Related papers: Ouroboros Spaces: An Intuitive Approach to Self-Re…

Previously, we have introduced a very small number of examples of what we call Ouroboros functions. Using our already established theory of Ouroboros spaces and their functions, we will provide a set of families of Ouroboros functions that…

In this paper, I aim to articulate and investigate the philosophical implications and inherent symbolism surrounding the mathematical properties of Ouroboros spaces and their respective functions. Initially, I provide a brief historical…

Ouroboros functions have shown some interesting properties when subjected to conventional operations. The aim of this paper is to continue our investigation and prove some additional properties of these functions. Using algebraic methods,…

The Hilbert space of probability mass functions (pmf) is introduced in this thesis. A factorization method for multivariate pmfs is proposed by using the tools provided by the Hilbert space of pmfs. The resulting factorization is special…

The aim of this work is to provide a unified framework for ordinal representations of uncertainty lying at the crosswords between possibility and probability theories. Such confidence relations between events are commonly found in monotonic…

The Perron-Frobenius theorem plays an important role in many areas of management science and operations research. This paper provides a probabilistic perspective on the theorem, by discussing a proof that exploits a probabilistic…

The notion of probability plays an important role in almost all areas of science and technology. In modern mathematics, however, probability theory means nothing other than measure theory, and the operational characterization of the notion…

We introduce a category Prob of probability spaces whose objects are all probability spaces and arrows are corresponding to measurable functions satisfying an absolutely continuous requirement. We can consider a Prob-arrow as an evolving…

At the core of the Ouroboros Model lies a self-referential recursive process with alternating phases of data acquisition and evaluation. Memory entries are organized in schemata. Activation at a time of part of a schema biases the whole…

It is well-known that a random variable, i.e., a function defined on a probability space, with values in a Borel space, can be represented on the special probability space consisting of the unit interval with Lebesgue measure. We show an…

This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…

In spite of its fundamental importance, inference has not been an inherent function of multidimensional models and analytical applications. These models are mainly aimed at numeric (quantitative) analysis where the notions of inference and…

This paper develops upper and lower bounds for the probability of Boolean functions by treating multiple occurrences of variables as independent and assigning them new individual probabilities. We call this approach dissociation and give an…

The purpose of this paper is to make an introduction to univalent function theory for readers of any level, assuming only foundational knowledge in real and complex analysis. In particular, we state and proof (with details) important…

In this paper we describe a theory of a cumulative distribution function on a space with an order from a probability measure defined in this space. This distribution function plays a similar role to that played in the classical case.…

Over the decades, Functional Analysis has been enriched and inspired on account of demands from neighboring fields, within mathematics, harmonic analysis (wavelets and signal processing), numerical analysis (finite element methods,…

This work proposes a view of probability as a relative measure rather than an absolute one. To demonstrate this concept, we focus on finite outcome spaces and develop three fundamental axioms that establish requirements for relative…

Causal spaces have recently been introduced as a measure-theoretic framework to encode the notion of causality. While it has some advantages over established frameworks, such as structural causal models, the theory is so far only developed…

In this paper we examine the problem of inference in Bayesian Networks with discrete random variables that have very large or even unbounded domains. For example, in a domain where we are trying to identify a person, we may have variables…

The aim of this paper is to establish a theory of random variables on domains. Domain theory is a fundamental component of theoretical computer science, providing mathematical models of computational processes. Random variables are the…