Related papers: When is a Bol loop Moufang?
Non-associative finite invertible loops (NAFIL) are loops whose every element has a unique two-sided inverse. Not much is known about the class of NAFIL loops which includes the familiar IP (Inverse Property), Moufang, and Bol loops. Our…
Positive maps applied to a subsystem of a bipartite quantum state constitute a central tool in characterising entanglement. In the multipartite case, however, the direct application of a positive but not completely positive map cannot…
We quantize the electromagnetic field in the presence of a static magnetic monopole, within the loop-representation formalism. We find that the loop-dependent wave functional becomes multivalued, in the sense that it acquires a dependence…
For most (and possibly all) non-associative finite simple Moufang loops, three generators of order 3 can be chosen so that each two of them generate a group isomorphic to $(3, 3 | 3, p)$. The subgroup structure of $(3, 3 | 3, p)$ depends on…
Information flow properties express the capability for an agent to infer information about secret behaviours of a partially observable system. In a language-theoretic setting, where the system behaviour is described by a language, we define…
In math.GR/0510298, we showed that every loop isotopic to an F-quasigroup is a Moufang loop. Here we characterize, via two simple identities, the class of F-quasigroups which are isotopic to groups. We call these quasigroups FG-quasigroups.…
We consider an evolution of two elementary quantum particles and ask the question: under what conditions such a system behaves as a single object? It is obvious that if the attraction between the particles is stronger than any other force…
A restatement of the Algebraic Dichotomy Conjecture, due to Maroti and McKenzie, postulates that if a finite algebra A possesses a weak near-unanimity term, then the corresponding constraint satisfaction problem is tractable. A binary…
Buchsteiner loops are those which satisfy the identity $x\backslash (xy \cdot z) = (y \cdot zx)/ x$. We show that a Buchsteiner loop modulo its nucleus is an abelian group of exponent four, and construct an example where the factor achieves…
A simple classical, deterministic, local situation violating the Bell inequality is described. The detectors used in the experiment are ideal and the observers who decide which pair of measuring devices to choose for a given pair of…
We prove an inverse relation and a family of convolution formulas involving partial Bell polynomials. Known and some presumably new combinatorial identities of convolution type are discussed. Our approach relies on an interesting…
Given word on $n$ letters, we study groups which satisfiy "iterated identity" $w$, meaning that for all $x_1, \dots, x_n$ there exists $m$ such that $m$-the iteration of $w$ of Engel type, applied to $x_1, \dots, x_n$, is equal to the…
We establish necessary and sufficient conditions for a semigroup identity to hold in the monoid of $n\times n$ upper triangular tropical matrices, in terms of equivalence of certain tropical polynomials. This leads to an algorithm for…
Explainable systems expose information about why certain observed effects are happening to the agents interacting with them. We argue that this constitutes a positive flow of information that needs to be specified, verified, and balanced…
It was recently shown that the theory of linear stochastic systems can be viewed as a particular case of the theory of linear systems on a certain commutative ring of power series in a countable number of variables. In the present work we…
We give a combinatorial characterization of the identities holding in the semiring of all upper triangular Boolean $n\times n$-matrices and apply the characterization to computational complexity of identity checking, finite axiomatizability…
Traditional mathematical notation can lead to confusion. Expressions that appear to define composite functions sometimes do not. A particular example with engineering applications is studied in detail.
The world is structured in countless ways. It may be prudent to enforce corresponding structural properties to a learning algorithm's solution, such as incorporating prior beliefs, natural constraints, or causal structures. Doing so may…
In this article we address the problem of automatic answer checking in interactive learning systems that support mathematical notation. This problem consists of the problem of establishing identities in formal mathematical systems and hence…
We introduce two entanglement conditions that take the form of inequalities involving expectation values of operators. These conditions are sufficient conditions for entanglement, that is if they are satisfied the state is entangled, but if…