Over-Specification of Small Cardinalities in Referential Communication

The paper presents experimental evidence for the over-specification of small cardinalities in referential communication. The first experiment shows that when presented with a small set (2, 3, or 4) of unique objects, the speaker includes a numeral denoting a small cardinality into the description of given objects, although it is over-informative for the hearer (e.g., “three stars”). On the contrary, when presented with a large set of unique objects, the speaker does not include a numeral denoting a large cardinality into their description, so she produces a bare plural (e.g., “stars”). The effect of small cardinalities resembles the effect of over-specifying color in referential communication, which has been extensively studied in recent years (cf. Tarenskeen et al., 2015; Rubio-Fernández, 2016, among many others). This suggests that, like color, small cardinalities are absolute and salient. The second experiment demonstrates that when presented with an identical small set of monochrome objects, the speaker over-specifies a small cardinality to a much greater extent than a color. This suggests that small cardinalities are even more salient than color. The third experiment reveals that when slides are flashed on the screen one by one, highlighted objects of small cardinalities are still over-specified. We argue that a plausible explanation for the salience of small cardinalities is a subitizing effect, which is the human capacity to instantaneously grasp small cardinalities.

Overspecification of small cardinalities in reference production

This paper presents experimental evidence for overspecification of small cardinalities in refer-ence production. The idea is that when presented with a small set of unique objects (2, 3 or 4), the speaker includes a small cardinality while describing given objects, although it is overin-formative for the hearer (e.g., 'three stars'). On the contrary, when presented with a large set of unique objects, the speaker does not include cardinality in their description – so she produces a bare plural (e.g. 'stars'). The effect of overspecifying small cardinalities resembles the effect of overspecifying color in reference production which has been extensively studied in recent years (cf. Rubio-Fernandez 2016, Tarenskeen et al. 2015). When slides are flashed on the screen one by one, highlighted objects are still overspecified. We argue that one of the main reasons lies in subitizing effect, which is a human capacity to instantaneously grasp small cardinalities.

Ordinal compactness

We introduce a new covering property, defined in terms of order types of sequences of open sets, rather than in terms of cardinalities. The most general form depends on two ordinal parameters. Ordinal compactness turns out to be a much more varied notion than cardinal compactness. We prove many nontrivial results of the form ?every [?,?]-compact topological space is [?',?']-compact?, for ordinals ?,?, ?'and ?' while only trivial results of the above form hold, if we restrict to regular cardinals. Counterexamples are provided showing that many results are optimal. Many spaces satisfy the very same cardinal compactness properties, but have a broad range of distinct behaviors, as far as ordinal compactness is concerned. A much more refined theory is obtained for T1 spaces, in comparison with arbitrary topological spaces. The notion of ordinal compactness becomes partly trivial for spaces of small cardinality.

NONLINEAR NYBERG CONSTRUCTION TRANSFORMS OVER ISOMORPHIC REPRESENTATIONS OF FIELDS GALOIS

Further development of cryptographic algorithms based on the principles of many-valued logic requires more accurate research of non-binary cryptographic primitives – S-boxes. One of the most promising constructions for the synthesis of S-boxes is the Nyberg construction, which ensures high quality of the designed S-boxes in the binary case. The disadvantage of the Nyberg construction is the small cardinality of the classes of the constructed S-boxes. Nevertheless, this disadvantage can be overcome by considering all the isomorphic representations of the main field, substantially expanding the choice of available high-quality S-boxes. The research carried out in this paper has shown that the advantages of the Nyberg construction can be easily transferred to a many-valued case. Thus, we construct complete sets of S-boxes of the Nyberg construction over all isomorphic representations of fields GF(pᵏ), р= 3,5, and research their nonlinear characteristics. As a criterion of nonlinearity, we measure the distances from the component many-valued functions to the set of Vilenkin–Chrestenson functions that are considered to be the most linear. The correlation coefficients of the output and input vectors of the obtained S-boxes are calculated. The researches performed have shown the high quality of the constructed cryptographic primitives and allow recommendation of them for use in cryptoalgorithms based on the principles of many-valued logic.

Multitarget Classifiers for Mining in Bioinformatics

Building effective multitarget classifiers is still an on-going research issue: this chapter proposes the use of the knowledge gleaned from a human expert as a practical way for decomposing and extend the proposed binary strategy. The core is a greedy feature selection approach that can be used in conjunction with different classification algorithms, leading to a feature selection process working independently from any classifier that could then be used. The procedure takes advantage from the Minimum Description Length principle for selecting features and promoting accuracy of multitarget classifiers. Its effectiveness is asserted by experiments, with different state-of-the-art classification algorithms such as Bayesian and Support Vector Machine classifiers, over dataset publicly available on the Web: gene expression data from DNA micro-arrays are selected as a paradigmatic example, containing a lot of redundant features due to the large number of monitored genes and the small cardinality of samples. Therefore, in analysing these data, like in text mining, a major challenge is the definition of a feature selection procedure that highlights the most relevant genes in order to improve automatic diagnostic classification.

Construction of Codes Identifying Sets of Vertices

In this paper the problem of constructing graphs having a $(1,\le \ell)$-identifying code of small cardinality is addressed. It is known that the cardinality of such a code is bounded by $\Omega\left({\ell^2\over\log \ell}\log n\right)$. Here we construct graphs on $n$ vertices having a $(1,\le \ell)$-identifying code of cardinality $O\left(\ell^4 \log n\right)$ for all $\ell \ge 2$. We derive our construction from a connection between identifying codes and superimposed codes, which we describe in this paper.