Low-Rank Approximation of Integral Operators by Interpolation

A central component of the analysis of panel clustering techniques for the approximation of integral operators is the so-called -admissibility condition min {diam(),diam()} 2dist(,) that ensures that the kernel function is approximated only on those parts of the domain that are far from the singularity. Typical techniques based on a Taylor expansion of the kernel function require a subdomain to be far enough from the singularity such that the parameter has to be smaller than a given constant depending on properties of the kernel function. In this paper, we demonstrate that any is sufficient if interpolation instead of Taylor expansionisused for the kernel approximation, which paves the way for grey-box panel clustering algorithms.     

More Church–Rosser Proofs

The proofs of the Church–Rosser theorems for , , and reduction in untyped -calculus are formalized in Isabelle/HOL, an implementation of Higher Order Logic in the generic theorem prover Isabelle. For -reduction, both the standard proof and Takahashi's are given and compared. All proofs are based on a general theory of commutating relations that supports an almost geometric style of reasoning about confluence diagrams.     

Reasoning about programs in continuation-passing style

Plotkin's _v -calculus for call-by-value programs is weaker than the -calculus for the same programs in continuation-passing style (CPS). To identify the call-by-value axioms that correspond to on CPS terms, we define a new CPS transformation and an inverse mapping, both of which are interesting in their own right. Using the new CPS transformation, we determine the precise language of CPS terms closed under -transformations, as well as the call-by-value axioms that correspond to the so-called administrative -reductions on CPS terms. Using the inverse mapping, we map the remaining and equalities on CPS terms to axioms on call-by-value terms. On the pure (constant free) set of -terms, the resulting set of axioms is equivalent to Moggi's computational -calculus. If the call-by-value language includes the control operatorsabort andcall-with-current-continuation, the axioms are equivalent to an extension of Felleisenet al.'s _v -C-calculus and to the equational subtheory of Talcott's logic IOCC.This article is a revised and extended version of the conference paper with the same title [42]. The technical report of the same title contains additional material.The authors were supported in part by NSF grant CCR 89-17022 and by Texas ATP grant 91-003604014.     

Decision procedures for elementary sublanguages of set theory: XIII. Model graphs,reflection and decidability

Positive solutions to the decision problem for a class of quantified formulae of the first order set theoretic language based on , , =, involving particular occurrences of restricted universal quantifiers and for the unquantified formulae of , , =, {...}, , where {...} is the tuple operator and is a general choice operator, are obtained. To that end a method is developed which also provides strong reflection principles over the hereditarily finite sets. As far as finite satisfiability is concerned such results apply also to the unquantified extention of , , =, {...}, , obtained by adding the operators of binary union, intersection and difference and the relation of inclusion, provided no nested term involving is allowed.     

A CUCH-machine: The automatic treatment of bound variables

This paper describes a machine for reducing a -formula (explicitly given or implicitly by a system of recursive equations) to principal --normal form, with particular attention to the memory structures needed for the purpose, and with some important features: (1) any kind of collision is permitted; (2) the processing of subformulas which will be thrown away [e.g., ((xy)x) in ((yz)(xy)x)] is avoided; (3) there is no need to introduce any fixed point operator like , etc. The machine structure entails: (1) some store to memorize as side-effects assignment statements with the r.h.s. of a given shape. (2) a number of stacks, one for every in the initial formula, partitioned naturally in classes (chains). These stacks admit as entries only words representing variables and they are peculiar in that the operations admitted on the top arewriting anderasing and the operations admitted on the pseudo-top arereading,read-protecting, andresetting readability (the last two operations are chain operations). This structure is critically motivated. (3) A workstack. (4) A pointerstack. The computation runs through four phases: -generation, -run, -generation, -run. Every generation- (run-) phase is rather recognition- (transformation-) oriented, but we found it more stimulating to emphasize technical similarities rather than methodological differences. Every phase is described and four examples are extensively developed.     

Monte Carlo modelling of electron beam lithography: a scaling law

The theorem of Dimensional Analysis, usually applied to the inference of physical laws, is for the first time applied to the derivation of interpolation curves of numerical data, leading to a simplified dependence on a reduced number of arguments , dimensionless combination of variables. In particular, Monte Carlo modelling of electron beam lithography is considered and the backscattering coefficient addressed, in case of a general substrate layer, in the elastic regime and in the energy range 5 to 100 keV. The many variables involved (electron energy, substrate physical constants and thickness) are demonstrated to ultimately enter in determining through asingle dimensionless parameter ₀. Thus, a scaling law is determined, an important guide in microsystem designing, indicating, if any part of the configuration is modified, how the other parameters should change (or scale) without affecting the result. Finally, a simple law =83 ₀ is shown to account for all variations of the parameters over all substrates of the periodic table.     

On a Stroboscopic Approach to Quantum Tomography of Qudits Governed by Gaussian Semigroups

In this paper, we discuss the minimal number of observables Q ₁, ..., Q , where expectation values at some time instants t ₁, ..., t _r determine the trajectory of a d-level quantum system (qudit) governed by the Gaussian semigroup . We assume that the macroscopic information about the system in question is given by the mean values E _j(Q _i) = tr(Q _i(t _j)) of n selfadjoint operators Q ₁, ..., Q _n at some time instants t ₁ < t ₂ < ... < t _r, where n < d ²– 1 and r deg (, ). Here (, ) stands for the minimal polynomial of the generator of the Gaussian flow (t).     

Transformation of programs for fault-tolerance

In this paper we describe how a program constructed for afault-free system can be transformed into afault-tolerant program for execution on a system which is susceptible to failures. A program is described by a set of atomic actions which perform transformations from states to states. We assume that a fault environment is represented by a programF. Interference by the fault environmentF on the execution of a programP can then be described as afault-transformation which transformsP into a program (P). This is proved to be equivalent to the programPP _F , whereP _F is derived fromP andF, and defines the union of the sets of actions ofP andF _P . A recovery transformation transformsP into a program (P) =PR by adding a set ofrecovery actions R, called arecovery program. If the system isfailstop and faults do not affect recovery actions, we have ((P))=(P)R=PP _F R We illustrate this approach to fault-tolerant programming by considering the problem of designing a protocol that guarantees reliable communication from a sender to a receiver in spite of faults in the communication channel between them.     

Reduction and unification in lambda calculi with a general notion of subtype

Reduction, equality, and unification are studied for a family of simply typed -calculi with subtypes. The subtype relation is required to relate base types only to base types and to satisfy some order-theoretic conditions. Constants are required to have a least type, that is, no overloading. We define the usual and a subtype-dependent -reduction. These are related to a typed equality relation and shown to be confluent in a certain sense. We present a generic algorithm for preunification modulo -conversion and an arbitrary subtype relation. Furthermore it is shown that unification with respect to any subtype relation is universal.     

The growth of configurations

The transition ruleF of a cellular automaton may sometimes be regarded as a rule of growth of a crystal from a seed. A study is made of the iterates,F,F ² .For certain one-dimensional growth rules, the limiting shapes of the crystals are computed, and an asymptotic formula for the size of the crystal as a function of time is obtained.     

Reaping the whirlwind: Reply to Harnad's “other bodies,other minds”

Harnad's proposed robotic upgrade of Turing's Test (TT), from a test of linguistic capacity alone to a Total Turing Test (TTT) of linguisticand sensorimotor capacity, conflicts with his claim that no behavioral test provides even probable warrant for attributions of thought because there is no evidence of consciousness besides private experience. Intuitive, scientific, and philosophical considerations Harnad offers in favor of his proposed upgrade are unconvincing. I agree with Harnad that distinguishing real from as if thought on the basis of (presence or lack of) consciousness (thus rejecting Turing (behavioral) testing as sufficient warrant for mental attribution)has the skeptical consequence Harnad accepts — there is in factno evidence for me that anyone else but me has a mind. I disagree with hisacceptance of it! It would be better to give up the neo-Cartesian faith in private conscious experience underlying Harnad's allegiance to Searle's controversial Chinese Room Experiment than give up all claim to know others think. It would be better to allow that (passing) Turing's Test evidences — evenstrongly evidences — thought.     

Utilizing deontic operators in information systems specification

One major task in requirements specification is to capture the rules relevant to the problem at hand. Declarative, rule-based approaches have been suggested by many researchers in the field. However, when it comes to modeling large systems of rules, not only for the behavior of the computer system but also for the organizational environment surrounding it, current approaches have problems with limited expressiveness, flexibility, and poor comprehensibility. Hence, rule-based approaches may benefit from improvements in two directions: (1) improvement of the rule languages themselves and (2) better integration with other, complementary modeling approaches.In this article, both issues are addressed in an integrated manner. The proposal is presented in the context of the Tempora project on rule-based information systems development, but has also been integrated with PPP. Tempora has provided a rule language based on an executable temporal logic working on top of a temporal database. The rule language is integrated with static (ER-like) and dynamic (SA/RT-like) modeling approaches. In the current proposal, the integration with complementary modeling approaches is extended by including organization modeling (actors, roles), and the expressiveness of the rule language is increased by introducing deontic operators and rule hierarchies. The main contribution of the article is not seen as any one of the above-mentioned extensions, but as the resulting comprehensive modeling support. The approach is illustrated by examples taken from an industrial case study done in connection with Tempora.C. List of Symbols Subset of set - Not subset of set - Element of set - Not element of set - Equivalent to - Not equivalent to - ¬ Negation - Logical and - Logical or - Implication - Sometime in past - Sometime in future - Always in past - Always in future - Just before - Just after - u Until - s Since - Trigger - Condition - _s State condition - Consequence - _a Action - _s State - Role - Actor - ¬ - General deontic operator - O Obligatory - R Recommended - P Permitted - D Discouraged - F Forbidden - (/–) General rule - t _R Real time - t _M Model time     

The existence of solutions,stability, and linearization of volterra systems

LetB be a Banach space ofR _n valued continuous functions on [0, ) withfB. Consider the nonlinear Volterra integral equation (^*)x(t)+ _o ^t K(t,s,x(s))ds. We use the implicit function theorem to give sufficient conditions onB andK (t,s,x) for the existence of a unique solutionxB to (^*) for eachf B with f ^B sufficiently small. Moreover, there is a constantM>0 independent off with Mf^B.Part of this work was done while the author was visiting at Wright State University.     

Constructing sets of functions which have a givenF-cardinality

The termF-cardinality of (=F-card()) is introduced whereF: ^{n n} is a partial function and is a set of partial functionsf: ^{n n} . TheF-cardinality yields a lower bound for the worst-case complexity of computingF if only functionsf can be evaluated by the underlying abstract automaton without conditional jumps. This complexity bound isindependent from the oracles available for the abstract machine. Thus it is shown that any automaton which can only apply the four basic arithmetic operations needs (n logn) worst-case time to sortn numbers; this result is even true if conditional jumps witharbitrary conditions are possible. The main result of this paper is the following: Given a total functionF: ^{n n} and a natural numberk, it is almost always possible to construct a set such that itsF-cardinality has the valuek; in addition, can be required to be closed under composition of functionsf,g . Moreover, ifF is continuous, then consists of continuous functions.     

Probabilistic analysis of the application of the cross ratio to model based vision: Misclassification

The cross ratio of four colinear points is of fundamental importance in model based vision, because it is the simplest numerical property of an object that is invariant under projection to an image. It provides a basis for algorithms to recognise objects from images without first estimating the position and orientation of the camera.A quantitative analysis of the effectiveness of the cross ratio in model based vision is made. A given imageI of four colinear points is classified by making comparisons between the measured cross ratio of the four image points and the cross ratios stored in the model database. The imageI is accepted as a projection of an objectO with cross ratio if |–|ntu, wheren is the standard deviation of the image noise,t is a threshold andu=. The performance of the cross ratio is described quantitatively by the probability of rejectionR, the probability of false alarmF and the probability of misclassificationp (), defined for two model cross ratios , . The trade off between these different probabilities is determined byt.It is assumed that in the absence of an object the image points have identical Gaussian distributions, and that in the presence of an object the image points have the appropriate conditional densities. The measurements of the image points are subject to small random Gaussian perturbations. Under these assumptions the trade offs betweenR,F andp () are given to a good approximation byR=2(1–(t)),F=r _F t, t|–|^–1, where is the relative noise level, is cumulative distribution function for the normal distribution,r _F is constant, ande is a function of only. The trade off betweenR andF is obtained in Maybank (1994). In this paper the trade off betweenR andp () is obtained.It is conjectured that the general form of the above trade offs betweenR,F andp () is the same for a range of invariants useful in model based vision. The conjecture prompts the following definition: an invariant which has trade offs betweenR,F,p () of the above form is said to benon-degenerate for model based vision.The consequences of the trade off betweenR andp () are examined. In particular, it is shown that for a fixed overall probability of misclassification there is a maximum possible model cross ratio _m , and there is a maximum possible numberN of models. Approximate expressions for _m andN are obtained. They indicate that in practice a model database containing only cross ratio values can have a size of order at most ten, for a physically plausible level of image noise, and for a probability of misclassification of the order 0.1.     

From Conditional Events to Conditional Measures: A New Axiomatic Approach

Our starting point is a definition of conditional event EH which differs from many seemingly similar ones adopted in the relevant literature since 1935, starting with de Finetti. In fact, if we do not assign the same third value u (undetermined) to all conditional events, but make it depend on EH, it turns out that this function t(EH) can be taken as a general conditional uncertainty measure, and we get (through a suitable – in a sense, compulsory – choice of the relevant operations among conditional events) the natural axioms for many different (besides probability) conditional measures.     

On Skolemization in constrained logics

Quantification in first-order logic always involves all elements of the universe. However, it is often more natural to just quantify over those elements of the universe which satisfy a certain condition. Constrained logics therefore provide restricted quantifiers _X:R F and _X:R F whereX is a set of variables, and which can be read as F holds for all elements satisfying the restrictionR and F holds if there exists an element which satisfiesR. In order to test satisfiability of a set of such formulas by means of an appropriately extended resolution principle, one needs a procedure which transforms them into a set of clauses with constraints. Such a procedure essentially differs from the classical transformation of first-oder formulas into a set of clauses, in particular since quantification over the empty set may occur and since the needed Skolemization procedure has to take the restrictions of restricted quantifiers into account. In the first part of this article we present a procedure that transforms formulas with restricted quantifiers into a set of clauses with constraints while preserving satisfiability. The thus obtained clauses are of the formC R whereC is an ordinary clause andR is a restriction, and can be read as C holds ifR holds. These clauses can now be tested on unsatisfiability via the existingconstrained resolution principle. In the second part we generalize the constrained resolution principle in such a way that it allows for further optimization, and we introduce a combination of unification and constraint solving that can be employed to instantiate this kind of optimization.     

Deterministic sequential functions

The simple rational partial functions accepted by generalized sequential machines are shown to coincide with the compositions _P ^–1 , where _P consists of the prefix codings. The rational functions accepted by generalized sequential machines are proved to coincide with the compositions _P ^–1 , where is the family of endmarkers and is the family of removals of endmarkers. (The compositions are read from left to right). We also show that _P ^–1 is the family of the subsequential functions.This work was partially supported by the Esprit Basic Research Action Working Group No. 3166 ASMICS, the CNRS and the Academy of Finland     

Maintaining Longest Paths Incrementally

Modeling and programming tools for neighborhood search often support invariants, i.e., data structures specified declaratively and automatically maintained incrementally under changes. This paper considers invariants for longest paths in directed acyclic graphs, a fundamental abstraction for many applications. It presents bounded incremental algorithms for arc insertion and deletion which run in O( + || log||) time and O() time respectively, where || and are measures of the change in the input and output. The paper also shows how to generalize the algorithm to various classes of multiple insertions/deletions encountered in scheduling applications. Preliminary experimental results show that the algorithms behave well in practice.     

MAAN: A Multi-Attribute Addressable Network for Grid Information Services

Recent structured Peer-to-Peer (P2P) systems such as Distributed Hash Tables (DHTs) offer scalable key-based lookup for distributed resources. However, they cannot be simply applied to grid information services because grid resources need to be registered and searched using multiple attributes. This paper proposes a Multi-Attribute Addressable Network (MAAN) that extends Chord to support multi-attribute and range queries. MAAN addresses range queries by mapping attribute values to the Chord identifier space via uniform locality preserving hashing. It uses an iterative or single attribute dominated query routing algorithm to resolve multi-attribute based queries. Each node in MAAN only has O(logN) neighbors for N nodes. The number of routing hops to resolve a multi-attribute range query is O(logN+N×s_min), where s_min is the minimum range selectivity on all attributes. When s_min=, it is logarithmic to the number of nodes, which is scalable to a large number of nodes and attributes. We also measured the performance of our MAAN implementation and the experimental results are consistent with our theoretical analysis.