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.     

The dynamic clusters method in nonhierarchical clustering

Given a finite setE R ⁿ, the problem is to find clusters (or subsets of similar points inE) and at the same time to find the most typical elements of this set. An original mathematical formulation is given to the problem. The proposed algorithm operates on groups of points, called samplings (samplings may be called multiple centers or cores); these samplings adapt and evolve into interesting clusters. Compared with other clustering algorithms, this algorithm requires less machine time and storage. We provide some propositions about nonprobabilistic convergence and a sufficient condition which ensures the decrease of the criterion. Some computational experiments are presented.     

Data structures as sets with repeating elements

Data structures are interpreted as sets which may contain repeating elements. An algebraic system close to the integer ring is constructed on these sets.Translated from Kibernetika, No. 4, pp. 82–88, July–August, 1990.     

Multicriterion optimization of complex systems with parameters ranked by descending importance

A multicriterion optimization method is proposed for complex systems with parameters ranked by descending importance. This method requires weaker expert estimates for choosing an optimal alternative from the set of equally good solutions by formal specification of functional dependence between ranked parameter weights.Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 167–170, November–December, 1991.     

Sometime = always + recursion ≡ always on the equivalence of the intermittent and invariant assertions methods for proving inevitability properties of programs

Summary We propose and compare two induction principles called always and sometime for proving inevitability properties of programs. They are respective formalizations and generalizations of Floyd invariant assertions and Burstall intermittent assertions methods for proving total correctness of sequential programs whose methodological advantages or disadvantages have been discussed in a number of previous papers. Both principles are formalized in the abstract setting of arbitrary nondeterministic transition systems and illustrated by appropriate examples. The sometime method is interpreted as a recursive application of the always method. Hence always can be considered as a special case of sometime. These proof methods are strongly equivalent in the sense that a proof by one induction principle can be rewritten into a proof by the other one. The first two theorems of the paper show that an invariant for the always method can be translated into an invariant for the sometime method even if every recursive application of the later is required to be of finite length. The third and main theorem of the paper shows how to translate an invariant for the sometime method into an invariant for the always method. It is emphasized that this translation technique follows the idea of transforming recursive programs into iterative ones. Of course, a general translation technique does not imply that the original sometime invariant and the resulting always invariant are equally understandable. This is illustrated by an example.     

Fuzzy measurement in the Mishnah and the Talmud

I discuss the attitude of Jewish law sources from the 2nd–:5th centuries to the imprecision of measurement. I review a problem that the Talmud refers to, somewhat obscurely, as impossible reduction. This problem arises when a legal rule specifies an object by referring to a maximized (or minimized) measurement function, e.g., when a rule applies to the largest part of a divided whole, or to the first incidence that occurs, etc. A problem that is often mentioned is whether there might be hypothetical situations involving more than one maximal (or minimal) value of the relevant measurement and, given such situations, what is the pertinent legal rule. Presumption of simultaneous occurrences or equally measured values are also a source of embarrassment to modern legal systems, in situations exemplified in the paper, where law determines a preference based on measured values. I contend that the Talmudic sources discussing the problem of impossible reduction were guided by primitive insights compatible with fuzzy logic presentation of the inevitable uncertainty involved in measurement. I maintain that fuzzy models of data are compatible with a positivistic epistemology, which refuses to assume any precision in the extra-conscious world that may not be captured by observation and measurement. I therefore propose this view as the preferred interpretation of the Talmudic notion of impossible reduction. Attributing a fuzzy world view to the Talmudic authorities is meant not only to increase our understanding of the Talmud but, in so doing, also to demonstrate that fuzzy notions are entrenched in our practical reasoning. If Talmudic sages did indeed conceive the results of measurements in terms of fuzzy numbers, then equality between the results of measurements had to be more complicated than crisp equations. The problem of impossible reduction could lie in fuzzy sets with an empty core or whose membership functions were only partly congruent. Reduction is impossible may thus be reconstructed as there is no core to the intersection of two measures. I describe Dirichlet maps for fuzzy measurements of distance as a rough partition of the universe, where for any region A there may be a non-empty set of - _A (upper approximation minus lower approximation), where the problem of impossible reduction applies. This model may easily be combined with probabilistic extention. The possibility of adopting practical decision standards based on -cuts (and therefore applying interval analysis to fuzzy equations) is discussed in this context. I propose to characterize the uncertainty that was presumably capped by the old sages as U-uncertainty, defined, for a non-empty fuzzy set A on the set of real numbers, whose -cuts are intervals of real numbers, as U(A) = 1/h(A) ₀ ^h(A) log [1+(A)]d, where h(A) is the largest membership value obtained by any element of A and (A) is the measure of the -cut of A defined by the Lebesge integral of its characteristic function.     

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.     

Sparse Two-Scale FEM for Homogenization Problems

We analyze two-scale Finite Element Methods for the numerical solution of elliptic homogenization problems with coefficients oscillating at a small length scale 1. Based on a refined two-scale regularity on the solutions, two-scale tensor product FE spaces are introduced and error estimates which are robust (i.e., independent of ) are given. We show that under additional two-scale regularity assumptions on the solution, resolution of the fine scale is possible with substantially fewer degrees of freedom and the two-scale full tensor product spaces can be thinned out by means of sparse interpolation preserving at the same time the error estimates.     

ART: A Hybrid Classification Model

This paper presents a new family of decision list induction algorithms based on ideas from the association rule mining context. ART, which stands for Association Rule Tree, builds decision lists that can be viewed as degenerate, polythetic decision trees. Our method is a generalized Separate and Conquer algorithm suitable for Data Mining applications because it makes use of efficient and scalable association rule mining techniques.     

LAR: A logic of algorithmic reasoning

Summary Reasoning about programs involves some logical framework which seems to go beyond classical predicate logic. LAR is an extension of predicate logic by additional concepts which are to formalize our natural reasoning about algorithms. Semantically, this extension introduces an underlying time scale on which formulas are considered and time shifting connectives. Besides a full model-theoretic treatment, a consistent and complete formal system for LAR is given. The pure logical system can serve as a basis for various theories. As an example, a theory of while program schemes is developed which contains Hoare's correctness proof system.     

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.     

A Stylometric Analysis of Ya?ar Kemal’s ? nce Memed Tetralogy

We analyze four nce Memed novels of Yaar Kemal using six style markers: most frequent words, syllable counts, word type – or part of speech – information, sentence length in terms of words, word length in text, and word length in vocabulary. For analysis we divide each novel into five thousand word text blocks and count the frequencies of each style marker in these blocks. The style markers showing the best separation are most frequent words and sentence lengths. We use stepwise discriminant analysis to determine the best discriminators of each style marker. We then use these markers in cross validation based discriminant analysis. Further investigation based on multiple analysis of variance (MANOVA) reveals how the attributes of each style marker group distinguish among the volumes.     

Continuous reductions among combinatorial optimization problems

Summary Many reductions among combinatorial problems are known in the context of NP-completeness. These reductions preserve the optimality of solutions. However, they may change the relative error of approximative solutions dramatically. In this paper, we apply a new type of reductions, called continuous reductions. When one problem is continuously reduced to another, any approximation algorithm for the latter problem can be transformed into an approximation algorithm for the former. Moreover, the performance ratio is preserved up to a constant factor. We relate the problem Minimum Number of Inverters in CMOS-Circuits, which arises in the context of logic synthesis, to several classical combinatorial problems such as Maximum Independent Set and Deletion of a Minimum Number of Vertices (Edges) in Order to Obtain a Bipartite (Partial) Subgraph.     

Nonlockability in Multirings and Hypercubes at Serial Transmission of Data Blocks

For the multiring and hypercube, a method of conflictless realization of an arbitrary permutation of large data items that can be divided into many smaller data blocks was considered, and its high efficiency was demonstrated.     

A Typology of Translation Problems for Eurotra Translation Machines

This paper presents a detailed study of Eurotra Machine Translation engines, namely the mainstream Eurotra software known as the E-Framework, and two unofficial spin-offs – the C,A,T and Relaxed Compositionality translator notations – with regard to how these systems handle hard cases, and in particular their ability to handle combinations of such problems. In the C,A,T translator notation, some cases of complex transfer are wild, meaning roughly that they interact badly when presented with other complex cases in the same sentence. The effect of this is that each combination of a wild case and another complex case needs ad hoc treatment. The E-Framework is the same as the C,A,T notation in this respect. In general, the E-Framework is equivalent to the C,A,T notation for the task of transfer. The Relaxed Compositionality translator notation is able to handle each wild case (bar one exception) with a single rule even where it appears in the same sentence as other complex cases.     

The plane with parallel coordinates

By means ofParallel Coordinates planar graphs of multivariate relations are obtained. Certain properties of the relationship correspond tothe geometrical properties of its graph. On the plane a point line duality with several interesting properties is induced. A new duality betweenbounded and unbounded convex sets and hstars (a generalization of hyperbolas) and between Convex Unions and Intersections is found. This motivates some efficient Convexity algorithms and other results inComputational Geometry. There is also a suprising cusp inflection point duality. The narrative ends with a preview of the corresponding results inR ^N .     

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.     

Properties of Ridges and Cores for Two-Dimensional Images

Pizer and Eberly introduced the core as the analogue of the medial axis for greyscale images. For two-dimensional images, it is obtained as the ridge of a medial function defined on 2 + 1-dimensional scale space. The medial function is defined using Gaussian blurring and measures the extent to which a point is in the center of the object measured at a scale. Numerical calculations indicate the core has properties quite different from the medial axis. In this paper we give the generic properties of ridges and cores for two-dimensional images and explain the discrepancy between core and medial axis properties. We place cores in a larger relative critical set structure, which coherently relates disjoint pieces of core. We also give the generic transitions which occur for sequences of images varying with a parameter such as time. The genericity implies the stability of the full structure in any compact viewing area of scale space under sufficiently small L2 perturbations of the image intensity function. We indicate consequences for finding cores and also for adding markings to completely determine the structure of the medial function.     

Theory and benefits of recursive certificate structures

Processing of a set of multi-level digital certificates, particularly path construction and validation, can be excessively resource consuming, and even impractical in some cases. This article introduces classifications of certificate sets as minimal, surplus, and deficient and explains the new paradigm of a recursive certificate structure designed to provide the equivalent of a minimal set of conventional certificates containing only the necessary and sufficient information to minimize the effort to validate a certificate sequence, with a potential avoidance of duplication of validation previously handled by related Certification Authorities.     

Maximum entropy two-station cyclic queues with multiple general servers

Summary The efficient implementation and extension of various approximate methods for general queueing networks require the study of two-station cyclic queues. In this paper maximum entropy formalism is used to analyse two-station cyclic queues with multiple general servers and a fixed number of jobs. New robust one step recursions for the queue length distribution are derived and asymptotic connections to infinite capacity queues are established. Links with Birth-Death and global balance solutions are determined and extensions to load dependent servers with Bernoulli feedback are presented. Numerical examples provide useful information on how critically system behaviour is affected by the distributional form of service times and simple bounds for typical performance measures such as throughout and mean queue length are defined. Moreover, the utility of the work as a building block for the approximate analysis of a general central server model is demonstrated.Some of the material included in this paper has been orally presented to the International Workshop on Computer Performance Evaluation, 28–30 April 1986, Sophia-Antipolis (INRIA), France [1]This work is jointly supported by Science and Engineering Research Council (SERC), UK and Metron Technology Ltd., UK, under grants GR/D/12422 and GR/AA/772, respectively