We studied whether temporal sequences can be learned implicitly using a process dissociation procedure (PDP). Participants performed repeated serial recalls of sequential stimuli with a random ordinal structure and fixed temporal structure. Explicit knowledge was evaluated through verbal questions and PDP analysis of two generation tasks (inclusion and exclusion). Participants were divided into...

This is the second of two papers establishing structural properties of R2, the structure giving rise to pure patterns of resemblance of order two, which partially underly the results in [2] and [3] as well as other work in the area. For the entire paper, we will assume ρ is an arbitrary additively indecomposable ordinal and α is an epsilon number greater than ρ. By Lemma 5.8 of [4], κα is addit...

If α is an ordinal, then the space of all ordinals less than or equal to α is a compact Hausdorff space when endowed with the order topology. Let C(α) be the space of all continuous real-valued functions defined on the ordinal interval [0, α]. We characterize the symmetric sequence spaces which embed into C(α) for some countable ordinal α. A hierarchy (Eα) of symmetric sequence spaces is constr...

Ordinal computability uses ordinals instead of natural numbers in abstract machines like register or Turing machines. We give an overview of the computational strengths of α-β-machines, where α and β bound the time axis and the space axis of some machine model. The spectrum ranges from classical Turing computability to ∞-∞-computability which corresponds to Gödel’s model of constructible sets. ...

envelopment analysis (dea) is a very eective method to evaluate the relative eciency of decision-making units (dmus). dea models divided all dmus in two categories: ecient and inecientdmus, and don't able to discriminant between ecient dmus. on the other hand, the observedvalues of the input and output data in real-life problems are sometimes imprecise or vague, suchas interval data, ...

Ordinal notations and provability of well-foundedness have been a central tool in the study of the consistency strength and computational strength of formal theories of arithmetic. This development began with Gentzen’s consistency proof for Peano arithmetic based on the well-foundedness of ordinal notations up to ǫ0. Since the work of Gentzen, ordinal notations and provable wellfoundedness have...

We study strategic games where players' preferences are weak orders which need not admit utility representations. First of all, we extend Voorneveld's concept of best-response potential from cardinal to ordinal games and derive the analogue of his characterization result: An ordinal game is a best-response potential game if and only if it does not have a best-response cycle. The characterizatio...

Probability distributions produced by the crossentropy loss for ordinal classification problems can possess undesired properties. We propose a straightforward technique to constrain discrete ordinal probability distributions to be unimodal via the use of the Poisson and binomial probability distributions. We evaluate this approach in the context of deep learning on two large ordinal image datas...

Using the Schreier families (Sξ)ξ<ω1 , we define subclasses of weakly compact and Rosenthal operators between two Banach spaces. These subclasses give rise to ordinal ranks defined on each ideal. We prove several results concerning the analytic properties of this rank and give examples of spaces on which the ranks are bounded and unbounded.