event structures and trace monoids event structures are a poset based model for describing the behaviour of distributed systems they give rise to a well understood class of scott domains event structures are also related to petri nets in a fundamental way trace monoids are a string based formalism for describing the behaviour of distributed systems they have an independent theory rooted in the theory of formal languages here we obtain a representation of trace monoids in terms of a subclass of labelled event structures

goal programming for decision making an overview of the current state of the art there have been significant advances in the theory of goal programming gp in recent years particularly in the area of intelligent modelling and solution analysis the intention of this paper is to provide an overview of these developments to detail and assess the current state of the art in the subject and to highlight areas which seem promising for future research modelling techniques such as detection and restoration of pareto efficiency normalisation redundancy checking and non standard utility function modelling are overviewed the connection between gp and other multi objective programming techniques as well as a utility interpretation of gp are examined the rationality of ranking multi criteria decision making techniques and of placing gp in such a ranking is discussed

di domains as prime information systems abstract this paper introduces prime information systems prime information systems determine di domains and stable approximable mappings give stable functions and vice versa the notion of rigid embedding is captured by a subsystem relation under this relation prime information systems form a complete partial order cpo constructions like lifting sum product and function space are proposed which induce continuous functions on the cpo in this way recursive prime information systems can be defined using fixed point theory

formulating generalised goal games against nature an illustration from decision making under uncertainty in agriculture abstract the games against nature approach to the analysis of uncertainty in decision making relies on the assumption that the behaviour of a decision maker can be explained by concepts such as maximin minimax regret or a similarly defined criterion in reality however these criteria represent a spectrum and the actual behaviour of a decision maker is most likely to embody a mixture of such idealisations this paper proposes that in game theoretic approach to decision making under uncertainty a more realistic representation of a decision maker s behaviour can be achieved by synthesising games against nature with goal programming into a single framework the proposed formulation is illustrated by using a well known example from the literature on mathematical programming models for agricultural decision making

a fast monte carlo method with a reduced basis of control variates applied to uncertainty propagation and bayesian estimation abstract the reduced basis control variate monte carlo method was introduced recently in s boyaval t lelievre a variance reduction method for parametrized stochastic differential equations using the reduced basis paradigm commun math sci 8 2010 735 762 special issue mathematical issues on complex fluids as an improved monte carlo method for the fast estimation of many parametrized expected values at many parameter values we provide here a more complete analysis of the method including precise error estimates and convergence results we also numerically demonstrate that it can be useful to some parametric frameworks in uncertainty quantification in particular i the case where the parametrized expectation is a scalar output of the solution to a partial differential equation pde with stochastic coefficients an uncertainty propagation problem and ii the case where the parametrized expectation is the bayesian estimator of a scalar output in a similar pde context moreover in each case a pde has to be solved many times for many values of its coefficients this is costly and we also use a reduced basis of pde solutions like in s boyaval c le bris y maday n nguyen a patera a reduced basis approach for variational problems with stochastic parameters application to heat conduction with variable robin coefficient comput methods appl mech eng 198 2009 3187 3206 to our knowledge this is the first combination of various reduced basis ideas with a view to reducing as much as possible the computational cost of a simple versatile monte carlo approach to uncertainty quantification

karhunen loeve approximation of random fields by generalized fast multipole methods kl approximation of a possibly instationary random field a x l2 dp l d subject to prescribed meanfield ea x a x dp and covariance va x x a x ea x a x ea x dp in a polyhedral domain d rd is analyzed we show how for stationary covariances va x x ga x x with ga z analytic outside of z 0 an m term approximate kl expansion am x of a x can be computed in log linear complexity the approach applies in arbitrary domains d and for nonseparable covariances ca it involves galerkin approximation of the kl eigenvalue problem by discontinuous finite elements of degree p 0 on a quasiuniform possibly unstructured mesh of width h in d plus a generalized fast multipole accelerated krylov eigensolver the approximate kl expansion am x of a x has accuracy o exp bm1 d if ga is analytic at z 0 and accuracy o m k d if ga is ck at zero it is obtained in o mn logn b operations where n o h d

quasi prime algebraic domains abstract the purpose of this paper is to introduce a new class of domains called quasi prime algebraic domains we show that this class is a good candidate for the purpose of denotational semantics of programming languages this is achieved by exhibiting many constructions usually needed for denotational semantics on quasi prime algebraic domains in the first part we motivate the notion of quasi primes and quasi prime algebraic domains by studying the effect of linear functions on domains that are not prime algebraic in the second part we study categories of quasi prime algebraic domains by representing them as irreducible information systems we introduce a symmetric monoidal closed category of quasi prime algebraic domains with quasi linear functions we show further that with the usual scott continuous functions as morphisms quasi prime algebraic domains are cartesian closed in the third part we show the existence of a saturated quasi prime algebraic domain and introduce a framework for solving domain equations in quasi prime algebraic domains it is then possible to give for example a model for the un typed lambda calculus with a reflexive quasi prime algebraic domain

well behaved flow event structures for parallel composition and action refinement flow event structures were introduced as a model for giving semantics to process algebras however it turned out that certain restrictions have to be made to make them suitable for this purpose in this paper we investigate subclasses of flow event structures which are both suited for the process algebraic composition operators and for action refinement as a means of regarding processes on different levels of abstraction first suitable subclasses are characterised then two specific subclasses are proposed the larger class generalises the one from castellani and zhang theoret comput sci 179 1997 203 215 which is not suitable for action refinement the smaller one is still sufficiently expressive for dealing with all standard process algebras and action refinement

a partial ordering semantics for ccs a new operational semantics for pure ccs is proposed that considers the parallel operator as a first class one and permits a description of the calculus in terms of partial orderings the new semantics also for unguarded agents is given in the sos style via the partial ordering derivation relation ccs agents are decomposed into sets of sequential subagents the new derivations relate sets of subagents and describe their actions and the casual dependencies among them the computations obtained by composing partial ordering derivations are observed either as interleaving or partial orderings of events interleavings coincide with milner s many step derivations and linearizations of partial orderings are all and only interleavings abstract semantics are obtained by introducing two relations of observational equivalence and congruence that preserve concurrency these relations are finer than milner s in that they distinguish interleaving of sequential nondeterministic agents from their concurrent execution

determinism event structure isomorphism step sequence equivalence abstract a concurrent system s is called determinism if for all states s of s we have that whenever s can evolve from state s into states s and s by doing an action a it must be the case that s equals s it is well known that for deterministic concurrent systems most of the interleaved equivalences bisimulation failure trace equivalence coincide in this paper we prove in the setting of event structures that also most of the non interleaved equivalences coincide with each other on this domain in the last section of the paper we show that as a consequence of our result the causal structure of a deterministic concurrent system can be unravelled by observers who are capable of observing the beginning and termination of events

a reduced basis approach for variational problems with stochastic parameters application to heat conduction with variable robin coefficient in this work a reduced basis rb approach is used to solve a large number of boundary value problems bvps parametrized by a stochastic input expressed as a karhunen loeve expansion in order to compute outputs that are smooth functionals of the random solution fields the rb method proposed here for variational problems parametrized by stochastic coefficients bears many similarities to the rb approach developed previously for deterministic systems however the stochastic framework requires the development of new a posteriori estimates for statistical outputs such as the first two moments of integrals of the random solution fields these error bounds in turn permit efficient sampling of the input stochastic parameters and fast reliable computation of the outputs in particular in the many query context

stochastic model reduction for chaos representations abstract this paper addresses issues of model reduction of stochastic representations and computational efficiency of spectral stochastic galerkin schemes for the solution of partial differential equations with stochastic coefficients in particular an algorithm is developed for the efficient characterization of a lower dimensional manifold occupied by the solution to a stochastic partial differential equation spde in the hilbert space spanned by wiener chaos a description of the stochastic aspect of the problem on two well separated scales is developed to enable the stochastic characterization on the fine scale using algebraic operations on the coarse scale with such algorithms at hand the solution of spde s becomes both computationally manageable and efficient moreover a solid foundation is thus provided for the adaptive error control in stochastic galerkin procedures different aspects of the proposed methodology are clarified through its application to an example problem from solid mechanics

a new iterative method for solving multiobjective linear programming problem in the paper we present a new iterative method for solving multiobjective linear programming problems with an arbitrary number of decision makers the method is based on the principles of game theory each step of the method yields a unique solution which respects the aspirations of decision makers within the frame of given possibilities each decision maker is assigned an objective indicator which shows the reality of his aspiration and which may be used to define the strategy for the next step the method can be easily extended to general nonlinear multiobjective programming problems but the numerical application would require further research on computational methods

configuration structures event structures and petri nets in this paper the correspondence between safe petri nets and event structures due to nielsen plotkin and winskel is extended to arbitrary nets without self loops under the collective token interpretation to this end we propose a more general form of event structure matching the expressive power of such nets these new event structures and nets are connected by relating both notions with configuration structures which can be regarded as representations of either event structures or nets that capture their behaviour in terms of action occurrences and the causal relationships between them but abstract from any auxiliary structure a configuration structure can also be considered logically as a class of propositional models or equivalently as a propositional theory in disjunctive normal from converting this theory to conjunctive normal form is the key idea in the translation of such a structure into a net for a variety of classes of event structures we characterise the associated classes of configuration structures in terms of their closure properties as well as in terms of the axiomatisability of the associated propositional theories by formulae of simple prescribed forms and in terms of structural properties of the associated petri nets

on an open problem of amadio and curien the finite antichain condition more than a dozen years ago amadio bifinite domains stable case in lecture notes in computer science vol 530 1991 pp 16 33 see amadio and curien domains and lambda calculi cambridge tracts in theoretical computer science vol 46 cambridge university press 1998 as well raised the question of whether the category of stable bifinite domains of amadio droste r m amadio bifinite domains stable case in lecture notes in computer science vol 530 1991 pp 16 33 m droste on stable domains theor comput sci 111 1993 89 101 m droste cartesian closed categories of stable domains for polymorphism preprint universitat ghs essen is the largest cartesian closed full sub category of the category of w algebraic meet cpos with stable functions an affirmative solution to this problem has two major steps 1 show that for any w algebraic meet cpo d if all higher order stable function spaces built from d are w algebraic then d is finitary i e it satisfies the so called axiom i 2 show that for any w algebraic meet cpo d if d violates mi then d d violates either m or i we solve the first part of the problem in this paper i e for any w algebraic meet cpo d if the stable function space d d satisfies m then d is finitary our notion of mub meet closed set which is introduced for step 1 will also be used for treating some example cases in step 2

on maximal stable functions abstract this note studies maximal elements in di domains especially maximal stable functions first a sufficient condition for a stable function to be maximal is provided the condition requires that the function be total in the sense that it preserves maximal elements examples are then given to demonstrate that being total is not necessary for a stable function to be maximal secondly a characterization is given for di domains for which maximal also implies total finally topological properties of maximal elements are investigated di domains for which maximal is the same as total are those having a certain hausdorff property

a semi analytical framework for structural reliability analysis abstract estimation of the probability of failure of structural systems can often be computationally intensive and time consuming hence alternative techniques for efficient computation of the probability of failure of complex structures while retaining the accuracy is of paramount importance to structural engineering community this paper presents a semi analytical approach for computing failure probability of structure the proposed approach utilizes i polynomial correlated function expansion a novel surrogate modelling technique to determine the moments and ii maximum entropy method to determine an analytical expression for the response probability density function pdf once the analytical expression for the pdf is obtained failure probability is calculated by numerically integrating the pdf in the failure domain as a special case when only the first two moments of response are considered an analytical formula for the probability of failure is also proposed four structural engineering problems are shown to illustrate the performance of the proposed approach it is observed that the proposed approach outperforms other existing approaches

construction of probability distributions in high dimension using the maximum entropy principle applications to stochastic processes random fields and random matrices the construction of probabilistic models in computational mechanics requires the effective construction of probability distributions of random variables in high dimension this paper deals with the effective construction of the probability distribution in high dimension of a vector valued random variable using the maximum entropy principle the integrals in high dimension are then calculated in constructing the stationary solution of an ito stochastic differential equation associated with its invariant measure a random generator of independent realizations is explicitly constructed in this paper three fundamental applications are presented the first one is a new formulation of the stochastic inverse problem related to the construction of the probability distribution in high dimension of an unknown non stationary random time series random accelerograms for which the velocity response spectrum is given the second one is also a new formulation related to the construction of the probability distribution of positive definite band random matrices finally we present an extension of the theory when the support of the probability distribution is not all the space but is any part of the space the third application is then a new formulation related to the construction of the probability distribution of the karhunen loeve expansion of non gaussian positive valued random fields

petri nets event structures and domains part i abstract the general aim of this paper is to find a theory of concurrency combining the approaches of petri and scott and others in part i we introduce our formalisms to connect the abstract ideas of events and domains of information we show how casual nets induce certain kinds of domains where the information points are certain sets of events this allows translations between the languages of net theory and domain theory following the idea that events of causal nets are occurrences we generalise causal nets to occurrence nets by adding forwards conflict just as infinite flow charts unfold finite ones so transition nets can be unfolded into occurrence nets next we extend the above connections between nets and domains to these new nets event structures which are intermediate between nets and domains play an important part in all our work finally as an example of how concepts translate from one formalism to the other we show how petri s notion of confusion ties up with kahn and plotkin s concrete domains in part ii we shall continue the job of connecting up notions within net theory and the theory of domains in particular we shall examine the idea of states of computations

on the construction and analysis of stochastic models characterization and propagation of the errors associated with limited data this paper investigates the predictive accuracy of stochastic models in particular a formulation is presented for the impact of data limitations associated with the calibration of parameters for these models on their overall predictive accuracy in the course of this development a new method for the characterization of stochastic processes from corresponding experimental observations is obtained specifically polynomial chaos representations of these processes are estimated that are consistent in some useful sense with the data the estimated polynomial chaos coefficients are themselves characterized as random variables with known probability density function thus permitting the analysis of the dependence of their values on further experimental evidence moreover the error in these coefficients associated with limited data is propagated through a physical system characterized by a stochastic partial differential equation spde this formalism permits the rational allocation of resources in view of studying the possibility of validating a particular predictive model a bayesian inference scheme is relied upon as the logic for parameter estimation with its computational engine provided by a metropolis hastings markov chain monte carlo procedure

a generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations we propose a new robust technique for solving stochastic partial differential equations the solution is approximated by a series of terms each of which being the product of a scalar stochastic function by a deterministic function none of these functions are fixed a priori but determined by solving a problem which can be interpreted as an extended eigenvalue problem this technique generalizes the classical spectral decomposition namely the karhunen loeve expansion ad hoc iterative techniques to build the approximation inspired by the power method for classical eigenproblems then transform the problem into the resolution of a few uncoupled deterministic problems and stochastic equations this method drastically reduces the calculation costs and memory requirements of classical resolution techniques used in the context of galerkin stochastic finite element methods finally this technique is particularly suitable to non linear and evolution problems since it enables the construction of a relevant reduced basis of deterministic functions which can be efficiently reused for subsequent resolutions

finite elements for elliptic problems with stochastic coefficients abstract we describe a deterministic finite element fe solution algorithm for a stochastic elliptic boundary value problem sbvp whose coefficients are assumed to be random fields with finite second moments and known piecewise smooth two point spatial correlation function separation of random and deterministic variables parametrization of the uncertainty is achieved via a karhunen loeve kl expansion an o n log n algorithm for the computation of the kl eigenvalues is presented based on a kernel independent fast multipole method fmm truncation of the kl expansion gives an m 1 wiener polynomial chaos pc expansion of the stochastic coefficient and is shown to lead to a high dimensional deterministic boundary value problem dbvp analyticity of its solution in the stochastic variables with sharp bounds for the domain of analyticity are used to prescribe variable stochastic polynomial degree r r1 rm in an m r wiener pc expansion for the approximate solution pointwise error bounds for the fem approximations of kl eigenpairs the truncation of the kl expansion and the fe solution to the dbvp are given numerical examples show that m depends on the spatial correlation length of the random diffusion coefficient the variable polynomial degree r in pc stochastic galerkin fem allows to handle kl expansions with m up to 30 and r1 up to 10 in moderate time

preconditioning markov chain monte carlo simulations using coarse scale models we study the preconditioning of markov chain monte carlo mcmc methods using coarse scale models with applications to subsurface characterization the purpose of preconditioning is to reduce the fine scale computational cost and increase the acceptance rate in the mcmc sampling this goal is achieved by generating markov chains based on two stage computations in the first stage a new proposal is first tested by the coarse scale model based on multiscale finite volume methods the full fine scale computation will be conducted only if the proposal passes the coarse scale screening for more efficient simulations an approximation of the full fine scale computation using precomputed multiscale basis functions can also be used comparing with the regular mcmc method the preconditioned mcmc method generates a modified markov chain by incorporating the coarse scale information of the problem the conditions under which the modified markov chain will converge to the correct posterior distribution are stated in the paper the validity of these assumptions for our application and the conditions which would guarantee a high acceptance rate are also discussed we would like to note that coarse scale models used in the simulations need to be inexpensive but not necessarily very accurate as our analysis and numerical simulations demonstrate we present numerical examples for sampling permeability fields using two point geostatistics the karhunen loeve expansion is used to represent the realizations of the permeability field conditioned to the dynamic data such as production data as well as some static data our numerical examples show that the acceptance rate can be increased by more than 10 times if mcmc simulations are preconditioned using coarse scale models

a model and variance reduction method for computing statistical outputs of stochastic elliptic partial differential equations we present a model and variance reduction method for the fast and reliable computation of statistical outputs of stochastic elliptic partial differential equations our method consists of three main ingredients 1 the hybridizable discontinuous galerkin hdg discretization of elliptic partial differential equations pdes which allows us to obtain high order accurate solutions of the governing pde 2 the reduced basis method for a new hdg discretization of the underlying pde to enable real time solution of the parameterized pde in the presence of stochastic parameters and 3 a multilevel variance reduction method that exploits the statistical correlation among the different reduced basis approximations and the high fidelity hdg discretization to accelerate the convergence of the monte carlo simulations the multilevel variance reduction method provides efficient computation of the statistical outputs by shifting most of the computational burden from the high fidelity hdg approximation to the reduced basis approximations furthermore we develop a posteriori error estimates for our approximations of the statistical outputs based on these error estimates we propose an algorithm for optimally choosing both the dimensions of the reduced basis approximations and the sizes of monte carlo samples to achieve a given error tolerance we provide numerical examples to demonstrate the performance of the proposed method

on the expressiveness of higher dimensional automata in this paper i compare the expressive power of several models of concurrency based on their ability to represent causal dependence to this end i translate these models in behaviour preserving ways into the model of higher dimensional automata hda which is the most expressive model under investigation in particular i propose four different translations of petri nets corresponding to the four different computational interpretations of nets found in the literature i also extend various equivalence relations for concurrent systems to hda these include the history preserving bisimulation which is the coarsest equivalence that fully respects branching time causality and their interplay as well as the st bisimulation a branching time respecting equivalence that takes causality into account to the extent that it is expressible by actions overlapping in time through their embeddings in hda it is now well defined whether members of different models of concurrency are equivalent

an event structure semantics for general petri nets abstract in this paper we address the following question what type of event structures are suitable for representing the behaviour of general petri nets as a partial answer to this question we define a new class of event structures called local event structures and identify a subclass called ul event structures we propose that ul event structures are appropriate for capturing the behaviour of general petri nets our answer is a partial one in that in the proposed event structure semantics auto concurrency is filtered out from the behaviour of petri nets it turns out that this limited event structure semantics for petri nets is nevertheless a non trivial and conservative extension of the prime event structure semantics of 1 safe petri nets provided in nielsen et al 1981 we also show that the strong relationship between prime event structures and 1 safe petri nets established in a categorical framework in winskel 1987 can be extended to the present setting provided we restrict our attention to the subclass of petri nets whose behaviours do not exhibit any auto concurrency finally we show that winskel s general and stable event structures can be smoothly related to local event structures and that similarly prime event structures can be related to ul event structures

galerkin methods for linear and nonlinear elliptic stochastic partial differential equations abstract stationary systems modelled by elliptic partial differential equations linear as well as nonlinear with stochastic coefficients random fields are considered the mathematical setting as a variational problem existence theorems and possible discretisations in particular with respect to the stochastic part are given and investigated with regard to stability different and increasingly sophisticated computational approaches involving both wiener s polynomial chaos as well as the karhunen loeve expansion are addressed in conjunction with stochastic galerkin procedures and stability within the galerkin framework is established new and effective algorithms to compute the mean and covariance of the solution are proposed the similarities and differences with better known monte carlo methods are exhibited as well as alternatives to integration in high dimensional spaces hints are given regarding the numerical implementation and parallelisation numerical examples serve as illustration

dimensionality reduction and polynomial chaos acceleration of bayesian inference in inverse problems we consider a bayesian approach to nonlinear inverse problems in which the unknown quantity is a spatial or temporal field endowed with a hierarchical gaussian process prior computational challenges in this construction arise from the need for repeated evaluations of the forward model e g in the context of markov chain monte carlo and are compounded by high dimensionality of the posterior we address these challenges by introducing truncated karhunen loeve expansions based on the prior distribution to efficiently parameterize the unknown field and to specify a stochastic forward problem whose solution captures that of the deterministic forward model over the support of the prior we seek a solution of this problem using galerkin projection on a polynomial chaos basis and use the solution to construct a reduced dimensionality surrogate posterior density that is inexpensive to evaluate we demonstrate the formulation on a transient diffusion equation with prescribed source terms inferring the spatially varying diffusivity of the medium from limited and noisy data

a representation of sfp this chapter introduces a representation of the category of sfp domains it uses structures similar to but more general than scott s information systems distilled from gentzen s sequent calculi a basic structure called a sequent structure is produced sequent structures determine a major part of the axioms of information systems a category of special kind of sequent structures called the strongly finite ones is shown to be equivalent to the category of sfp domains constructions like the plotkin power domain and the function space are given as well as a complete partial order of such structures to give solutions to recursively defined systems

hybrid uncertain static analysis with random and interval fields abstract uncertain static analysis of an engineering structure with diverse type of non deterministic system parameter is investigated in this study unlike the traditional hybrid uncertain static analysis involving random and interval variables the concept of random and interval fields has been implemented to model the spatially dependent uncertainties associated with the system inputs a novel computational approach namely the extended unified interval stochastic sampling x uiss method is proposed to calculate the statistical characteristics i e mean and standard deviation of the extreme bounds i e lower and upper bounds of the concerned responses e g displacement and stress of engineering structure involving hybrid spatially dependent uncertainties subsequently by utilizing either parametric or nonparametric statistical analysis the probability density functions pdfs as well as the cumulative distribution functions cdfs of the extreme bounds of the concerned structural responses can be effectively established consequently the upper and lower bounds of either the concerned responses of the engineering structure at any particular percentile of probability or the structural reliability against any specified capacities can be effectively secured the applicability and effectiveness of the proposed computational analysis framework are illustrated through the numerical investigations on various examples

a representation of l domains by information systems in this paper we propose the notion of l information systems which provides a concrete representation of l domains in particular we prove that the category of l information systems with approximable mappings as morphisms is equivalent to that of l domains with scott continuous functions as morphisms

information systems revisited the general continuous case in this paper a new notion of continuous information system is introduced it is shown that the information systems of this kind generate exactly the continuous domains the new information systems are of the same logic oriented style as the information systems first introduced by scott in 1982 they consist of a set of tokens a consistency predicate and an entailment relation satisfying a set of natural axioms it is shown that continuous information systems are closely related to abstract bases indeed both categories are equivalent since it is known that the categories of abstract bases and or continuous domains are equivalent it follows that the category of continuous information systems is also equivalent to that of continuous domains in applications mostly subclasses of continuous domains are considered for example the domains have to be pointed algebraic bounded complete or fs conditions are presented that when fulfilled by a continuous information system force the generated domain to belong to the required subclass in most cases the requirements are not only sufficient but also necessary

re visiting axioms of information systems based on the investigation of the axioms used in the theory of information system the notion of simplified continuous information system is introduced which is considered as a generalization of continuous information systems just like the continuous information system it is also a concrete representation of continuous domains and categorically equivalent to the category of continuous domains and scott continuous functions what is more all types of information systems studied in the literature so far turn out to be special cases of the new type by defining linear information systems and their entailment functions we show that the states of a scott style information system are exactly the fixpoints of its entailment function some axioms about an entailment relation can be characterized by the properties of the corresponding entailment function and in particular the simplified continuous information systems are solely determined by the idempotence of entailment functions

a logical approach to stable domains building on earlier work by guo qiang zhang on disjunctive information systems and by thomas ehrhard pasquale malacaria and the first author on stable stone duality we develop a framework of disjunctive propositional logic in which theories correspond to algebraic l domains disjunctions in the logic can be indexed by arbitrary sets as in geometric logic but must be provably disjoint this raises several technical issues which have to be addressed before clean notions of axiom system and theory can be defined we show soundness and completeness of the proof system with respect to distributive disjunctive semilattices and prove that every such semilattice arises as the lindenbaum algebra of a disjunctive theory via stable stone duality we show how to use disjunctive propositional logic for a logical description of algebraic l domains

weak algebraic information systems and a new equivalent category of dom of domains abstract in this paper concepts of generalized algebraic information system in short ga inf and weak algebraic information system in short wa inf are introduced relationships among several algebraicities of information systems are explored main results are 1 a dcpo d is an algebraic domain iff d is represented by an algebraic information system in short a inf and iff d is represented by a ga inf 2 every a inf is a ga inf and a wa inf 3 every c inf s d b induced by a domain with a basis b is a wa inf 4 the category wainf of wa infs and approximable mappings is equivalent to the category dom of domains and scott continuous functions 5 every wa inf s satisfying condition mt is a retract of w s the information structure induced by s in category wainf of wa infs and approximable mappings particularly c inf s d b induced by a domain d with a basis b is a retract of a inf w s d b in category wainf

the largest cartesian closed category of stable domains abstract berry s category of di domains with stable functions is a relatively intricate yet elegant framework for semantics of programming languages despite over 15 years of work in the area the exact reasons for distributivity axiom d and finitariness axiom i have not been fully explicated this paper shows that axiom d and axiom i are important when one works within the realm of scott domains in particular it has been shown that i if d s d has a countable basis then d must be finitary for any scott domain d ii if d s d is bounded complete then d must be distributive for any finitary scott domain d therefore the category of di domains is the largest cartesian closed category within omega algebraic bounded complete domains with the exponential being the stable function space

a stochastic collocation method for elliptic partial differential equations with random input data in this paper we propose and analyze a stochastic collocation method to solve elliptic partial differential equations with random coefficients and forcing terms input data of the model the input data are assumed to depend on a finite number of random variables the method consists in a galerkin approximation in space and a collocation in the zeros of suitable tensor product orthogonal polynomials gauss points in the probability space and naturally leads to the solution of uncoupled deterministic problems as in the monte carlo approach it can be seen as a generalization of the stochastic galerkin method proposed in i babuscka r tempone and g e zouraris siam j numer anal 42 2004 pp 800 825 and allows one to treat easily a wider range of situations such as input data that depend nonlinearly on the random variables diffusivity coefficients with unbounded second moments and random variables that are correlated or even unbounded we provide a rigorous convergence analysis and demonstrate exponential convergence of the probability error with respect to the number of gauss points in each direction in the probability space under some regularity assumptions on the random input data numerical examples show the effectiveness of the method

true concurrency probabilistic models branching cells and distributed probabilities for event structures this paper is devoted to probabilistic models for concurrent systems under their true concurrency semantics here we address probabilistic event structures we consider a new class of event structures called locally finite that extend confusion free event structure in locally finite event structures maximal configurations can be tiled with branching cells branching cells are minimal and finite sub structures capturing the choices performed while scanning a maximal configuration the probabilistic event structures that we introduce have the property that concurrent processes are independent in the probabilistic sense

quasi monte carlo finite element methods for a class of elliptic partial differential equations with random coefficients in this paper quasi monte carlo qmc methods are applied to a class of elliptic partial differential equations pdes with random coefficients where the random coefficient is parametrized by a co