polymorphic lambda calculus and subtyping we present a denotational model for f the extension of second order lambda calculus with subtyping defined in cardelli and wegner acm comput surveys 17 4 1985 471 522 types are interpreted as arbitrary cpos and elements of types as natural transformations we prove the soundness of our model with respect to the equational theory of f cardelli et al internat conf on theoretical aspects of computer software lecture notes in computer science vol 526 springer berlin 1991 pp 750 770 and show coherence our model is of independent interest because it integrates ad hoc and parametric polymorphism in an elegant fashion admits nontrivial records and record update operations and formalizes an order faithfulness criterion for well behaved multiple subtyping

the dependent product construction in various categories of domains coquand gunter and winskel show how to use the class s of all countably based scott domains as a model for the polymorphic lambda calculus in particular a type which contrains n free type variables is interpreted as a continuous functor f s n s the category of continuous sections of the corresponding grothendieck fibration is shown to be isomorphic to a scott domain we show that this construction does not work for bifinite domains or algebraic l domains

recursion over realizability structures abstract realizability structures play a major role in the metamathematics of intuitionistic systems and they are a basic tool in the extraction of the computational content of constructive proofs besides their rich categorical structure and effectiveness properties provide a privileged mathematical setting for the semantics of data types of programming languages in this paper we emphasize the modelling of recursive definitions of programs and types a realizability model for a language including girard s system f and an operator of recursion on types is given and some of its local properties are studied

why add anything to nothing the arcsine difference as a measure of treatment effect in meta analysis with zero cells for clinical trials with binary endpoints there are a variety of effect measures for example risk difference risk ratio and odds ratio or the choice of metric is not always straightforward and should reflect the clinical question additional issues arise if the event of interest is rare in systematic reviews trials with zero events in both arms are encountered and often excluded from the meta analysis the arcsine difference as is a measure which is rarely considered in the medical literature it appears to have considerable promise because it handles zeros naturally and its asymptotic variance does not depend on the event probability this paper investigates the pros and cons of using the as as a measure of intervention effect we give a pictorial representation of its meaning and explore its properties in relation to other measures based on analytical calculation of the variance of the arcsine transformation a more conservative variance estimate for the rare event setting is proposed motivated by a published meta analysis in cardiac surgery we examine the statistical properties of the various metrics in the rare event setting we find the variance estimate of the as to be more stable than that of the log or even if events are rare however parameter estimation is biased if the groups are markedly unbalanced though from a theoretical viewpoint the as is a natural choice its practical use is likely to continue to be limited by its less direct interpretation

state feedback control of systems with multiplicative noise via linear matrix inequalities we consider lti systems perturbed by parametric uncertainties modeled as white noise disturbances we show how to maximize via state feedback control the smallest norm of the noise intensity vector producing instability in the mean square sense using convex optimization over linear matrix inequalities we also show how to maximize performance robustness where performance is measured by expected output energy with either bounded initial conditions and zero inputs classical lqg cost or zero initial conditions and deterministic inputs of bounded energy a generalization of the h norm

an empirical comparison of univariate and multivariate meta analyses for categorical outcomes treatment effects for multiple outcomes can be meta analyzed separately or jointly but no systematic empirical comparison of the two approaches exists from the cochrane library of systematic reviews we identified 45 reviews including 1473 trials and 258 675 patients that contained two or three univariate meta analyses of categorical outcomes for the same interventions that could also be analyzed jointly eligible were meta analyses with at least seven trials reporting all outcomes for which the cross classification tables were exactly recoverable e g outcomes were mutually exclusive or one was a subset of the other this ensured known correlation structures outcomes in 40 reviews had an is subset of relationship and those in 5 were mutually exclusive we analyzed these data with univariate and multivariate models based on discrete and approximate likelihoods discrete models were fit in the bayesian framework using slightly informative priors the summary effects for each outcome were similar with univariate and multivariate meta analyses both using the approximate and discrete likelihoods however the multivariate model with the discrete likelihood gave smaller between study variance estimates and narrower predictive intervals for new studies when differences in the summary treatment effects were examined the multivariate models gave similar summary estimates but considerably longer shorter uncertainty intervals because of positive negative correlation between outcome treatment effects it is unclear whether any of the examined reviews would change their overall conclusions based on multivariate versus univariate meta analyses because extra analytical and context specific considerations contribute to conclusions and secondarily because numerical differences were often modest

linear matrix inequalities riccati equations and indefinite stochastic linear quadratic controls this paper deals with an optimal stochastic linear quadratic lq control problem in infinite time horizon where the diffusion term in dynamics depends on both the state and the control variables in contrast to the deterministic case we allow the control and state weighting matrices in the cost functional to be indefinite this leads to an indefinite lq problem which may still be well posed due to the deep nature of uncertainty involved the problem gives rise to a stochastic algebraic riccati equation sare which is however fundamentally different from the classical algebraic riccati equation as a result of the indefinite nature of the lq problem to analyze the sare we introduce linear matrix inequalities lmis whose feasibility is shown to be equivalent to the solvability of the sare moreover we develop a computational approach to the sare via a semi definite programming associated with the lmis finally numerical experiments are reported to illustrate the proposed approach

stochastic receding horizon control of constrained linear systems with state and control multiplicative noise we develop a receding horizon control approach to stochastic linear systems with control and state multiplicative noise that also contain constraints our receding horizon formulation is based upon an on line optimization that utilizes open loop plus linear feedback and is solved as a semi definite programming problem we also provide a characterization of stability performance and constraint satisfaction properties of the receding horizon controlled system under a specific choice of terminal weight and terminal constraint a simple numerical example is used to illustrate the approach

term graph rewriting and garbage collection using opfibrations the categorical semantics of an abstract version of the general term graph rewriting language dactl is investigated the operational semantics is reformulated in order to reveal its universal properties the technical dissonance between the matchings of left hand sides of rules to redexes and the properties of rewrite rules themselves is taken as the impetus for expressing the core of the model as a grothendieck opfibration of a category of general rewrites over a base of general rewrite rules garbage collection is examined in this framework in order to reconcile the treatment with earlier approaches it is shown that term rewriting has particularly good garbage theoretic properties that do not generalise to all cases of graph rewriting and that this has been a stumbling block for aspects of some earlier models for graph rewriting

categories of embeddings abstract we present a categorical generalisation of the notion of domains which is closed under suitable exponentiation the goal was originally to generalise girard s model of polymorphism to f if we specialise this notion in the poset case we get new cartesian closed categories of domains

scenario reduction in stochastic programming an approach using probability metrics given a convex stochastic programming problem with a discrete initial probability distribution the problem of optimal scenario reduction is stated as follows determine a scenario subset of prescribed cardinality and a probability measure based on this set that is the closest to the initial distribution in terms of a natural or canonical probability metric arguments from stability analysis indicate that fortet mourier type probability metrics may serve as such canonical metrics efficient algorithms are developed that determine optimal reduced measures approximately numerical experience is reported for reductions of electrical load scenario trees for power management under uncertainty for instance it turns out that after 50 reduction of the scenario tree the optimal reduced tree still has about 90 relative accuracy

a full continuous model of polymorphism we introduce a model of the second order lambda calculus such a model is a scott domain whose elements are themselves scott domains and in it polymorphic maps are interpreted by generic continous maps

iterative generalized least squares for meta analysis of survival data at multiple times a method is presented for joint analysis of survival proportions reported at multiple times in published studies to be combined in a meta analysis generalized least squares is used to fit linear models including between trial and within trial covariates using current fitted values iteratively to derive correlations between times within studies multi arm studies and nonrandomized historical controls can be included with no special handling the method is illustrated with data from two previously published meta analyses in one an early treatment difference is detected that was not apparent in the original analysis

universal profinite domains abstract we introduce a bicartesian closed category of what we call profinite domains study of these domains is carried out through the use of an equivalent category of pre orders in a manner similar to the information systems approach advocated by dana scott and others a class of universal profinite domains is defined and used to derive sufficient conditions for the profinite solution of domain equations involving continuous operators as a special instance of this construction a universal domain for the category sfp is demonstrated necessary conditions for the existence of solutions for domain equations over the profinites are also given and used to derive results about solutions of some equations a new universal bounded complete domain is also demonstrated using an operator which has bounded complete domains as its fixed points

the system f of variable types fifteen years later the semantic study of system f stumbles on the problem of variable types for which there was no convincing interpretation we develop here a semantics based on the category theoretic idea of direct limit so that the behaviour of a variable type on any domain is determined by its behaviour on finite ones thus getting rid of the circularity of variable types to do so one has first to simplify somehow the extant semantic ideas replacing scott domains by the simpler and more finitary qualitative domains the interpretation obtained is extremely compact as shown on simple examples the paper also contains the definitions of a very small universal model of lambda calculus and investigates the concept totality

adequacy for a lazy functional language with recursive and polymorphic types abstract we consider a lazy functional language with both recursive and polymorphic types for this language we give an operational semantics and a denotational semantics based on information systems and establish adequacy i e that a term converges denotationally if and only if it converges operationally in the presence of universal types the usual approach taken is to apply the technique of reducibility candidates but at this point we take a different approach the concreteness of our model allows us to define a notion of size of tokens of information systems based on this notion an appropriate logical relation can be defined by good old well founded recursion the proof of adequacy then follows by standard techniques

quantitative domains and infinitary algebras abstract we describe a class of models of the lambda calculus that generalize and simplify the quantitative domains of girard 1988 their salient feature is that these domains do not have enough points in the sense that a map of domains is not entirely determined by its value on the points i e the morphisms from the terminal object of the category we construct a universal domain whose structure is particularly simple and describe some of the features of the untyped lambda calculus associated to it finally we show how linear logic can be interpreted in these domains and construct another category of domains that supports linear logic

quantifying heterogeneity in a meta analysis the extent of heterogeneity in a meta analysis partly determines the difficulty in drawing overall conclusions this extent may be measured by estimating a between study variance but interpretation is then specific to a particular treatment effect metric a test for the existence of heterogeneity exists but depends on the number of studies in the meta analysis we develop measures of the impact of heterogeneity on a meta analysis from mathematical criteria that are independent of the number of studies and the treatment effect metric we derive and propose three suitable statistics h is the square root of the chi2 heterogeneity statistic divided by its degrees of freedom r is the ratio of the standard error of the underlying mean from a random effects meta analysis to the standard error of a fixed effect meta analytic estimate and i2 is a transformation of h that describes the proportion of total variation in study estimates that is due to heterogeneity we discuss interpretation interval estimates and other properties of these measures and examine them in five example data sets showing different amounts of heterogeneity we conclude that h and i2 which can usually be calculated for published meta analyses are particularly useful summaries of the impact of heterogeneity one or both should be presented in published meta analyses in preference to the test for heterogeneity

the category theoretic solution of recursive domain equations recursive specifications of domains plays a crucial role in denotational semantics as developed by scott and strachey and their followers the purpose of the present paper is to set up a categorical framework in which the known techniques for solving these equations find a natural place the idea is to follow the well known analogy between partial orders and categories generalizing from least fixed points of continuous functions over cpos to initial ones of continuous functors over omega categories to apply these general ideas we introduce wand s bf o categories where the morphism sets have a partial order structure and which include almost all the categories occurring in semantics the idea is to find solutions in a derived category of embeddings and we give order theoretic conditions which are easy to verify and which imply the needed categorical ones the main tool is a very general form of the limit colimit coincidence remarked by scott in the concluding section we outline how compatibilit

stochastic linear quadratic control via semidefinite programming we study stochastic linear quadratic lq optimal control problems over an infinite time horizon allowing the cost matrices to be indefinite we develop a systematic approach based on semidefinite programming sdp a central issue is the stability of the feedback control and we show this can be effectively examined through the complementary duality of the sdp furthermore we establish several implication relations among the sdp complementary duality the generalized riccati equation and the optimality of the lq control problem based on these relations we propose a numerical procedure that provides a thorough treatment of the lq control problem via primal dual sdp it identifies a stabilizing feedback control that is optimal or determines that the problem possesses no optimal solution for the latter case we develop an epsilon approximation scheme that is asymptotically optimal

on functors expressible in the polymorphic typed lambda calculus abstract given a model of the polymorphic typed lambda calculus based upon a cartesian closed category k there will be functors from k to k whose action on objects can be expressed by type expressions and whose action on morphisms can be expressed by ordinary expressions we show that if t is such a functor then there is a weak initial t algebra and if in addition k possesses equalizers of all subsets of its morphism sets then there is an initial t algebra these results are used to establish the impossibility of certain models including those in which types denote sets and s s denotes the set of all functions from s to s

domain theoretic models of polymorphism abstract we give an illustration of a construction useful in producing and describing models of girard and reynolds polymorphic calculus the key unifying ideas are that of a grothendieck fibration and the category of continuous sections associated with it constructions used in indexed category theory the universal types of the calculus are interpreted as the category of continuous sections of the fibration as a major example a new model for the polymorphic calculus is presented in it a type is interpreted as a scott domain in fact understanding universal types of the polymorphic calculus as categories of continuous sections appears to be useful generally for example the technique also applies to the finitary projection model of bruce and longo and a recent model of girard indeed the work here was inspired by girard s and arose through trying to extend the construction of his model to scott domains it is hoped that by pin pointing a key construction this paper will help towards a deeper understanding of models for the polymorphic calculus and the relations between them

the semantics of second order lambda calculus abstract in the second order polymorphic typed lambda calculus lambda abstraction over type variables leads to terms denoting polymorphic functions straightforward cardinality considerations show that a naive set theoretic interpretation of the calculus is impossible we give two definitions of semantic models for this language and prove them equivalent our syntactical environment model definition and a more algebraic combinatory model definition for the polymorphic calculus correspond to analogous model definitions for untyped lambda calculus soundness and completeness theorems are proved using the environment model definition we verify that some specific interpretations of the calculus proposed in the literature indeed yield models in our sense

a method for the meta analysis of mutually exclusive binary outcomes meta analyses of multiple outcomes need to take into account the within study correlation across the different outcomes here we focus on the meta analysis of dichotomous outcomes that are mutually exclusive and exhaustive correlations between effect sizes for mutually exclusive outcomes are negative and can be obtained from data already available we present both fixed effects and random effects methods that account for the negative correlations and yield correct simultaneous confidence intervals for both the marginal outcome specific effect sizes and the relative effect sizes between outcomes formulae for the odds ratio risk ratio risk difference and the differences in the arcsin transformed risks are provided an example of a meta analysis of randomized trials of radiotherapy and mastectomy with axillary lymph node clearance versus only mastectomy with axillary clearance for early breast cancer is presented the mutually exclusive outcomes of breast cancer deaths and deaths secondary to other causes are examined in separate meta analyses and also by taking the between outcome correlation into account we argue that mutually exclusive outcomes in the meta analyses of binary data are optimally analyzed in a multinomial setting this may also be applicable when a meta analysis examines only one out of several mutually exclusive outcomes for large sample sizes and or low event counts the covariances between outcome specific effect sizes are small and either ignoring them or accounting for them would result in similar estimates for any practical purpose however meta analysts should explore the robustness of the findings from individual meta analyses when mutually exclusive outcomes are assessed

building continuous webbed models for system f we present here a large family of concrete models for girard and reynolds polymorphism system f in a noncategorical setting the family generalizes the construction of the model of barbanera and berardi tech report university of turin 1997 hence it contains complete models for f a complete model for system f preprint june 1998 and we conjecture that it contains models which are complete for f it also contains simpler models the simplest of them e2 being a second order variant of the engeler plotkin model e all the models here belong to the continuous semantics and have underlying prime algebraic domains all have the maximum number of polymorphic maps the class contains models which can be viewed as two intertwined compatible webbed models of untyped calculus in the sense of berline from computations to foundations the calculus and its webbed models revised version theoret comput sci 86 pp to appear but it is much larger than this finally many of its models might he read as two intertwined strict intersection type systems

a higher order calculus and theory abstraction abstract we present a higher order calculus ecc which naturally combines coquand huet s calculus of constructions and martin lof s type theory with universes ecc is very expressive both for structured abstract reasoning and for program specification and construction in particular the strong sum types together with the type universes provide a useful module mechanism for abstract description of mathematical theories and adequate formalization of abstract mathematics this allows comprehensive structuring of interactive development of specifications programs and proofs after a summary of the meta theoretic properties of the calculus an set realizability model of ecc is described to show how its essential properties can be captured set theoretically the model construction entails the logical consistency of the calculus and gives some hints on how to adequately formalize abstract mathematics theory abstraction in ecc is discussed as a pragmatic application

the largest cartesian closed category of domains the main result of this paper provides a necessary and sufficient condition that the function space d d of a domain algebraic cpo d be again a domain the condition confirming a conjecture of plotkin is that d be strongly algebraic sfp the importance of this is that it enables us to conclude that sfp is the largest category of domains that is closed under the constructions of interest in semantics in the final section we briefly consider how our results may need to be extended if our admittedly rather restrictive notion of category of domains is relaxed in certain ways

a natural semantics of first order type dependency abstract we develop a natural model of first order type dependency by considering types as stable families of di domains indexed on a di domain or in an equivalent way as stable functors from a di domain to the category of di domains with rigid embedding projections the fundamental idea of the interpretation is to interpret any construction in the type system by an algebraic construction in this category we present here a model of the so called generalised algebraic fragment of martin lof s and we replace it in the d category general framework