Related papers: Stratified Algebra
An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic…
Despite their impressive performance, contemporary neural networks often lack structural safeguards that promote stable learning and interpretable behavior. In this work, we introduce a reformulation of layer-level transformations that…
I introduce a novel mathematical framework integrating topological dynamics, operator algebras, and ergodic geometry to study lattices of asynchronous metric dynamical systems. Each node in the lattice carries an internal flow represented…
Text analytical tasks like word embedding, phrase mining, and topic modeling, are placing increasing demands as well as challenges to existing database management systems. In this paper, we provide a novel algebraic approach based on…
A novel algebra underlying integrable systems is shown to generate and unify a large class of quantum integrable models with given $R$-matrix, through reductions of an ancestor Lax operator and its different realizations. Along with known…
In this paper we develop a structure called Link Algebra, in which we present a Set with two binary operations and an axiom system developed from the study of graph theory and set/antiset theory, sowing main theorems and definitions. Once…
In this paper we present the set of intervals as a normed vector space. We define also a four-dimensional associative algebra whose product gives the product of intervals in any cases. This approach allows to give a notion of divisibility…
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…
Motivated by some recent developments in abstract theories of quadratic forms, we start to develop in this work an expansion of Linear Algebra to multivalued structures (a multialgebraic structure is essentially an algebraic structure but…
Interaction models describe distributed systems as algebraic terms, with gates marking interaction points between local views. Composing local models into a coherent global one requires aligning these gates while respecting the algebraic…
A new class of integrable mappings and chains is introduced. Corresponding $(1+2)$ integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in…
A stratified space is a kind of topological space together with a partition into smooth manifolds. These kinds of spaces naturally arise in the study of singular algebraic varieties, symplectic reduction, and differentiable stacks. In this…
We investigate stratified-algebraic vector bundles on a real algebraic variety X. A stratification of X is a finite collection of pairwise disjoint, Zariski locally closed subvarieties whose union is X. A topological vector bundle on X is…
In this paper, we propose a framework to extract the algebra of the transformations of worlds from the perspective of an agent. As a starting point, we use our framework to reproduce the symmetry-based representations from the…
In this work, we leverage the linear algebraic structure of distributed word representations to automatically extend knowledge bases and allow a machine to learn new facts about the world. Our goal is to extract structured facts from…
In this paper, we advocate the use of stratified logical theories for representing probabilistic models. We argue that such encodings can be more interpretable than those obtained in existing frameworks such as Markov logic networks. Among…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
Superstring compactifications have been vigorously studied for over four decades, and have flourished involving an active iterative feedback between physics and (complex) algebraic geometry. This led to an unprecedented wealth of…
A foundation is investigated for the application of loosely structured data on the Web. This area is often referred to as Linked Data, due to the use of URIs in data to establish links. This work focuses on emerging W3C standards which…
This paper combines the classical model of labeled transition systems with the epistemic model for reasoning about knowledge. The result is a unifying framework for modeling and analyzing multi-agent, knowledge-based, dynamic systems. On…