spectral shape discrimination by hearing impaired and normal hearing listeners the ability to discriminate between sounds with different spectral shapes was evaluated for normal hearing and hearing impaired listeners listeners discriminated between a standard stimulus and a signal stimulus in which half of the standard components were decreased in level and half were increased in level in one condition the standard stimulus was the sum of six equal amplitude tones equal spl and in another the standard stimulus was the sum of six tones at equal sensation levels re audiometric thresholds for individual subjects equal sl spectral weights were estimated in conditions where the amplitudes of the individual tones were perturbed slightly on every presentation sensitivity was similar in all conditions for normal hearing and hearing impaired listeners the presence of perturbation and equal sl components increased thresholds for both groups but only small differences in weighting strategy were measured between the groups depending on whether the equal spl or equal sl condition was tested the average data suggest that normal hearing listeners may rely more on the central components of the spectrum whereas hearing impaired listeners may have been more likely to use the edges however individual weighting functions were quite variable especially for the hi listeners perhaps reflecting difficulty in processing changes in spectral shape due to hearing loss differences in weighting strategy without changes in sensitivity suggest that factors other than spectral weights such as internal noise or difficulty encoding a reference stimulus also may dominate performance

the effects of amplitude perturbation and increasing numbers of components in profile analysis in a profile analysis task the effect of randomly perturbing the amplitudes of the components of multi tone stimuli was studied in two experiments in the first experiment thresholds for a signal added in phase to the central component of a standard were measured for different numbers of components in two conditions in one condition thresholds were measured in blocks for six different jagged standards and in another thresholds were measured when one of the six standards was chosen randomly on a presentation by presentation basis regardless of condition thresholds did not depend on the numbers of components and increased magnitude of perturbation increased thresholds moreover the slope relating thresholds to number of components did not increase with increasing magnitude of perturbation in the second experiment the signal consisted of an increase in amplitude of the central components and a decrease in amplitude of the outer components of the standard a stimulus type which has been shown to maximize the change in threshold with increasing number of components the amplitudes of component tones were selected randomly on a presentation by presentation basis thresholds fell with increases in the number of components but the slope relating thresholds to numbers of components did not change as the magnitude of perturbation increased the latter result contrasts with that reported by kidd et al j acoust soc am 90 1340 1354 1991

causal inference by using invariant prediction identification and confidence intervals summary what is the difference between a prediction that is made with a causal model and that with a non causal model suppose that we intervene on the predictor variables or change the whole environment the predictions from a causal model will in general work as well under interventions as for observational data in contrast predictions from a non causal model can potentially be very wrong if we actively intervene on variables here we propose to exploit this invariance of a prediction under a causal model for causal inference given different experimental settings e g various interventions we collect all models that do show invariance in their predictive accuracy across settings and interventions the causal model will be a member of this set of models with high probability this approach yields valid confidence intervals for the causal relationships in quite general scenarios we examine the example of structural equation models in more detail and provide sufficient assumptions under which the set of causal predictors becomes identifiable we further investigate robustness properties of our approach under model misspecification and discuss possible extensions the empirical properties are studied for various data sets including large scale gene perturbation experiments

causal diagrams for empirical research summary the primary aim of this paper is to show how graphical models can be used as a mathematical language for integrating statistical and subject matter information in particular the paper develops a principled nonparametric framework for causal inference in which diagrams are queried to determine if the assumptions available are sufficient for identifying causal effects from nonexperimental data if so the diagrams can be queried to produce mathematical expressions for causal effects in terms of observed distributions otherwise the diagrams can be queried to suggest additional observations or auxiliary experiments from which the desired inferences can be obtained

monotone schwarz iterates for a semilinear parabolic convection diffusion problem this paper deals with a discrete monotone iterative algorithm for solving a nonlinear singularly perturbed convection diffusion problem of parabolic type on each time level the monotone method known as the method of lower and upper solutions is applied to computing a nonlinear upwind difference scheme obtained after discretisation of the continuous problem a monotone domain decomposition algorithm based on a modification of the schwarz alternating method is constructed the rate of convergence of the monotone schwarz method is estimated uniform convergence properties of the monotone domain decomposition algorithm are studied numerical experiments are presented

a parallel schwarz method for a convection diffusion problem this paper describes a parallel convection diffusion solver which may be used as part of a navier stokes solver for three dimensional channel flow at moderately large reynolds numbers s turek efficient solvers for incompessible flow problems an algorithmic approach in view of computational aspects springer verlag 1999 the solver uses a multiplicative schwarz domain decomposition with overlapping subdomains to solve singularly perturbed convection diffusion equations where convection is dominant upwind finite differences are used for the spatial discretization the algorithm uses special features of the singularly perturbed convection diffusion operator the error due to a local perturbation of the boundary conditions decays extremely fast in the upwind as well as the crosswind direction so the overlap in the domain decomposition can be kept to a minimum the algorithm parallelizes well and is particularly suited for applications in three dimensions results of two and three dimensional numerical experiments are presented

individual differences in the improvement in spectral shape discrimination due to increasing number of nonsignal tones the effect of the number of nonsignal tones on the just discriminable difference in spectral shape was evaluated for 12 naive subjects the signal was an intensity increment to the center tone of a multitone complex the tones were spaced at equal frequency ratios and except for the signal increment were equal in level the number of nonsignal tones ranged from 2 to 20 consistent with previous studies using equally spaced components group mean thresholds improved monotonically with increasing number of tones group mean thresholds improved about 8 db over the range of reference spectra employed large differences were found across subjects in overall performance and in the magnitude of the improvement with increasing number of nonsignal tones the greatest intersubject variability was observed for the stimuli composed of the fewest components it was concluded that the differences reported in the literature concerning the presence and magnitude of the improvement are due both to differences in the pr

evaluation of simple models of auditory profile analysis using random reference spectra this article describes further study of the finding reported by green et al j acoust soc am 73 639 643 1983 and others that in certain conditions the threshold of detectability for an intensity increment to the center tone of a multitone reference spectrum decreased as the number of nonsignal tones increased that result was considered remarkable since critical band theory would predict that these nonsignal tones spaced outside the critical band containing the signal would have no effect on or at most slightly decrease within band detectability and certainly could not account for the result of improved detectability found in the study cited above recently henn and turner j acoust soc am 88 126 131 1990 were unable to replicate the result described above concluding that the phenomenon exists only in limited conditions and that it is highly individual in nature further they speculated that the most likely reason for the discrepancy between their study and previous s

a domain decomposition taylor galerkin finite element approximation of a parabolic singularly perturbed differential equation in this paper we deal with a discrete monotone iterative domain decomposition midd method based on schwarz alternating algorithm for solving parabolic singularly perturbed partial differential equations a discrete iterative algorithm is proposed which combines the monotone approach and the iterative non overlapping domain decomposition method ddm based on the schwarz alternating procedure using three step taylor galerkin finite element 3tgfe approximation for solving parabolic singularly perturbed partial differential equations the subdomain boundary conditions are updated through well defined interface problems the convergence of the midd method has been established further the proposed 3tgfe based midd method has been successfully implemented on three test problems

on an uniform multidomain decomposition method applied to a singularly perturbed problem with regular boundary layers this paper deals with an iterative algorithm for multidomain decomposition applied to the solution of a singularly perturbed convection diffusion problem uniform convergent properties of the algorithm are established numerical results are presented

spectral peak selection in spectral shape discrimination by normal hearing and hearing impaired listeners spectral shape discrimination thresholds were measured in the presence and absence of noise to determine whether normal hearing and hearing impaired listeners rely primarily on spectral peaks in the excitation pattern when discriminating between stimuli with different spectral shapes standard stimuli were the sum of 2 4 6 8 10 20 or 30 equal amplitude tones with frequencies fixed between 200 and 4000hz signal stimuli were generated by increasing and decreasing the levels of every other standard component the function relating the spectral shape discrimination threshold to the number of components n showed an initial decrease in threshold with increasing n and then an increase in threshold when the number of components reached 10 and 6 for normal hearing and hearing impaired listeners respectively the presence of a 50 db spl hz noise led to a 1 7db increase in threshold for normal hearing listeners and a 3 5db increase for hearing impaired listeners multichannel modeling and the relatively s

conditional independence and chain event graphs graphs provide an excellent framework for interrogating symmetric models of measurement random variables and discovering their implied conditional independence structure however it is not unusual for a model to be specified from a description of how a process unfolds i e via its event tree rather than through relationships between a given set of measurements here we introduce a new mixed graphical structure called the chain event graph that is a function of this event tree and a set of elicited equivalence relationships this graph is more expressive and flexible than either the bayesian network equivalent in the symmetric case or the probability decision graph various separation theorems are proved for the chain event graph these enable implied conditional independencies to be read from the graph s topology we also show how the topology can be exploited to tease out the interesting conditional independence structure of functions of random variables associated with the underlying event tree

random walks and percolation on trees there is a way to define an average number of branches per vertex for an arbitrary infinite locally finite tree it equals the exponential of the hausdorff dimension of the boundary in an appropriate metric its importance for probabilistic processes on a tree is shown in several ways including random walk and percolation where it provides points of phase transition

computation causation and discovery in science business and policymaking anywhere data are used in prediction two sorts of problems requiring very different methods of analysis often arise the first problems of recognition and classification concerns learning how to use some features of a system to accurately predict other features of that system the second problems of causal discovery concerns learning how to predict those changes to some features of a system that will result if an intervention changes other features this book is about the second more difficult type of problem typical problems of causal discovery are how will a change in commission rates affect the total sales of a company how will a reduction in cigarette smoking among older smokers affect their life expectancy how will a change in the formula a college uses to award scholarships affect its dropout rate these sorts of changes are interventions that directly alter some features of the system and perhaps and this is the question indirectly alter others the contributors discuss recent research and applications using bayes nets or directed graphic representations including representations of feedback of recursive systems the book contains a thorough discussion of foundational issues algorithms proof techniques and applications to economics physics biology educational research and other areas

causal inference without counterfactuals abstract a popular approach to the framing and answering of causal questions relies on the idea of counterfactuals outcomes that would have been observed had the world developed differently for example if the patient had received a different treatment by definition one can never observe such quantities nor assess empirically the validity of any modeling assumptions made about them even though one s conclusions may be sensitive to these assumptions here i argue that for making inference about the likely effects of applied causes counterfactual arguments are unnecessary and potentially misleading an alternative approach based on bayesian decision analysis is presented properties of counterfactuals are relevant to inference about the likely causes of observed effects but close attention then must be given to the nature and context of the query as well as to what conclusions can and cannot be supported empirically in particular even in the absence of statistical uncertainty such inferences m

auditory profile analysis of irregular sound spectra the discrimination of changes in the shapes of sound spectra is reported the change was always an intensity increment to the 948 hz component of a multitone complex first the ability of naive listeners to learn to discriminate a change in a regular background or reference spectrum equal level tones equally spaced in logarithmic frequency was measured as a function of the number of trials on the average threshold improved about 10 db over 3000 trials with about 50 of the decrease in threshold occurring during the first 750 trials in a subsequent series of experiments the overall pattern of spectral shape of the background was varied randomly two kinds of perturbations in spectral shape were employed 1 randomly choosing the frequencies of the reference spectra and 2 randomly choosing the amplitudes of the components of the reference spectra the experimental manipulations involved fixing the random spectra across a block of trials varying the reference spectra from interval to interval of each trial and providing extensive practice in discriminating specific randomly perturbed reference spectra the results of the spectrum learning and random perturbation experiments provide insight into the roles of critical band filtering sensory variability and short term and long term memory representations in auditory profile analysis further the appropriateness of the generalization of a simple energy detection model is discussed

effect of temporal position proportional variance and proportional duration on decision weights in temporal pattern discrimination two experiments investigated how listeners allocate their attention to different segments of a temporal pattern the experiments allowed a direct test of the predictions of the proportion of total duration ptd rule and the component relative entropy core model listeners had to decide whether two sequences of nine tones had the same or different temporal patterns tone duration 25 ms tone frequency 1000 hz a sequence s temporal pattern was determined by the time intervals between each tone s offset and the next tone s onset on same trials the time intervals at corresponding temporal positions in the two sequences were identical on different trials the corresponding time intervals were randomly varied listener attention to different temporal positions within a sequence was assessed by calculating the decision weights at each position the results supported the core model and were inconsistent with the ptd rule manipulating the mean of the time intervals within the sequence had no consistent ef

a finite element solver and energy stable coupling for 3d and 1d fluid models the paper develops a solver based on conforming finite element method fem for a 3d 1d coupled incompressible flow problem new coupling conditions are introduced to ensure a suitable bound for the cumulative energy of the model we study the stability and the accuracy of the discretization method and the performance of some state of the art linear algebraic solvers for such flow configurations motivated by the simulation of the flow over inferior vena cava ivc filter we consider the coupling of a 1d fluid model and a 3d fluid model posed in a domain with anisotropic inclusions the relevance of our approach to realistic cardiovascular simulations is demonstrated by computing blood flows over a model ivc filter

maximum norm stability of difference schemes for parabolic equations on overset nonmatching space time grids in this paper theoretical results are described on the maximum norm stability and accuracy of finite difference discretizations of parabolic equations on overset nonmatching space time grids we consider parabolic equations containing a linear reaction term on a space time domain 0 t which is decomposed into an overlapping collection of cylindrical subregions of the form l 0 t for l 1 p each of the space time domains l 0 t are assumed to be independently grided in parallel according to the local geometry and space time regularity of the solution yielding space time grids with mesh parameters hl and l in particular the different space time grids need not match on the regions of overlap and the time steps l can differ from one grid to the next we discretize the parabolic equation on each local grid by employing an explicit or implicit scheme in time and a finite difference scheme in space satisfying a discrete maximum principle the local discretizations are coupled together without the use of lagrange multipliers by requiring the boundary values on each space time grid to match a suitable interpolation of the solution on adjacent grids the resulting global discretization yields a large system of coupled equations which can be solved by a parallel schwarz iterative procedure requiring some communication between adjacent subregions our analysis employs a contraction mapping argument applications of the results are briefly indicated for reaction diffusion equations with contractive terms and heterogeneous hyperbolic parabolic approximations of parabolic equations

the number of components in profile analysis tasks the central issue of this paper is how detection of a change in spectral shape depends on the number of components m that define the spectrum first a channel theory is reviewed and the predictions relating the detectability of such a change as a function of the number of components are derived second the existing literature is reviewed most of it concerns the detection of an increment in a single tone of an m component equal amplitude complex the data are close 2 db to the predictions of the theory which suggests that there is a relatively small change in threshold as the number of components increases the consistency of the data is also discussed and hypotheses for discrepancies are presented finally the results of an experiment measuring the detectability of a special spectral shape change is explored in this case all the changes are equal in size but some are opposite in sign so that the summed change is zero the results using this balanced spectral change are also consistent with the predictions of the theory and show that for this special kind of spectral change thresholds improve by nearly 7 db as m increases from 4 to 24 components

flexible multiple semicoarsening for three dimensional singularly perturbed problems we present robust parallel multigrid based solvers for 3d scalar partial differential equations the robustness is obtained by combining multiple semicoarsening strategies matrix dependent transfer operators and a krylov subspace acceleration the basis for the 3d preconditioner is a 2d method with multiple semicoarsened grids based on the mg s method from c w oosterlee appl numer math 19 1995 pp 115 128 and t washio and c w oosterlee gmd arbeitspapier 949 gmd st augustin germany 1995 the 2d method is generalized to three dimensions with a line smoother in the third dimension the method based on semicoarsening has been parallelized with the grid partitioning technique j linden b steckel and k stuben parallel comput 7 1988 pp 461 475 o a mcbryan et al impact comput sci engrg 3 1991 pp 1 75 and is evaluated as a solver and as a preconditioner on a mimd machine the robustness of the 3d method is shown for finite volume and finite difference discretizations of 3d anisotropic diffusion equations and convection dominated convection diffusion problems

causal analysis with chain event graphs as the chain event graph ceg has a topology which represents sets of conditional independence statements it becomes especially useful when problems lie naturally in a discrete asymmetric non product space domain or when much context specific information is present in this paper we show that it can also be a powerful representational tool for a wide variety of causal hypotheses in such domains furthermore we demonstrate that as with causal bayesian networks cbns the identifiability of the effects of causal manipulations when observations of the system are incomplete can be verified simply by reference to the topology of the ceg we close the paper with a proof of a back door theorem for cegs analogous to pearl s back door theorem for cbns

decision strategies of hearing impaired listeners in spectral shape discrimination the ability to discriminate between sounds with different spectral shapes was evaluated for normal hearing and hearing impaired listeners listeners detected a 920 hz tone added in phase to a single component of a standard consisting of the sum of five tones spaced equally on a logarithmic frequency scale ranging from 200 to 4200 hz an overall level randomization of 10 db was either present or absent in one subset of conditions the no perturbation conditions the standard stimulus was the sum of equal amplitude tones in the perturbation conditions the amplitudes of the components within a stimulus were randomly altered on every presentation for both perturbation and no perturbation conditions thresholds for the detection of the 920 hz tone were measured to compare sensitivity to changes in spectral shape between normal hearing and hearing impaired listeners to assess whether hearing impaired listeners relied on different regions of the spectrum to discriminate between sounds spectral weights were estimated from the perturbed standards by correlating the listener s responses with the level differences per component across two intervals of a two alternative forced choice task results showed that hearing impaired and normal hearing listeners had similar sensitivity to changes in spectral shape on average across frequency correlation functions also were similar for both groups of listeners suggesting that as long as all components are audible and well separated in frequency hearing impaired listeners can use information across frequency as well as normal hearing listeners analysis of the individual data revealed however that normal hearing listeners may be better able to adopt optimal weighting schemes this conclusion is only tentative as differences in internal noise may need to be considered to interpret the results obtained from weighting studies between normal hearing and hearing impaired listeners

a schwarz alternating procedure for singular perturbation problems we show that the schwarz alternating procedure offers a good algorithm for the numerical solution of singular perturbation problems provided the domain decomposition is properly designed to resolve the boundary and transition layers we give sharp estimates for the optimal position of the domain boundaries and study the convergence rates of the algorithm for various linear second order singular perturbation problems we report on implementation results for a turning point problem and a combustion problem

the solution of a semilinear evolutionary convection diffusion problem by a monotone domain decomposition algorithm abstract this paper deals with a monotone domain decomposition algorithm for solving a semilinear singularly perturbed convection diffusion problem of parabolic type on each time level the monotone method known as the method of lower and upper solutions is applied to computing a nonlinear upwind difference scheme obtained after discretization of the continuous problem a monotone domain decomposition algorithm based on a modification of the schwarz alternating method is constructed the rate of convergence of the monotone algorithm is estimated uniform convergence properties of the monotone domain decomposition algorithm are studied numerical experiments are presented

an evaluation of parallel multigrid as a solver and a preconditioner for singularly perturbed problems in this paper we try to achieve h independent convergence with preconditioned gmres y saad and m h schultz siam j sci comput 7 1986 pp 856 869 and bicgstab h a van der vorst siam j sci comput 13 1992 pp 63 644 for two dimensional 2d singularly perturbed equations three recently developed multigrid methods are adopted as a preconditioner they are also used as solution methods in order to compare the performance of the methods as solvers and as preconditioners two of the multigrid methods differ only in the transfer operators one uses standard matrix dependent prolongation operators from j e dendy jr j comput phys 48 1982 pp 366 386 w hackbusch multi grid methods and applications springer berlin 1985 the second uses upwind prolongation operators developed in p m de zeeuw j comput appl math 33 1990 pp 1 27 both employ the galerkin coarse grid approximation and an alternating zebra line gauss seidel smoother the third method is based on the block lu decomposition of a matrix and on an approximate schur complement this multigrid variant is presented in a reusken a multigrid method based on incomplete gaussian elimination university of eindhoven the netherlands 1995 all three multigrid algorithms are algebraic methods the eigenvalue spectra of the three multigrid iteration matrices are analyzed for the equations solved in order to understand the convergence of the three algorithms furthermore the construction of the search directions for the multigrid preconditioned gmres solvers is investigated by the calculation and solution of the minimal residual polynomials for poisson and convection diffusion problems all solution methods are investigated and evaluated for finite volume discretizations on fine grids the methods have been parallelized with a grid partitioning technique and are compared on an mimd machine

maximum norm analysis of overlapping nonmatching grid discretizations of elliptic equations in this paper we provide a maximum norm analysis of a finite difference scheme defined on overlapping nonmatching grids for second order elliptic equations we consider a domain which is the union of p overlapping subdomains where each subdomain has its own independently generated grid the grid points on the subdomain boundaries need not match the grid points from adjacent subdomains to obtain a global finite difference discretization of the elliptic problem we employ standard stable finite difference discretizations within each of the overlapping subdomains and the different subproblems are coupled by enforcing continuity of the solutions across the boundary of each subdomain by interpolating the discrete solution on adjacent subdomains if the subdomain finite difference schemes satisfy a strong discrete maximum principle and if the overlap is sufficiently large we show that the global discretization converges in optimal order corresponding to the largest truncation errors of the local interpolation maps and discretizations our discretization scheme and the corresponding theory allows any combination of lower order and higher order finite difference schemes in different subdomains we describe also how the resulting linear system can be solved iteratively by a parallel schwarz alternating method or a schwarz preconditioned krylov subspace iterative method several numerical results are included to support the theory

schwarz alternating algorithms for a convection diffusion problem abstract this paper deals with iterative domain decomposition algorithms for solving a singularly perturbed convection diffusion problem the algorithms are based on schwarz alternating procedure applied to a discrete approximations of the continuous problem convergence properties of the algorithms are established and their parallel implementations are discussed numerical results for a test singularly perturbed problem are presented

sources of variation in profile analysis i individual differences and extended training this study investigated two sources of variance in the ability to discriminate auditory profiles individual differences and extended training the goals of the study were 1 to determine the range and origins of individual differences in profile analysis and 2 to determine whether those who initially had poor sensitivity to changes in spectral shape could eventually acquire finer sensitivity profile stimuli had 11 components with equal log spacing from 200 2200 hz thresholds ranged from 1 to 25 db signal level relative to the context level across 46 listeners the correlation between spectral shape discrimination thresholds after 2000 trials and pure tone intensity discrimination thresholds was 0 36 the range of individual differences for pure tone intensity discrimination and spectral shape discrimination was about the same two groups of listeners were given extended practice on the profile task one group that showed low thresholds after an initial 2000 trials of practice and another that showed much higher initial thresholds all listeners improved during the course of the first 2000 trials of training most of the poor listeners continued to improve during 9000 trials of training individual differences in the listeners sensitivity to changes in spectral shape still existed after the extended practice

on possible cues in profile analysis identification of the incremented component the ability to identify the frequency of the incremented component in a multitone complex was assessed in two conditions both using the same 11 tone complexes fixed frequency equilog spaced random phases in the standard plus signal complex all components had equal level except one of the inner nine which was incremented in level by an in phase addition of a sinusoid of the same frequency the signal the overall level and signal position were randomly varied on each presentation in the standard absent condition the standard plus signal complex was presented first and it was followed by a single sinusoid either at the signal frequency or at that of an adjacent component below or above in the standard present condition a complex with equal level components the standard complex was also presented on each trial either before or after the standard plus signal complex in random order these two complexes were followed by the single sinusoid in both conditions the subjects had to indica

detection of random alterations to time varying musical instrument spectra the time varying spectra of eight musical instrument sounds were randomly altered by a time invariant process to determine how detection of spectral alteration varies with degree of alteration instrument musical experience and spectral variation sounds were resynthesized with centroids equalized to the original sounds with frequencies harmonically flattened and with average spectral error levels of 8 16 24 32 and 48 listeners were asked to discriminate the randomly altered sounds from reference sounds resynthesized from the original data for all eight instruments discrimination was very good for the 32 and 48 error levels moderate for the 16 and 24 error levels and poor for the 8 error levels when the error levels were 16 24 and 32 the scores of musically experienced listeners were found to be significantly better than the scores of listeners with no musical experience also in this same error level range discrimination was significantly affected by the instrument tested for error levels of 16 and 24 discrimination scores were significantly but negatively correlated with measures of spectral incoherence and normalized centroid deviation on unaltered instrument spectra suggesting that the presence of dynamic spectral variations tends to increase the difficulty of detecting spectral alterations correlation between discrimination and a measure of spectral irregularity was comparatively low

a block monotone domain decomposition algorithm for a semilinear convection diffusion problem this paper deals with discrete monotone iterative algorithms for solving a nonlinear singularly perturbed convection diffusion problem a block monotone domain decomposition algorithm based on a schwarz alternating method and on block iterative scheme is constructed this monotone algorithm solves only linear discrete systems at each iterative step of the iterative process and converges monotonically to the exact solution of the nonlinear problem the rate of convergence of the block monotone domain decomposition algorithm is estimated numerical experiments are presented

pressure schur complement preconditioners for the discrete oseen problem we consider several preconditioners for the pressure schur complement of the discrete steady oseen problem two of the preconditioners are well known from the literature and the other is new supplemented with an appropriate approximate solve for an auxiliary velocity subproblem these approaches give rise to a family of the block preconditioners for the matrix of the discrete oseen system in the paper we critically review possible advantages and difficulties of using various schur complement preconditioners we recall existing eigenvalue bounds for the preconditioned schur complement and prove such for the newly proposed preconditioner these bounds hold both for lbb stable and stabilized finite elements results of numerical experiments for several model two dimensional and three dimensional problems are presented in the experiments we use lbb stable finite element methods on uniform triangular and tetrahedral meshes one particular conclusion is that in spite of essential improvement in comparison with simple scaled mass matrix preconditioners in certain cases none of the considered approaches provides satisfactory convergence rates in the case of small viscosity coefficients and a sufficiently complex e g circulating advection vector field

causal identifiability via chain event graphs we present the chain event graph ceg as a complementary graphical model to the causal bayesian network for the representation and analysis of causally manipulated asymmetric problems our focus is on causal identifiability finding conditions for when the effects of a manipulation can be estimated from a subset of events observable in the unmanipulated system ceg analogues of email protected s back door and front door theorems are presented applicable to the class of singular manipulations which includes both email protected s basic do intervention and the class of functional manipulations possible on bayesian networks these theorems are shown to be more flexible than their bayesian network counterparts both in the types of manipulation to which they can be applied and in the nature of the conditioning sets which can be used

iterative domain decomposition algorithms for a convection diffusion problem abstract this paper deals with iterative algorithms for domain decomposition applied to the solution of a singularly perturbed convection diffusion problem with regular boundary layers these algorithms are based on a finite difference domain decomposition approach and on a modified schwarz alternating method convergence properties of the algorithm are established and their parallel implementations are discussed numerical results for a test singularly perturbed problem are presented