In 1991 Stute introduced a class of estimators called conditional U –statistics. They can be seen as a generalization of the Nadaraya-Watson estimator for the regression function, and he proved their strong pointwise consistency to Very recently, Giné and Mason introduced the notion of a local U –process, which generalizes that of a local empirical process, and obtained central limit theorems a...

The present study aims at insights into the nature of incremental learning in the context of Gold’s model of identification in the limit. With a focus on natural requirements such as consistency and conservativeness, incremental learning is analysed both for learning from positive examples and for learning from positive and negative examples. The results obtained illustrate in which way differe...

We analyze the consistency strength of regularity on the basis of Feferman’s operational set theory OST. Our main result shows that regularity over OST for operations corresponds to regularity with respect to set-theoretic functions in frameworks like Kripke-Platek set theory. As a consequence, we obtain that OST plus the operational axiom (Inac) is consistency-equivalent to Kripke-Platek set t...

Strengthening a result of Amir Leshem [7], we prove that the consistency strength of holding GCH together with definable tree property for all successors of regular cardinals is precisely equal to the consistency strength of existence of proper class many Π 1 reflecting cardinals. Moreover it is proved that if κ is a supercompact cardinal and λ > κ is measurable, then there is a generic extensi...

The hypothesis that students who cheat will externalize the cause of this behavior was tested by contrasting the causal inferences of cheating students and noncheating students. The results supported Kelley’s attributional model, for cheaters tended to note the high distinctiveness, high consensus, and low consistency of their actions, while noncheaters noted the low distinctiveness, low consen...

The present study aims at insights into the nature of incremental learning in the context of Gold’s model of identification in the limit. With a focus on natural requirements such as consistency and conservativeness, incremental learning is analysed both for learning from positive examples and for learning from positive and negative examples. The results obtained illustrate in which way differe...

We give two results on guessing unbounded subsets of λ+. The first is a positive result and applies to the situation of λ regular and at least equal to א3, while the second is a negative consistency result which applies to the situation of λ a singular strong limit with 2 > λ+. The first result shows that in ZFC there is a guessing of unbounded subsets of S + λ . The second result is a consiste...

We revisit the squeezed-limit non-Gaussianity in single-field non-attractor inflation models from viewpoint of cosmological soft theorem. In attractor models, inflaton's trajectories with different initial conditions effectively converge into a single trajectory phase space, and hence there is only one \emph{clock} degree freedom (DoF) scalar part. Its long-wavelength perturbations can be absor...

Fundamental measure theory (FMT) for hard particles has great potential for predicting the phase behavior of colloidal and nanometric shapes. The modern versions of FMT are usually derived from the zero-dimensional limit, a system of at most one particle confined in a collection of cavities in the limit that all cavities shrink to the size of the particle. In Phys. Rev. E 85, 041150 (2012), a d...