partitioned runge kutta methods with stiffness detection and stepsize control for the numerical solution of autonomous initial value problems partitioned runge kutta methods are studied consisting of ana stable rosenbrock wanner method for the treatment of the stiff components and a customary runge kutta method for the nonstiff part the equations of condition including the coupling conditions are presented an automatic stiffness detection and a stepsize control for two different algorithms are developed the first algorithm prk4 of order 3 4 possesses an automatic componentwise stiffness detection the second algorithm rkf4rw treats the whole system as nonstiff or as stiff rkf4rw is based on the well known runge kutta fehlberg pair of order 4 5 additionally a row method of order 3 4 with ana stable fourth order approximation is embedded usually rkf4rw is the faster algorithm and the system stiffness detection works more reliable than the componentwise stiffness detection in prk4

a new approach to quantitative and credible diagnosis for multiple faults of components and sensors abstract many practical applications of system diagnosis require the credible identification of multiple faults of nonlinear components and sensors in quantitative measures however the state of the art of diagnosis technique is considered to be still insufficient to meet these severe requirements the approach of diagnosis using the traditional linear system identification theory can diagnose the disturbed parameters of a system in detail and evaluate the quantitative amplitude of the disturbance however it hardly provides the diagnosis of the multiple faults and the diagnosis of the components having high nonlinearity on the other hand some recent model based diagnosis approaches can diagnose the multiple faults even for highly nonlinear components though they do not provide the detailed diagnosis of elements indivisibly involved in components and the quantitative amplitudes of the faults the method proposed in this paper provides an efficient remedy to achieve all of the practical requirements i e the credible detailed and quantitative diagnosis of multiple faults of nonlinear components and sensors our study newly proposes the frameworks of optimal constraints and causal ordering of physical systems also a systematic and strict theory to synthesize these frameworks together with the model based diagnosis is provided to characterize an optimal consistency checking method in diagnosis and to evaluate quantitative amplitudes of faulty disturbances first the detection of faulty behaviors of an objective component is performed based on the quantitative consistency checking between observations and the optimal constraints called as minimal overconstraints consisting of first principles in the components second once if some inconsistencies are detected a mathematical operation of model based diagnosis derives the candidates of faulty elements and functions even under multiple fault conditions third the anomalous quantities directly disturbed by the faulty elements are identified systematically based on causal ordering furthermore the quantitative deviations of these quantities are evaluated by using the minimal over constraints the performance of the proposed method is demonstrated through an example to diagnose an electric water heater the ability of this diagnosis has been confirmed for the multiple faults in nonlinear and dynamic systems

theories of causal ordering abstract this paper is a response to iwasaki and simon 14 which criticizes de kleer and brown 8 we argue that many of their criticisms particularly concerning causality modeling and stability originate from the difference of concerns between engineering and economics our notion of causality arises from considering the interconnections of components not equations when no feedback is present the ordering produced by our qualitative physics is similar to theirs however when feedback is present our qualitative physics determines a causal ordering around feedback loops as well causal ordering is a general technique not only applicable to qualitative reasoning therefore we also explore the relationship between causal ordering and propagation of constraints upon which the methods of qualitative physics are based

the development version of the chevie package of gap3 abstract i describe the current state of the development version of the chevie package which allows to transform the theories of coxeter groups reductive algebraic groups complex reflection groups hecke algebras braid monoids etc into actual computations examples are given showing the code to check some results of lusztig

complex reflection groups braid groups hecke algebras presentations a la coxeter are given for all irreducible nite com plex re ection groups they provide presentations for the corresponding generalized braid groups for all but six cases which allow us to generalize some of the known properties of nite coxeter groups and their associated braid groups such as the computation of the center of the braid group and the construction of deformations of the nite group algebra hecke algebras we introduce monodromy representations of the braid groups which factorize through the hecke algebras extending results of cherednik opdam kohno and others summary introduction complex re ection groups and their presentations a background from complex re ection groups b presentations braid groups and their diagrams a generalities about hyperplane complements b generalities about the braid groups c the braid diagrams proofs of the main theorems for the braid groups b de e r a notation and prerequisites b computation of b de e r and of its center for d c computation of b e e r and of its center hecke algebras a background from di erential equations and monodromy b a family of monodromy representations of the braid group c hecke algebras diagrams and tables appendix generators of the monodromy around a divisor appendix tables to mathematics subject classi cation primary g we thank jean michel peter orlik pierre vogel for useful conversations and the isaac newton institute for its hospitality while the last version of this manuscript was written up the second named author gratefully acknowledges nancial support by the fondation alexander von humboldt for his stays in paris michel brou e gunter malle raphael rouquier

order conditions for numerical methods for partitioned ordinary differential equations motivated by the consideration of runge kutta formulas for partitioned systems the theory of p series is studied this theory yields the general structure of the order conditions for numerical methods for partitioned systems and in addition for nystrom methods fory f y y for rosenbrock type methods with inexact jacobian w methods it is a direct generalization of the theory of butcher series 7 8 in a later publication the theory ofp series will be used for the derivation of order conditions for runge kutta type methods for volterra integral equations 1

runge kutta theory for volterra integrodifferential equations the present paper develops the theory of general runge kutta methods for volterra integrodifferential equations the local order is characterized in terms of the coefficients of the method we investigate the global convergence of mixed and extended runge kutta methods and give results on asymptotic error expansions in a further section we construct examples of methods up to order 4

runge kutta theory for volterra integral equations of the second kind the present paper develops the theory of general runge kutta methods for volterra integral equations of the second kind the order conditions are derived by using the theory of p series which for our problem reduces to the theory of v series these results are then applied to two special classes of runge kutta methods introduced by pouzet and by bel tyukov

implicit explicit runge kutta methods for financial derivatives pricing models abstract implicit explicit runge kutta methods are investigated for application to financial derivatives pricing models in the partial differential equations approach the methods are showed to be an alternative to other existing procedures for the numerical valuation of american type contracts we follow the method of lines in order to have a numerical method that can be used with a variety of state variable discretizations including finite elements finite differences and finite volume methods some numerical experiments are presented

causality as a key to the frame problem abstract in a formal description of actions and changes there is a famous problem known as the frame problem in its generalized form the frame problem is that it is practically impossible to describe or infer all the necessary preconditions qualification problem and all the possible consequences of a given action ramification problem it is not only difficult to determine what changes and what does not change it is also difficult to determine what is relevant our observations show that even humans cannot solve the frame problem humans simply behave as if there were no such problem the solution is to use some kind of heuristics we claim that the notion of causality is the heuristics necessary to solve the frame problem the most important working hypothesis is that causality is not a logical relation as one of the heuristics it is subject to change as more information becomes available there are two kinds of nonmonotonicity in the reasoning of changes one due to a lack of information the other due to change itself we need separate mechanisms for them because they are used in combination to solve the frame problem

non crossing partitions of type e e r abstract we investigate a new lattice of generalised non crossing partitions constructed using the geometry of the complex reflection group g e e r for the particular case e 2 resp r 2 our lattice coincides with the lattice of simple elements for the type d n resp i 2 e dual braid monoid using this lattice we construct a garside structure for the braid group b e e r as a corollary one may solve the word and conjugacy problems in this group

a composite runge kutta method for the spectral solution of semilinear pdes a new composite runge kutta rk method is proposed for semilinear partial differential equations such as korteweg de vries nonlinear schrodinger kadomtsev petviashvili kp kuramoto sivashinsky ks cahn hilliard and others having high order derivatives in the linear term the method uses fourier collocation and the classical fourth order rk method except for the stiff linear modes which are treated with a linearly implicit rk method the composite rk method is simple to implement indifferent to the distinction between dispersive and dissipative problems and as efficient on test problems for ks and kp as any other generally applicable method

natural continuous extensions of runge kutta methods for volterra integral equations of the second kind and their applications we consider a very general class of runge kutta methods for the numerical solution of volterra integral equations of the second kind which includes as special cases all the more important methods which have been considered in the literature the main purpose of this paper is to define and prove the existence of the natural continuous extensions nce s of runge kutta methods i e piecewise polynomial functions which extend the approximation at the grid points to the whole interval of integration the particular properties required of the nce s allow us to construct the tail approximations which are quite efficient in terms of kernel evaluations

causality and model abstraction abstract much of science and engineering is concerned with characterizing processes by equations describing the relations that hold among parameters of objects and govern their behavior over time in formal descriptions of processes in terms of parameters and equations the notion of causality is rarely made explicit formal treatments of the foundations of sciences have avoided discussions of causation and spoken only of functional relations among variables nevertheless the notion of causality plays an important role in our understanding of phenomena even when we describe the behavior of a system formally in terms of acausal mathematical relations we often give an informal intuitive explanation of why the system behaves the way it does in terms of cause effect relations in this paper we will present an operational definition of causal ordering the definition allows us to extract causal dependency relations among variables implicit in a model of a system when a model is represented as a set of acausal mathematical relations our approach is based on the theory of causal ordering first presented by simon 22 the paper shows how to use the theory and its extension in reasoning about physical systems further the paper studies the relation of the theory to the problems of model aggregation

unconditional contractivity in the maximum norm of diagonally split runge kutta methods we consider the new class of diagonally split runge kutta dsrk methods 1 5 for the standard initial value problem 1 1 by using the theory of p series we derive the order conditions on the method s coefficients stability analysis is also carried out by showing that the method is unconditionally contractive in the maximum norm if and only if the method is based on particular pairs of discrete and continuous runge kutta methods for an effective implementation of the method an iteration scheme is proposed which preserves the contractivity of any iterate

causality in device behavior abstract this paper shows how formal characterizations of causality and of the method of comparative statics long used in econometrics thermodynamics and other domains can be applied to clarify and make rigorous the qualitative causal calculus recently proposed by de kleer and brown 2 the formalization shows exactly what assumptions are required to carry out causal analysis of a system of interdependent variables in equilibrium and to propagate disturbances through such a system the intuitive concepts of causality captured by de kleer and brown provide a rough approximation to the standard analytic techniques that are used in the treatment of simultaneous algebraic and differential equations

a dynamic systems perspective on qualitative simulation abstract this paper presents a simple geometric interpretation of qualitative simulation qs based on the phase space representation of dynamic systems theory qs consists of two steps transition analysis determines the sequence of qualitative states that a system traverses and global interpretation derives its long term behavior i recast transition analysis as a search problem in phase space and replace the assorted transition rules with two algebraic conditions the first condition determines transitions between arbitrarily shaped regions in phase space as opposed to qs which only handles n dimensional rectangles it also provides more accurate results by considering only the boundaries between regions the second condition determines whether nearby trajectories approach a fixed point asymptotically it obtains better results than qs by exploiting local stability properties i recast global interpretation of dissipative systems as a search for attractors in phase space and present a global interpretation strategy for the subset of these systems whose local behavior determines global behavior uniquely although limited in scope this strategy handles many systems that appear in the qs literature

highly continuous interpolants for one step ode solvers and their application to runge kutta methods we suggest a general method for the construction of highly continuous interpolants for one step methods applied to the numerical solution of initial value problems of odes of arbitrary order for the construction of these interpolants one uses along with the numerical data of the discrete solution of a problem provided by a typical one step method at endstep points high order derivative approximations of this solution this approach has two main advantages it allows an easy way of construction of high order runge kutta and nystrom interpolants with reduced cost in additional function evaluations that also preserve the one step nature of the underlying discrete ode solver moreover for problems which are known to possess a solution of high smoothness the approximating interpolant resembles this characteristic a property that on occasion might be desirable an analysis of the stability behavior of such interpolatory processes is carried out in the general case a new numerical technique concerning the accurate determination of the stability behavior of numerical schemes involving higher order derivatives and or approximations of the solution from previous grid points over nonequidistant meshes is presented this technique actually turns out to be of a wider interest as it allows us to infer in certain cases more accurate results concerning the stability of for example the bdf formulas over variable stepsize grids moreover it may be used as a framework for analyzing more complex and supposedly more promising types of methods as they are the general linear methods for first and second order differential equations many particular variants of the new method for first order differential equations that have good prospects of finding a practical implementation are fully analyzed with respect to their stability characteristics a detailed application concerning the construction of c 2 and c 3 continuous extensions for some fifth and sixth order runge kutta pairs supplemented by a detailed study of the local truncation error characteristics of a class of interpolants of this type is also provided various numerical examples show in these cases several advantages of the newly proposed technique with respect to function evaluation cost and global error behavior in comparison with others currently in use

interval garside structures related to the affine artin groups of type a abstract garside theory emerged from the study of artin groups and their generalizations finite type artin groups admit two types of interval garside structures corresponding to their standard and dual presentations concerning affine artin groups digne established interval garside structures for two families of these groups by using their dual presentations recently mccammond established that none of the remaining dual presentations except for one additional case correspond to interval garside structures in this paper shifting attention from dual presentations to other nice presentations for the affine artin group of type a discovered by shi and corran lee lee i will construct interval garside structures related to this group this construction is the first successful attempt to establish interval garside structures not related to the dual presentations in the case of affine artin groups

a neural network model of causality this paper proposes a model for commonsense causal reasoning based on the basic idea of neural networks after an analysis of the advantages and limitations of existing accounts of causality a fuzzy logic based formalism fel is proposed that takes into account the inexactness and the cumulative evidentiality of commonsense causal reasoning overcoming the limitations of existing accounts analyses concerning how fel handles various aspects of commonsense causal reasoning are performed in an abstract way fel can be implemented naturally in a neural connectionist network this work also serves to link rule based reasoning with neural network models in that a rule encoding scheme fel is equated directly to a neural network model

automatic qualitative analysis of dynamic systems using piecewise linear approximations abstract this paper explores automating the qualitative analysis of physical systems it describes a program called plr for piecewise linear reasoner that formalizes an analysis strategy employed by experts plr takes parameterized ordinary differential equations as input and produces a qualitative description of the solutions for all initial values it approximates intractable nonlinear systems with piecewise linear ones analyzes the approximations and draws conclusions about the original systems it chooses approximations that are accurate enough to reproduce the essential properties of their nonlinear prototypes yet simple enough to be analyzed completely and efficiently it derives additional properties such as boundedness or periodicity by theoretical methods plr s analysis depends on abstract properties of systems rather than on specific numeric values this makes its conclusions more robust and enables it to handle parameterized equations transparently i demonstrate plr on several common nonlinear systems and on published examples from mechanical engineering

temporal constraint satisfaction on causal models abstract causal models play a fundamental role in many intelligent problem solving activities such as diagnosis or simulation although the notion of causation is strictly related to the notion of time temporal knowledge and temporal reasoning have been often disregarded in problem solvers operating on causal models in this page we propose an approach to temporal constraint satisfaction on causal models the approach departs significantly from traditional approaches to temporal constraint satisfaction in our approach in fact we use synchronization mechanisms for dealing with events caused by a conjunction of other events in the paper we analyze the computation complexity of temporal constraint satisfaction on causal models showing that such a form of reasoning is intrinsically intractable i e it is intractable even if one limits the attention to a simple form of causal model and of consistency constraints however we show that it is possible to define sufficient conditions for temporal consistency that can be checked in polynomial time interestingly such conditions allow us to relate our approach to traditional approaches to temporal constraint satisfaction

on the stability of volterra runge kutta methods we investigate the stability of extended runge kutta methods for volterra integral equations of the second kind as test equations we choose linear convolution equations with positive definite l 1 kernels our results are strongly connected with the contractivity of runge kutta methods for nonlinear dissipative differential equations

causality tests and observationally equivalent representations of econometric models abstract this article deals with the problem of observational equivalence of alternative econometric equation systems on the same data as a practical obstacle to econometricians success in applying definitions of causality by simon 1953 strotz and wold 1960 and granger 1969 to economic time series

gaussian groups and garside groups two generalisations of artin groups it is known that a number of algebraic properties of the braid groups extend to arbitrary finite coxeter type artin groups here we show how to extend the results to more general groups that we call garside groups define a gaussian monoid to be a finitely generated cancellative monoid where the expressions of a given element have bounded lengths and where left and right lowest common multiples exist a garside monoid is a gaussian monoid in which the left and right lowest common multiples satisfy an additional symmetry condition a gaussian group is the group of fractions of a gaussian monoid and a garside group is the group of fractions of a garside monoid braid groups and more generally finite coxeter type artin groups are garside groups we determine algorithmic criteria in terms of presentations for recognizing gaussian and garside monoids and groups and exhibit infinite families of such groups we describe simple algorithms that solve the word problem in a gaussian group show that these algorithms have a quadratic complexity if the group is a garside group and prove that garside groups have quadratic isoperimetric inequalities we construct normal forms for gaussian groups and prove that in the case of a garside group the language of normal forms is regular symmetric and geodesic has the 5 fellow traveller property and has the uniqueness property this shows in particular that garside groups are geodesically fully biautomatic finally we consider an automorphism of a finite coxeter type artin group derived from an automorphism of its defining coxeter graph and prove that the subgroup of elements fixed by this automorphism is also a finite coxeter type artin group that can be explicitly determined 1991 mathematics subject classification primary 20f05 20f36 secondary 20b40 20m05

conditions for the coefficients of runge kutta methods for systems of n th order differential equations abstract to derive order conditions for runge kutta methods of nystrom or fehlberg type applicable to arbitrary order differential equations a theory similar to that about runge kutta methods for first order systems due to butcher 1 is developed by a new definition of elementary differentials which is independent of the order of the given system each condition to be satisfied by the coefficients of the method directly follows from the representation of the corresponding elementary differential

a note on the correctness of the causal ordering algorithm in this paper we examine in detail the algorithm of simon h a simon causal ordering and identifiability in w c hood t c koopmans eds studies in econometric method cowles commission for research in economics monograph no 14 john wiley sons inc new york 1953 pp 49 74 chapter iii called the causal ordering algorithm coa used for constructing the causal ordering of a system given a complete specification of the system in terms of a set of structural equations that govern the variables in the system this algorithm constructs a graphical characterization of the model in a form that we call a partial causal graph simon argued in h a simon causal ordering and identifiability in w c hood t c koopmans eds studies in econometric method cowles commission for research in economics monograph no 14 john wiley sons inc new york 1953 pp 49 74 chapter iii and subsequent papers that a graph so generated explicates causal structure among variables in the model we formalize this claim further by proving that any causal model based on a one to one correspondence between equations and variables must be consistent with the coa