a class of bidiagonal schemes for solving the euler equations a class of implicit bidiagonal schemes is developed for the conservative euler equations the schemes are based on a predictor corrector approach for the characteristic variables adapted according to the sign of the characteristic speeds of information they are second order accurate in space and time and have intrinsic dissipative properties a new fully implicit boundary treatment is developed for this class of schemes allowing high cfl numbers in all regions of the flow domain results are presented for the quasi one dimensional flow in a nozzle n recent years substantial progress has been made in the development of numerical methods for solving conservative systems of hyperbolic equations such as the euler equations describing inviscid fluid flow m one of the main achievements has been the development of implicit methods based on tridiagonal solution procedures 2 the use of explicit impl icit artificial viscosity5 and of implicit boundary conditions6 7 has made these algorithms very robust and efficient recently an implicit method based on a bidiagonal solution technique has been introduced by maccormack 1 the first part of this paper is concerned with further developments related to the bidiagonal solution technique a general class of second order accurate bidiagonal schemes is proposed containing a class of implicit schemes and one of semiexplicit schemes it is shown that these schemes are in trinsically dissipative so that no artificial viscosity is necessary for linear stability the second part of the paper introduces an implicit boundary treatment for these bidiagonal schemes that preserves the stability properties of the interior scheme in deed while a number of successful boundary procedures have been proposed for explicit and tridiagonal implicit schemes this stability remained an unsolved problem in earlier ap plications of bidiagonal techniques 8 9 numerical experiments for the euler flow in a nozzle confirm the unconditional linear stability allowing the use of very high cfl numbers

an implicit bidiagonal numerical method for solving the navier stokes equations in recent years much progress has been made in solving fluid dynamical problems using finite difference methods solving inviscid compressible problems in two and three dimensions has become almost routine with many suitable methods explicit or implicit available the problem of compressible viscous flows in complicated geometries remains however a major challenge here fine mesh spacing in the viscous flow regions makes the explicit methods with their simple boundary conditions extremely costly existing implicit methods can make use of large time steps but require inversions of large block tridiagonal matrices a method recently developed by maccormack eliminates this disadvantage by introducing a predictor corrector scheme requiring the inversion of only block bidiagonal matrices it is the aim of present work to extend this method to allow solution of viscous compressible problems in general coordinates for arbitrary two dimensional geometries

grid generation techniques in computational fluid dynamics revue des differentes methodes on montre que les regions tridimensionnelles sont mieux traitees par fragmentation du champ en sous regions avec generation de grilles dans chaque sous region interet des grilles adaptatives couplees a des solutions physiques

nonparametric probabilistic approach of uncertainties for elliptic boundary value problem the paper is devoted to elliptic boundary value problems with uncertainties such a problem has already been analyzed in the context of the parametric probabilistic approach of system parameters uncertainties or for random media model uncertainties are induced by the mathematical physical process which allows the boundary value problem to be constructed from the design system if experiments are not available the bayesian approach cannot be used to take into account model uncertainties recently a nonparametric probabilistic approach of both the model uncertainties and system parameters uncertainties has been proposed by the author to analyze uncertain linear and non linear dynamical systems nevertheless the use of this concept that has to be developed for dynamical systems cannot directly be applied for elliptic boundary value problem for instance for a linear elastostatic problem relative to an elastic bounded domain we then propose an extension of the nonparametric probabilistic approach in order to take into account model uncertainties for strictly elliptic boundary value problems the theory and its validation are presented

a regularized monotonic fuzzy support vector machine model for data mining with prior knowledge incorporating prior knowledge into data mining is an interesting but challenging problem and this study proposes a novel fuzzy support vector machine svm model to explore this issue it considers the fact that in many applications each input point may not be exactly labeled as one particular class and thus it applies a fuzzy membership to each input point it also utilizes expert knowledge concerning the monotonic relations between the response and predictor variables which is represented in the form of monotonicity constraints we formulate the classification problem of a monotonically constrained fuzzy svm called a monotonic fsvm derive its dual optimization problem and theoretically analyze its monotonic property the tikhonov regularization method is further applied to ensure that the solution is unique and bounded a new measure i e the frequency monotonicity rate is proposed to evaluate the ability of the model to retain the monotonicity the results of the experiments on real world and synthetic datasets show that this method which considers different contributions of each data and the prior knowledge of the monotonicity has a number of advantages with regard to predictive ability and retaining monotonicity over the original fsvm and svm models when applied to classification problems

on measures of nonlinearity effects for uncertain dynamical systems application to a vibro impact system the transient dynamics of a linear dynamical system with elastic barriers is studied the system is excited by a deterministic transient force whose fourier transform is limited to a narrow frequency band as the system responds it may impact the elastic barrier therefore the system behavior is nonlinear in order to measure the degree of nonlinearity of the system one looks for the mechanical energy transferred outside the frequency band of excitation as a function of the parameter eta defined by epsilon a in which epsilon is the size of the barrier gap and a is the amplitude of the excitation force the mechanical energy transferred outside the frequency band of excitation can potentially be a source of excitation for other subsystems consequently quantification of this energy transfer is an important step in developing an understanding of the nonlinear dynamical system behavior in addition it is well known that this type of nonlinear dynamical system is very sensitive to uncertainties for this reason the system is considered to be deterministic and also stochastic in order to take into account random uncertainties the proposed analysis is applied to a timoshenko beam having its motion constrained by a symmetric elastic barrier at its free end the confidence region of the random mechanical energy transferred outside the excitation band is shown as a function of eta for several levels of model and data uncertainties from this the robustness of the predictions can be analyzed with respect to model and data uncertainties

rank discrimination measures for enforcing monotonicity in decision tree induction monotone classification is a relatively recent topic in machine learning in which the classification function to learn is asked to guarantee a sort of monotonicity of the class with respect to attribute values nevertheless real datasets are quite far from being monotone and this can sharply limit the performance of purely monotone classifiers while standard classifiers are simply insensitive to monotonicity here we focus on rank discrimination measures to be used in decision tree induction i e functions able to measure the discrimination power of an attribute with respect to the class taking into account the monotonicity of the class with respect to the attribute three new measures are studied in detail and a hierarchical construction model is derived allowing the formal definition of a general rank discrimination measure our measures have been compared with other well known proposals quantifying both the accuracy and the monotonicity of the resulting binary decision tree classifiers

robust ordinal regression for dominance based rough set approach to multiple criteria sorting we present a new multiple criteria sorting method deriving from dominance based rough set approach drsa the preference information supplied by the decision maker dm is a set of possibly imprecise and inconsistent assignment examples on a subset of reference alternatives relatively well known to the dm to structure the data we use drsa and subsequently represent the assignment examples by all minimal sets of rules covering all alternatives from the lower approximations of class unions such a set of rules is called minimal cover set it is one of the instances of the preference model compatible with dm s preference information in this way we implement the principle of robust ordinal regression ror to decision rule preference model for each alternative we derive the necessary and possible assignments specifying the range of classes to which the alternative is assigned by all or at least one compatible set of rules respectively as well as class acceptability indices we also introduce the notion of a representative compatible minimal cover set of rules whose selection builds on the results of ror addressing the robustness concern application of the approach is demonstrated by classifying 69 land zones in 4 classes representing different risk levels

generalized probabilistic approach of uncertainties in computational dynamics using random matrices and polynomial chaos decompositions a new generalized probabilistic approach of uncertainties is proposed for computational model in structural linear dynamics and can be extended without difficulty to computational linear vibroacoustics and computational non linear structural dynamics this method allows the prior probability model of each type of uncertainties model parameter uncertainties and modeling errors to be separately constructed and identified the modeling errors are not taken into account with the usual output prediction error method but with the nonparametric probabilistic approach of modeling errors recently introduced and based on the use of the random matrix theory the theory an identification procedure and a numerical validation are presented then a chaos decomposition with random coefficients is proposed to represent the prior probabilistic model of random responses the random germ is related to the prior probability model of model parameter uncertainties the random coefficients arc related to the prior probability model of modeling errors and then depends on the random matrices introduced by the nonparametric probabilistic approach of modeling errors a validation is presented finally a future perspective is introduced when experimental data are available the prior probability model of the random coefficients can be improved in constructing a posterior probability model using the bayesian approach

induction of ordinal classification rules from decision tables with unknown monotonicity abstract we are considering induction of ordinal classification rules which assign objects to preference ordered decision classes within the dominance based rough set approach in order to extract such rules it is necessary to define dominance inconsistencies with respect to a set of condition attributes containing at least one ordinal condition attribute furthermore it is also assumed that we know if there exist increasing or decreasing monotonicity relationships between the values of ordinal condition and decision attributes very often however this information is unknown a priori one solution to this issue is to transform the ordinal condition attributes with unknown directions of preference to pairs of attributes with supposed inverse monotonic relationships both local and global monotonicity relationships can be represented by decision rules induced from transformed decision tables however in some cases transforming a decision table in this way is overcomplex in this paper we propose the inconsistency rates based on dominance and fuzzy preference relations that have the capacity of discovering monotonic relationships directly from data rather than induced decision rules moreover we propose a refined transformation method by introducing an additional monotonicity checking using these inconsistency rates to determine whether an ordinal condition attribute should be cloned or not experiments are also provided to evaluate the usefulness of the refined transformation method

dominance based rough set approach for group decisions the objective of this paper is to propose an approach to support group multicriteria classification the approach is composed of three phases the first phase exploits the knowledge provided by each decision maker to individually approximate the decision classes using rough approximation the second phase seeks to combine the outputs of individual approximation phase into a collective decision table by using an appropriate aggregation procedure the third phase uses the collective decision table in order to infer a set of collective decision rules which synthesize the judgements and perspectives of the different decision makers and to permit the classification of all decision objects the proposed approach relies on the dominance based rough set approach drsa which is used at two different levels first the drsa is used during the first phase to approximate the input data relative to each decision maker second the drsa is used during the third phase to approximate the collective decision table and generate the collective decision rules this paper presents the theoretical foundation of the proposed approach three case studies using real world data and a comparative study of recent similar proposals

stochastic modeling of uncertainties in computational structural dynamics recent theoretical advances this paper deals with a short overview on stochastic modeling of uncertainties we introduce the types of uncertainties the variability of real systems the types of probabilistic approaches the representations for the stochastic models of uncertainties the construction of the stochastic models using the maximum entropy principle the propagation of uncertainties the methods to solve the stochastic dynamical equations the identification of the prior and the posterior stochastic models the robust updating of the computational models and the robust design with uncertain computational models we present recent theoretical advances in this field concerning the parametric and the nonparametric probabilistic approaches of uncertainties in computational structural dynamics for the construction of the prior stochastic models of both the uncertainties on the computational model parameters and on the modeling uncertainties and for their identification with experimental data we also present the construction of the posterior stochastic model of uncertainties using the bayesian method

second order accurate boundary conditions for compressible flows the accuracy and the consistency of the methods commonly used for the numerical application of the boundary conditions on the surface of solid bodies immerged in an inviscid compressible flow is examined a new method is proposed for the application of second order accurate boundary conditions in the case of isentropic irrotational compressible flows the method is applied to a circular cylinder in uniform subsonic and low transonic flows the conservation law equations are solved using the second order accurate difference scheme of maccormack the results indicate a definite improvement over lower accuracy methods the method can be easily generalized to apply on three dimensional solid surfaces

rough approximation of a preference relation by dominance relations an original methodology for using rough sets to preference modeling in multi criteria decision problems is presented this methodology operates on a pairwise comparison table pct including pairs of actions described by graded preference relations on particular criteria and by a comprehensive preference relation it builds up a rough approximation of a preference relation by graded dominance relations decision rules derived from the rough approximation of a preference relation can be used to obtain a recommendation in multi criteria choice and ranking problems the methodology is illustrated by an example of multi criteria programming of water supply systems

partially monotonic decision trees abstract in multicriteria decision tasks certain features are linearly ordered according to the decision and are called criteria whereas others called regular attributes are not in practice regular attributes and criteria coexist in most classification tasks in this paper we propose a rank inconsistent rate that distinguishes attributes from criteria furthermore it represents the directions of the monotonic relationships between criteria and decisions we design a partially monotonic decision tree algorithm to extract decision rules for partially monotonic classification tasks experimental results show that the proposed algorithm is effective and efficient

nonoscillatory solution of the steady state inviscid burgers equation by mathematical programming abstract numerical solution of the steady state inviscid burgers equation u2 0 on 0 1 u 0 g0 u 1 g1 g0 g1 is considered to obtain the physically relevant discontinuous solution of this problem the equation is singularly perturbed by adding a small amount of viscosity u u2 0 a cell entered finite difference scheme that uses two points for the inviscid part and four points for the viscous part is proposed the overdetermined nonlinear system that results is solved by a homotopy based on the newton linearizer and a linear programming algorithm used to solve l problems difficulties in capturing interior layers centered at node points are observed however the computational results for interior layers centered between node points and for boundary layers show accurate nonoscillatory solutions with discontinuities captured in one cell on both coarse and fine grids the amount of artificial viscosity required to obtain these solutions is small 10 9 compared to the amount of artificial viscosity required by standard methods a partial proof of pointwise and l1 0 1 convergence of the linear spline interpolant of the numerical solution to the inviscid solution h 0 and h 0 is given for one case

karhunen loeve decomposition of coupled axial bending vibrations of beams subject to impacts abstract this work presents a study of the oscillations of a vertical slender beam clamped in its upper extreme pinned in its lower one and constrained inside an outer cylinder in its lower portion the beam is subject to distributed axial loads due to its own weight leading to geometric softening of its lower portion and thus yielding a large number of vibroimpacts with the outer cylinder this is due to the axial bending coupling often called geometric stiffening and largely discussed in the last two decades here it is accounted for by using a non linear finite element model proposed in a previous work in which non linear strain displacement relations are considered to help understand this non linear coupled vibro impact problem the karhunen loeve decomposition also known as the proper orthogonal decomposition is applied to its simulated dynamics the results show that the micro impacts accompanying the beam hole impacts and mainly due to the beam compressive softening and the reaction forces at the top and bottom positions are well represented only when using a non linear axial bending coupling it is also shown that 15 proper orthogonal modes are sufficient to reconstruct the dynamics of the impacting beam under a 3 error margin

boundary approximations for implicit schemes for one dimensional inviscid equations of gasdynamics the applicability to practical calculations of recent theoretical developments in the stability analysis of difference approximations is examined for initial boundary value problems of the hyperbolic type for the numerical experiments the one dimensional inviscid gasdynamic equations in conservation law form are selected a class of implicit schemes based on linear multistep methods for ordinary differential equations is chosen and the use of space or space time extrapolations as implicit or explicit boundary schemes is emphasized some numerical examples with various inflow outflow conditions highlight the commonly discussed issues explicit vs implicit boundary schemes and unconditionally stable schemes hen finite difference schemes are used to solve initial boundary value problems for the equations of fluid dynamics it is well known that most methods require more boundary conditions than those required by the governing partial differential equations these additional boundary conditions for the finite difference equations are often called numerical boundary conditions the numerical boundary conditions cannot be imposed arbitrarily but are determined in general using interior information for example by extrapolation or uncentered approximations in this paper any numerical procedure used to provide a numerical boundary condition will be called a boundary scheme whatever schemes are used for the numerical boundary conditions it is a common practice to assume that the boundary scheme has a local effect and will not affect the solution globally during the early 1970s kreiss 1 2 osher 3 gustafsson et al 4 varah 5 and gustafsson6 published a series of papers establishing methods for checking the stability and accuracy of difference approximations with boundary schemes included since then further progress has been made in the theory of linear difference approximations for initial boundary value problems of the hyperbolic and parabolic type 7 12 because improper treatment of the boundary conditions can lead to instability and inaccuracy even though we start with a stable interior scheme i e scheme for the interior points it is appropriate to adopt an approach that includes the stability and accuracy of the combined interior and boundary schemes surveys of recent developments and extensive bibliographies are included in papers by coughran13 and yee 14 the purpose of this paper is to examine the applicability to practical calculations for nonlinear gasdynamic problems of recent theoretical stability analyses of implicit difference approximations for initial boundary value problems of the hyperbolic type as numerical computations have progressed the use of the conservative form of the gasdynamic equations has gained popularity for physical reasons it is sometimes desirable to specify boundary conditions in the nonconservative variables and to compute with conservative variables in the interior we will consider the additional complications introduced by this procedure

sequential covering rule induction algorithm for variable consistency rough set approaches we present a general rule induction algorithm based on sequential covering suitable for variable consistency rough set approaches this algorithm called vc domlem can be used for both ordered and non ordered data in the case of ordered data the rough set model employs dominance relation and in the case of non ordered data it employs indiscernibility relation vc domlem generates a minimal set of decision rules these rules are characterized by a satisfactory value of the chosen consistency measure we analyze properties of induced decision rules and discuss conditions of correct rule induction moreover we show how to improve rule induction efficiency due to application of consistency measures with desirable monotonicity properties

equitability mutual information and the maximal information coefficient how should one quantify the strength of association between two random variables without bias for relationships of a specific form despite its conceptual simplicity this notion of statistical equitability has yet to receive a definitive mathematical formalization here we argue that equitability is properly formalized by a self consistency condition closely related to data processing inequality mutual information a fundamental quantity in information theory is shown to satisfy this equitability criterion these findings are at odds with the recent work of reshef et al reshef dn et al 2011 science 334 6062 1518 1524 which proposed an alternative definition of equitability and introduced a new statistic the maximal information coefficient mic said to satisfy equitability in contradistinction to mutual information these conclusions however were supported only with limited simulation evidence not with mathematical arguments upon revisiting these claims we prove that the mathematical definition of equitability proposed by reshef et al cannot be satisfied by any nontrivial dependence measure we also identify artifacts in the reported simulation evidence when these artifacts are removed estimates of mutual information are found to be more equitable than estimates of mic mutual information is also observed to have consistently higher statistical power than mic we conclude that estimating mutual information provides a natural and often practical way to equitably quantify statistical associations in large datasets

feature selection for monotonic classification monotonic classification is a kind of special task in machine learning and pattern recognition monotonicity constraints between features and decision should be taken into account in these tasks however most existing techniques are not able to discover and represent the ordinal structures in monotonic datasets thus they are inapplicable to monotonic classification feature selection has been proven effective in improving classification performance and avoiding overfitting to the best of our knowledge no technique has been specially designed to select features in monotonic classification until now in this paper we introduce a function which is called rank mutual information to evaluate monotonic consistency between features and decision in monotonic tasks this function combines the advantages of dominance rough sets in reflecting ordinal structures and mutual information in terms of robustness then rank mutual information is integrated with the search strategy of min redundancy and max relevance to compute optimal subsets of features a collection of numerical experiments are given to show the effectiveness of the proposed technique

a pearson s correlation coefficient based decision tree and its parallel implementation abstract in this paper a pearson s correlation coefficient based decision tree pcc tree is established and its parallel implementation is developed in the framework of map reduce mr pcc tree the proposed methods employ pearson s correlation coefficient as a new measure of feature quality to confirm the optimal splitting attributes and splitting points in the growth of decision trees besides the proposed mr pcc tree adopts map reduce technology to every component during the decision trees learning process for parallel computing which mainly consists of a parallel pearson s correlation coefficient based splitting rule and a parallel splitting data method the experimental analysis is conducted on a series of uci benchmark data sets with different scales in contrast to several traditional decision tree classifiers including bft c4 5 lad sc and nbt on 17 data sets the proposed pcc tree is no worse than the traditional models as a whole furthermore the experimental results on other 8 data sets show the feasibility of the proposed mr pcc tree and its good parallel performance on reducing computational time for large scale data classification problems

multi criteria classification a new scheme for application of dominance based decision rules abstract we are considering the problem of multi criteria classification in this problem a set of if then decision rules is used as a preference model to classify objects evaluated by a set of criteria and regular attributes given a sample of classification examples called learning data set the rules are induced from dominance based rough approximations of preference ordered decision classes according to the variable consistency dominance based rough set approach vc drsa the main question to be answered in this paper is how to classify an object using decision rules in situation where it is covered by i no rule ii exactly one rule iii several rules the proposed classification scheme can be applied to both learning data set to restore the classification known from examples and testing data set to predict classification of new objects a hypothetical example from the area of telecommunications is used for illustration of the proposed classification method and for a comparison with some previous proposals

euler equations implicit schemes and boundary conditions implicit boundary condition procedures are presented for use with implicit finite difference schemes for the unsteady euler equations this new boundary point treatment is based on the mathematical theory of characteristics for hyperbolic systems of equations along with the theoretical background the practical application of the method to several types of boundaries is also explained using several examples the specific boundary conditions covered include subsonic inflow and outflow surface tangency and shock waves the example problems include one dimensional laval nozzle flow dual throat rocket engine nozzle flow and supersonic flow past a sphere the implicit boundary treatment permits the use of large time steps allowing the finite difference algorithm to converge to the asymptotic steady state much faster than schemes that use explicitly applied boundary conditions at least an order of magnitude increase in computational speed is demonstrated in the examples shown background t he growing popularity of solutions to the euler equations in transonics and their continued application in supersonics have increased the need for quicker solutions the potential of implicit schemes in this direction has not been fully exploited for want of correct implicit application of boundary conditions the predominant use of implicit algorithms for the navier stokes equations has partly been responsible for the neglect of implicit boundary point treatment for the euler equations thus there is a need for correct and stable procedures for the easy implicit application of boundary conditions such methods will serve the two purposes of 1 reaching time asymptotic steady state faster and 2 permitting a time step for truly unsteady flow that is not necessarily restricted by the cfl stability criterion but is based upon the magnitude of the transients for clues and information on how to construct such boundary condition procedures one must turn to the mathematical theory of characteristi cs for hyperbolic systems of equations the unsteady euler equations belong to this category the theory for hyperbolic systems is rich with information on signal propagation directions the characteristics theory clearly points to the number of boundary conditions that may and need be prescribed without overdetermining the solution boundary condition procedures based on this theory have been known and applied for several years by kentzer 1 porter and coakley 2 de neef 3 and others in earlier work by this author 4 5 easily understood and implementable methods for boundary point treatment were presented however all of the above techniques were developed for explicit finite difference schemes it seems that it must be easy to extend such methodologies based on mathematical theory for hyperbolic systems to implicit finite difference schemes and indeed it is simple enough the rest of this paper describes such implicit boundary condition procedures the given examples illustrate in detail the application of the proposed methodology to specific types of boundaries and demonstrate the merits of the new scheme

random matrix theory for modeling uncertainties in computational mechanics this paper deals with data uncertainties and model uncertainties issues in computational mechanics if data uncertainties can be modeled by parametric probabilistic methods for a given mean model a nonparametric probabilistic approach can be used for modeling model uncertainties the first part is devoted to random matrix theory for which we summarize previous published results and for which two new ensembles of random matrices useful for the nonparametric models are introduced in a second part the nonparametric probabilistic approach of random uncertainties is presented for linear dynamical systems and for nonlinear dynamical systems constituted of a linear part with additional localized nonlinearities in a third part a new method is proposed for estimating the parameters of the nonparametric approach from experiments finally examples with experimental comparisons are given

reply by authors to g degrez references 1 casier f deconinck h and hirsch ch a class of bidiagonal schemes for solving the euler equations aiaa journal vol 22 nov 1984 pp 1556 1563 2 maccormack r w the effect of viscosity in hypervelocity impact cratering aiaa paper 69 354 april 1969 3 maccormack r w a numerical method for solving the equations of compressible viscous flow aiaa journal vol 20 sept 1982 pp 1275 1281

calculation of shocked one dimensional flows on abruptly changing grids by mathematical programming abstract the steady state inviscid and nearly inviscid burgers equations and the euler equations for steady state shocked flow in a quasi 1 dimensional nozzle are discretized by cell centered finite differences on the cells of an arbitrarily spaced grid inviscid and viscous terms are approximated to second order by 2 point schemes and 4 point schemes respectively there results an overdetermined system of nonlinear algebraic equations this system is solved by a mathematical programming procedure that minimizes a weighted sum of the absolute values of the residuals the l 1 norm of the vector of residuals in this algorithm which is nonconservative no upwinding switches arbitrary constants or heuristic quantities are used the artificial viscosity used to solve the inviscid burgers equation is small 10 15 u no artificial viscosity of any kind is used for the euler equations the numerical solutions of both the viscous and the inviscid problems are accurate and nonoscillatory on grids with abrupt refinements in mesh length by factors as high as 10 4 shocks are invariably captured in one cell and this cell is rarely more than three cells away from the cell in which the physical shock occurs