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We consider the defect theorem in the context of labelled
polyominoes, i.e., two-dimensional figures. The classical version of
this property states that if a set of n words is not a code then
the words can be expressed as a product of at most n - 1 words, the
smaller set being a code. We survey several two-dimensional
extensions exhibiting the boundaries where the theorem fails. In
particular, we establish the defect property in the case of three
dominoes (n × 1 or 1 × n rectangles).
Second of a series of articles laying down the bases for classical first order model theory. A language is defined basically as a tuple made of an integer-valued function (adicity), a symbol of equality and a symbol for the NOR logical connective. The only requests for this tuple to be a language is that the value of the adicity in = is -2 and that its preimage (i.e. the variables set) in 0 is infinite. Existential quantification will be rendered (see [11]) by mere prefixing a formula with a letter....
This text includes the definition and basic notions of product of posets, chain-complete and flat posets, flattening operation, and the existence theorems of recursive call using the flattening operator. First part of the article, devoted to product and flat posets has a purely mathematical quality. Definition 3 allows to construct a flat poset from arbitrary non-empty set [12] in order to provide formal apparatus which eanbles to work with recursive calls within the Mizar langauge. To achieve this...
A fuzzy method for the text error correction problem is introduced. The method is able to handle insert, delete and substitution errors. Moreover, it uses the measurement level output that an Isolated Character Classifier can provide. The method is based on a Deformed System, in particular, a deformed fuzzy automaton is defined to model the possible errors in the words of the texts. Experimental results show good performance in correcting the three types of errors.
Probability logic studies the properties resulting from the probabilistic interpretation of logical argument forms. Typical examples are probabilistic Modus Ponens and Modus Tollens. Argument forms with two premises usually lead from precise probabilities of the premises to imprecise or interval probabilities of the conclusion. In the contribution, we study generalized inference forms having three or more premises. Recently, Gilio has shown that these generalized forms “degrade” – more premises...
We prove two cases of a strong version of Dejean's conjecture
involving extremal letter frequencies. The results are that there
exist an infinite -free word over a 5 letter
alphabet with letter frequency and an infinite
-free word over a 6 letter alphabet with
letter frequency .
We show that Dejean's conjecture
holds for n ≥ 27. This brings the final resolution of the conjecture by the approach of Moulin Ollagnier within range of the computationally feasible.
2000 Mathematics Subject Classification: 68T01, 62H30, 32C09.Locally Linear Embedding (LLE) has gained prominence as a tool in unsupervised non-linear dimensional reduction. While the algorithm aims to preserve certain proximity relations between the observed points, this may not always be desirable if the shape in higher dimensions that we are trying to capture is observed with noise. This note suggests that a desirable first step is to remove or at least reduce the noise in the observations before...
We show that the standard normalization-by-evaluation construction for the simply-typed -calculus has a natural counterpart for the untyped -calculus, with the central type-indexed logical relation replaced by a “recursively defined” invariant relation, in the style of Pitts. In fact, the construction can be seen as generalizing a computational-adequacy argument for an untyped, call-by-name language to normalization instead of evaluation.In the untyped setting, not all terms have normal forms,...
We show that the standard normalization-by-evaluation construction for the
simply-typed λβη-calculus
has a natural counterpart for the untyped
λβ-calculus, with the central type-indexed logical relation
replaced by a “recursively defined” invariant relation, in
the style of Pitts. In fact, the construction can be seen as
generalizing a computational-adequacy argument for an untyped,
call-by-name language to normalization instead of evaluation.In the untyped setting, not all terms have normal...
The denotational semantics of a programming language which manages fuzzy data is presented. The introduction of blocks poses problems regarding transmission, both for the degree at which the work is carried out and for triangular operations necessary for the evaluation of the degrees of the fuzzy data. We propose some solutions. The possibility of defining linguistic variables is provided.
We propose a feature selection method for density estimation with
quadratic loss. This method relies on the study of unidimensional
approximation models and on the definition of confidence regions for
the density thanks to these models. It is quite general and includes
cases of interest like detection of relevant wavelets coefficients
or selection of support vectors in SVM. In the general case, we
prove that every selected feature actually improves the performance
of the estimator. In the case...
We investigate the density of critical factorizations of infinite sequences of words. The density of critical factorizations of a word is the ratio between the number of positions that permit a critical factorization, and the number of all positions of a word. We give a short proof of the Critical Factorization Theorem and show that the maximal number of noncritical positions of a word between two critical ones is less than the period of that word. Therefore, we consider only words of index one,...
We investigate the density of critical factorizations of infinite
sequences of words. The density of critical factorizations
of a word is the ratio between the number of positions
that permit a critical factorization, and the number of
all positions of a word.
We give a short proof of the Critical Factorization Theorem
and show that the maximal number of noncritical positions
of a word between two critical ones is less than the period
of that word. Therefore, we consider only words of...
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