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We introduce the notion of generalized bialgebra, which includes the classical notion of bialgebra (Hopf algebra) and many others. We prove that, under some mild conditions, a connected generalized bialgebra is completely determined by its…
Functional analysis, especially the theory of Hilbert spaces and of operators on these, form an important area in mathematics. We formalized the Isabelle/HOL library Complex_Bounded_Operators containing a large amount of theorems about…
We provide a simple recipe for obtaining all self-adjoint extensions, together with their resolvent, of the symmetric operator $S$ obtained by restricting the self-adjoint operator $A:\D(A)\subseteq\H\to\H$ to the dense, closed with respect…
We show how to calculate the operator algebra and the operator Lie algebra of a stochastic labelled-graph grammar. More specifically, we carry out a generic calculation of the product (and therefore the commutator) of time-evolution…
The $\mathcal{B}_p$-algebras are a family of vertex operator algebras parameterized by $p\in \mathbb Z_{\geq 2}$. They are important examples of logarithmic CFTs and appear as chiral algebras of type $(A_1, A_{2p-3})$ Argyres-Douglas…
We present some general theorems about operator algebras that are algebras of functions on sets, including theories of local algebras, residually finite dimensional operator algebras and algebras that can be represented as the scalar…
The Operator axioms have produced new real numbers with new operators. New operators naturally produce new equations and thus extend the traditional mathematical models which are selected to describe various scientific rules. So new…
Let $k$ be a field of characteristic $p$. We construct a new inflation functor for cohomological Mackey functors for finite groups over $k$. Using this inflation functor, we give an explicit presentation of the graded algebra of self…
Augmenting Transformers with linguistic structures effectively enhances the syntactic generalization performance of language models. Previous work in this direction focuses on syntactic tree structures of languages, in particular…
We extend homological perturbation theory to encompass algebraic structures governed by operads and cooperads. The main difficulty is to find a suitable notion of algebra homotopy that generalizes to algebras over operads O. To solve this…
The usual Laurent expansion of the analytic tensors on the complex plane is generalized to any closed and orientable Riemann surface represented as an affine algebraic curve. As an application, the operator formalism for the $b-c$ systems…
We introduce a formal operational semantics that describes the fused execution of variable contraction problems, which compute indexed arithmetic over a semiring and generalize sparse and dense tensor algebra, relational algebra, and graph…
We prove two extension theorems for positive maps from operator systems into matrix algebras
We postulate a new type of operator algebra with a non-abelian extension. This algebra generalizes the Kac--Moody algebra in string theory and the Mickelsson--Faddeev algebra in three dimensions to higher-dimensional extended objects…
We provide an extension of the Gromov--Zimmer Embedding Theorem for Cartan geometries of [3] to tractor bundles carrying any invariant connection, including tractor connections and prolongation connections of first BGG operators for…
We propose a transition-based bubble parser to perform coordination structure identification and dependency-based syntactic analysis simultaneously. Bubble representations were proposed in the formal linguistics literature decades ago; they…
Covering and elimination inequalities are central to combinatorial optimization, yet their role has largely been studied in problem-specific settings or via no-good cuts. This paper introduces a unified perspective that treats these…
Every CSP(B) for a finite structure B is either in P or it is NP-complete but the proofs of the finite-domain CSP dichotomy by Andrei Bulatov and Dimitryi Zhuk not only show the computational complexity separation but also confirm the…
Extended multi-adjoint logic programming arises as an extension of multi-adjoint normal logic programming where constraints and a special type of aggregator operator have been included. The use of this general aggregator operator permits to…
Causal discovery seeks to uncover causal relations from data, typically represented as causal graphs, and is essential for predicting the effects of interventions. While expert knowledge is required to construct principled causal graphs,…