Related papers: A Note on the Ideals E^a Which Are Discrete
It has been pointed out by counterexamples in a 2013 paper in the IEEE Transactions on Computers [1], that there is an error in the previously ibid.\ in 2005 published paper [2] on the construction of valid digit selection tables for SRT…
This article appears as chapter 21 of Prince (2023, Understanding Deep Learning); a complete draft of the textbook is available here: http://udlbook.com. This chapter considers potential harms arising from the design and use of AI systems.…
Comment on ``Microarrays, Empirical Bayes and the Two-Groups Model'' [arXiv:0808.0572]
Comment on ``Microarrays, Empirical Bayes and the Two-Groups Model'' [arXiv:0808.0572]
For a singular integral equation on an interval of the real line, we study the behavior of the error of a delta-delta discretization. We show that the convergence is non-uniform, between order $O(h^{2})$ in the interior of the interval and…
This study proposes an analysis of the different types of ethical approaches involved in the ethics of AI, and situates their interests and limits. First, the author introduces to the contemporary need for and meaning of ethics. He…
In this note we extend to arbitrary dimensions a couple of results due respectively to Mattei-Moussu and to Camara-Scardua in dimension 2. We also provide examples of singular foliations having a Siegel-type singularity and answering in the…
This paper is concerned with ideals in a commutative Noetherian ring $R$ of prime characteristic. The main purpose is to show that the Frobenius closures of certain ideals of $R$ generated by regular sequences exhibit a desirable type of…
For a discrete group $G$, we use the natural correspondence between ideals in the Boolean algebra $ \mathcal{P}_G$ of subsets of $G$ and closed subsets in the Stone-$\check{C}$ech compactifi-cation $\beta G$ as a right topological semigroup…
As a natural extension of the ongoing development of a theory of ideals in commutative quantales with an identity element, this article aims to study into the analysis of certain topological properties exhibited by distinguished classes of…
Neural ideals, originally defined in arXiv:1212.4201, give a way of translating information about the firing pattern of a set of neurons into a pseudomonomial ideal in a polynomial ring. We give a simple criterion for determining whether a…
We consider elliptic problems with complicated, discontinuous diffusion tensor $A_{\scriptscriptstyle 0} $. One of the standard approaches to numerically treat such problems is to simplify the coefficient by some approximation, say…
The main aim of this paper is to classify Ulrich ideals and Ulrich modules over two-dimensional Gorenstein rational singularities (rational double points) from a geometric point of view. To achieve this purpose, we introduce the notion of…
In this thesis, we focus on the study of some classes of monomial ideals, namely lexsegment ideals and monomial ideals with linear quotients.
These informal notes deal with some topics related to analysis on metric spaces.
As a capability coming from computation, how does AI differ fundamentally from the capabilities delivered by rule-based software program? The paper examines the behavior of artificial intelligence (AI) from engineering points of view to…
It is demonstrated that remarks and criticism in work [1] (arXiv:1005.2436 nucl-th) have resulted from inattentive reading of work [2] (Phys. Rev.C 81, 035501 (2010)) or just some misunderstanding and do not influence conclusions of work…
This paper is an appendix to the paper "Reasoning with Justifiable Exceptions in Contextual Hierarchies" by Bozzato, Serafini and Eiter, 2018. It provides further details on the language, the complexity results and the datalog translation…
A number of internal inconsistencies, misleading conclusions and lack of completeness in the analyses of the small $x$ deep inelastic data in recent papers of HERA physicists, particularly in a very recent one by the H1 collaboration are…
We study the structure of ideals generated by some classes of 2 \times 2 permanents of hypermatrices. This generalizes [9] on 2 x 2 permanental ideal of generic matrices. We compare the obtained structure to that of the corresponding…