States and the free orthogonality monoid

Let (X, #) be an orthogonality space such that the lattice C(X, #) of closed subsets of (X, #) is orthomodular and let (, ) denote the free orthogonality monoid over (X, #). Let C₀(, ) be the subset of C(, ), consisting of all closures of bounded orthogonal sets. We show that C₀(, ) is a suborthomodular lattice of C(, ) and we provide a necessary and sufficient condition for C₀(, ) to carry a full set of dispersion free states.The work of the second author on this paper was supported by National Science Foundation Grant GP-9005.     

A variotherm mold for micro metal injection molding

In this paper, a variotherm mold was designed and fabricated for the production of 316L stainless steel microstructures by micro metal injection molding (MIM). The variotherm mold incorporated a rapid heating/cooling system, vacuum unit, hot sprue and cavity pressure transducer. The design of the variotherm mold and the process cycle of MIM using the variotherm mold were described. Experiments were conducted to evaluate the molded microstructures produced using variotherm mold and conventional mold. The experiments showed that microstructures of higher aspect ratio such as 60 m × height 191 m and 40 m × height 174 m microstructures could be injection molded with complete filling and demolded successfully using the variotherm mold. Molded microstructures with dimensions of 60 m × height 191 m were successfully debound and sintered without visual defects.     

Generating Boolean \mu-expressions

In this paper, we consider the class of Boolean -functions, which are the Boolean functions definable by -expressions (Boolean expressions in which no variable occurs more than once). We present an algorithm which transforms a Boolean formulaE into an equivalent -expression-if possible-in time linear in E times , where E is the size ofE andn _m is the number of variables that occur more than once inE. As an application, we obtain a polynomial time algorithm for Mundici's problem of recognizing -functions fromk-formulas [17]. Furthermore, we show that recognizing Boolean -functions is co-NP-complete for functions essentially dependent on all variables and we give a bound close to co-NP for the general case.     

Über die Konvergenz des Relaxationsverfahrens bei nicht-negativen und diagonaldominanten Matrizen

Zusammenfassung In der folgenden Arbeit werden zunächst die Begriffe Gesamtschrittverfahren, Einzelschrittverfahren und Relaxationsverfahren allgemein formuliert und dann auf allgemeine lineare Gleichungssysteme angewandt. Im Spezialfall einer Matrix mit verschwindender Hauptdiagonale erhält man so die bekanntenJacobi-, Gauss-Seidel- und Relaxationsverfahren. Satz 1 macht eine Aussage über die Konvergenz des Einzelschrittverfahrens bei allgemeinen, nicht-negativen Matrizen. Der Beweis verläuft ähnlich wie in einem bereits 1948 vonStein undRosenberg [2] behandelten Spezialfall. Als Korollar ergibt sich eine Aussage über die Konvergenz des Relaxationsverfahrens bei nicht-negativen Matrizen. Es wird ferner der Satz 2 über die Konvergenz des Relaxationsverfahrens bei diagonaldominanten Matrizen beweisen.

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Summary In this paper we give a general definition what is meant by total-step-, single-step- and successive relaxation iterative method and we apply these concepts on systems of linear equations. In the special case of a matrix with zero diagonal entries we obtain the well knownJacobi-, Gauss-Seidel- and Relaxation iterative method. Theorem 1 gives conditions for the convergence of the singlestep-iterative method for general, non-negative matrices. The proof is similar to that given byStein andRosenberg in [2] (1948) for a special case. A corollary gives conditions for the convergence of the relaxation-iterative method for non-negative matrices. Further on we prove theorem 2 about the convergence of the relaxation-iterative method with diagonally dominant matrices.

     

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.     

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.     

Supporting the sense of presence in control environments

This paper proposes a notion of presence which overcomes its strict interpretation in terms of physical projection and perception, and interprets the sense of being there as the understanding of the meaning of what is going on there. The domain of control environments is considered to illustrate this point and to propose technological solutions combining principles and techniques taken from Artificial Intelligence and Computer Supported Cooperative Work to enhance the interpretation and cooperation capabilities of the involved actors.     

Personalized and Adaptive Services on Board a Car: An Application for Tourist Information

Personalization and adaptation techniques are an interesting opportunity to design new services on-board vehicles. In this context, in fact, the need of an individual user to receive the right service at the right time and in the right way is more critical than in other cases, where personalization and adaptation already showed interesting advantages. At the same time, this context of application can provide new interesting insights for user modeling and adaptation. In the paper we present an architecture for providing personalized services on-board vehicles and we discuss an application to the case of tourist information. We focus on the choices we made to design an on-board system which was as less intrusive and distracting as possible and that could adapt its recommendations, the way it presents them and its own behavior to the user's preferences/interests and to the context of interaction (especially the driving conditions).     

Schedulers for larger classes of pinwheel instances

The pinwheel is a hard-real-time scheduling problem for scheduling satellite ground stations to service a number of satellites without data loss. Given a multiset of positive integers (instance)A={a₁,..., a_n}, the problem is to find an infinite sequence (schedule) of symbols from {1,2,...,n} such that there is at least one symboli within any interval of a_i symbols (slots). Not all instancesA can be scheduled; for example, no successful schedule exists for instances whose density,(A)= _i ⁱ (l/a_i), is larger than 1. It has been shown that all instances whose densities are less than a 0.5 density threshold can always be scheduled. If a schedule exists, another concern is the design of a fast on-line scheduler (FOLS) which can generate each symbol of the schedule in constant time. Based on the idea of integer reduction, two new FOLSs which can schedule different classes of pinwheel instances, are proposed in this paper. One uses single-integer reduction and the other uses double-integer reduction. They both improve the previous 0.5 result and have density thresholds of 13/20 and2/3, respectively. In particular, if the elements inA are large, the density thresholds will asymptotically approach In 2 and 1/R2, respectively.This research was supported in part by ONR Grant N00014-87-K-0833, and was done while Francis Chin was visiting the Computer Science Program, The University of Texas at Dallas, Richardson, TX 75083, USA.     

Meaningful Alignments

We propose a method for detecting geometric structures in an image, without any a priori information. Roughly speaking, we say that an observed geometric event is meaningful if the expectation of its occurences would be very small in a random image. We discuss the apories of this definition, solve several of them by introducing maximal meaningful events and analyzing their structure. This methodology is applied to the detection of alignments in images.     

End-to-end communications management using TMN “X” interfaces

The ongoing integration of LANs and WANs to support global communications and businesses and the emergence of integrated broadband communication services has created an increased demand for cooperation between customers, network and service providers to achieve end-to-end service management. Such a cooperation between autonomous authorities, each defining their own administrative management domains, requires the application of an open standardized framework to facilitate and regulate interworking. Such a framework is given by the ITU-T recommendations on TMN, where the so-called X interface is of particular importance for inter-domain management. In this paper, we explain the role of the TMN X interface within an inter-domain TMN architecture supporting end-to-end communications management. We identify the important issues that need to be addressed for the definition and realization of TMN X interfaces and report about our practical experiences with the implementation of TMN X interfaces in the PREPARE project.     

Enhancing the performance of an agent-based manufacturing system through learning and forecasting

Agent-based technology has been identified as an important approach for developing next generation manufacturing systems. One of the key techniques needed for implementing such advanced systems will be learning. This paper first discusses learning issues in agent-based manufacturing systems and reviews related approaches, then describes how to enhance the performance of an agent-based manufacturing system through learning from history (based on distributed case-based learning and reasoning) and learning from the future (through system forecasting simulation). Learning from history is used to enhance coordination capabilities by minimizing communication and processing overheads. Learning from the future is used to adjust promissory schedules through forecasting simulation, by taking into account the shop floor interactions, production and transportation time. Detailed learning and reasoning mechanisms are described and partial experimental results are presented.     

Logic Based Abstractions of Real-Time Systems

When verifying concurrent systems described by transition systems, state explosion is one of the most serious problems. If quantitative temporal information (expressed by clock ticks) is considered, state explosion is even more serious. We present a notion of abstraction of transition systems, where the abstraction is driven by the formulae of a quantitative temporal logic, called qu-mu-calculus, defined in the paper. The abstraction is based on a notion of bisimulation equivalence, called , n-equivalence, where is a set of actions and n is a natural number. It is proved that two transition systems are , n-equivalent iff they give the same truth value to all qu-mu-calculus formulae such that the actions occurring in the modal operators are contained in , and with time constraints whose values are less than or equal to n. We present a non-standard (abstract) semantics for a timed process algebra able to produce reduced transition systems for checking formulae. The abstract semantics, parametric with respect to a set of actions and a natural number n, produces a reduced transition system , n-equivalent to the standard one. A transformational method is also defined, by means of which it is possible to syntactically transform a program into a smaller one, still preserving , n-equivalence.     

Axiomatising finite delay operators

Summary In a simple language for finite automata based on SCCS we introduce three different delay operators , , . The operators , are two different versions of an unbounded but finite delay operator. It is argued that the usual notion of bisimulation is inadequate and two generalisations are proposed. In both cases we give a complete axiomatisation for finite terms of the language and prove that certain forms of induction are sound. In one case we give a complete axiomatisation.     

Unitary immersions of nonlinear systems

In this paper, we define what we call a unitary immersion of a nonlinear system. We observe that, for classical Hamiltonian systems, this notion contains, in some sense, the concept of quantization. We restrict our attention to degree-zero unitary immersions, where all observation functions must be represented by operators of the type multiplication by a function. We show that the problem of classifying such degree-zero unitary immersions of a given nonlinear system is not obvious. In some cases, we solve this problem.Chargé de Recherche au CNRS.Maître de Conférences.     

Data encodings and their costs

Summary This paper is devoted to developing and studying a precise notion of the encoding of a logical data structure in a physical storage structure, that is motivated by considerations of computational efficiency. The development builds upon the notion of an encoding of one graph in another. The cost of such an encoding is then defined so as to reflect the structural compatibility of the two graphs, the (externally specified) costs of implementing the host graph, and the (externally specified) set of intended usage patterns of the guest graph. The stability of the constructed framework is demonstrated in terms of a number of results; the faithfulness of the formalism is argued in terms of a number of examples from the literature; and the tractability of the model is hinted at by several results and by further references to the literature.     

Beyond unimodular transformations

This paper presents an approach to modeling loop transformations using linear algebra. Compound transformations are modeled as integer matrices. The nonsingular linear transformations presented here subsume the class of unimodular transformations. The loop transformations included are the unimodular transformations-reversal, skewing, and permutation- and a new transformation, namelystretching. Nonunimodular transformations (with determinant 1) create holes in the transformed iteration space, rendering code generation difficult. We solve this problem by suitably changing the step size of loops in order to skip these holes when traversing the transformed iteration space. For the class of nonunimodular loop transformations, we present algorithms for deriving the loop bounds, the array access expressions, and the step sizes of loops in the nest. To derive the step sizes, we compute the Hermite normal form of the transformation matrix; the step sizes are the entries on the diagonal of this matrix. We then use the theory of Hessenberg matrices in the derivation of exact loop bounds for nonunimodular transformations. We illustrate the use of this approach in several problems such as the generation of tile sets and distributed-memory code generation. This approach provides a framework for optimizing programs for a variety of architectures.Supported in part by an NSF Young Investigator Award CCR-9457768, an NSF grant CCR-9210422, and by the Louisiana Board of Regents through contract LEQSF (1991–94)-RD-A-09.     

Tight bounds for oblivious routing in the hypercube

We prove that in anyN-node communication network with maximum degreed, any deterministic oblivious algorithm for routing an arbitrary permutation requires (N/d) parallel communication steps in the worst case. This is an improvement upon the (N/d ^3/2) bound obtained by Borodin and Hopcroft. For theN-node hypercube, in particular, we show a matching upper bound by exhibiting a deterministic oblivious algorithm that routes any permutation in (N/logN) steps. The best previously known upper bound was (N). Our algorithm may be practical for smallN (up to about 2¹⁴ nodes).C. Kaklamanis was supported in part by NSF Grant NSF-CCR-87-04513. T. Tsantilas was supported in part by NSF Grants NSF-DCR-86-00379 and NSF-CCR-89-02500.     

Indecomposable local maps of tessellation automata

Indecomposable local maps of one-dimensional tessellation automata are studied. The main results of this paper are the following. (1) For any alphabet containing two or more symbols and for anyn 1, there exist indecomposable scope-n local maps over . (2) If is a finite field of prime order, then a linear scope-n local map over is indecomposable if and only if its associated polynomial is an irreducible polynomial of degreen – 1 over , except for a trivial case. (3) Result (2) is no longer true if is a finite field whose order is not prime.     

Finding Global Minima of Maximum Functions by Using Exclusion Functions without Derivatives

The first part of the paper introduces a new exclusion function without derivatives and describes its fundamental characteristics. The second part uses the new notion for finding global minimum of a real function of few variables g : [a, b] Rm R, g(x) = max{g1(x),...,gn(x)}, x [a, b], where g1(x),...,gn(x) are special multivariant real functions. The structure of the Maple program and some numerical examples are also presented in this part.