Recent reports from electrophysiological and psychophysical experiments provide evidence that repeated exposure to an ordered sequence of morphed stimuli may over time adapt a prelearned object category such that the category may generalise the entire sequence as belonging to the same object. Here, a new protocol that includes a single exposure to a morphing sequence is presented. Subjects expo...

The classical (Bancilhon-Spyratos) correspondence between view update translations and views with a constant complement reappears more generally as the correspondence between update strategies and meet complements in the order based setting of S. Hegner. We show that these two theories of database view updatability are linked by the notion of “lens” which is an algebra for a monad. We generaliz...

Filtered colimits, i.e., colimits over schemes D such that D-colimits in Set commute with finite limits, have a natural generalization to sifted colimits: these are colimits over schemes D such that D-colimits in Set commute with finite products. An important example: reflexive coequalizers are sifted colimits. Generalized varieties are defined as free completions of small categories under sift...

Exemplar sequencing effects in incidental and intentional unsupervised category learning were investigated to illuminate how people form categories without an external teacher. Stimuli were perfectly separable into 2 categories based on 1 of 2 dimensions of variation. Sequencing of the first 20 training stimuli was manipulated. In the blocked condition, 10 Category A stimuli were followed by 10...

For an arbitrary partially ordered set P its dual P ∗ is built as the collection of all monotone mappings P → 2 where 2 = {0, 1} with 0 < 1. The set of mappings P ∗ is proved to be a complete lattice with respect to the pointwise partial order. The second dual P ∗∗ is built as the collection of all morphisms of complete lattices P ∗ → 2 preserving universal bounds. Then it is proved that the pa...

When customers are classified into ordered categories, which are defined from the outset, it may happen that the majority belongs to a single category. If a market researcher is interested in the correlation between the classification and individual characteristics, the natural question is whether one needs to collect data for all customers in that particular category. We address this question ...

Introduction. In the theory of i7„-sets three main theorems stand out: I. An tya-set is universal for totally ordered sets of power not exceeding fc$„. II. Two r/a-sets of power tí« are isomorphic. III. If Na is regular and if ^2s<a 2s« ^Ka, then an rja-set of power Sa exists. These results were proved by Hausdorff [15, pp. 180-185] and Gillman [10]. Clearly they may be viewed as theorems about...

Mitchell characterized all finite partially ordered sets with incidence ring of Hochschild dimension 0, 1, and 2. Cheng characterized all finite partially ordered sets of cohomological dimension one. There are no conjectures in other dimensions. This article contains the algorithms for calculating the dimensions of finite partially ordered sets by elementary operations over rows and columns of ...

We use ordered categories to study semidirect decompositions of finite ordered semigroups. We obtain ordered analogues of the derived category theorem and of the delay theorem. Next we prove that the ordered analogues of semilattices and of J -trivial monoids constitute local varieties, and we derive some decomposition theorems from these results. In [10], Pin and Weil initiated a study of the ...

NexClass is a multi-criteria methodology and decision support system developed to classification into predefined nominal (non-ordered) categories. In this paper we introduce an extension of at problems ordinal (ordered) For each category entrance threshold defined by maker, which indicates its boundary with respect the evaluation criteria. Then, assignment alternatives classes based on concept ...