Mesh Selection for a Nearly Singular Boundary Value Problem

In this paper, we investigate the numerical solution of a model equation u _xx = exp(– ) (and several slightly more general problems) when 1 using the standard central difference scheme on nonuniform grids. In particular, we are interested in the error behaviour in two limiting cases: (i) the total mesh point number N is fixed when the regularization parameter 0, and (ii) is fixed when N. Using a formal analysis, we show that a generalized version of a special piecewise uniform mesh 12 and an adaptive grid based on the equidistribution principle share some common features. And the optimal meshes give rates of convergence bounded by |log()| as 0 and N is given, which are shown to be sharp by numerical tests.     

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).     

‘Use’ discourses in system development: Can communication be improved?

This paper aims to provide a basis for renewed talk about use in computing. Four current discourse arenas are described. Different intentions manifest in each arena are linked to failures in translation, different terminologies crossing disciplinary and national boundaries non-reflexively. Analysis of transnational use discourse dynamics shows much miscommunication. Conflicts like that between the Scandinavian System Development School and the usability approach have less current salience. Renewing our talk about use is essential to a participatory politics of information technology and will lead to clearer perception of the implications of letting new systems becoming primary media of social interaction.     

Evaluation of Queries under Closed-World Assumption

The minimal entailment Min has been characterized elsewhere by where Cn is the first-order consequence operation, P is a set of clauses (indefinite deductive data base; in short: a data base), is a clause (a query), and Pos is the set of positive (that is, bodiless) ground clauses. In this paper, we address the problem of the computational feasibility of criterion (1). Our objective is to find a query evaluation algorithm that decides P Min by what we call indefinite modeling, without actually computing all ground positive consequences of P and P {}. For this purpose, we introduce the concept of minimal indefinite Herbrand model MP of P, which is defined as the set of subsumption-minimal ground positive clauses provable from P. The algorithm first computes MP by finding the least fixed-point of an indefinite consequence operator TIP. Next, the algorithm verifies whether every ground positive clause derivable from MP {} by one application of the parallel positive resolution rule (in short: the PPR rule) is subsumed by an element of MP. We prove that the PPR rule, which can derive only positive clauses, is positively complete, that is, every positive clause provable from a data base P is derivable from P by means of subsumption and finitely many applications of PPR. From this we conclude that the presented algorithm is partially correct and that it eventually halts if both P and MP are finite. Moreover, we indicate how the algorithm can be modified to handle data bases with infinite indefinite Herbrand models. This modification leads to a concept of universal model that allows for nonground clauses in its Herbrand base and appears to be a good candidate for representation of indefinite deductive data bases.     

Generalized lowness and highness and probabilistic complexity classes

We introduce generalized notions of low and high complexity classes and study their relation to structural questions concerning bounded probabilistic polynomial-time complexity classes. We show, for example, that for a bounded probabilistic polynomial-time complexity class =BP _k ^P ,L =H implies that the polynomial hierarchy collapses to . This extends Schöning's result for = _k ^P (L andH are the low and high sets defined by ). We also show, with one exception, that containment relations between the bounded probabilistic classes and the polynomial hierarchy are preserved by their low and high counterparts.LBPP andLBPNP are characterized asNP BPP andNP co-BPNP, respectively. These characterizations are then used to recover Boppana, Hastad, and Zachos's result that if co-NP BPNP, then the polynomial hierarchy collapses toBPNP, and Ko's result that ifNP BPP, then the polynomial hierarchy collapses toBPP.     

Unextendible Product Bases and Locally Unconvertible Bound Entangled States

Mutual convertibility of bound entangled states under local quantum operations and classical communication (LOCC) is studied. We focus on states associated with unextendible product bases (UPB) in a system of three qubits. A complete classification of such UPBs is suggested. We prove that for any pair of UPBs S and T the associated bound entangled states _S and _T cannot be converted to each other by LOCC, unless S and T coincide up to local unitaries. More specifically, there exists a finite precision (S,T) > 0 such that for any LOCC protocol mapping _S into a probabilistic ensemble (p, ), the fidelity between _T and any possible final state satisfies F(_T, ) = 1 - (S,T).PACS: 03.65.Bz; 03.67.-a; 89.70+c.     

Specification and verification of database dynamics

Summary A framework is proposed for the structured specification and verification of database dynamics. In this framework, the conceptual model of a database is a many sorted first order linear tense theory whose proper axioms specify the update and the triggering behaviour of the database. The use of conceptual modelling approaches for structuring such a theory is analysed. Semantic primitives based on the notions of event and process are adopted for modelling the dynamic aspects. Events are used to model both atomic database operations and communication actions (input/output). Nonatomic operations to be performed on the database (transactions) are modelled by processes in terms of trigger/reaction patterns of behaviour. The correctness of the specification is verified by proving that the desired requirements on the evolution of the database are theorems of the conceptual model. Besides the traditional data integrity constraints, requirements of the form Under condition W, it is guaranteed that the database operation Z will be successfully performed are also considered. Such liveness requirements have been ignored in the database literature, although they are essential to a complete definition of the database dynamics.

Notation

Classical Logic Symbols (Appendix 1) for all (universal quantifier) - exists at least once (existential quantifier) - ¬ no (negation) - implies (implication) - is equivalent to (equivalence) - and (conjunction) - or (disjunction) Tense Logic Symbols (Appendix 1) G always in the future - G ₀ always in the future and now - F sometime in the future - F ₀ sometime in the future or now - H always in the past - H ₀ always in the past and now - P sometime in the past - P ₀ sometime in the past or now - X in the next moment - Y in the previous moment - L always - M sometime Event Specification Symbols (Sects. 3 and 4.1) (x) means immediately after the occurrence of x - (x) means immediately before the occurrence of x - (x) means x is enabled, i.e., x may occur next - { } ({w ₁} x{w ₂}) states that if w ₁ holds before the occurrence of x, then w ₂ will hold after the occurrence of x (change rule) - [ ] ([oa₁, ..., oa_n]x) states that only the object attributes oa₁, ..., oa _n are modifiable by x (scope rule) - {{ }} ({{w}}x) states that if x may occur next, then w holds (enabling rule) Process Specification Symbols (Sects. 5.3 and 5.4) :: for causal rules - for behavioural rules Transition-Pattern Composition Symbols (Sects. 5.2 and 5.3) ; sequential composition - ¦ choice composition - parallel composition - :| guarded alternative composition Location Predicates (Sect. 5.2) (z) means immediately after the occurrence of the last event of z (after) - (z) means immediately before the occurrence of the first event of z (before) - (z) means after the beginning of z and before the end of z (during) - ( z) means before the occurrence of an event of z (at)     

Linear Interval Tolerance Problem and Linear Programming Techniques

In this paper, we consider the linear interval tolerance problem, which consists of finding the largest interval vector included in ([A], [b]) = {x R ⁿ | A [A], b [b], Ax = b}. We describe two different polyhedrons that represent subsets of all possible interval vectors in ([A], [b]), and we provide a new definition of the optimality of an interval vector included in ([A], [b]). Finally, we show how the Simplex algorithm can be applied to find an optimal interval vector in ([A], [b]).     

Factorisation of finite state machines under strong and observational equivalences

The factorisation problem is to construct the specification of a submoduleX when the specifications of the system and all submodules butX are given. It is usually described by the equation where P and X are submodules of system Q, ¦ is a composition operator, and is the equivalence criterion. In this paper we use a finite state machine (FSM) model consistent with CCS and study two factorisation problems:P |||P Q andP |||P Q, where ||| is a derived CCS composition operator, and represent strong and observational equivalences. Algorithms are presented and proved correct to find the most general specification of submoduleX forP |||P Q withQ -deterministic and forP |||P Q withQ deterministic. Conditions on the submachines of the most general solutions that remain solutions toP |||P Q(P |||P Q) are given. This paper extends and is based on the work of M. W. Shields.     

Property preserving abstractions for the verification of concurrent systems

We study property preserving transformations for reactive systems. The main idea is the use of simulations parameterized by Galois connections (, ), relating the lattices of properties of two systems. We propose and study a notion of preservation of properties expressed by formulas of a logic, by a function mapping sets of states of a systemS into sets of states of a systemS'. We give results on the preservation of properties expressed in sublanguages of the branching time -calculus when two systemsS andS' are related via (, )-simulations. They can be used to verify a property for a system by verifying the same property on a simpler system which is an abstraction of it. We show also under which conditions abstraction of concurrent systems can be computed from the abstraction of their components. This allows a compositional application of the proposed verification method.This is a revised version of the papers [2] and [16]; the results are fully developed in [28].This work was partially supported by ESPRIT Basic Research Action REACT.Verimag is a joint laboratory of CNRS, Institut National Polytechnique de Grenoble, Université J. Fourier and Verilog SA associated with IMAG.     

The “explicit-implicit” distinction

Much of traditional AI exemplifies the explicit representation paradigm, and during the late 1980's a heated debate arose between the classical and connectionist camps as to whether beliefs and rules receive an explicit or implicit representation in human cognition. In a recent paper, Kirsh (1990) questions the coherence of the fundamental distinction underlying this debate. He argues that our basic intuitions concerning explicit and implicit representations are not only confused but inconsistent. Ultimately, Kirsh proposes a new formulation of the distinction, based upon the criterion ofconstant time processing.The present paper examines Kirsh's claims. It is argued that Kirsh fails to demonstrate that our usage of explicit and implicit is seriously confused or inconsistent. Furthermore, it is argued that Kirsh's new formulation of the explicit-implicit distinction is excessively stringent, in that it banishes virtually all sentences of natural language from the realm of explicit representation. By contrast, the present paper proposes definitions for explicit and implicit which preserve most of our strong intuitions concerning straightforward uses of these terms. It is also argued that the distinction delineated here sustains the meaningfulness of the abovementioned debate between classicists and connectionists.     

The network complexity and the Turing machine complexity of finite functions

Summary Let L(f) be the network complexity of a Boolean function L(f). For any n-ary Boolean function L(f) let . Hereby p ranges over all relative Turing programs and ranges over all oracles such that given the oracle , the restriction of p to inputs of length n is a program for L(f). p is the number of instructions of p. T _p (n) is the time bound and S _p of the program p relative to the oracle on inputs of length n. Our main results are (1) L(f) O(TC(L(f))), (2) TC(f) O(L(f) ^{2 2+}) for every O.The results of this paper have been reported in a main lecture at the 1975 annual meeting of GAMM, April 2–5, Göttingen     

Almost surely continuous solutions of a nonlinear stochastic integral equation

A nonlinear stochastic integral equation of the Hammerstein type in the formx(t; ) = h(t, x(t; )) + _s k(t, s; )f(s, x(s; ); )d(s) is studied wheret S, a measure space with certain properties, , the supporting set of a probability measure space (,A, P), and the integral is a Bochner integral. A random solution of the equation is defined to be an almost surely continuousm-dimensional vector-valued stochastic process onS which is bounded with probability one for eacht S and which satisfies the equation almost surely. Several theorems are proved which give conditions such that a unique random solution exists. AMS (MOS) subject classifications (1970): Primary; 60H20, 45G99. Secondary: 60G99.     

Regions-of-Interest and Spatial Layout for Content-Based Image Retrieval

To date most content-based image retrieval (CBIR) techniques rely on global attributes such as color or texture histograms which tend to ignore the spatial composition of the image. In this paper, we present an alternative image retrieval system based on the principle that it is the user who is most qualified to specify the query content and not the computer. With our system, the user can select multiple regions-of-interest and can specify the relevance of their spatial layout in the retrieval process. We also derive similarity bounds on histogram distances for pruning the database search. This experimental system was found to be superior to global indexing techniques as measured by statistical sampling of multiple users' satisfaction ratings.     

Shallow circuits and concise formulae for multiple addition and multiplication

A theory is developed for the construction of carry-save networks with minimal delay, using a given collection of carry-save adders each of which may receive inputs and produce outputs using several different representation standards.The construction of some new carry-save adders is described. Using these carry-save adders optimally, as prescribed by the above theory, we get {, , }-circuits of depth 3.48 log₂ n and {, , }-circuits of depth 4.95 log₂ n for the carry-save addition ofn numbers of arbitrary length. As a consequence we get multiplication circuits of the same depth. These circuits put out two numbers whose sum is the result of the multiplication. If a single output number is required then the depth of the multiplication circuits increases respectively to 4.48 log₂ n and 5.95 log₂ n.We also get {, , }-formulae of sizeO (n ^3.13) and {, }-formulae of sizeO (n ^4.57) for all the output bits of a carry-save addition ofn numbers. As a consequence we get formulae of the same size for the majority function and many other symmetric Boolean functions.     

Fast exponentiation using the truncation operation

Given an integerk, and anarbitrary integer greater than , we prove a tight bound of on the time required to compute with operations {+, –, *, /, ·, }, and constants {0, 1}. In contrast, when the floor operation is not available this computation requires (k) time. Using the upper bound, we give an time algorithm for computing log loga, for alln-bit integersa. This upper bound matches the lower bound for computing this function given by Mansour, Schieber, and Tiwari. To the best of our knowledge these are the first non-constant tight bounds for computations involving the floor operation.     

Two and three-quarter dimensional meshing facilitators

This paper presents generated enhancements for robust two and three-quarter dimensional meshing, including: (1) automated interval assignment by integer programming for submapped surfaces and volumes, (2) surface submapping, and (3) volume submapping. An introduction to the simplex method, an optimization technique of integer programming, is presented. Simplification of complex geometry is required for the formulation of the integer programming problem. A method of i-j unfolding is defined which explains how irregular geometry can be realigned into a simplified form that is suitable for submap interval assignment solutions. Also presented is the processes by which submapping eliminates the decomposition of surface geometry, through a pseudodecomposition process, producing suitable mapped meshes. The process of submapping involves the creation of interpolated virtual edges, user defined vertex types and i-j-k space traversals. The creation of interpolated virtual edges is the method by which submapping automatically subdivides surface geometry. The interpolated virtual edge is formulated according to an interpolation scheme using the node discretization of curves on the surface. User defined vertex types allow direct user control of surface decomposition and interval assignment by modifying i-j-k space traversals. Volume submapping takes the geometry decomposition to a higher level by using mapped virtual surfaces to eliminate decomposition of complex volumes.     

Separating complexity classes related to bounded alternating ω-branching programs

We develop a theory of communication within branching programs that provides exponential lower bounds on the size of branching programs that are bounded alternating. Our theory is based on the algebraic concept of -branching programs, : , a semiring homomorphism, that generalizes ordinary branching programs, -branching programs [M2] andMOD _p-branching programs [DKMW].Due to certain exponential lower and polynomial upper bounds on the size of bounded alternating -branching programs we are able to separate the corresponding complexity classesN _ba ,co-N _{ba ba} , andMOD _p - _ba ,p prime, from each other, and from that classes corresponding to oblivious linear length-bounded branching programs investigated in the past.     

Fast Theta-Subsumption with Constraint Satisfaction Algorithms

Relational learning and Inductive Logic Programming (ILP) commonly use as covering test the -subsumption test defined by Plotkin. Based on a reformulation of -subsumption as a binary constraint satisfaction problem, this paper describes a novel -subsumption algorithm named Django,¹ which combines well-known CSP procedures and -subsumption-specific data structures. Django is validated using the stochastic complexity framework developed in CSPs, and imported in ILP by Giordana et Saitta. Principled and extensive experiments within this framework show that Django improves on earlier -subsumption algorithms by several orders of magnitude, and that different procedures are better at different regions of the stochastic complexity landscape. These experiments allow for building a control layer over Django, termed Meta-Django, which determines the best procedures to use depending on the order parameters of the -subsumption problem instance. The performance gains and good scalability of Django and Meta-Django are finally demonstrated on a real-world ILP task (emulating the search for frequent clauses in the mutagenesis domain) though the smaller size of the problems results in smaller gain factors (ranging from 2.5 to 30).     

Context-free text grammars

A text is a triple=(, ₁, ₂) such that is a labeling function, and ₁ and ₂ are linear orders on the domain of ; hence may be seen as a word (, ₁) together with an additional linear order ₂ on the domain of . The order ₂ is used to give to the word (, ₁) itsindividual hierarchical representation (syntactic structure) which may be a tree but it may be also more general than a tree. In this paper we introducecontext-free grammars for texts and investigate their basic properties. Since each text has its own individual structure, the role of such a grammar should be that of a definition of a pattern common to all individual texts. This leads to the notion of ashapely context-free text grammar also investigated in this paper.