Related papers: On ring-like structures of lattice-ordered numeric…
In computer science, especially when dealing with quantum computing or other non-standard models of computation, basic notions in probability theory like "a predicate" vary wildly. There seems to be one constant: the only useful example of…
Probabilities to find a chosen number of electrons in flexible domains of space are calculated for highly correlated wave functions. Quantum mechanics can produce higher probabilities for chemically relevant arrangements of electrons in…
We consider random boolean cellular automata on the integer lattice, i.e., the cells are identified with the integers from 1 to $N$. The behaviour of the automaton is mainly determined by the support of the random variable that selects one…
We analyze Fock-state lattices (FSLs) from an algebraic viewpoint. Starting from a Lie algebra, we associate a FSL constructed from the action of its generators: diagonal (Cartan) generators define the lattice sites, while off-diagonal…
This paper pursues an investigation on groups equipped with an $L$-ordered relation, where $L$ is a fixed complete complete Heyting algebra. First, by the concept of join and meet on an $L$-ordered set, the notion of an $L$-lattice is…
We celebrate this year hundred years of quantum mechanics but there is still no consensus regarding its interpretation and limitations. In this article we advocate the statistical contextual interpretation which is free of paradoxes. State…
F. Labourie [arXiv:1212.5015] characterized the Hitchin components for $\operatorname{PSL}(n, \mathbb{R})$ for any $n>1$ by using the swapping algebra, where the swapping algebra should be understood as a ring equipped with a Poisson…
In this paper we introduce a new kind of topological space, called 'structured space', which locally resembles various kinds of algebraic structures. This can be useful, for instance, to locally study a space that cannot be globally endowed…
Many machine learning applications require the ability to learn from and reason about noisy multi-relational data. To address this, several effective representations have been developed that provide both a language for expressing the…
In this paper using the connections between some subvarieties of residuated lattices, we investigated some properties of the lattice of ideals in commutative and unitary rings. We give new characterizations for commutative rings $A$ in…
Given a model in algebraic statistics and some data, the likelihood function is a rational function on a projective variety. Algebraic algorithms are presented for computing all critical points of this function, with the aim of identifying…
Let A be a finite set with at least two elements. The composition of two classes I and J of operations on A, is defined as the set of all compositions of functions in I with functions in J. This binary operation gives a monoid structure to…
We study, in the context of algorithmic randomness, the closed amenable subgroups of the symmetric group $S_\infty$ of a countable set. In this paper we address this problem by investigating a link between the symmetries associated with…
We introduce a foundational sheaf theoretical scheme for the comprehension of quantum event structures, in terms of localization systems consisting of Boolean coordinatization coverings induced by measurement. The scheme is based on the…
Covering is a common type of data structure and covering-based rough set theory is an efficient tool to process this data. Lattice is an important algebraic structure and used extensively in investigating some types of generalized rough…
We study a connection between the algebraic probability and classical stochastic processes described by master equations. Introducing a definition of a state which has not been used for quantum cases, the classical stochastic processes can…
In the paper "An Abelian Loop for Non-Composites" (arXiv:110.14716), we introduced a group-like structure consisting of odd prime numbers and 1, with properties that allowed us to prove analogous results to well known theorems in Number…
We present a classical probability model appropriate to the description of quantum randomness. This tool, that we have called stochastic gauge system, constitutes a contextual scheme in which the Kolmogorov probability space depends upon…
The class of skew lattices can be seen as an algebraic category. It models an algebraic theory in the category of Sets where the Green's relation D is a congruence describing an adjunction to the category of Lattices. In this paper we will…
Although quantum states nicely explain experiments, the outcomes of experiments are not states. Instead, outcomes correspond to probability distributions. Twenty years ago we proved categorically that probability distributions leave open a…