optimal matching with minimal deviation from fine balance in a study of obesity and surgical outcomes in multivariate matching fine balance constrains the marginal distributions of a nominal variable in treated and matched control groups to be identical without constraining who is matched to whom in this way a fine balance constraint can balance a nominal variable with many levels while focusing efforts on other more important variables when pairing individuals to minimize the total covariate distance within pairs fine balance is not always possible that is it is a constraint on an optimization problem but the constraint is not always feasible we propose a new algorithm which returns a minimum distance finely balanced match when one is feasible and otherwise minimizes the total distance among all matched samples that minimize the deviation from fine balance perhaps we can come very close to fine balance when fine balance is not attainable moreover in any event because our algorithm is guaranteed to come as close as possible to fine balance the investigator may perform one match and on that basis judge whether the best attainable balance is adequate or not we also show how to incorporate an additional constraint the algorithm is implemented in two similar ways first as an optimal assignment problem with an augmented distance matrix second as a minimum cost flow problem in a network the case of knee surgery in the obesity and surgical outcomes study motivated the development of this algorithm and is used as an illustration in that example two of 47 hospitals had too few nonobese patients to permit fine balance for the nominal variable with 47 levels representing the hospital but our new algorithm came very close to fine balance moreover in that example there was a shortage of nonobese diabetic patients and incorporation of an additional constraint forced the match to include all of these nonobese diabetic patients thereby coming as close as possible to balance for this important but recalcitrant covariate

bootstrap tests for distributional treatment effects in instrumental variable models this article considers the problem of assessing the distributional consequences of a treatment on some outcome variable of interest when treatment intake is possibly nonrandomized but there is a binaryinstrument available for the researcher such a scenario is common in observational studies and in randomized experiments with imperfect compliance one possible approach to this problem is to compare the counterfactual cumulative distribution functions of the outcome with and without the treatment this article shows how to estimate these distributions using instrumental variable methods and a simple bootstrap procedure is proposed to test distributional hypotheses such as equality of distributions first order and second order stochastic dominance these tests and estimators are applied to the study of the effects of veteran status on the distribution of civilian earnings the results show a negative effect of military service during the vietnam era that appears to be concentrated on the lower tail of

a co induction principle for recursively defined domains abstract this paper establishes a new property of predomains recursively defined using the cartesian product disjoint union partial function space and convex powerdomain constructors we prove that the partial order on such a recursive predomain d is the greatest fixed point of a certain monotone operator associated to d this provides a structurally defined family of proof principles for these recursive predomains to show that one element of d approximates another it suffices to find a binary relation containing the two elements that is a post fixed point for the associated monotone operator the statement of the proof principles is independent of any of the various methods available for explicit construction of recursive predomains following milner and tofte 1991 the method of proof is called co induction it closely resembles the way bisimulations are used in concurrent process calculi milner 1989 two specific instances of the co induction principle already occur in the work of abramsky 1990 1991 in the form of internal full abstraction theorems for denotational semantics of sccs and lazy lambda calculus in the first case post fixed binary relations are precisely abramsky s partial bisimulations whereas in the second case they are his applicative bisimulations the co induction principle also provides an apparently useful tool for reasoning about equality of elements of recursively defined datatypes in strict or lazy higher order functional programming languages

full abstraction for pcf an intensional model for the programming language pcf is described in which the types of pcf are interpreted by games and the terms by certain history free strategies this model is shown to capture definability in pcf more precisely every compact strategy in the model is definable in a certain simple extension of pcf we then introduce an intrinsic preorder on strategies and show that it satisfies some striking properties such that the intrinsic preorder on function types coincides with the pointwise preorder we then obtain an order extensional fully abstract model of pcf by quotienting the intensional model by the intrinsic preorder this is the first syntax independent description of the fully abstract model for pcf hyland and ong have obtained very similar results by a somewhat different route independently and at the same time we then consider the effective version of our model and prove a universality theorem every element of the effective extensional model is definable in pcf equivalently every recursive strategy is definable up to observational equivalence

musings around the geometry of interaction and coherence we introduce the danos regnier category dr m of a linear inverse monoid m as a categorical description of geometries of interaction goi inspired from the weight algebra the natural setting for goi is that of a so called weakly cantorian linear inverse monoid in which case dr m is a kind of symmetrized version of the classical abramsky haghverdi scott construction of a weak linear category from a goi situation it is well known that goi is perfectly suited to describe the multiplicative fragment of linear logic and indeed dr m will be a autonomous category in this case it is also well known that the categorical interpretation of the other linear connectives conflicts with goi interpretations we make this precise and show that dr m has no terminal object no cartesian product of any two objects and no exponential whatever m is unless m is trivial however a form of coherence completion of dr m a la hu joyal which for additives resembles a layered approach a la hughes van glabbeek provides a model of full classical linear logic as soon as m is weakly cantorian one finally notes that girard s notion of coherence is pervasive and instrumental in every aspect of this work

on global solutions of the maxwell dirac equations we prove for the maxwell dirac equations in 1 3 dimensions that modified wave operators exist on a domain of small entire test functions of exponential type and that the cauchy problem inr r3 has a unique solution for each initial condition att 0 which is in the image of the wave operator the modification of the wave operator which eliminates infrared divergences is given by approximate solutions of the hamilton jacobi equation for a relativistic electron in an electromagnetic potential the modified wave operator linearizes the maxwell dirac equations to their linear part

causal inference in paired two arm experimental studies under noncompliance with application to prognosis of myocardial infarction motivated by a study about prompt coronary angiography in myocardial infarction we propose a method to estimate the causal effect of a treatment in two arm experimental studies with possible noncompliance in both treatment and control arms we base the method on a causal model for repeated binary outcomes before and after the treatment which includes individual covariates and latent variables for the unobserved heterogeneity between subjects moreover given the type of noncompliance the model assumes the existence of three subpopulations of subjects compliers never takers and always takers we estimate the model using a two step estimator at the first step we estimate the probability that a subject belongs to one of the three subpopulations on the basis of the available covariates at the second step we estimate the causal effects through a conditional logistic method the implementation of which depends on the results from the first step the estimator is approximately consistent and under certain circumstances exactly consistent we provide evidence that the bias is negligible in relevant situations we compute standard errors on the basis of a sandwich formula the application shows that prompt coronary angiography in patients with myocardial infarction may significantly decrease the risk of other events within the next 2 years with a log odds of about 2 given that noncompliance is significant for patients being given the treatment because of high risk conditions classical estimators fail to detect or at least underestimate this effect copyright 2013 john wiley sons ltd

weighted models for higher order computation abstract we study a class of quantitative models for higher order computation lafont categories with infinite biproducts each of these has a complete internal semiring and can be enriched over its modules we describe a semantics of nondeterministic pcf weighted over this semiring in which fixed points are obtained from the bifree algebra over its exponential structure by characterizing them concretely as infinite sums of approximants indexed over nested finite multisets we prove computational adequacy we can construct examples of our semantics by weighting existing models such as categories of games over a complete semiring this transition from qualitative to quantitative semantics is characterized as a change of base of enriched categories arising from a monoidal functor from coherence spaces to modules over a complete semiring for example the game semantics of idealized algol is coherence space enriched and thus gives rise to to a weighted model which is fully abstract

doubly robust estimation of the local average treatment effect curve we consider estimation of the causal effect of a binary treatment on an outcome conditionally on covariates from observational studies or natural experiments in which there is a binary instrument for treatment we describe a doubly robust locally efficient estimator of the parameters indexing a model for the local average treatment effect conditionally on covariates v when randomization of the instrument is only true conditionally on a high dimensional vector of covariates x possibly bigger than v we discuss the surprising result that inference is identical to inference for the parameters of a model for an additive treatment effect on the treated conditionally on v that assumes no treatment instrument interaction we illustrate our methods with the estimation of the local average effect of participating in 401 k retirement programs on savings by using data from the us census bureau s 1991 survey of income and program participation

innocent game models of untyped λ calculus we present a new denotational model for the untyped l calculus using the techniques of game semantics the strategies used are innocent in the sense of hyland and ong inform and comput to appear and nickau hereditarily sequential functionals a game theoretic approach to sequentiality shaker verlag 1996 dissertation universitat gesamthochschule siegen shaker verlag 1996 but the traditional distinction between question and answer moves is removed we first construct models d and drec as global sections of a reflexive object in the categories a and arec of arenas and innocent and recursive innocent strategies respectively we show that these are sensible le algebras but are neither extensional nor universal we then introduce a new representation of innocent strategies in an economical form we show a strong connexion between the economical form of the denotation of a term in the game models and a variable free form of the nakajima tree of the term using this we show that the definable elements of drec are precisely what we call effectively almost everywhere copycat eac strategies the category aeac with these strategies as morphisms gives rise to a model deac which we show has the same expressive power as d i e the equational theory of deac is the maximal consistent sensible theory h we show that the model deac is sensible order extensional and universal i e every strategy is the denotation of some term to our knowledge this is the first syntax free model of the untyped calculus with the universality property copyright 2002 elsevier science b v

a theory of sequentiality abstract we show that the notion of sequentiality as presented in concrete data structures may be carried to a more general domain theoretic framework cells are replaced by some linear maps on a domain which turns out to be a di domain in a first phase we do not require the cells to be enabled as they are in cdss and we get a weak form of cartesian closedness then by enriching the structure we get the standard one

on the completeness of order theoretic models of the λ calculus scott discovered his domain theoretic models of the l calculus isomorphic to their function space in 1969 a natural completeness problem then arises whether any two terms equal in all scott models are convertible there is also an analogous consistency problem whether every equation between two terms consistent with the l calculus has a scott model we consider such questions for wider sets of sentences and wider classes of models the pointed completely partially ordered ones a negative result for a set of sentences shows the impossibility of finding scott models for that class a positive result gives evidence that there might be enough scott models we find for example that the order extensional pointed w cpo models are complete for p 1 sentences with positive matrices whereas the consistency question for s 1 sentences with equational matrices depends on the consistency of certain critical sentences asserting the existence of certain functions analogous to the generalized mal cev operators first considered in the context of the l calculus by selinger

instrumental variable estimators for binary outcomes instrumental variables ivs can be used to construct estimators of exposure effects on the outcomes of studies affected by nonignorable selection of the exposure estimators that fail to adjust for the effects of nonignorable selection will be biased and inconsistent such situations commonly arise in observational studies but are also a problem for randomized experiments affected by nonignorable noncompliance in this article we review iv estimators for studies in which the outcome is binary and consider the links between different approaches developed in the statistics and econometrics literatures the implicit assumptions made by each method are highlighted and compared within our framework we illustrate our findings through the reanalysis of a randomized placebo controlled trial and highlight important directions for future work in this area

finitary pcf is not decidable the question of the decidability of the observational ordering of finitary pcf was raised jung and stoughton in m bezem j f groote eds typed lambda calculi and applications lecture notes in computer science vol 664 springer berlin 1993 pp 230 244 to give mathematical content to the full abstraction problem for pcf milner theoret comput sci 4 1977 1 22 we show that the ordering is in fact undecidable this result places limits on how explicit a representation of the fully abstract model can be it also gives a slight strengthening of the author s earlier result on typed ability loader in a anderson m zeleny eds church memorial volume kluwer academic press dordrecht to appear copyright 2001 elsevier science b v

bounded efficient and multiply robust estimation of average treatment effects using instrumental variables instrumental variables ivs are widely used for estimating causal effects in the presence of unmeasured confounding under the standard iv model however the average treatment effect ate is only partially identifiable to address this we propose novel assumptions that allow for identification of the ate our identification assumptions are clearly separated from model assumptions needed for estimation so that researchers are not required to commit to a specific observed data model in establishing identification we then construct multiple estimators that are consistent under three different observed data models and multiply robust estimators that are consistent in the union of these observed data models we pay special attention to the case of binary outcomes for which we obtain bounded estimators of the ate that are guaranteed to lie between 1 and 1 our approaches are illustrated with simulations and a data analysis evaluating the causal effect of education on earnings

on falsification of the binary instrumental variable model instrumental variables are widely used for estimating causal effects in the presence of unmeasured confounding the discrete instrumental variable model has testable implications for the law of the observed data however current assessments of instrumental validity are typically based solely on subject matter arguments rather than these testable implications partly due to a lack of formal statistical tests with known properties in this paper we develop simple procedures for testing the binary instrumental variable model our methods are based on existing techniques for comparing two treatments such as the formula see text test and the gail simon test we illustrate the importance of testing the instrumental variable model by evaluating the exogeneity of college proximity using the national longitudinal survey of young men

scattering theory for the schrodinger equation in some external time dependent magnetic fields abstract we study the theory of scattering for a schrodinger equation in an external time dependent magnetic field in the coulomb gauge in space dimension 3 the magnetic vector potential is assumed to satisfy decay properties in time that are typical of solutions of the free wave equation and even in some cases to be actually a solution of that equation that problem appears as an intermediate step in the theory of scattering for the maxwell schrodinger ms system we prove in particular the existence of wave operators and their asymptotic completeness in spaces of relatively low regularity we also prove their existence or at least asymptotic results going in that direction in spaces of higher regularity the latter results are relevant for the ms system as a preliminary step we study the cauchy problem for the original equation by energy methods using as far as possible time derivatives instead of space derivatives

syntax vs semantics a polarized approach we present a notion of sliced proof nets for the polarized fragment of linear logic and a corresponding game model we show that the connection between them is very strong through an equivalence of categories this contains soundness full completeness and faithful completeness

relative definability of boolean functions via hypergraphs the aim of this work is to show how hypergraphs can be used as a systematic tool in the classification of continuous boolean functions according to their degree of parallelism intuitively f is less parallel than g if it can be defined by a sequential program using g as its only free variable it turns out that the poset induced by this preorder is as for the degrees of recursion a sup semilattice although hypergraphs have already been used in bucciarelli theoret comput sci to appear as a tool for studying degrees of parallelism no general result relating the former to the latter has been proved in that work we show that the sup semilattice of degrees has a categorical counterpart we define a category of hypergraphs such that every object represents a monotone boolean function finite coproducts in this category correspond to lubs of degrees unlike degrees of recursion where every set has a recursive upper bound monotone boolean functions may have no sequential upper bound however the ones which do have a sequential upper bound can be nicely characterised in terms of hypergraphs these subsequential functions play a major role in the proof of our main result namely that f is less parallel than g if there exists a morphism between their associated hypergraphs

domain semantics of possibility computations the purpose of this paper is to introduce a kind of computational model called possibility computation to deal with non determinism both its denotational and logical semantics in the framework of domain theory are established and their equivalence is verified in this approach the denotational semantics will be set up by assigning to programs possibility state transformers i e scott continuous functions from the domain of input states to the possibility powerdomain of the codomain of final states this possibility powerdomain of a dcpo will consist of all possibility valuations ordered pointwise of this dcpo the logical semantics will be given by fuzzy predicate transformers introduced by the first author and jung following dijkstra s predicate transformers two semantics equivalence will be verified in terms of the integration of fuzzy predicates with respect to possibility valuations the categorical monad of the possibility powerdomain will be investigated

bounds on treatment effects from studies with imperfect compliance abstract this article establishes nonparametric formulas that can be used to bound the average treatment effect in experimental studies in which treatment assignment is random but subject compliance is imperfect the bounds provided are the tightest possible given the distribution of assignments treatments and responses the formulas show that even with high rates of noncompliance experimental data can yield useful and sometimes accurate information on the average effect of a treatment on the population

on a preference based instrumental variable approach in reducing unmeasured confounding by indication treatment preferences of groups e g clinical centers have often been proposed as instruments to control for unmeasured confounding by indication in instrumental variable iv analyses however formal evaluations of these group preference based instruments are lacking unique challenges include the following i correlations between outcomes within groups ii the multi value nature of the instruments iii unmeasured confounding occurring between and within groups we introduce the framework of between group and within group confounding to assess assumptions required for the group preference based iv analyses our work illustrates that when unmeasured confounding effects exist only within groups but not between groups preference based ivs can satisfy assumptions required for valid instruments we then derive a closed form expression of asymptotic bias of the two stage generalized ordinary least squares estimator when the ivs are valid simulations demonstrate that the asymptotic bias formula approximates bias in finite samples quite well particularly when the number of groups is moderate to large the bias formula shows that when the cluster size is finite the iv estimator is asymptotically biased only when both the number of groups and cluster size go to infinity the bias disappears however the iv estimator remains advantageous in reducing bias from confounding by indication the bias assessment provides practical guidance for preference based iv analyses to increase their performance one should adjust for as many measured confounders as possible consider groups that have the most random variation in treatment assignment and increase cluster size to minimize the likelihood for these ivs to be invalid one should minimize unmeasured between group confounding copyright 2014 john wiley sons ltd

two stage instrumental variable methods for estimating the causal odds ratio analysis of bias we present closed form expressions of asymptotic bias for the causal odds ratio from two estimation approaches of instrumental variable logistic regression i the two stage predictor substitution 2sps method and ii the two stage residual inclusion 2sri approach under the 2sps approach the first stage model yields the predicted value of treatment as a function of an instrument and covariates and in the second stage model for the outcome this predicted value replaces the observed value of treatment as a covariate under the 2sri approach the first stage is the same but the residual term of the first stage regression is included in the second stage regression retaining the observed treatment as a covariate our bias assessment is for a different context from that of terza j health econ 2008 27 3 531 543 who focused on the causal odds ratio conditional on the unmeasured confounder whereas we focus on the causal odds ratio among compliers under the principal stratification framework our closed form bias results show that the 2sps logistic regression generates asymptotically biased estimates of this causal odds ratio when there is no unmeasured confounding and that this bias increases with increasing unmeasured confounding the 2sri logistic regression is asymptotically unbiased when there is no unmeasured confounding but when there is unmeasured confounding there is bias and it increases with increasing unmeasured confounding the closed form bias results provide guidance for using these iv logistic regression methods our simulation results are consistent with our closed form analytic results under different combinations of parameter settings

a stable programming language it is well known that stable models as di domains qualitative domains and coherence spaces are not fully abstract for the language pcf this fact is related to the existence of stable parallel functions and of stable functions that are not monotone with respect to the extensional order which cannot be defined by programs of pcf in this paper a paradigmatic programming language named st pcf is proposed which extends the language pcf with two additional operators the operational description of the extended language is presented in an effective way although the evaluation of one of the new operators cannot be formalized in a pcf like rewrite system since st pcf can define all finite cliques of coherence spaces the above gap with stable models is filled consequently stable models are fully abstract for the extended language

local instrumental variables and latent variable models for identifying and bounding treatment effects this paper examines the relationship between various treatment parameters within a latent variable model when the effects of treatment depend on the recipient s observed and unobserved characteristics we show how this relationship can be used to identify the treatment parameters when they are identified and to bound the parameters when they are not identified

from algol to polymorphic linear lambda calculus in a linearly typed functional language one can define functions that consume their arguments in the process of computing their results this is reminiscent of state transformations in imperative languages where execition of an assignment statement alters the contents of the store we explore this connection by translating two variations on algol 60 into a purely functional language with polymorphic linear types on the one hand the translations lead to a semantic analysis of algol like programs in terms of a model of the linear language on the other hand they demonstrate that a linearly typed functional language can be at least as expressive as algol

bayesian inference for causal effects in randomized experiments with noncompliance for most of this century randomization has been a cornerstone of scientific experimentation especially when dealing with humans as experimental units in practice however noncompliance is relatively common with human subjects complicating traditional theories of inference that require adherence to the random treatment assignment in this paper we present bayesian inferential methods for causal estimands in the presence of noncompliance when the binary treatment assignment is random and hence ignorable but the binary treatment received is not ignorable we assume that both the treatment assigned and the treatment received are observed we describe posterior estimation using em and data augmentation algorithms also we investigate the role of two assumptions often made in econometric instrumental variables analyses the exclusion restriction and the monotonicity assumption without which the likelihood functions generally have substantial regions of maxima we apply our procedures to real and artificial data thereby demonstrating the technology and showing that our new methods can yield valid inferences that differ in practically important ways from those based on previous methods for analysis in the presence of noncompliance including intention to treat analyses and analyses based on econometric instrumental variables techniques finally we perform a simulation to investigate the operating characteristics of the competing procedures in a simple setting which indicates relatively dramatic improvements in frequency operating characteristics attainable using our bayesian procedures

hierarchies of total functionals over the reals we compare two natural constructions the a hierarchy and the r hierarchy of hereditarily total continuous and extensional functionals of finite types over the reals the a hierarchy is based on the closed interval domain representation of the reals while the r hierarchy is based on the binary negative digit representation we show that the two hierarchies share a common maximal core to this end we construct an alternative to the r hierarchy and prove a density theorem for this alternative hierarchy

game semantics for dependent types abstract we present a model of dependent type theory dtt with 1 and intensional id types which is based on a slight variation of the call by name category of ajm games and history free winning well bracketed strategies the model satisfies streicher s criteria of intensionality and refutes function extensionality the principle of uniqueness of identity proofs is satisfied we show it contains a submodel as a full subcategory which gives a faithful interpretation of dtt with 1 and intensional id types and additionally finite inductive type families this smaller model is fully and faithfully complete with respect to the syntax at the type hierarchy built without id types as well as at the more general class of types where we allow for one strictly positive occurrence of an id type definability for the full type hierarchy with id types remains to be investigated

global existence and asymptotic behavior of solutions for the maxwell schrodinger equations in three space dimensions in this paper we study the global existence and asymptotic behavior of solutions for the maxwell schrodinger equations under the coulomb gauge condition in three space dimensions with the final states given att this leads to the construction of the modified wave operator for certain scattered data it is also shown that for the initial data in the range of the modified wave operator the initial value problem of the maxwell schrodinger equations has the global solutions in time

strichartz estimates for the magnetic schrodinger equation abstract we prove global scale invariant strichartz estimates for the linear magnetic schrodinger equation with small time dependent magnetic field this is done by constructing an appropriate parametrix as an application we show a global regularity type result for schrodinger maps in dimensions n 6

what is a model of the lambda calculus an elementary purely algebraic definition of model for the untyped lambda calculus is given this definition is shown to be equivalent to the natural semantic definition based on environments these definitions of model are consistent with and yield a completeness theorem for the standard axioms for lambda convertibility a simple construction of models for lambda calculus is reviewed the algebraic formulation clarifies the relation between combinators and lambda terms

a fully abstract denotational semantics for the calculus of higher order communicating systems abstract in this paper we study the calculus of higher order communicating systems chocs thomsen proc of popl 89 acm 1989 pp 143 154 inform comput 116 1 1995 38 57 in a denotational setting we present a construction of a denotational semantics for chocs which resides in a domain constructed using the standard constructions of separated sum cartesian product the plotkin power domain constructor and recursively defined domains we show under mild restrictions that the denotational semantics and the operational semantics of chocs are fully abstract we have previously proved using bisimulation arguments that processes as first class objects are powerful enough to simulate recursion however the proof is very long and tedious to demonstrate the power of the denotational approach we use it to obtain a very simple proof of the simulation of recursion result

regression and weighting methods for causal inference using instrumental variables please see the supplementary material for a correction and a new result recent researches in econometrics and statistics have gained considerable insights into the use of instrumental variables ivs for causal inference a basic idea is that ivs serve as an experimental handle the turning of which may change each individual s treatment status and through and only through this effect also change observed outcome the average difference in observed outcome relative to that in treatment status gives the average treatment effect for those whose treatment status is changed in this hypothetical experiment we build on the modern iv framework and develop two estimation methods in parallel to regression adjustment and propensity score weighting in the case of treatment selection based on covariates the iv assumptions are made explicitly conditional on covariates to allow for the fact that instruments can be related to these background variables the regression method focuses on the relationship between respo

operational domain theory and topology of sequential programming languages a number of authors have exported domain theoretic techniques from denotational semantics to the operational study of contextual equivalence and order we further develop this and moreover we additionally export topological techniques in particular we work with an operational notion of compact set and show that total programs with values on certain types are uniformly continuous on compact sets of total elements we apply this and other conclusions to prove the correctness of non trivial programs that manipulate infinite data what is interesting is that the development applies to sequential programming languages in addition to languages with parallel features

long range scattering for the modified schrodinger map in two space dimensions we study the asymptotic behaviour in time of solutions and the theory of scattering for the modified schrodinger map in two space dimensions we solve the cauchy problem with large finite initial time up to infinity in time and we determine the asymptotic behaviour in time of the solutions thereby obtained as a by product we obtain global existence for small data in hk fhk with k 1 we also solve the cauchy problem with infinite initial time namely we construct solutions defined in a neighborhood of infinity in time with prescribed asymptotic behaviour of the previous type

a relative pcf definability result for strongly stable functions and some corollaries we prove that in the hierarchy of simple types based on the type of natural numbers any finite strongly stable function is equal to the application of the semantics of a pcf definable functional to some strongly stable generally not pcf definable functionals of type two applying a logical relation technique we derive from this result that the strongly stable model of pcf is the extensional collapse of its sequential algorithms model

long range scattering for nonlinear schrodinger equations in one space dimension we consider the scattering problem for the nonlinear schrodinger equation in 1 1 dimensions open image in new window where x r 0 r p 3 we show that modified wave operators for exist on a dense set of a neighborhood of zero in the lebesgue spacel2 r or in the sobolev spaceh1 r the modified wave operators are introduced in order to control the long range nonlinearity u 2u

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

marginal and nested structural models using instrumental variables the objective of many scientific studies is to evaluate the effect of a treatment on an outcome of interest ceteris paribus instrumental variables ivs serve as an experimental handle independent of potential outcomes and potential treatment status and affecting potential outcomes only through potential treatment status we propose marginal and nested structural models using ivs in the spirit of marginal and nested structural models under no unmeasured confounding a marginal structural iv model parameterizes the expectations of two potential outcomes under an active treatment and the null treatment respectively for those in a covariate specific subpopulation who would take the active treatment if the instrument were externally set to each specific level a nested structural iv model parameterizes the difference between the two expectations after transformed by a link function and hence the average treatment effect on the treated at each instrument level we develop iv outcome regression iv propensi

adapting innocent game models for the bohm tree λ theory we present a game model of the untyped calculus with equational theory equal to the bohm tree theory b which is universal i e every element of the model is definable by some term this answers a question of di gianantonio franco and honsell we build on our earlier work which uses the methods of innocent game semantics to develop a universal model inducing the maximal consistent sensible theory h to our knowledge these are the first syntax independent universal models of the untyped calculus

combining a monad and a comonad we give a systematic treatment of distributivity for a monad and a comonad as arises in giving category theoretic accounts of operational and denotational semantics and in giving an intensional denotational semantics we do this axiomatically in terms of a monad and a comonad in a 2 category giving accounts of the eilenberg moore and kleisli constructions we analyse the eight possible relationships deducing that two pairs are isomorphic but that the other pairs are all distinct we develop those 2 categorical definitions necessary to support this analysis

comparing hierarchies of types in models of linear logic we show that two models m and n of linear logic collapse to the same extensional hierarchy of types when 1 their monoidal categories c and d are related by a pair of monoidal functors f c d g and transformations idc gf and idd fg and 2 their exponentials m and n are related by distributive laws nf f m and mg g n commuting to the promotion rule the key ingredient of the proof is a notion of back and forth translation between the hierarchies of types induced by m and n we apply this result to compare 1 the qualitative and the quantitative hierarchies induced by the coherence or hypercoherence space model 2 several paradigms of games semantics error free vs error aware alternated vs non alternated backtracking vs repetitive uniform vs nonuniform

constructing differential categories and deconstructing categories of games differential categories were introduced by blute cockett and seely to axiomatize categorically ehrhard and regnier s syntactic differential operator we present an abstract construction that takes a symmetric monoidal category and yields a differential category and show how this construction may be applied to categories of games in one instance we recover the category previously used to give a fully abstract model of a nondeterministic imperative language the construction exposes the differential structure already present in this model and shows how the differential combinator may be encoded in the imperative language the second instance corresponds to a new cartesian differential category of games we give a model of a simply typed resource calculus resource pcf in this category and show that it possesses the finite definability property comparison with a semantics based on bucciarelli ehrhard and manzonetto s relational model reveals that the latter also possesses this property and is fully abstract

multigames and strategies coalgebraically coalgebraic games have been recently introduced as a generalization of conway games and other notions of games arising in different contexts using coalgebraic methods games can be viewed as elements of a final coalgebra for a suitable functor and operations on games can be analyzed in terms of generalized coiteration schemata coalgebraic games are sequential in nature i e at each step either the left l or the right r player moves global polarization moreover only a single move can be performed at each step recently in the context of game semantics concurrent games have been introduced where global polarization is abandoned and multiple moves are allowed in this paper we introduce coalgebraic multigames which are situated half way between traditional sequential games and concurrent games global polarization is still present however multiple moves are possible at each step i e a team of l r players moves in parallel coalgebraic operations such as sum and negation can be naturally defined on multigames interestingly sum on coalgebraic multigames turns out to be related to conway s selective sum on games rather than the usual sequential disjoint sum selective sum has a parallel nature in that at each step the current player performs a move in at least one component of the sum game while on disjoint sum the current player performs a move in exactly one component at each step a presentation of strategies on coalgebraic games is given via a final coalgebra of a pair of mutually recursive functors and a suitable notion of simulation a monoidal closed category of coalgebraic multigames in the vein of a joyal category of conway games is then built the relationship between coalgebraic multigames and games is then formalized via an equivalence of the multigame category and a monoidal closed category of coalgebraic games where tensor is selective sum

robust causal inference with continuous instruments using the local instrumental variable curve instrumental variables are commonly used to estimate effects of a treatment afflicted by unmeasured confounding and in practice instruments are often continuous e g measures of distance or treatment preference however available methods for continuous instruments have important limitations they either require restrictive parametric assumptions for identification or else rely on modelling both the outcome and the treatment process well and require modelling effect modification by all adjustment covariates in this work we develop the first semiparametric doubly robust estimators of the local instrumental variable effect curve i e the effect among those who would take treatment for instrument values above some threshold and not below in addition to being robust to misspecification of either the instrument or treatment or outcome processes our approach also incorporates information about the instrument mechanism and allows for flexible data adaptive estimation of effect modification we discuss asymptotic properties under weak conditions and use the methods to study infant mortality effects of neonatal intensive care units with high versus low technical capacity using travel time as an instrument

the scott model of linear logic is the extensional collapse of its relational model we show that the extensional collapse of the relational model of linear logic is the model of prime algebraic complete lattices a natural extension to linear logic of the well known scott semantics of the lambda calculus

semiparametric instrumental variable estimation of treatment response models this article introduces a new class of instrumental variable iv estimators for linear and nonlinear treatment response models with covariates the rationale for focusing on nonlinear models is that if the dependent variable is binary or limited or if the effect of the treatment varies with covariates a nonlinear model is appropriate in the spirit of roehrig econometrica 56 1988 433 identification is attained nonparametrically and does not depend on the choice of the parametric specification for the response function of interest one virtue of this approach is that it allows the researcher to construct estimators that can be interpreted as the parameters of a well defined approximation to a treatment response function under functional form misspecification in contrast to some usual iv models heterogeneity of treatment effects is not restricted by the identification conditions the ideas and estimators in this article are illustrated using iv to estimate the effects of 401 k retirement programs on savings

reducing bias in observational studies using subclassification on the propensity score abstract the propensity score is the conditional probability of assignment to a particular treatment given a vector of observed covariates previous theoretical arguments have shown that subclassification on the propensity score will balance all observed covariates subclassification on an estimated propensity score is illustrated using observational data on treatments for coronary artery disease five subclasses defined by the estimated propensity score are constructed that balance 74 covariates and thereby provide estimates of treatment effects using direct adjustment these subclasses are applied within sub populations and model based adjustments are then used to provide estimates of treatment effects within these sub populations two appendixes address theoretical issues related to the application the effectiveness of subclassification on the propensity score in removing bias and balancing properties of propensity scores with incomplete data

long range scattering for the maxwell schrodinger system in the lorenz gauge without any restriction on the size of data abstract this paper concerns the scattering theory for the maxwell schrodinger ms system in the lorenz gauge or more precisely the existence of the modified wave operators for this system in r 3 1 space time we construct solutions to the ms system which behave as free maxwell and schrodinger waves with prescribed asymptotic states when t without any restriction on the size thereof since this system belongs to the borderline between the short range case and the long range case we need modification of phase for the schrodinger function

control function instrumental variable estimation of nonlinear causal effect models the instrumental variable method consistently estimates the effect of a treatment when there is unmeasured confounding and a valid instrumental variable a valid instrumental variable is a variable that is independent of unmeasured confounders and affects the treatment but does not have a direct effect on the outcome beyond its effect on the treatment two commonly used estimators for using an instrumental variable to estimate a treatment effect are the two stage least squares estimator and the control function estimator for linear causal effect models these two estimators are equivalent but for nonlinear causal effect models the estimators are different we provide a systematic comparison of these two estimators for nonlinear causal effect models and develop an approach to combing the two estimators that generally performs better than either one alone we show that the control function estimator is a two stage least squares estimator with an augmented set of instrumental variables if these augmented instrumental variables are valid then the control function estimator can be much more efficient than usual two stage least squares without the augmented instrumental variables while if the augmented instrumental variables are not valid then the control function estimator may be inconsistent while the usual two stage least squares remains consistent we apply the hausman test to test whether the augmented instrumental variables are valid and construct a pretest estimator based on this test the pretest estimator is shown to work well in a simulation study an application to the effect of exposure to violence on time preference is considered

parallel and serial hypercoherences abstract it is known that the strongly stable functions which arise in the semantics of pcf can be realized by sequential algorithms which can be considered as deterministic strategies in games associated to pcf types studying the connection between strongly stable functions and sequential algorithms two dual classes of hypercoherences naturally arise the parallel and serial hypercoherences the objects belonging to the intersection of these two classes are in bijective correspondence with the so called serial parallel graphs that can essentially be considered as games we show how to associate to any hypercoherence a parallel hypercoherence together with a projection onto the given hypercoherence and present some properties of this construction intuitively it makes explicit the computational time of a hypercoherence

identification and estimation of local average treatment effects we investigate conditions sufficient for identification of average treatment effects using instrumental variables first we show that the existence of valid instruments is not sufficient to identify any meaningful average treatment effect we then establish that the combination of an instrument and a condition on the relation between the instrument and the participation status is sufficient for identification of a local average treatment effect for those who can be induced to change their participation status by changing the value of the instrument finally we derive the probability limit of the standard iv estimator under these conditions it is seen to be a weighted average of local average treatment effects this abstract was borrowed from another version of this item

sensitivity analysis for instrumental variables regression with overidentifying restrictions instrumental variables regression iv regression is a method for making causal inferences about the effect of a treatment based on an observational study in which there are unmeasured confounding variables the method requires one or more valid instrumental variables ivs a valid iv is a variable that is associated with the treatment is independent of unmeasured confounding variables and has no direct effect on the outcome often there is uncertainty about the validity of the proposed ivs when a researcher proposes more than one iv the validity of these ivs can be tested through the overidentifying restrictions test although the overidentifying restrictions test does provide some information the test has no power versus certain alternatives and can have low power versus many alternatives due to its omnibus nature to fully address uncertainty about the validity of the proposed ivs we argue that a sensitivity analysis is needed a sensitivity analysis examines the impact of plausible amounts of

an exact correspondence between a typed pi calculus and polarised proof nets this paper presents an exact correspondence in typing and dynamics between polarised linear logic and a typed p calculus based on io typing the respective incremental constraints one on geometric structures of proof nets and one based on types precisely correspond to each other leading to the exact correspondence of the respective formalisms as they appear in olivier laurent 2003 27 for proof nets and kohei honda et al 2004 24 for the p calculus

exact real number computations relative to hereditarily total functionals we show that the continuous existential quantifier is not definable in escardo s real pcf from all functionals equivalent to a given total one in a uniform way we further prove that relative to any total functional of type i i i which gives the maximum value for any total input we may given a computable total functional of type r r r find a real pcf definable total equivalent to

the cauchy problem for the coupled maxwell schrodinger equations the cauchy problem for the coupled maxwell schrodinger equations in rd in the lorentz gauge is considered the viscosity method is used to establish local existence in one and two space dimensions global solutions are obtained

a type assignment system for game semantics we present a type assignment system that provides a finitary interpretation of lambda terms in a game semantics model traditionally type assignment systems describe the semantic interpretation of terms in domain theoretic models quite surprisingly the type assignment system presented in this paper is very similar to the traditional ones the main difference being the omission of the subtyping rules

a structural approach to reversible computation reversibility is a key issue in the interface between computation and physics and of growing importance as miniaturization progresses towards its physical limits most foundational work on reversible computing to date has focussed on simulations of low level machine models by contrast we develop a more structural approach we show how high level functional programs can be mapped compositionally i e in a syntax directed fashion into a simple kind of automata which are immediately seen to be reversible the size of the automaton is linear in the size of the functional term in mathematical terms we are building a concrete model of functional computation this construction stems directly from ideas arising in geometry of interaction and linear logic but can be understood without any knowledge of these topics in fact it serves as an excellent introduction to them at the same time an interesting logical delineation between reversible and irreversible forms of computation emerges from our analysis

a type theoretical alternative to iswim cuch owhy abstract the paper first written in 1969 and circulated privately concerns the definition axiomatization and applications of the hereditarily monotone and continuous functionals generated from the integers and the booleans plus undefined elements the system is formulated as a typed system of combinators or as a typed calculus with a recursion operator the least fixed point operator and its proof rules are contrasted to a certain extent with those of the untyped calculus for publication 1993 a new preface has been added and many bibliographical references and comments in footnotes have been appended

global existence and uniqueness of solutions to the maxwell schrodinger equations the time local and global well posedness for the maxwell schrodinger equations is considered in sobolev spaces in three spatial dimensions the strichartz estimates of koch and tzvetkov type are used for obtaining the solutions in the sobolev spaces of low regularities one of the main results is that the solutions exist time globally for large data

types and full abstraction for polyadic π calculus a type system for terms of the monadic p calculus is introduced and used to obtain a full abstraction result for the translation of the polyadic p calculus into the monadic calculus well sorted terms of the polyadic calculus are barbed congruent iff their translations are typed barbed congruent

existence of solutions for schrodinger evolution equations we study the existence uniqueness and regularity of the solution of the initial value problem for the time dependent schrodinger equationi u t 1 2 u v t x u u 0 u0 we provide sufficient conditions onv t x such that the equation generates a unique unitary propagatoru t s and such thatu t s u0ec1 l2 c0 h2 n foru0eh2 n the conditions are general enough to accommodate moving singularities of type x 2 n 4 or x n 2 n 3

global wellposedness in the energy space for the maxwell schrodinger system we prove that the maxwell schrodinger system in mathbb r 3 1 is globally well posed in the energy space the key element of the proof is to obtain a short time wave packet parametrix for the magnetic schrodinger equation which leads to linear bilinear and trilinear estimates these in turn are extended to larger time scales via a bootstrap argument

glueing and orthogonality for models of linear logic we present the general theory of the method of glueing and associated technique of orthogonality for constructing categorical models of all the structure of linear logic in particular we treat the exponentials in detail we indicate simple applications of the methods and show that they cover familiar examples

two categories of effective continuous cpos this paper presents two categories of effective continuous complete partial orders cpos we define a new criterion on the basis of a cpo so as to make the resulting category of consistently complete continuous cpos cartesian closed we also generalise to continuous cpos the definition of a complete set which was used as a definition of effective bifinite domains in hamrin and stoltenberg hansen cartesian closed categories of effective domains in h schwichtenberg r steinbruggen eds proof and system reliability kluwer academic publishers dordrecht 2002 pp 1 20 and investigate the closure results that can be obtained

a distributional approach for causal inference using propensity scores drawing inferences about the effects of treatments and actions is a common challenge in economics epidemiology and other fields we adopt rubin s potential outcomes framework for causal inference and propose two methods serving complementary purposes one can be used to estimate average causal effects assuming no confounding given measured covariates the other can be used to assess how the estimates might change under various departures from no confounding both methods are developed from a nonparametric likelihood perspective the propensity score plays a central role and is estimated through a parametric model under the assumption of no confounding the joint distribution of covariates and each potential outcome is estimated as a weighted empirical distribution expectations from the joint distribution are estimated as weighted averages or equivalently to first order regression estimates the likelihood estimator is at least as efficient and the regression estimator is at least as efficient and r

sequential algorithms and strongly stable functions intuitionistic proofs and pcf programs may be interpreted as functions between domains or as strategies on games the two kinds of interpretation are inherently different static vs dynamic extensional vs intentional it is thus extremely instructive to compare and to connect them in this article we investigate the extensional content of the sequential algorithm hierarchy sds introduced by berry and curien we equip every sequential game t sds of the hierarchy with a realizability relation between plays and extensions in this way the sequential game t sds becomes a directed acyclic graph instead of a tree this enables to define a hypergraph t hc on the extensions or terminal leaves of the game t sds we establish that the resulting hierarchy hc coincides with the strongly stable hierarchy introduced by bucciarelli and ehrhard we deduce from this a gametheoretic proof of ehrhard s collapse theorem which states that the strongly stable hierarchy coincides with the extensional collapse of the sequential algorithm hierarchy

strong normalisation in the π calculus we introduce a typed calculus where strong normalisation is ensured by typability strong normalisation is a useful property in many computational contexts including distributed systems in spite of its simplicity our type discipline captures a wide class of converging name passing interactive behaviour the proof of strong normalisability combines methods from typed calculi and linear logic with process theoretic reasoning it is adaptable to systems involving state non determinism polymorphism control and other extensions strong normalisation is shown to have significant consequences including finite axiomatisation of weak bisimilarity a fully abstract embedding of the simply typed calculus with products and sums and basic liveness in interaction strong normalisability has been extensively studied as a fundamental property in functional calculi term rewriting and logical systems this work is one of the first steps to extend theories and proof methods for strong normalisability to the context of name passing processes

kripke logical relations and pcf abstract sieber has described a model of pcf consisting of continuous functions that are invariant under certain finitary logical relations and shown that it is fully abstract for closed terms of up to third order types we show that one may achieve full abstraction at all types using a form of kripke logical relations introduced by jung and tiuryn to characterize definability

multiple robustness in factorized likelihood models we consider inference under a nonparametric or semiparametric model with likelihood that factorizes as the product of two or more variation independent factors we are interested in a finite dimensional parameter that depends on only one of the likelihood factors and whose estimation requires the auxiliary estimation of one or several nuisance functions we investigate general structures conducive to the construction of so called multiply robust estimating functions whose computation requires postulating several dimension reducing models but which have mean zero at the true parameter value provided one of these models is correct