countable nondeterminism and random assignment four semantics for a small programming language involving unbounded but countable nondeterminism are provided these comprise an operational semantics two state transformation semantics based on the egli milner and smyth orders respectively and a weakest precondition semantics their equivalence is proved a hoare like proof system for total correctness is also introduced and its soundness and completeness in an appropriate sense are shown finally the recursion theoretic complexity of the notions introduced is studied admission of countable nondeterminism results in a lack of continuity of various semantic functions and this is shown to be necessary for any semantics satisfying appropriate conditions in proofs of total correctness one resorts to the use of countable ordinals and it is shown that all recursive ordinals are needed

transition system specifications with negative premises abstract in this article the general approach to plotkin style operational semantics of groote and vaandrager 1989 is extended to transition system specifications tsss with rules that may contain negative premises two problems arise firstly the rules may be inconsistent and secondly it is not obvious how a tss determines a transition relation we present a general method based on the stratification technique in logic programming to prove consistency of a set of rules and we show how a specific transition relation can be associated with a tss in a natural way then a special format for the rules the ntyft ntyxt format is defined it is shown that for this format three important theorems hold the first theorem says that bisimulation is a congruence if all operators are defined using this format the second theorem states that under certain restrictions a tss in ntyft format can be added conservatively to a tss in pure ntyft ntyxt format finally it is shown that the trace congruence for image finite processes induced by the pure ntyft ntyxt format is precisely bisimulation equivalence

polar factorization and monotone rearrangement of vector valued functions given a probability space x p and a bounded domain r in rd equipped with the lebesgue measure 1 i normalized so that 10 i i it is shown under additional technical assumptions on x and q that for every vector valued function u e lp x p rd there is a unique polar factorization u v s where is a convex function defined on r and s is a measure preserving mapping from x p into q i i provided that u is nondegenerate in the sense that p u e 0 for each lebesgue negligible subset e of rd through this result the concepts of polar factorization of real matrices helmholtz decomposition of vector fields and nondecreasing rearrangements of real valued functions are unified the monge amgre equation is involved in the polar factorization and the proof relies on the study of an appropriate monge kantorovich problem

bi inductive structural semantics we propose a simple order theoretic generalization possibly non monotone of set theoretic inductive definitions this generalization covers inductive co inductive and bi inductive definitions and is preserved by abstraction this allows structural operational semantics to describe simultaneously the finite terminating and infinite diverging behaviors of programs this is illustrated on grammars and the structural bifinitary small big step trace relational operational semantics of the call by value l calculus for which co induction is shown to be inadequate

language preorder as a precongruence groote and vaandrager introduced the tyft format which is a congruence format for strong bisimulation equivalence this article proposes additional syntactic requirements on the tyft format extended with predicates to obtain a precongruence format for language preorder

the minkowski problem for polytopes abstract the traditional solution to the minkowski problem for polytopes involves two steps first the existence of a polytope satisfying given boundary data is demonstrated in the second step the uniqueness of that polytope up to translation is then shown to follow from the equality conditions of minkowski s inequality a generalized isoperimetric inequality for mixed volumes that is typically proved in a separate context in this article we adapt the classical argument to prove both the existence theorem of minkowski and his mixed volume inequality simultaneously thereby providing a new proof of minkowski s inequality that demonstrates the equiprimordial relationship between these two fundamental theorems of convex geometry

surveillance of nonhomogeneous poisson processes the use of varying sample size monitoring techniques for poisson count data has drawn a great deal of attention in recent years specifically these methods have been used in public health surveillance manufacturing and safety monitoring a number of approaches have been proposed from the traditional shewhart charts to cumulative sum cusum and exponentially weighted moving average ewma methods it is convenient to use techniques based on statistics that are invariant to the units of measurement since in most cases these units are arbitrarily selected a few of the methods reviewed in our expository article are not inherently invariant but most are easily modified to be invariant most importantly if methods are invariant to the choice of units of measurement they can be applied in situations where the in control poisson mean varies over time even if there is no associated varying sample size several examples are discussed to highlight the promising uses of invariant poisson control charting me

structural operational semantics for weak bisimulations in this study we present rule formats for four main notions of bisimulation with silent moves weak bisimulation is a congruence for any process algebra defined by wb cool rules we have similar results for rooted weak bisimulation milner s observational equivalence branching bisimulation and rooted branching bisimulation the theorems stating that say observational equivalence is an appropriate notion of equality for ccs are corollaries of the results of this paper we also give sufficient conditions under which equational axiom systems can be generated from operational rules indeed many equational axiom systems appearing in the literature are instances of this general theory

compositionality of hennessy milner logic by structural operational semantics this paper presents a method for the decomposition of hml formulas it can be used to decide whether a process algebra term satisfies a hml formula by checking whether subterms satisfy certain formulas obtained by decomposing the original formula the method uses the structural operational semantics of the process algebra the main contribution of this paper is the extension of an earlier decomposition method for the de simone format from the ph d thesis of larsen in 1986 to more general formats

the dual minkowski problem for symmetric convex bodies abstract the dual minkowski problem for even data asks what are the necessary and sufficient conditions on a prescribed even measure on the unit sphere for it to be the q th dual curvature measure of an origin symmetric convex body in r n a full solution to this is given when 1 q n the necessary and sufficient conditions turn out to be an explicit measure concentration condition to obtain the results a variational approach is used where the functional is the sum of a dual quermassintegral and an entropy integral the proof requires two crucial estimates the first is an estimate of the entropy integral which is obtained by using a spherical partition the second is a sharp estimate of the dual quermassintegrals for a carefully chosen barrier convex body

likelihood based ewma charts for monitoring poisson count data with time varying sample sizes many applications involve monitoring incidence rates of the poisson distribution when the sample size varies over time recently a couple of cumulative sum and exponentially weighted moving average ewma control charts have been proposed to tackle this problem by taking the varying sample size into consideration however we argue that some of these charts which perform quite well in terms of average run length arl may not be appealing in practice because they have rather unsatisfactory run length distributions with some charts the specified in control ic arl is attained with elevated probabilities of very short and very long runs as compared with a geometric distribution this is reflected in a larger run length standard deviation than that of a geometric distribution and an elevated probability of false alarms with short runs which in turn hurt an operator s confidence in valid alarms furthermore with many charts the ic arl exhibits considerable variations with different patterns of sam

a comparison of weighted cusum procedures that account for monotone changes in population size the cusum procedure has been popularly used for detecting a shift in the incidence rate of a rare health event many cusum methods are developed based on a poisson model with a constant mean number of events in practice the expected number of events is likely to vary over time as the population size at risk is not constant but often grows over time an increase in the baseline incidence rate tends to be masked by the population growth to efficiently detect an increase in the baseline incidence rate it is appealing to assign more weight to recent observations and less weight to older observations this paper compares weighted cusum wcusum and conventional cusum procedures in the presence of monotone changes in population size the simulation results show that the wcusum method may be more efficient than the conventional cusum methods in detecting increases in the incidence rate especially for small shifts an example based on mortality data from new mexico is used to illustrate the implementation of the wcusum method copyright 2010 john wiley sons ltd

lp dual curvature measures abstract a new family of geometric borel measures on the unit sphere is introduced special cases include the l p surface area measures which extend the classical surface area measure of aleksandrov and fenchel jessen and l p integral curvature which extends alkesandrov s integral curvature in the l p brunn minkowski theory it also includes the dual curvature measures which are the duals of federer s curvature measures in the dual brunn minkowski theory this partially unifies the classical theory of mixed volumes and the newer theory of dual mixed volumes

existence and uniqueness of monotone measure preserving maps introduction given a pair of borel probability measures and v on rd it is natural to ask whether v can be obtained from by redistributing its mass in a canonical way in the case of the line d 1 the answer is clear as long as both measures are free from atoms x v x 0mthere is a map y x of the line to itself for which uniquely determined almost everywhere this map may be taken to be nondecreasing by a suitable choice of y x e rw o at the remaining points interpreting and v as the initial and final distribution of a one dimensional fluid the transformation y x gives a rearrangement of fluid particles yielding final state v from the initial state this rearrangement is characterized by the fact that it preserves particle ordering obviating any need for two particles to cross although the generalization of this construction to higher dimensions is the focus of this paper the one dimensional case will be pursued slightly further when the measures are absolutely continuous with respect to lebesgue d x f x dx and dr y g y dymthen formally at least neglecting regularity issues the fundamental theorem of calculus yields

bisimulation can t be traced in the concurrent language ccs two programs are considered the same if they are bisimilar several years and many researchers have demonstrated that the theory of bisimulation is mathematically appealing and useful in practice however bisimulation makes too many distinctions between programs we consider the problem of adding operations to ccs to make bisimulation fully abstract we define the class of gsos operations generalizing the style and technical advantages of ccs operations we characterize gsos congruence in as a bisimulation like relation called ready simulation bisimulation is strictly finer than ready simulation and hence not a congruence for any gsos language

observable behaviors and equivalences of logic programs we first introduce a general semantic scheme for logic programs which provides a uniform framework for defining different compositional semantics parametrically with respect to a given notion of observability the equivalence of the operational top down and fixpoint bottom up construction of the semantics is ensured by the scheme provided a congruence property is verified we then define several observational equivalences on logic programs and investigate how they are related the equivalences are based on various observables successful derivations computed answers partial computed answers and call patterns and on a notion of program composition for each observational equivalence we study the relation with a suitable formal semantics by investigating correctness and full abstraction properties all the semantics we consider are obtained as instances of the general scheme

co induction in relational semantics abstract an application of the mathematical theory of maximum fixed points of monotonic set operators to relational semantics is presented it is shown how an important proof method which we call co induction a variant of park s 1969 principle of fixpoint induction can be used to prove the consistency of the static and the dynamic relational semantics of a small functional programming language with recursive functions

constructive design of a hierarchy of semantics of a transition system by abstract interpretation we construct a hierarchy of semantics by successive abstract interpretations starting from the maximal trace semantics of a transition system we derive the big step semantics termination and nontermination semantics plotkin s natural smyth s demoniac and hoare s angelic relational semantics and equivalent nondeterministic denotational semantics with alternative powerdomains to the egli milner and smyth constructions d scott s deterministic denotational semantics the generalized and dijkstra s conservative liberal predicate transformer semantics the generalized total and hoare s partial correctness axiomatic semantics and the corresponding proof methods all the semantics are presented in a uniform fixpoint form and the correspondences between these semantics are established through composable galois connections each semantics being formally calculated by abstract interpretation of a more concrete one using kleene and or tarski fixpoint approximation transfer theorems copyright 2002 elsevier science b v

on infinite computations in denotational semantics abstract finite and especially infinite computations in languages with iteration or recursion are studied in the framework of denotational semantics and a theorem is proved which relates their syntactic and semantic characterizations a general proof method is presented to establish this type of relations and it is shown how in an induction on the structure of the syntactic constructs of the language the recursive case follows from the non recursive one by applying a general definitional scheme the method is applicable to a variety of other problems concerning recursive constructs such as for example fixed point characterizations of several notions of weakest precondition also the connections with the theory of languages with infinite words are discussed in particular with a substitution theorem due to nivat 1978

handling convexity like constraints in variational problems we provide a general framework to construct finite dimensional approximations of the space of convex functions which also applies to the space of c convex functions and to the space of support functions of convex bodies we give precise estimates of the distance between the approximation space and the admissible set this framework applies to the approximation of convex functions by piecewise linear functions on a mesh of the domain and by other finite dimensional spaces such as tensor product splines we show how these discretizations are well suited for the numerical solution of problems of calculus of variations under convexity constraints our implementation relies on proximal algorithms and can be easily parallelized thus making it applicable to large scale problems in dimension two and three we illustrate the versatility and the efficiency of our approach on the numerical solution of three problems in calculus of variation three dimensional denoising the principal agent problem and optimizat

divide and congruence ii from decomposition of modal formulas to preservation of delay and weak bisimilarity abstract earlier we presented a method to decompose modal formulas for processes with the internal action and congruence formats for branching and bisimilarity were derived on the basis of this decomposition method the idea is that a congruence format for a semantics must ensure that the formulas in the modal characterisation of this semantics are always decomposed into formulas that are again in this modal characterisation in this follow up paper the decomposition method is enhanced to deal with modal characterisations that contain a modality a to derive congruence formats for delay and weak bisimilarity

proving congruence of bisimulation in functional programming languages we give a method for proving congruence of bisimulation like equivalences in functional programming languages the method applies to languages that can be presented as a set of expressions together with an evaluation relation we use this method to show that some generalizations of abramsky s applicative bisimulation are congruences whenever evaluation can be specified by a certain natural form of structured operational semantics one of the generalizations handles nondeterminism and diverging computations

optimal stopping times for detecting changes in distributions it is shown that page s stopping time is optimal for the detection of changes in distributions in a well defined sense this work is a generalization of an existing result where it was shown that page s stopping time is optimal asymptotically

a conservative look at operational semantics with variable binding we set up a formal framework to describe transition system specifications in the style of plotkin this framework has the power to express many sortedness general binding mechanisms and substitutions among other notions such as negative hypotheses and unary predicates on terms the framework is used to present a conservativity format in operational semantics which states sufficient criteria to ensure that the extension of a transition system specification with new transition rules does not affect the semantics of the original terms

uniform closures the notion of uniform closure operator is introduced and it is shown how this concept surfaces in two different areas of application of abstract interpretation notably in semantics design for logic programs and in the theory of abstract domain refinements in logic programming uniform closures permit generalization from an order theoretic perspective of the standard hierarchy of declarative semantics in particular we show how to reconstruct the model theoretic characterization of the well known s semantics using pure order theoretic concepts only as far as the systematic refinement operators on abstract domains are concerned we show that uniform closures capture precisely the property of a refinement of being invertible namely of admitting a related operator that simplifies as much as possible a given abstract domain of input for that refinement exploiting the same argument used to reconstruct the s semantics of logic programming we yield a precise relationship between refinements and their inverse operators we demonstrate that they form an adjunction with respect to a conveniently modified complete order among abstract domains

mass transport generated by a flow of gauss maps abstract let a r d d 2 be a compact convex set and let 0 d x be a probability measure on a equivalent to the restriction of lebesgue measure let 1 d x be a probability measure on b r x x r equivalent to the restriction of lebesgue measure we prove that there exists a mapping t such that t 1 and t n where a 0 r is a continuous potential with convex sub level sets and n is the gauss map of the corresponding level sets of moreover t is invertible and essentially unique our proof employs the optimal transportation techniques we show that in the case of smooth the level sets of are governed by the gauss curvature flow x s s d 1 1 s n 0 x k x n x where k is the gauss curvature as a by product one can reprove the existence of weak solutions to the classical gauss curvature flow starting from a convex hypersurface

declarative modeling of the operational behavior of logic languages abstract the paper defines a new declarative semantics for logic programs which is based on interpretations containing possibly non ground atoms two different interpretations are introduced and the corresponding models are defined and compared the classical results on the herbrand model semantics of logic programs are shown to hold in the new models too i e existence of a minimal model fixpoint characterization etc with the new models we have a stronger soundness and completeness result for sld resolution in particular one of the two models allows the set of computed answer substitutions to be characterized precisely

on the _ minkowski problem a volume normalized formulation of the lp minkowski problem is presented this formulation has the advantage that a solution is possible for all p 1 including the degenerate case where the index p is equal to the dimension of the ambient space a new approach to the lp minkowski problem is presented which solves the volume normalized formulation for even data and all p 1

a general sos theory for the specification of probabilistic transition systems this article focuses on the formalization of the structured operational semantics approach for languages with primitives that introduce probabilistic and non deterministic behavior we define a general theoretic framework and present the rule format that guarantees that bisimulation equivalence in the probabilistic setting is a congruence for any operator defined in this format we show that the bisimulation is fully abstract w r t the format and possibilistic trace equivalence in the sense that bisimulation is the coarsest congruence included in trace equivalence for any operator definable within the format in other words bisimulation is the smallest congruence relation guaranteed by the format we also provide a conservative extension theorem and show that languages that include primitives for exponentially distributed time behavior such as imc and markov automata based language fit naturally within our framework

weighted cumulative sum technique a class of weighted control schemes that generalizes the basic cumulative sum cusum technique is introduced the schemes of the first type in which the weights represent information concomitant with the data prove to be especially useful when handling charts corresponding to samples of varying sizes the schemes of the second type are based on giving greater weight to more recent information representatives of this class are shown to have better run length characteristics with respect to drift in the level of a controlled process than does the classical cusum while maintaining good sensitivity with respect to shifts analogous to the classical cusum scheme they admit a dual graphical representation that is the scheme can be applied by means of a one or two sided decision interval or via a v mask a special case of this type of scheme designated the geometric cusum is considered in detail it can be viewed as a cusum type counterpart of the exponentially weighted moving average

a general conservative extension theorem in process algebras with inequalities we prove a general conservative extension theorem for transition system based process theories with easy to check and reasonable conditions the core of this result is another general theorem which gives sufficient conditions for a system of operational rules and an extension of it in order to ensure conservativity that is provable transitions from an original term in the extension are the same as in the original system as a simple corollary of the conservative extension theorem we prove a completeness theorem we also prove a general theorem giving sufficient conditions to reduce the question of ground confluence modulo some equations for a large term rewriting system associated with an equational process theory to a small term rewriting system under the condition that the large system is a conservative extension of the small one we provide many applications to show that our results are useful the applications include but are not limited to various real and discrete time settings in acp atp and ccs and the notions projection renaming stage operator priority recursion the silent step autonomous actions the empty process divergence etc

divide and congruence from decomposition of modal formulas to preservation of branching and η bisimilarity we present a method for decomposing modal formulas for processes with the internal action t to decide whether a process algebra term satisfies a modal formula one can check whether its subterms satisfy formulas that are obtained by decomposing the original formula the decomposition uses the structural operational semantics that underlies the process algebra we use this decomposition method to derive congruence formats for two weak and rooted weak semantics branching and h bisimilarity

the spherical convex floating body abstract for a convex body on the euclidean unit sphere the spherical convex floating body is introduced the asymptotic behavior of the volume difference of a spherical convex body and its spherical floating body is investigated this gives rise to a new spherical area measure the floating area remarkably this floating area turns out to be a spherical analogue to the classical affine surface area from affine differential geometry several properties of the floating area are established

optimal detection of a change in distribution abstract document discusses a stopping rule that is a limit of bayes rules derived then an almost minimax rule is presented

a continuous semantics for unbounded nondeterminism abstract nondeterminism is introduced into an ordinary iterative programming language by treating procedure calls as nondeterministic assignment statements the effect of such assignment statements is assumed to be determined solely by the entry exit specifications of the corresponding procedures the nondeterminism which this approach yields is not necessarily bounded the paper discusses the problem of defining a denotational semantic for programming languages with this kind of possibly unbounded nondeterminism as an additional constraint the semantics is required to be continuous in the sense that the underlying semantic algebra is continuous it is shown how such a continuous semantics for unbounded nondeterminism can be derived from a simple operational semantics based on program execution trees

embedding sn into rn 1 with given integral gauss curvature and optimal mass transport on sn in a d aleksandrov convex polyhedra gittl moscow ussr 1950 in russian english translation a d aleksandrov convex polyhedra springer berlin new york 2005 a d aleksandrov raised a general question of finding variational statements and proofs of existence of polytopes with given geometric data the first goal of this paper is to give a variational solution to the problem of existence and uniqueness of a closed convex hypersurface in euclidean space with prescribed integral gauss curvature our solution includes the case of a convex polytope this problem was also first considered by aleksandrov and below it is referred to as aleksandrov s problem the second goal of this paper is to show that in variational form the aleksandrov problem is closely connected with the theory of optimal mass transport on a sphere with cost function and constraints arising naturally from geometric considerations

surveillance strategies for detecting changepoint in incidence rate based on exponentially weighted moving average methods surveillance is a major issue in the today s world the need to develop adequate surveillance strategies is genuine in many spheres of human activity in this article we focus on a specific problem of surveillance and discuss some related statistical issues this specific problem deals with a possible change in the incidence rate of an event to a higher value when a system is studied at discrete time points we apply the exponentially weighted moving average methods for detecting an increased incidence rate per exposure unit of an event different measures of evaluation suitable in different types of applications such as the expected delay out of control average run length and probability of successful detection are studied analytical bounds are provided for those measures of evaluation results from intensive simulations indicate that the analytical bounds perform fairly well when the weight parameter is large

ntyft ntyxt rules reduce to ntree rules groote and vaandrager introduced thetyft tyxt formatfor transition system specifications tsss and established that for each tss in this format that iswell founded the bisimulation equivalence it induces is a congruence in this paper we construct for each tss in tyft tyxt format an equivalent tss that consists oftree rulesonly as a corollary we can give an affirmative answer to an open question namely whether the well foundedness condition in the congruence theorem for tyft tyxt can be dropped these results extend to tyft tyxt with negative premises and predicates

a logic for default reasoning the need to make default assumptions is frequently encountered in reasoning about incompletely specified worlds inferences sanctioned by default are best viewed as beliefs which may well be modified or rejected by subsequent observations it is this property which leads to the non monotonicity of any logic of defaults in this paper we propose a logic for default reasoning we then specialize our treatment to a very large class of commonly occuring defaults for this class we develop a complete proof theory and show how to interface it with a top down resolution theorem prover finally we provide criteria under which the revision of derived beliefs must be effected

the meaning of negative premises in transition system specifications we present a general theory for the use of negative premises in the rules of transition system specifications tsss we formulate a criterion that should be satisfied by a tss in order to be meaningful that is to unequivocally define a transition relation we also provide powerful techniques for proving that a tss satisfies this criterion meanwhile constructing this transition relation both the criterion and the techniques originate from logic programming van gelder et al 1988 gelfond and lifschitz 1988 to which tsss are close in an appendix we provide an extensive comparison between them as in groote 1993 we show that the bisimulation relation induced by a tss is a congruence provided that it is in ntyft ntyxt format and can be proved meaningful using our techniques we also considerably extend the conservativity theorems of groote 1993 and groote and vaandrager 1992 as a running example we study the combined addition of priorities and abstraction to basic process algebra bpa under some reasonable conditions we show that this tss is indeed meaningful which could not be shown by other methods bloom et al 1995 groote 1993 finally we provide a sound and complete axiomatization for this example

non expansive e bisimulations for probabilistic processes e bisimulation equivalence has been proposed in the literature as a technique to study the concept of behavioral distance between probabilistic processes in this paper we first consider the generative model of probabilistic processes and introduce two stronger equivalence notions action e bisimulation and global e bisimulation for each of these three equivalence notions we propose an sos transition rule format ensuring the property of non expansiveness non expansiveness means that if the behavioral distance between s i and t i is e i then the behavioral distance between f s 1 s n and f t 1 t n is no more that e 1 e n as expected the stronger the e bisimulation considered the weaker the constraints of the transition rule format then we switch to the reactive model of probabilistic processes and we propose a rule format for e bisimulation and action e bisimulation arguing that global e bisimulation is not needed in such a context

geometric measures in the dual brunn minkowski theory and their associated minkowski problems a longstanding question in the dual brunn minkowski theory is what are the dual analogues of federer s curvature measures for convex bodies the answer to this is provided this leads naturally to dual versions of minkowski type problems what are necessary and sufficient conditions for a borel measure to be a dual curvature measure of a convex body sufficient conditions involving measure concentration are established for the existence of solutions to these problems

divide and congruence iii from decomposition of modal formulas to preservation of stability and divergence abstract in two earlier papers we derived congruence formats with regard to transition system specifications for weak semantics on the basis of a decomposition method for modal formulas the idea is that a congruence format for a semantics must ensure that the formulas in the modal characterisation of this semantics are always decomposed into formulas that are again in this modal characterisation the stability and divergence requirements that are imposed on many of the known weak semantics have so far been outside the realm of this method stability refers to the absence of a transition we show using the decomposition method how congruence formats can be relaxed for weak semantics that are stability respecting this relaxation for instance brings the priority operator within the range of the stability respecting branching bisimulation format divergence which refers to the presence of an infinite sequence of transitions escapes the inductive decomposition method we circumvent this problem by proving that a congruence format for a stability respecting weak semantics is also a congruence format for its divergence preserving counterpart

transforming semantics by abstract interpretation in 1997 cousot introduced a hierarchy where semantics are related with each other by abstract interpretation in this field we consider the standard abstract domain transformers devoted to refine abstract domains in order to include attribute independent and relational information respectively the reduced product and power of abstract domains as domain operations to systematically design and compare semantics of programming languages by abstract interpretation we first prove that natural semantics can be decomposed in terms of complementary attribute independent observables leading to an algebraic characterization of the symmetric structure of the hierarchy moreover we characterize some structural property of semantics such as their compositionality in terms of simple abstract domain equations this provides an equational presentation of most well known semantics which is parametric on the observable and structural property of the semantics making it possible to systematically derive abstract semantics e g for program analysis as solutions of abstract domain equations

an approximate cusum procedure for surveillance of health events the cusum method is frequently used by epidemiologists for detecting a shift in the incidence of rare health events an exact solution for a poisson process has been proposed by other works but potential applications have been limited by the fact that the size the structure of the at risk population and the baseline rate may not be constant during the period of surveillance furthermore for practical use tables of critical values are available only for some expected values and in any case less then 9 this paper proposes an approximate cusum procedure based on the normal approximation to a poisson process which may be an efficient solution of the problems previously pointed out analyses of simulated and actual data sets illustrate the usefulness of the proposed procedure an application to mortality data for respiratory diseases in a north tuscany area characterized by the presence of chemical plants is showed no shift in the mortality rate during the 1980 1989 period was detected compared with the 1970 1979 period in contrast with the result obtained with the standard cusum method for a poisson variate

making abstract interpretations complete completeness is an ideal although uncommon feature of abstract interpretations formalizing the intuition that relatively to the properties encoded by the underlying abstract domains there is no loss of information accumulated in abstract computations thus complete abstract interpretations can be rightly understood as optimal we deal with both pointwise completeness involving generic semantic operations and least fixpoint completeness completeness and fixpoint completeness are shown to be properties that depend on the underlying abstract domains only our primary goal is then to solve the problem of making abstract interpretations complete by minimally extending or restricting the underlying abstract domains under the weak and reasonable hypothesis of dealing with continuous semantic operations we provide constructive characterizations for the least complete extensions and the greatest complete restrictions of abstract domains as far as fixpoint completeness is concerned for merely monotone semantic operators the greatest restrictions of abstract domains are constructively characterized while it is shown that the existence of least extensions of abstract domains cannot be in general guaranteed even under strong hypotheses these methodologies which in finite settings give rise to effective algorithms provide advanced formal tools for manipulating and comparing abstract interpretations useful both in static program analysis and in semantics design a number of examples illustrating these techniques are given

monge s transport problem on a riemannian manifold monge s problem refers to the classical problem of optimally transporting mass given borel probability measures find the measurepreserving map s m m between them which minimizes the average distance transported set on a complete connected riemannian manifold m and assuming absolute continuity of an optimal map will be shown to exist aspects of its uniqueness are also established

turning sos rules into equations abstract many process algebras are defined by structural operational semantics sos indeed most such definitions are nicely structured and fit the gsos format of bloom et al j assoc comput mach to appear we give a procedure for converting any gsos language definition to a finite complete equational axiom system possibly with one infinitary induction principle which precisely characterizes strong bisimulation of processes

on the planar dual minkowski problem abstract in this paper we resolve the planar dual minkowski problem proposed by huang et al 2016 31 for all positive indices without any symmetry assumption more precisely given any q 0 and function f on s 1 bounded by two positive constants we show that there exists a convex body in the plane containing the origin in its interior whose dual curvature measure c q has density f in particular if f is smooth then is also smooth

the reduced relative power operation on abstract domains abstract in the context of standard abstract interpretation theory a reduced relative power operation for functionally composing abstract domains is introduced and studied the reduced relative power of two abstract domains d 1 the exponent and d 2 the base consists in a suitably defined lattice of monotone functions from d 1 to d 2 called dependencies and it is a generalization of the cousot and cousot reduced cardinal power operation the relationship between reduced relative power and nielson s tensor product of abstract domains is also investigated the case of autodependencies i e base and exponent are the same domain turns out to be particularly interesting under certain hypotheses the domain of autodependencies corresponds to a powerset like completion of the base abstract domain providing a compact set theoretic representation for autodependencies two relevant applications of the reduced relative power operation in the fields of logic program analysis and semantics design are presented notably it is proved that the wellknown abstract domain def for logic program ground dependency analysis can be characterized as the domain of autodependencies of the standard abstract domain representing plain groundness information only on the semantics side it is shown how reduced relative power can be exploited in order to systematically derive compositional semantics for logic programs

on the axiomatisability of priority iii priority strikes again abstract aceto et al proved that over the process algebra bccsp with the priority operator of baeten bergstra and klop the equational theory of order insensitive bisimilarity is not finitely based however it was noticed that by substituting the action prefixing operator of bccsp with bpa s sequential composition the infinite family of equations used to show that non finite axiomatisability result could be proved by a finite collection of sound equations that observation left as an open question the existence of a finite axiomatisation for order insensitive bisimilarity over bpa with the priority operator in this paper we provide a negative answer to this question we prove that in the presence of at least two actions order insensitive bisimilarity is not finitely based over bpa with priority

the geometry of optimal transportation introduction 113 1 summary of main results 120 2 background on optimal measures 126 part i strictly convex costs 133 3 existence and uniqueness of optimal maps 133 4 characterization of the optimal map 137 part ii costs which are strictly concave as a function of d i s t a n c e 141 5 the role of optimal maps 141 6 uniqueness of optimal solutions 144 part iii appendices 148 a legendre transforms and conjugate costs 148 b examples of c concave potentials 152 c regularity of c concave potentials 154 references 159