity of Friedmann's counterexamples is bounded, and indeed in most cases by very small numbers. This analysis strengthens in some sense Friedmann's results and shows that the discrete strategy improvement algorithm is even more limited than one might have thought. Not only does it require super-polynomial running time in the general case, where the problem of polynomial-time solvability is open, it even has super-polynomial lower time bounds on natural classes of parity games on which efficient algorithms are known.

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Discovering controlling factors of geospatial variables Efficient means of determining factors controlling spatial distribution of an environmental class variable are of significant interest in Earth science. In this paper, we present a method for automated discovery of controlling factors by mining for emerging patterns in a database constructed from the fusion of several explanatory datasets. We introduce a new definition of pattern support to account for spatial character of the data and systematically evaluate the effectiveness of our technique using a real-world application pertaining to density of vegetation cover. Experimental results show that our method can successfully identify controlling factors for the presence of high vegetation cover. Environmental variables are highly coupled through a complex chain of interactions resulting in their mutual interdependability. Efficient means of determining controlling factors which are responsible for spatial distribution of a selected class variable are of significant interest to domain experts. In order to understand the properties of a class variable, experts attempt to identify dominant controlling factors: explanatory variables that are predominantly responsible for spatial distribution of the class variable. For example, the density of vegetation (class variable) shows large regional variations due to changes in environmental variables such as various climate indicators and soil properties. Understanding the dominant factors behind geographical extent of high vegetation regions is of great interest from Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. ACM GIS '08, November [5] [6] [7] 2008 . Irvine, CA, USA Copyright 2008 ACM ISBN 978-1-60558-323-5/08/11 ...$5.00. a scientific as well as a practical point of view, such as the impact of global warming on vegetation cover.. Currently, such problems are addressed by painstaking manual analysis, but with an increasing access to data products describing terrain topography, climate, vegetation cover, lithology, soil properties, human impact, etc., a more comprehensive methodology, one that would distill all dependencies in the data and present an expert with a relevant summary needs to be developed. In this paper, we propose a method for machine-aided identification of dominant controlling factors for a geospatial class variable. The method extends the standard technique of mining for emerging patterns (EPs) [2, 3] to geospatial domain.. Identifying EPs in spatial datasets presents challenges. Firstly, all databases of interest are spatial databases; this requires modification of standard EPs methods. Secondly, relevant geospatial databases contain continuous variables that need to be categorized in order to be subjected to association analysis. Categorization inevitably leads to information loss as it introduces sharp boundaries between different regions (for example, regions of high vegetation and low vegetation) where in reality the regions are not mutually exclusive, but instead they gradually transit into each other. We address these challenges by generalizing the definition of pattern support. The new definition takes into account spatial autocorrelation -a common feature in spatially extended variables. The overall goal of the method described in this paper is to provide means for discovering a set of dominant controlling factors that provides comprehensive and systematic knowledge for building empirical models of a chosen phenomena.. We illustrate our method by applying it to a real-world case study of finding factors exerting control over the density of vegetation cover in the continental United States. Continuing with the example given above, a territory of the United States can be divided into two sets based on the values of a class variable: high vegetation density region, and not-high vegetation density region. The patterns to be considered are the collections of the values of environmental explanatory variables. The goal is to identify patterns that are relatively frequent in the high vegetation region but rare in the low vegetation region. Examination of patterns related to the high vegetation provides a summary of data dependencies that helps to develop a better empirical models of the vegetation growth.

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From Bi-ideals to Periodicity The necessary and sufficient conditions are extracted for periodicity of bi-ideals. By the way two proper subclasses of uniformly recurrent words are introduced. The periodicities are fundamental objects, due to their primary importance in word combinatorics [8, 9] as well as in various applications. The study of periodicities is motivated by the needs of molecular biology [6] and computer science. Particularly, we mention here such fields as string matching algorithms [4] , text compression [14] and cryptography [12] . In different areas of mathematics, people consider a lot of hierarchies which are typically used to classify some objects according to their complexity. Here we deal with hierarchy B ⊃ R u ⊃ P , where B -the class of bi-ideals, R u -the class of uniformly recurrent words, P -the class of periodic words. This hierarchy comes from combinatorics on words, where these classes are being investigated intensively (cf. [2, 8, 9, 10] ). Bi-ideal sequences have been considered, with different names, by several authors in algebra and combinatorics [1, 3, 7, 13, 17] . We refine the hierarchy B ⊃ R u ⊃ P to the chain. B b -the class of bounded bi-ideals, B f -the class of finitely generated bi-ideals. So we localize the class of uniformly recurrent words by means of bi-ideals. Corollary 7 gives one method how the words of B f can be generated. At first we characterize periodic finitely generated bi-ideals: we give one necessary condition [

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Development of correlation-based clustering method and its application to software sensing The individuality of production devices should be taken into account when soft-sensors are designed for parallelized devices. Since it is expressed as differences of the correlation among measured variables, it is useful to cluster samples on the basis of the correlation among variables for adopting a multi-model approach. In addition, changes in process characteristics can be coped with in the same way. In the present work, a new clustering method, referred to as NC-spectral clustering, is proposed by integrating the nearest correlation (NC) method and spectral clustering. Spectral clustering is a graph partitioning method that can be used for sample classification when an affinity matrix of a weighted graph is given. The NC method can detect samples that are similar to the query from the viewpoint of the correlation without a teacher signal. In the proposed method, the NC method is used for constructing the weighted graph that expresses the correlation-based similarities between samples and the constructed graph is partitioned by using spectral clustering. In addition, a new soft-sensor design method is proposed on the basis of the proposed NCspectral clustering. The usefulness of the proposed methods is demonstrated through a numerical example and a case study of parallelized batch processes. The performance of the proposed correlation-based method is better than that of the conventional distance-based methods. Soft-sensors have been widely used for estimating product quality or other key variables. Partial least squares (PLS) and artificial neural network (ANN) have been widely accepted as useful techniques for softsensor design [1] [2] [3] [4] [5] . In addition, the application of subspace identification (SSID) to soft-sensor design has been reported [6, 7] .. Even if a good soft-sensor is developed successfully, its estimation performance deteriorates as process characteristics change. In chemical processes, process characteristics are changed by catalyst deactivation, scale adhesion and so on. In semiconductor manufacturing processes, periodic cleaning of equipment changes the process characteristics dramatically. Therefore, maintenance of soft-sensors is very important to keep their estimation performance. They should be updated as the process characteristics change. However, repeated and manual construction of them should be avoided due to heavy workload [8] .. To cope with changes in process characteristics and to update statistical models automatically, recursive PLS [9] and Just-In-Time (JIT) modeling [10] [11] [12] have been proposed. Recursive PLS updates a PLS model recursively, and JIT modeling builds a local model from neighbor samples around the query only when an estimate is requested. Although these methods can adapt models to new operating conditions, they cannot always achieve high estimation performance.. Recently, a new JIT modeling method, referred to as Correlation-based JIT (CoJIT) modeling, has been proposed [13] . Since changes in process characteristics are expressed as differences of the correlation among variables, CoJIT modeling builds a local model from samples whose correlation can properly describe the query.. In addition, the individuality of production devices should be taken into account. In semiconductor processes, for example, tens of parallelized production devices are used, and they have different characteristics even if their catalog specifications are the same. In such a case, a soft-sensor developed for one device is not always applicable to another device, and it is very laborious to construct soft-sensors for each device. Therefore, a practical soft-sensor design method that can cope with the individuality of production devices should be developed.. If there are some devices whose characteristics are similar to each other, the same soft-sensor may be applicable to them. That is, to construct soft-sensors that can cope with the individuality of production devices, it is useful to cluster operation data of parallelized processes into a few classes according to their characteristics and to construct a model for each class. In addition, the number of developed soft-sensors can be reduced by comparison with the case where soft-sensors are constructed for each device.. The k-means method has been used for sample classification. Although it can cluster samples on the basis of the distance, it does not take into account the correlation among variables. Recently, self-organizing map (SOM) has been proposed [14] . SOM is a machine learning process that imitates the brain learning process, and it can visualize high dimensional data as a map on the basis of similarities between samples. However, SOM does not always give clear boundaries between clusters on the map. In addition, it requires high computational load, and its parameter tuning and data preprocessing are complicated.. In the present work, a new clustering method, referred to as NC-spectral clustering, is proposed. In the proposed method, the nearest correlation (NC) method [15] that can detect samples whose correlation is similar to the query and spectral clustering [16, 17] that can partition a weighted graph are integrated. The proposed NC-spectral clustering can classify samples according to their correlation among variables without teacher signals. In addition, a new soft-sensor design method based on NC-spectral clustering is developed. The usefulness of the proposed methods is demonstrated through a case study of parallelized batch processes. A new clustering method is proposed by integrating the NC method and spectral clustering. The proposed NC-spectral clustering can accurately discriminate the correlation among variables. In addition, a new softsensor design method based on NC-spectral clustering is proposed. Since NC-spectral clustering can discriminate the individuality of production devices, the proposed soft-sensor design method can improve the estimation performance. The usefulness of the proposed methods is demonstrated through numerical examples and a case study of parallelized batch processes.

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Design of Content-Based Publish/Subscribe Systems over Structured Overlay Networks The management of subscriptions and events is an important task in the cobased publish/subscribe system . A good management mechanism can not only produce lower matching costs to speed up the delivery of matched events to the interested subscribers but can also induce good load balancing for subscription storage. In this paper, we consider the construction of this kind of system over a peer-to-peer overlay network and propose two message-to-node mapping schemes for system management. We both analyze and simulate the performance of the proposed schemes .The simulation results show the superiority of our schemes over existing ones.key words: publish/subscribe, peer-to-peer, overlay networks , load balancing The content-based p/s system is a very appealing interaction model and its capability can be fully enhanced over a P2P overlay network. The performance of this kind of system is dominated by the message-to-node mapping schemes. We found that the existing schemes either have high event delivery costs or high subscription storing costs. In this paper, we proposed two new mapping schemes: Hybrid and IIM. Hybrid performs well when the most of attributes are of equal type. IIM outperforms Hybrid if most attributes are of range type.. In the future, we will extend the work to both the location-dependent service environment and the mobile ad hoc network environment.. The new challenges include the location tracking, filtering of location-dependent criteria , and handling of node mobility.

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Two-View Multibody Structure from Motion Abstract. We present an algebraic geometric approach to 3-D motion estimation and segmentation of multiple rigid-body motions from noise-free point correspondences in two perspective views. Our approach exploits the algebraic and geometric properties of the so-called multibody epipolar constraint and its associated multibody fundamental matrix, which are natural generalizations of the epipolar constraint and of the fundamental matrix to multiple motions. We derive a rank constraint on a polynomial embedding of the correspondences, from which one can estimate the number of independent motions as well as linearly solve for the multibody fundamental matrix. We then show how to compute the epipolar lines from the first-order derivatives of the multibody epipolar constraint and the epipoles by solving a plane clustering problem using Generalized PCA (GPCA). Given the epipoles and epipolar lines, the estimation of individual fundamental matrices becomes a linear problem. The clustering of the feature points is then automatically obtained from either the epipoles and epipolar lines or from the individual fundamental matrices. Although our approach is mostly designed for noise-free correspondences, we also test its performance on synthetic and real data with moderate levels of noise. A classic problem in visual motion analysis is to estimate a motion model for a set of 2-D feature points as they move in a video sequence. When the scene is static, the problem of fitting a 3-D model compatible with the structure and motion of the scene is well understood (Hartley and Zisserman, 2000; Ma et al., 2003) . For instance, it is well-known that two views of a scene are related by the so-called epipolar constraint and that the motion of the camera can be estimated using linear techniques such as the eight-point algorithm (LonguetHiggins, 1981) . However, these techniques can not deal with dynamic scenes in which different regions of the image obey different motion models due to depth discontinuities, perspective effects, multiple moving objects, etc.. Motion estimation and segmentation refers to the problem of fitting multiple motion models to the scene, without knowing which feature points are moving according to the same model. Previous work (Feng and Perona, 1998) solves this problem by first clustering the features corresponding to the same motion using K -means or spectral clustering, and then estimating a single motion model for each group. This can also be done in a probabilistic framework (Torr, 1998) in which a maximum-likelihood estimate of the parameters of each motion model is sought by alternating between feature clustering and single-body motion estimation using the Expectation Maximization (EM) algorithm. However, the convergence of EM to the global maximum depends strongly on initialization (Torr et al., 2001) .. In order to deal with the initialization problem, recent work has concentrated on the study of the geometry of dynamic scenes. Even for drastically simplified motion models, such as multiple points moving linearly with constant speed (Han and Kanade, 2000; Shashua and Levin, 2001) or in a conic section (Avidan and Shashua, 2000) , multiple points moving in a plane (Sturm, 2002) , or multiple translating planes , the geometric aspects of the problem are nontrivial. More general motion models have only been studied in the case of orthographic cameras observing multiple rigid-body motions (Costeira and Kanade, 1995; Kanatani, 2001; Vidal and Hartley, 2004) and in the case of two perspective cameras observing two rigid-body motions .. In this paper, we present an algebraic geometric approach to the estimation and segmentation of an unknown number of rigid-body motions from a set of noise-free point correspondences in two perspective views. Rather than alternating between feature clustering and single-body motion estimation, our approach algebraically eliminates the feature clustering stage and directly solves for the motion parameters in an algebraic fashion. This is achieved by fitting a multibody motion model to all the image measurements and then factorizing this model to obtain the individual motion parameters. The final result is a natural generalization of the geometry of the classical two-view structure from motion problem (epipolar constraint, fundamental matrix and eight-point algorithm) to the case of multiple rigid-body motions.. Section 2 studies the geometry and algebra of the multibody structure from motion problem. We introduce the multibody epipolar constraint as a geometric relationship between the motion parameters and the image points that is satisfied by all the correspondences, regardless of the body with which they are associated. We show that the multibody epipolar constraint is bilinear on a polynomial embedding of the correspondences and linear on the so-called multibody fundamental matrix F, an algebraic structure encoding the parameters of all rigid-body motions. We then study the geometric properties of F and prove that the embedded epipoles of each independent motion are the intersection of the left null space of F with the so-called Veronese surface.. Section 3 presents an algebraic geometric algorithm for estimating the number of motions, the motion parameters and the clustering of the correspondences. We first derive a rank constraint on the matrix of embedded correspondences from which one can estimate the number of independent motions n as well as linearly solve for the multibody fundamental matrix F. Given n and F, we show that one can estimate the epipolar line associated with each correspondence from the first-order derivatives of the multibody epipolar constraint at the correspondence. By applying this process to all the correspondences, we obtain a collection of epipolar lines that must intersect at the n epipoles. The estimation of the epipoles is then equivalent to a plane clustering problem, which we solve algebraically using Generalized Principal Component Analysis (GPCA) . Given the epipoles and epipolar lines, the estimation of individual fundamental matrices becomes a linear problem. The clustering of the feature points is then automatically obtained from either the epipoles and epipolar lines or from the individual fundamental matrices. Since our technique is based Two-View Multibody Structure from Motion 9 on solving linear systems, taking derivatives of multivariate polynomials, and computing roots of univariate polynomials, 3-D motion segmentation can be solved in closed form if and only if the number of motions is at most four.. Although our 3-D motion segmentation algorithm is mostly designed for noise-free correspondences, in Section 4 we present experiments on synthetic data that evaluate the performance of our approach with respect to moderate levels of noise. We also apply our algorithm to the segmentation of an indoor sequence.. Remark 1. Although the proposed algebraic geometric algorithm is algebraically equivalent to the factorization of symmetric tensors, we avoid the use of tensorial notation throughout the paper, because algorithms based on polynomial algebra are computationally more straightforward and better established. As a consequence, this paper requires little background beyond conventional linear and polynomial algebra.

O B I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O B I I O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Experimental study of market reputation mechanisms We experimentally compare low-information, high-information and self-reporting reputation mechanisms. The results indicate players strategically reacted to the reputation mechanisms, with higher information mechanisms increasing market efficiency. We conducted 8 experimental sessions. The first had 8 subjects. The rest had at least 12 subjects. In all experiments, market prices converged reasonably well to equilibrium within 3 periods. While rapid convergence is expected for the market [7] , this may not have been the case with the our addition of non-binding contracts.. As expected, all experiments exhibit strong end-game effects. Subjects were told when the game would end two periods ahead of time. Fulfillment decreased sharply around 4 periods before the end of an experiment. We expect people are more likely to fulfill contracts when more information about their actions is available to people deciding whether to transact future business with them. This matches our observation of lower fulfillment with the low information policy, where subjects can safely reason that only people with whom they had unfulfilled contracts know of their "bad" record. Thus, not fulfilling a contract is less costly to future business than the case with full information. This is also strong evidence that people react to strategic implications of how information is used by other people. The figure shows an example of our experimental results. Fulfillment rates in the self-reporting treatment are similar to the high information treatment. This is consistent with observations on Internet auction sites such as eBay where the amount of negative feedback is only about 1%. This is not direct evidence that cheating is rare since feedback does not have to be 100% accurate. Similarly, reports in our experiment were not always accurate. However, they were, on average, a good representation of how likely a subject is going to fulfill contracts. Our experimental design allowed us to also observe endogenous macroeconomic effects: when fulfillment decreased, the contracted volume also increased but prices remained nearly constant. Market efficiencies responded to the level of fulfillment in a highly nonlinear fashion.

O O O O B O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


The effectiveness of online shopping characteristics and well-designed websites on satisfaction Much research has been done to understand the motivations of consumers to choose among online retailers and the retailer factors driving customer satisfaction (e.g., Kim et al. 2009; Kotha et al. 2004; Pan et al. 2002; Qu et al. 2008; Smith et al. 2000; Wolfinbarger and Gilly 2003) .Concentrating on e-tailing service quality, Wolfinbarger and Gilly (2003) argue that four factors-website design, fulfillment/reliability, privacy/security, and customer service-strongly predict customer satisfaction. Kotha et al. (2004) study the role of online buying experience as a competitive advantage along five dimensions: website usability, customer confidence in the web business, the selection of goods and services on the site, the effectiveness of relationship services such as virtual community building and site personalization, and the extent of price leadership. They conclude that website usability and product selection can be easily competed away via imitation, while superior customer service can lead to a sustainable competitive advantage. Devaraj et al. (2002) find that the usefulness and ease-of-use of online shopping, together with high service quality, are factors affecting consumer satisfaction and, subsequently, their channel preference. Price can also play a role in customer satisfaction. Because online stores are only a mouse click away, many studies have argued that price is an important factor in a customer's decision-making process (Lee and Overby 2004) . Using BizRate data, Jiang and Rosenbloom (2005) find that after-delivery satisfaction and price perception have a stronger impact on customer satisfaction than at-checkout satisfaction. Combining the aforementioned studies while integrating their similar dimensions, 1 we review three retailer characteristics, namely website design, customer service, and pricing, and we provide theoretical background for this research.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O


Coherence time-based cooperative MAC protocol 1 for wireless ad hoc networks In this article, we address the goal of achieving performance gains under heavy-load and fast fading conditions. CoopMACI protocol proposed in Proceedings of the IEEE International Conference on Communications (ICC), Seoul, Korea, picks either direct path or relay path based on rate comparison to enhance average throughput and delay performances. However, CoopMACI performance deteriorates under fading conditions because of lower direct path or relay path reliability compared to UtdMAC (Agarwal et al. LNCS, 4479, 415-426, 2007). UtdMAC was shown to perform better than CoopMACI in terms of average throughput and delay performances because of improved transmission reliability provided by the backup relay path. Although better than CoopMACI, UtdMAC does not fully benefit from higher throughput relay path (compared to the direct path), since it uses relay path only as a secondary backup path. In this article, we develop a cooperative MAC protocol (termed as instantaneous relaybased cooperative MAC-IrcMAC) that uses channel coherence time and estimates signal-to-noise ratio (SNR) of source-to-relay, relay-to-destination, and source-to-destination links, to reliably choose between relay path or direct path for enhanced throughput and delay performances. Unique handshaking is used to estimate SNR and single bit feedbacks resolve contentions among relay nodes, which further provides source node with rate (based on SNR) information on source-to-destination, source-to-relay, and relay-to-destination links. Simulation results clearly show that IrcMAC significantly outperforms the existing CoopMACI and the UtdMAC protocols in wireless ad hoc network. Results show average throughput improvements of 41% and 64% and average delay improvementd of 98.5% and 99.7% compared with UtdMAC and CoopMACI, respectively. Ever-increasing demand for higher throughput and lower delay in wireless ad hoc networks led to an extensive research into newer techniques, algorithms, and technologies. One such significant contribution is the notion of "Cooperative Communication" in ad hoc networks. Cooperative communication harnesses the broadcast nature of the wireless channel and uses spatial diversity of independent paths to mitigate channel impairments (mean signal loss and fading), enhances throughput capacity of the network, and reduces retransmission latency [1, 2] . In cooperative communication paradigm, nodes cooperate with the source and destination nodes at physical layer and/or MAC layer to improve throughput, delay, and coverage. Nodes cooperating at the physical layer receive packets and combine them together using different techniques (e.g., linear or random coding) for transmission to the destination nodes. Destination node can use multiple copies of the transmitted packet to decode with high reliability. Cooperation at physical layer has led to a specialized field of network coding [3] .. In general, for single hop ad hoc networks cooperative MAC protocols can be classified into two major categories: (1) protocols that invoke relay node when transmission time via relay path is better than the direct path, and (2) protocols that invoke the relay node for backup transmission when direct transmission fails due to fading or interference. Cooperative communication is different from multihop communication in the sense that although source-destination pair can communicate directly at some rate, but the relay node is still invoked to achieve enhanced data rate. Nodes cooperating at MAC level simply relay the received packets for improved throughput and coverage reliability. Specifically, MAC level cooperation improves performance when source-destination nodes are separated by a distance that prevents the source node from directly transmitting to the destination node at high data rates. Using any intermediate node that is appropriately located (and is willing to cooperate) can allow transmission at higher data rates compared to the direct transmission.. CoopMACI protocol falls under category one and is the most suitable for networks with mobile nodes [4, 5] . It is based on slight modification of IEEE 802.11 distributed coordination function (DCF) that benefits from cooperation between nodes in infrastructure-based wireless LAN (WLAN). CoopMACI uses a table-driven approach. Source node updates table entries by measuring path losses between the source and the relay nodes. Path losses allow estimation of possible rates using a rate look-up table. Further, the achievable rate between the relay node and the access point (AP) is obtained by listening to physical layer header transmissions between the relay and the AP. Once the source node has a packet to transmit, it compares the transmission times (using the relay table) between direct and indirect (via relay) transmissions and then picks the path (direct path or indirect path) that maximizes the rate. However, it is noted that CoopMACI only uses either direct path or indirect path for packet transmission based on updated table. Korakis et al. [6] extended CoopMACI for ad hoc network environment. It is very similar to CoopMACI approach, but adds some minor features in data and control planes. Reference [7] is a category two cooperative MAC protocol that opportunistically invokes the relay when direct transmission fails (termed as Utd-MAC). UtdMAC does not invoke any particular relay which can support higher data rate to the destination, but assumes that the relay will cooperate if present. Zhu and Cao [8] propose that rDCF protocol that requires periodic broadcast of willing list by each node to its one-hop neighbors. Further, the protocol piggybacks the data rate information to its request-to-send (RTS) and clear-to-send (CTS) packets which add more overhead and requires modifications to the legacy IEEE 802.11 MAC protocol. Zhu and Cao [9] propose infrastructurebased rpcf protocol, where a node reports to the AP with the sensed channel information. The AP then informs the node about the feasible rate for the relay through the polling packet.. It was shown in [7] that under Rayleigh fading conditions, UtdMAC protocol outperforms CoopMACI in terms of throughput. It is worth mentioning here that UtdMAC assumes that nodes have already agreed to cooperate and so does not consider relay management overhead when comparing results with the CoopMACI protocol. Results show that UtdMAC performs better because it uses diversity of the relay paths for backup transmissions. On the other hand, CoopMACI picks either the direct path or the relay path (indirect path) for reduced transmission time and does not invoke diversity for backup transmission. Although, the relay path can provide higher data rate, it is more susceptible to transmission failure due to independent fading on source-to-relay and relay-to-destination links. Hence, the relay path in CoopMACI can provide higher throughput, but with lower probability of packet success. In contrast, UtdMAC has higher probability of packet success due to backup relay path, but provides lower data rate depending upon source-destination separation. In essence, both CoopMACI and UtdMAC protocols lack in providing higher throughput with higher probability of success under fast fading conditions.. In this article, we develop IrcMAC protocol that measures signal-to-noise ratio (SNR) on source-to-destination, source-to-relay, and relay-to-destination links to evaluate packet transmission opportunities through direct and the candidate relay paths. A relay path becomes a candidate only when the channel coherence time is greater than the total transmission time through the relay path. Once, IrcMAC selects the best candidate relay path, the packet is then transmitted through the path (direct or indirect) that incurs minimum transmission time. In case, no candidate relay path is available, the IrcMAC protocol transmits directly to the destination node at the rate estimated during the handshake procedure. Protocol details are provided in later sections. In this article, we have proposed a novel cooperative protocol termed as IrcMAC for ad hoc networks. In contrast to UtdMAC and CoopMACI protocols, Irc-MAC protocol monitors instantaneous SNR during handshake procedure and picks a relay path only when it incurs total transmission time (based on SNR) less than the channel coherence time and the direct path transmission time. Thus, the relay is tapped only when it can offer reliable transmission path; otherwise, direct transmission takes place. Furthermore, given that all the nodes are at least within the mutual communication range, the proposed protocol introduces RR frame that resolves contentions among candidate relay nodes and allows contending relays located in close proximity at the time to communicate instantaneous rate information to the source node through single-bit feedbacks. Simulation results show average throughput improvement of 41% and 64% and average delay improvement of 98.5% and 99.7% compared to UtdMAC and CoopMACI protocols, respectively. In future, we plan to evaluate all the scenarios beyond nodes in mutual communication range.. Abbreviations AP: access point; CTS: clear-to-send; DCF: distributed coordination function; NAV: network allocation vector; RRF: relay response frame; RTS: request-tosend; SIFS: short interframe space; SNR: signal-to-noise ratio; WLAN: wireless LAN.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O


Arm load magnitude affects selective shoulder muscle activation Abstract For isometric tasks, shoulder muscle forces are assumed to scale linearly with the external arm load magnitude, i.e., muscle force ratios are constant. Inverse dynamic modeling generally predicts such linear scaling behavior, with a critical role for the arbitrary load sharing criteria, i.e., the ''cost function''. We tested the linearity of the relation between external load magnitude exerted on the humerus and shoulder muscle activation. Six isometric force levels ranging from 17 to 100% of maximal arm force were exerted in 24 directions in a plane perpendicular to the longitudinal axis of the humerus. The direction of maximum muscle activation, the experimentally observed so called Principal Action (PA), was determined for each force magnitude in 12 healthy subjects. This experiment was also simulated with the Delft Shoulder and Elbow Model (DSEM) using two cost functions: (1) minimizing muscle stress and (2) a compound, energy related cost function. PA, both experimental (PA exp ) and simulated (PA sim ), was expected not to change with arm forces magnitudes. PA exp of the mm. trapezius pars descendens, deltoideus pars medialis and teres major changed substantially as a function of external force magnitude, indicating external load dependency of shoulder muscle activation. In DSEM simulations, using the stress cost function, small non-linearities in the muscle forceexternal load dependency were observed, originating from gravitational forces working on clavicular and scapular bone masses. More pronounced non-linearities were introduced by using the compound energy related cost function, but no similarity was observed between PA exp and PA sim . Individual muscle forces change with armload direction. This load direction dependency was used to study muscle coordination in healthy subjects [1, 4, 10, 14, 18] and subjects with shoulder pathologies [5, 20] . The Principal Action (PA), which comprehends load direction dependent electromyography (EMG) parameters [4, 14] , is used as a descriptive parameter for muscle coordination. In practice, repeated measurements are performed before and after an intervention, while maximum force around the shoulder may be altered by the intervention, e.g., by pain reduction or muscle tendon transfers [20] . In the comparison of these experiments, we assume that muscle forces scale linearly with external force magnitude. External forces may differ considerably in pre-post measurements [5, 20] and interindividually [4, 18] . So linearity is a pre-requisite, or should be predictable if muscle contraction patterns are to be compared under these different loading conditions. In the jaw, linear scaling of muscle activity (EMG) and external load was indeed demonstrated [2, 25] . However, non-linear muscle activation scaling with external arm load was reported in the upper extremity [8] .. In shoulder inverse dynamic modeling, linearity is generally assumed and incorporated in the load sharing criteria that are needed to mathematically solve the redundancy problem in order to reach a unique muscle activation pattern [3, [7] [8] [9] 21] . Praagman et al. [19] introduced a combination of a linear stress and a quadratic energy cost function, which turned out to fit best with non-linear in vivo obtained muscle energy expenditure around the elbow using near infrared spectroscopy. They stated that most cost functions are chosen rather arbitrary, mainly due to the fact that validation is difficult since muscle force cannot be measured accurately in vivo. The EMG based PA method offers an alternative method to compare in vivo observed activation simulated muscle activation, in order to interpret the experimental results and to predict possible load dependencies of shoulder muscle activation patterns in future studies [3, 4] .. In the present study, we experimentally test the assumption that relative shoulder muscle forces do not change with armload magnitude. The experiment was numerically simulated, using the Delft Shoulder and Elbow Model (DSEM) with both a linear and an energy related cost function [19, [22] [23] [24] . We used the PA, i.e. the direction of maximum muscle activation assessed by either EMG (experiment) or force (simulation), respectively PA exp and PA sim , as a parameter for muscle coordination. Activation of three shoulder muscles appeared to be load dependent. This has consequences for the interpretation of muscle contraction patterns as measured in patients with shoulder disorders before and after intervention. In shoulder model simulations (DSEM) of the present experiment, non-linearities in the muscle force-external load relationships were not found using a quadratic stress cost function except when gravitational forces working on clavicular and scapular bone mass were incorporated. More pronounced non-linearities were introduced using a compound energy related cost function, however not leading to a better resemblance of PA exp to PA sim . The average maximum force performed within the study population was 65 N (SD = 22.3). PA exp for all muscles and loading conditions, as well as the number of observations after exclusion of outliers, is presented in Table 2 . Mm. trapezius pars descendens, deltoideus pars medialis and teres major showed a significant shift of PA exp as a function of external load. The maximum observed effect (m. teres major) of external loading on PA exp was b = -1.08, i.e. -1.08°per % of F max . The PA exp dependency was described by a linear regression model (Table 3 ).. In Fig. 2 changes in PA with respect to PA at the first force level (PA at 17% of F max = 0 o ) are presented. PA exp are shown (blue circles), together with PA sim , obtained using both a quadratic stress cost function (green upwardpointing triangles) and a compound energy cost function (black downward-pointing triangles). DSEM simulations with a quadratic stress cost function showed very small, but noticeable non-linear scaling. In our model, we simulated gravity compensation of the humerus, but the observed non-linearities could still be introduced by gravity working on the clavicle and scapular bone, which was obviously not controlled for in the in vivo experiments. To make this effect more clearly visible, we performed model simulations including only one force direction, i.e., a force acting downwards on the arm, with two different magnitudes, i.e., 10 and 20 N. We subsequently compared estimated muscle forces in a model with gravity working on the clavicle and scapular bone masses, and a model without. Indeed, we found non-linear external load dependence introduced in the first model in contrast to the simulation with full gravity compensation ( Table 4) .. The compound 'energy cost function' appeared to result in a non-linear relation between PA sim and external load. Except for the m. supraspinatus no similarity was observed between PA exp and PA sim (Fig. 2) . Subjects were seated with the dominant arm in a splint with the elbow in 90°of flexion (Fig. 1) . The set-up allowed for static, isometric contractions of shoulder muscles while loading the arm with a force of different magnitudes in different directions in a plane perpendicular to the humerus [3, 4, 18] . The humeral plane of elevation was approximately 60°rotated externally from the para-sagittal plane and the humerus was 60°abducted. The forearm was 45°e xternally rotated relative to the horizontal plane (see Fig. 1 ). The objective of the set-up was to record only forces perpendicular to the longitudinal axis of the humerus. In rest, the arm was fully supported by means of a weight and pulley system to compensate for all gravitational forces and moments [4, 18] . The arm splint was attached to a 3D force transducer (AMTI-300, Advanced Mechanical Technology, Inc., Watertown MA, USA) by means of a low friction ball and socket joint. The transducer was mounted on a low friction rail in line with the humerus. This construction allowed for movement of the arm along four degrees of freedom (three rotations and a translation), while translations along the axes perpendicular to the humerus long arm were constrained. These forces controlled the position of a cursor on a computer screen placed in front of the subjects [4, 18] (Fig. 1) .. EMG activity of 12 shoulder muscles was recorded (Table 1) , and off-line post-processed [4, 18] . Nine shoulder muscles were recorded with the use of bipolar silver bar surface electrodes (DelSys, Bagnoli-16, Boston MA, USA, analog filter: 20 Hz high pass, 450 Hz low pass, 10 mm electrode length, inter-electrode distance of 10 mm). ; the subject had the arm in a splint, which was connected to a force transducers. Subjects were required to bring the arm force driven red cursor into the blue target area. The force, perpendicular to the humerus long axis, was recorded with a 6-dof force transducer (AMTI). The target indicated force direction (n = 24) and force magnitude, i.e., radius (n = 6), resulting in 144 combinations Sample rate of analog filtered EMG and force data was 1,000 Hz. Before placement of the electrodes, the skin was abraded, cleaned and a skin preparation gel (Skin Pure, Nihon Kohden) was used. The EMG of the three rotatorcuff muscles was recorded by means of bi-polar wire electrodes ( Table 1 ). The wires were made of Teflon coated stainless steel with bare tips of 2-mm length and were inserted with a sharp hollow needle. The electrode tips were bent in a sharp angle, so that after withdrawal of the needles, the wires would remain in situ. The wires for the m. subscapularis were inserted with a curved needle underneath the medial border of the scapula [12] . Before insertion of the needles, the skin was anaesthetized with a 5% lidocaine solution. The needles for the mm. subscapularis and infraspinatus were inserted until the scapular bone was touched.

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