Related papers: Remarks on Fixed Point Assertions in Digital Topol…
This paper corrects an error in the authors' earlier work, by proving stronger forms of the basic lemmas
In this work, we Extend Pawlak approximation spaces by topological spaces. Also, Rough Membership, equality and inclusion relations are extended using topological near open sets. In addition, new extended measures of accuracy and quality of…
We present new computational methods for proving diffeomorphy of triangulated 4-manifolds, including algorithms and topological software that can for the first time effectively handle the complexities that arise in dimension four and be…
Comment: Elaboration on Two Points Raised in ``Classifier Technology and the Illusion of Progress'' [math.ST/0606441]
We define and study trivial points on towers of curves over number fields, and we show their finiteness in some cases. We relate these to the unboundeness of the gonality of the curves, which we show under some hypothesis. The problem is…
We propose a rigorous decomposition of predictive error, highlighting that not all 'irreducible' error is genuinely immutable. Many domains stand to benefit from iterative enhancements in measurement, construct validity, and modeling. Our…
The unfolding problem formulation for correcting experimental data distortions due to finite resolution and limited detector acceptance is discussed. A novel validation of the problem solution is proposed. Attention is drawn to fact that…
The most important problems for society are describable only in vague terms, dependent on subjective positions, and missing highly relevant data. This thesis is intended to revive and further develop the view that giving non-trivial,…
Explainable artificial intelligence techniques are developed at breakneck speed, but suitable evaluation approaches lag behind. With explainers becoming increasingly complex and a lack of consensus on how to assess their utility, it is…
Automated simplification models aim to make input texts more readable. Such methods have the potential to make complex information accessible to a wider audience, e.g., providing access to recent medical literature which might otherwise be…
We criticize the article "Quantifying sustainability: Resilience, efficiency and the return of information theory" (Ulanowicz et al., Ecological Complexity, 2009) for its presentation of information theory to an audience of ecologists. We…
We are pleased to see that Jeckelmann has made many changes to the original version of his comment on our paper as a result of our response. Here is a copy of this powerful response that reveals problems in his previous results. However,…
We prove extension-dimensional versions of finite dimensional selection and approximation theorems. As applications, we obtain several results on extension dimension.
The introduction of explicit notions of rejection, or disbelief, into logics for knowledge representation can be justified in a number of ways. Motivations range from the need for versions of negation weaker than classical negation, to the…
There are some inaccuracies and errors in my article "Dual and almost-dual homogeneous spaces". Here I will describe in detail how to correct incorrect statements from this article and which statements there will have to be reformulated in…
Incremental computation has recently been studied using the concepts of change structures and derivatives of programs, where the derivative of a function allows updating the output of the function based on a change to its input. We…
A comment has been recently posted on the arXiv (arXiv:1902.07504) that discuss our recent work on encircling multiple exceptional points in Nat. Commun. 9, 4808 (2018). In that comment, the authors claim that our approach is prone to…
Argumentation frameworks, consisting of arguments and an attack relation representing conflicts, are fundamental for formally studying reasoning under conflicting information. We use methods from mathematical logic, specifically…
Even though offline evaluation is just an imperfect proxy of online performance -- due to the interactive nature of recommenders -- it will probably remain the primary way of evaluation in recommender systems research for the foreseeable…
Asaf Karagila pointed out that Remark 3.4 [1], directly contradicts Theorem 3.3 (c) [2] which was incorrectly stated. This note contains a proof of this remark. [1] Miller, Arnold W.; A Dedekind Finite Borel Set, Arch. Math. Logic 50…