Related papers: Unreal Probabilities: Partial Truth with Clifford …

We extend the notion of Clifford index to reduced curves with planar singularities by considering rank 1 torsion free sheaves. We investigate the behaviour of the Clifford index with respect to the combinatorial properties of the curve and…

We use Clifford algebras to construct a unified formalism for studying constant extrinsic curvature immersed surfaces in riemannian and semi-riemannian $3$-manifolds in terms of immersed bilegendrian surfaces in their unitary bundles. As an…

The definition of the conditional probability is very important in the theory of the probability. This definition is based on the fact, that random events can be simultaneously measurable. This paper deal with the problem of conditioning…

Clifford algebras are naturally associated with quadratic forms. These algebras are Z_2-graded by construction. However, only a Z_n-gradation induced by a choice of a basis, or even better, by a Chevalley vector space isomorphism Cl(V) <->…

For the complex Clifford algebra Cl(p,q) of dimension n=p+q we define a Hermitian scalar product. This scalar product depends on the signature (p,q) of Clifford algebra. So, we arrive at unitary spaces on Clifford algebras. With the aid of…

We provide a careful analysis of the structure theorem for the $n$-qudit projective Clifford group and various encoding schemes for its elements. In particular, we derive formulas for evaluation, composition, and inversion. Our results…

The aim of this article is to promote the use of probabilistic methods in the study of problems in mathematical general relativity. Two new and simple singularity theorems, whose features are different from the classical singularity…

Some quantum algebras build from deformed oscillator algebras may be described in terms of a particular case of extended umbral calculus. We give here an example of a specific relation between such certain quantum algebras and generalized…

We provide a generalized definition for the quantized Clifford algebra introduced by Hayashi using another parameter $k$ that we call the twist. For a field of characteristic not equal to $2$, we provide a basis for our quantized Clifford…

A positive integer is expressed as a sum of squares of positive integers in a unique way applying a special technique. The expression, thus obtained is resolved into two factors using the concept of the Clifford algebra. This technique is…

The Principle of Complementarity of Probabilities based on of noncommutative probability is introduced.

In this paper, we study Clifford algebra construction from the perspective of adjunctions motivated by the general framework of Krashen and Lieblich. We introduce a category of weighted polynomial laws whose associated Clifford algebra…

We analyze selected iterated conditionals in the framework of conditional random quantities. We point out that it is instructive to examine Lewis's triviality result, which shows the conditions a conditional must satisfy for its probability…

In this paper, we introduce a novel generalization of the classical property of algebras known as "being alternative," which we term "partially alternative." This new concept broadens the scope of alternative algebras, offering a fresh…

Division algebras have demonstrated their utility in studying non-associative algebras and their connection to the Standard Model through complex Clifford algebras. This article focuses on exploring the connection between these complex…

A description of the real, complete modules over the Clifford algebra of a Hilbert space, with the elements of the latter acting by skew-symmetric operators.

In this article, the structure of the Clifford-Weyl superalgebras and their associated Lie superalgebras will be investigated. These superalgebras have a natural supersymmetric inner product which is invariant under their Lie superalgebra…

Uncertainty representation and quantification are paramount in machine learning and constitute an important prerequisite for safety-critical applications. In this paper, we propose novel measures for the quantification of aleatoric and…

We present necessary and sufficient conditions for the existence of a countably additive measure on a complete Boolean algebra.

Quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with support containing a finite number of elements. If in the quantization some of the elements in the support are…