Related papers: On interpretation of complex numbers
We introduce a hierarchy of fast-growing complexity classes and show its suitability for completeness statements of many non elementary problems. This hierarchy allows the classification of many decision problems with a non-elementary…
In this paper we investigate the complexity of abduction, a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining the world's behavior it aims at finding an explanation for some observed manifestation.…
This paper presents concentration inequalities and laws of large numbers under weak assumptions of irrelevance, expressed through lower and upper expectations. The results are variants and extensions of De Cooman and Miranda's recent…
A new application of polytope theory to Lie theory is presented. Exponential sums of convex lattice polytopes are applied to the characters of irreducible representations of simple Lie algebras. The Brion formula is used to write a polytope…
In this note we augment the poly-Bernoulli family with two new combinatorial objects. We derive formulas for the relatives of the poly-Bernoulli numbers using the appropriate variations of combinatorial interpretations. Our goal is to show…
In this paper, we advocate the use of stratified logical theories for representing probabilistic models. We argue that such encodings can be more interpretable than those obtained in existing frameworks such as Markov logic networks. Among…
As a contribution to interpretable machine learning research, we develop a novel optimization framework for learning accurate and sparse two-level Boolean rules. We consider rules in both conjunctive normal form (AND-of-ORs) and disjunctive…
The purpose of this paper is to combine classical methods from transcendental number theory with the technique of restriction to real scalars. We develop a conceptual approach relating transcendence properties of algebraic groups to results…
It is not commonly realized that the algebra of complex numbers can be used in an elegant way to represent the images of ordinary 3-dimensional figures, orthographically projected to the plane. We describe these ideas here, both using…
The real theory of the Dunkl operators has been developed very extensively, while there still lacks the corresponding complex theory. In this paper we introduce the complex Dunkl operators for certain Coxeter groups. These complex Dunkl…
Supervised machine learning models boast remarkable predictive capabilities. But can you trust your model? Will it work in deployment? What else can it tell you about the world? We want models to be not only good, but interpretable. And yet…
We define the class of multivariate group entropies as a novel set of information - theoretical measures, which extends significantly the family of group entropies. We propose new examples related to the "super-exponential" universality…
We introduce a remarkable new family of norms on the space of $n \times n$ complex matrices. These norms arise from the combinatorial properties of symmetric functions, and their construction and validation involve probability theory,…
A solution is proposed for the problem of composition of ordinary generating functions. A new class of functions that provides a composition of ordinary generating functions is introduced; main theorems are presented; compositae are written…
A new approach to complex systems aimed to resolve their paradoxes is proposed. Yet, the major inference is the prohibition of informational perpetuum mobile
A new notion of typicality for arbitrary probability measures on standard Borel spaces is proposed, which encompasses the classical notions of weak and strong typicality as special cases. Useful lemmas about strong typical sets, including…
We evaluate binomial series with harmonic number coefficients, providing recursion relations, integral representations, and several examples. The results are of interest to analytic number theory, the analysis of algorithms, and…
We survey commutative and non-commutative analogs of uniform algebras in the Archimedean settings and also offer some non-Archimedean examples. Constraints on the development of non-complex uniform algebras are also discussed.
The goal of the article is to get a satisfactory theory of cosupport in the derived category $\mathrm{D}(R)$, this is done by introducing another versions of the "big" and "small" cosupport for complexes. We provide some properties for…
We examine a generalization of the binomial distribution associated with a strictly increasing sequence of numbers and we prove its Poisson-like limit. Such generalizations might be found in quantum optics with imperfect detection. We…