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We consider a generalisation of the self-affine iterated function systems of Lalley and Gatzouras by allowing for a countable infinity of non-conformal contractions. It is shown that the Hausdorff dimension of the limit set is equal to the…
Fractional processes have gained popularity in financial modeling due to the dependence structure of their increments and the roughness of their sample paths. The non-Markovianity of these processes gives, however, rise to conceptual and…
An economic interpretation of the Caputo derivatives of non-integer orders is proposed. The suggested economic interpretation of the fractional derivatives is based on a generalization of average and marginal values of economic indicators.…
Attribution-based explanation techniques capture key patterns to enhance visual interpretability; however, these patterns often lack the granularity needed for insight in fine-grained tasks, particularly in cases of model misclassification,…
Functional representations of the capacity monad based on the max and min operations were considered in \cite{Ra1} and \cite{Ny1}. Nykyforchyn considered in \cite{Ny2} some alternative monad structure for the possibility capacity functor…
Numerous approaches have been recently proposed for learning fair representations that mitigate unfair outcomes in prediction tasks. A key motivation for these methods is that the representations can be used by third parties with unknown…
In this paper, a new axiomatization for unbounded functional calculi is proposed and the associated theory is elaborated comprising, among others, uniqueness and compatibility results and extension theorems of algebraic and topological…
Inspired by recent strides in empirical efficacy of implicit learning in many robotics tasks, we seek to understand the theoretical benefits of implicit formulations in the face of nearly discontinuous functions, common characteristics for…
Dummett's argument for intuitionism is well known. There is a concern that the argument proves too much, specifically, that it supports the extreme and apparently incoherent position of strict finitism. The central question is how to…
We here first study the state space realization of a tensor-product of a pair of rational functions. At the expense of "inflating" the dimensions, we recover the classical expressions for realization of a regular product of rational…
Asymptotic equivalence theory developed in the literature so far are only for bounded loss functions. This limits the potential applications of the theory because many commonly used loss functions in statistical inference are unbounded. In…
Defeasible logics provide several linguistic features to support the expression of defeasible knowledge. There is also a wide variety of such logics, expressing different intuitions about defeasible reasoning. However, the logics can only…
We survey the different properties of an intuitive notion of redundancy, as a function of the precise semantics given to the notion of partial implication. The final version of this survey will appear in the Proceedings of the Int. Conf.…
Recent years have witnessed the introduction and development of extremely fast rational function algorithms. Many ideas in this realm arose from polynomial-based linear-algebraic algorithms. However, polynomial approximation is occasionally…
Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on…
While belief functions may be seen formally as a generalization of probabilistic distributions, the question of the interactions between belief functions and probability is still an issue in practice. This question is difficult, since the…
We design an expansion of Belnap--Dunn logic with belief and plausibility functions that allow non-trivial reasoning with inconsistent and incomplete probabilistic information. We also formalise reasoning with non-standard probabilities and…
The notion of $\ast$-measure on a compact Hausdorff space can be defined for arbitrary continuous triangular norm $\ast$. The well-known Hutchinson-Barnsley theory deals with the iterated function systems (IFSs) of probability measures and…
Paradoxically, while the assumptions of second-order stationarity and isotropy appear outdated in light of modern spatial data, they remain remarkably robust in practice, as nonstationary methods often provide marginal improvements in…
Accepting a proposition means that our confidence in this proposition is strictly greater than the confidence in its negation. This paper investigates the subclass of uncertainty measures, expressing confidence, that capture the idea of…