Related papers: Taming Multirelations
We introduce a multiple conjugation biquandle, and show that it is the universal algebra to define a semi-arc coloring invariant for handlebody-links. A multiple conjugation biquandle is a generalization of a multiple conjugation quandle.…
Large bilingual parallel texts (also known as bitexts) are usually stored in a compressed form, and previous work has shown that they can be more efficiently compressed if the fact that the two texts are mutual translations is exploited.…
We aim at studying collections of algebraic structures defined over a commutative ring and investigating the complexity of significant constructions carried out on these objects. The assignment of measures of size, via a multiplicity…
We define a type of biquandle which is a generalization of symplectic quandles. We use the extra structure of these bilinear biquandles to define new knot and link invariants and give some examples.
This paper has a twofold purpose: to present an overview of the theory of absolutely summing operators and its different generalizations for the multilinear setting, and to sketch the beginning of a research project related to an objective…
Complex systems are characterized by many interacting units that give rise to emergent behavior. A particularly advantageous way to study these systems is through the analysis of the networks that encode the interactions among the system's…
An algebraic formalism for the study of a system of charged particles interacting with an external quantum field is developed. The notion of monoidal categories with duality is used for the description of composite systems and corresponding…
We study the combinatorics of an analogue of Green's $\mathcal{J}$-relation (a.k.a. the two-sided relation) for the bicategory of finite-dimensional bimodules over finite-dimensional associative algebras over a fixed field. In particular,…
We derive a separability criterion for bipartite quantum systems which generalizes the already known criteria. It is based on observables having generic commutation relations. We then discuss in detail the relation among these criteria.
The paper explores categorical interconnections between lattice-valued Relational systems and algebras of Fitting's lattice-valued modal logic. We define lattice-valued boolean systems, and then we study co-adjointness, adjointness of…
We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…
In this paper, we discuss the generalization of finitary $2$-representation theory of finitary $2$-categories to finitary birepresentation theory of finitary bicategories. In previous papers on the subject, the classification of simple…
We learn multiple hypotheses for related tasks under a latent hierarchical relationship between tasks. We exploit the intuition that for domain adaptation, we wish to share classifier structure, but for multitask learning, we wish to share…
We learn multiple hypotheses for related tasks under a latent hierarchical relationship between tasks. We exploit the intuition that for domain adaptation, we wish to share classifier structure, but for multitask learning, we wish to share…
Multipartite entanglement holds great importance in quantum information processing. The distribution of entanglement among subsystems can be characterized by monogamy relations. Based on the $\beta$th power of concurrence and negativity, we…
We define the category of partitioned binary relations and show that it contains many classical diagram categories, including categories of binary relations, maps, injective maps, partitions, (oriented) Brauer diagrams and (oriented)…
We study different notions of quantum correlations in multipartite systems of distinguishable and indistinguishable particles. Based on the definition of quantum coherence for a single particle, we consider two possible extensions of this…
Detecting and exploiting similarities between seemingly distant objects is without doubt an important human ability. This paper develops \textit{from the ground up} an abstract algebraic and qualitative notion of similarity based on the…
The connections between Tarski's relation algebras and Thompson's groups F, T, V, and his monoid M are reviewed here, along with Jonsson-Tarski algebras, fork algebras, true pairing algebras, and tabular relation algebras. All of these…
We shall discuss how the notions of multicategories and their linear representations are related with tensor categories. When one focuses on the ones arizing from planar diagrams, it particularly implies that there is a natural one-to-one…