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.     

Sound and Complete Qualitative Simulation Needs “Quantitative” Filtering

The AI methodology of qualitative reasoning furnishes useful tools to scientists and engineers who need to deal with incomplete system knowledge during design, analysis, or diagnosis tasks. Qualitative simulators have a theoretical soundness guarantee; they cannot overlook any concrete equation implied by their input. On the other hand, the basic qualitative simulation algorithms have been shown to suffer from the incompleteness problem; they may allow non-solutions of the input equation to appear in their output. The question of whether a simulator with purely qualitative input which never predicts spurious behaviors can ever be achieved by adding new filters to the existing algorithm has remained unanswered. In this paper, we show that, if such a sound and complete simulator exists, it will have to be able to handle numerical distinctions with such a high precision that it must contain a component that would better be called a quantitative, rather than qualitative reasoner. This is due to the ability of the pure qualitative format to allow the exact representation of the members of a rich set of numbers.     

Comparing text editions with the aid of the computer

The aim of this paper is to reveal the limitations of relying on fingerprint formulas or signature positions to identify printed editions, in the manner of the STCN project. The paper proposes that scanned images of texts be used to identify editions.Ben J. P. Salemans is a philologist with special interest in the use of the computer as a scientific tool in literary, philological and cultural-historical research. His Ph.D. project is a study of automated text-genealogical research. He works as a computer consultant at the UCI computer centre of the University of Nijmegen.Dedicated to the memory of Marcel te Wilt ( 1993).     

Redesign of a Systems Engineering Language: Formalisation of χ

This paper describes the redesign of a systems engineering language called . This is an engineering language designed to specify and analyse industrial systems. The main objective of this redesign was to enable mathematical reasoning about specifications. We discuss the original language, the requirements and design decisions, and the resulting syntax and semantics of the new version of , called . In particular, we elaborate on semantical aspects of s time model.     

The impact of artificial intelligence on leisure

Two views of AI in leisure and the work-place and two views of society are discussed. There is a conceptualisation of AI systems enhancing people in their work and leisure and another of AI automata which tends to degrade and replace human activity. Researchers tend to resolve into Optimists who work within a micro-sociological view and see AI systems as inevitable and beneficent. Others are Pessimists who adopt a macro-sociological view and see AI in its automata role and deliterious social consequences. These polarised perspectives must be integrated as only enhancing AI is socially acceptable.     

Informatik als Grundbildung

Im Teil II Bildung von Elementarsätzen wird der Teil Namengebung und Kennzeichnung vorbereitet. Seine Überschrift könnte auch lauten: Was sind Nominatoren und wie kommen sie zustande? Teil V ist wie seine Vorgänger Teil III Gleichheit und Abstraktion und Teil IV Objektsprache/Metasprache als eine Erweiterung einer rationalen Grammatik aufzufassen. Der noch folgende Teil VI Logik und Geltungsicherung von Behauptungen schließt die Serie Informatik als Grundbildung ab.     

A Genetic Algorithm Based Approach to Optimal Toll Level and Location Problems

The derivative based approach to solve the optimal toll problem is demonstrated in this paper for a medium scale network. It is shown that although the method works for most small problems with only a few links tolled, it fails to converge for larger scale problems. This failure led to the development of an alternative genetic algorithm (GA) based approach for finding optimal toll levels for a given set of chargeable links. A variation on the GA based approach is used to identify the best toll locations making use of location indices suggested by Verhoef (2002).     

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.     

A priori Probability That Two Qubits Are Unentangled

In a previous study (P. B. Slater, Eur. Phys. J. B. 17, 471 (2000)), several remarkably simple exact results were found, in certain specialized m-dimensional scenarios (m 4), for the a priori probability that a pair of qubits is unentangled/separable. The measure used was the volume element of the Bures metric (identically one-fourth the statistical distinguishability [SD] metric). Here, making use of a newly-developed (Euler angle) parameterization of the 4 × 4 density matrices of Tilma, Byrd and Sudarshan, we extend the analysis to the complete 15-dimensional convex set (C) of arbitrarily paired qubits—the total SD volume of which is known to be ⁸ / 1680 = ⁸/2⁴ 3 5 7 5.64794. Using advanced quasi-Monte Carlo procedures (scrambled Halton sequences) for numerical integration in this high-dimensional space, we approximately (5.64851) reproduce that value, while obtaining an estimate of 0.416302 for the SD volume of separable states. We conjecture that this is but an approximation to ⁶/2310 = ⁶ / (2 3 5 7 11) 0.416186. The ratio of the two volumes, 8/11²2 .0736881, would then constitute the exact Bures/SD probability of separability. The SD area of the 14-dimensional boundary of C is 142⁷/12285 = 2 71⁷/3³ 5 7 13 34.911, while we obtain a numerical estimate of 1.75414 for the SD area of the boundary of separable states. PACS: 03.67.-; 03.65.Ud; 02.60.Jh; 02.40.Ky     

Recognition of handwritten musical notes by a modified Neocognitron

A neural network for recognition of handwritten musical notes, based on the well-known Neocognitron model, is described. The Neocognitron has been used for the what pathway (symbol recognition), while contextual knowledge has been applied for the where (symbol placement). This way, we benefit from dividing the process for dealing with this complicated recognition task. Also, different degrees of intrusiveness in learning have been incorporated in the same network: More intrusive supervised learning has been implemented in the lower neuron layers and less intrusive in the upper one. This way, the network adapts itself to the handwriting of the user. The network consists of a 13×49 input layer and three pairs of simple and complex neuron layers. It has been trained to recognize 20 symbols of unconnected notes on a musical staff and was tested with a set of unlearned input notes. Its recognition rate for the individual unseen notes was up to 93%, averaging 80% for all categories. These preliminary results indicate that a modified Neocognitron could be a good candidate for identification of handwritten musical notes.     

‘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.     

Virtual Connections and a Traffic Optimization Model for an ATM Network

The number of virtual connections in the nodal space of an ATM network of arbitrary structure and topology is computed by a method based on a new concept—a covering domain having a concrete physical meaning. The method is based on a network information sources—boundary switches model developed for an ATM transfer network by the entropy approach. Computations involve the solution of systems of linear equations. The optimization model used to compute the number of virtual connections in a many-category traffic in an ATM network component is useful in estimating the resource of nodal equipment and communication channels. The variable parameters of the model are the transmission bands for different traffic categories.     

Nonblockability of Switches with the Cayley Graph Structure for Serial Transfer of Data Blocks. Generalized Hypercubes and Multidimensional Grids

A general method of conflictless arbitrary permutation of large data elements that can be divided into a multitude of smaller data blocks was considered for switches structured as the Cayley graphs. The method was specified for arbitrary permutations in the generalized hypercubes and multidimensional grids, and their characteristics were considered.     

A Full Bayesian Approach to Curve and Surface Reconstruction

When interpolating incomplete data, one can choose a parametric model, or opt for a more general approach and use a non-parametric model which allows a very large class of interpolants. A popular non-parametric model for interpolating various types of data is based on regularization, which looks for an interpolant that is both close to the data and also smooth in some sense. Formally, this interpolant is obtained by minimizing an error functional which is the weighted sum of a fidelity term and a smoothness term.The classical approach to regularization is: select optimal weights (also called hyperparameters) that should be assigned to these two terms, and minimize the resulting error functional.However, using only the optimal weights does not guarantee that the chosen function will be optimal in some sense, such as the maximum likelihood criterion, or the minimal square error criterion. For that, we have to consider all possible weights.The approach suggested here is to use the full probability distribution on the space of admissible functions, as opposed to the probability induced by using a single combination of weights. The reason is as follows: the weight actually determines the probability space in which we are working. For a given weight , the probability of a function f is proportional to exp(– f² _uu du) (for the case of a function with one variable). For each different , there is a different solution to the restoration problem; denote it by f. Now, if we had known , it would not be necessary to use all the weights; however, all we are given are some noisy measurements of f, and we do not know the correct . Therefore, the mathematically correct solution is to calculate, for every , the probability that f was sampled from a space whose probability is determined by , and average the different f's weighted by these probabilities. The same argument holds for the noise variance, which is also unknown.Three basic problems are addressed is this work: Computing the MAP estimate, that is, the function f maximizing Pr(f/D) when the data D is given. This problem is reduced to a one-dimensional optimization problem. Computing the MSE estimate. This function is defined at each point x as f(x)Pr(f/D) f. This problem is reduced to computing a one-dimensional integral.In the general setting, the MAP estimate is not equal to the MSE estimate. Computing the pointwise uncertainty associated with the MSE solution. This problem is reduced to computing three one-dimensional integrals.     

Uniform hardness versus randomness tradeoffs for Arthur-Merlin games

Impagliazzo and Wigderson proved a uniform hardness vs. randomness gap theorem for BPP. We show an analogous result for AM: Either Arthur-Merlin protocols are very strong and everything in can be proved to a subexponential time verifier, or else Arthur-Merlin protocols are weak and every language in AM has a polynomial time nondeterministic algorithm such that it is infeasible to come up with inputs on which the algorithm fails. We also show that if Arthur-Merlin protocols are not very strong (in the sense explained above) then Our technique combines the nonuniform hardness versus randomness tradeoff of Miltersen and Vinodchandran with instance checking. A key ingredient in our proof is identifying a novel resilience property of hardness vs. randomness tradeoffs.     

Estimating camera and object translation in the presence of camera rotation

This paper deals with stereo camera-based estimation of sensor translation in the presence of modest sensor rotation and moving objects. It also deals with the estimation of object translation from a moving sensor. The approach is based on Gabor filters, direct passive navigation, and Kalman filters.Three difficult problems associated with the estimation of motion from an image sequence are solved. (1) The temporal correspondence problem is solved using multi-scale prediction and phase gradients. (2) Segmentation of the image measurements into groups belonging to stationary and moving objects is achieved using the Mahalanobis distance. (3) Compensation for sensor rotation is achieved by internally representing the inter-frame (short-term) rotation in a rigid-body model. These three solutions possess a circular dependency, forming a cycle of perception. A seeding process is developed to correctly initialize the cycle. An additional complication is the translation-rotation ambiguity that sometimes exists when sensor motion is estimated from an image velocity field. Temporal averaging using Kalman filters reduces the effect of motion ambiguities. Experimental results from real image sequences confirm the utility of the approach.Financial support from the Natural Science and Engineering Research Council (NSERC) of Canada is acknowledged.     

Symbols and Computation A Critique of the Computational Theory of Mind

Over the past several decades, the philosophical community has witnessed the emergence of an important new paradigm for understanding the mind.¹ The paradigm is that of machine computation, and its influence has been felt not only in philosophy, but also in all of the empirical disciplines devoted to the study of cognition. Of the several strategies for applying the resources provided by computer and cognitive science to the philosophy of mind, the one that has gained the most attention from philosophers has been the Computational Theory of Mind (CTM). CTM was first articulated by Hilary Putnam (1960, 1961), but finds perhaps its most consistent and enduring advocate in Jerry Fodor (1975, 1980, 1981, 1987, 1990, 1994). It is this theory, and not any broader interpretations of what it would be for the mind to be a computer, that I wish to address in this paper. What I shall argue here is that the notion of symbolic representation employed by CTM is fundamentally unsuited to providing an explanation of the intentionality of mental states (a major goal of CTM), and that this result undercuts a second major goal of CTM, sometimes refered to as the vindication of intentional psychology. This line of argument is related to the discussions of derived intentionality by Searle (1980, 1983, 1984) and Sayre (1986, 1987). But whereas those discussions seem to be concerned with the causal dependence of familiar sorts of symbolic representation upon meaning-bestowing acts, my claim is rather that there is not one but several notions of meaning to be had, and that the notions that are applicable to symbols are conceptually dependent upon the notion that is applicable to mental states in the fashion that Aristotle refered to as paronymy. That is, an analysis of the notions of meaning applicable to symbols reveals that they contain presuppositions about meaningful mental states, much as Aristotle's analysis of the sense of healthy that is applied to foods reveals that it means conducive to having a healthy body, and hence any attempt to explain mental semantics in terms of the semantics of symbols is doomed to circularity and regress. I shall argue, however, that this does not have the consequence that computationalism is bankrupt as a paradigm for cognitive science, as it is possible to reconstruct CTM in a fashion that avoids these difficulties and makes it a viable research framework for psychology, albeit at the cost of losing its claims to explain intentionality and to vindicate intentional psychology. I have argued elsewhere (Horst, 1996) that local special sciences such as psychology do not require vindication in the form of demonstrating their reducibility to more fundamental theories, and hence failure to make good on these philosophical promises need not compromise the broad range of work in empirical cognitive science motivated by the computer paradigm in ways that do not depend on these problematic treatments of symbols.     

Interactive Speech Translation in the Diplomat Project

The Diplomat rapid-deployment speech-translation systemis intended to allow naï ve users to communicate across a languagebarrier, without strong domain restrictions, despite the error-pronenature of current speech and translation technologies. In addition,it should be deployable for new languages an order of magnitude morequickly than traditional technologies. Achieving this ambitious setof goals depends in large part on allowing the users to correct recognition and translation errors interactively. We present the Multi-Engine Machine Translation (MEMT) architecture, describing how it is well suited for such an application. We then discuss ourapproaches to rapid-deployment speech recognition and synthesis.Finally we describe our incorporation of interactive error correctionthroughout the system design. We have already developed workingbidirectional Croatian English and Spanish English systems, and have Haitian Creole English and Korean English versions under development.     

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.     

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)