Related papers: Unified inverse correspondence for DLE-Logics

In this paper we derive some basic results of circuit theory using `Implicit Linear Algebra' (ILA). This approach has the advantage of simplicity and generality. Implicit linear algebra is outlined in [1]. We denote the space of all vectors…

We study the linear differential system associated with the supersymmetric affine Toda field equations for affine Lie superalgebras, which has a purely odd simple root system. For an affine Lie algebra, the linear problem modified by…

We discuss the differential graded Lie algebra (DGLA) of Drinfeld modeled on the tensor algebra of the universal enveloping algebra of a Lie algebra g over any field K of characteristic zero. We explicitly analyze the first obstruction to…

Aligning large language models (LLMs) with human expectations without human-annotated preference data is an important problem. In this paper, we propose a method to evaluate the response preference by using the output probabilities of…

Let G be a connected reductive group over a non-archimedean local field K, and assume that G splits over an unramified extension of K. We establish a local Langlands correspondence for irreducible unipotent representations of G. It comes as…

In the literature on Kleene algebra (KA), a number of variants have been proposed such as Kleene algebra with tests, commutative KA, bi-KA, and concurrent KA. The equational theories of some of these structures have then been studied in the…

The Langlands correspondence for complex curves is traditionally formulated in terms of sheaves rather than functions. Recently, Langlands asked whether it is possible to construct a function-theoretic version. In this paper we use the…

Correspondence analysis (CA) is a popular technique to visualize the relationship between two categorical variables. CA uses the data from a two-way contingency table and is affected by the presence of outliers. The supplementary points…

In this paper, we introduce an algebra structure denoted by InvDer algebra whose which we twist an algebra thanks to an invertible derivation, where its inverse is also a derivation. We define InvDer Lie algebras, InvDer associated…

We propose a new training algorithm, named DualFL (Dualized Federated Learning), for solving distributed optimization problems in federated learning. DualFL achieves communication acceleration for very general convex cost functions, thereby…

Deep learning has emerged as a versatile tool for a wide range of NLP tasks, due to its superior capacity in representation learning. But its applicability is limited by the reliance on annotated examples, which are difficult to produce at…

The objective of this paper is, in the main, twofold: Firstly, to develop an algebraic setting for dealing with Bell polynomials and related extensions. Secondly, based on the author's previous work on multivariate Stirling polynomials…

With distributed computing and mobile applications becoming ever more prevalent, synchronizing diverging replicas of the same data is a common problem. Reconciliation -- bringing two replicas of the same data structure as close as possible…

The development of the relativistic all-order method where all single, double, and partial triple excitations of the Dirac-Hartree-Fock wave function are included to all orders of perturbation theory led to many important results for study…

Unitary dynamics with a strict causal cone (or "light cone") have been studied extensively, under the name of quantum cellular automata (QCAs). In particular, QCAs in one dimension have been completely classified by an index theory.…

Optimal control in general, and flatness-based control in particular, of robotic arms necessitate to compute the first and second time derivatives of the joint torques/forces required to achieve a desired motion. In view of the required…

We propose a generalization of first-order logic originating in a neglected work by C.C. Chang: a natural and generic correspondence language for any types of structures which can be recast as Set-coalgebras. We discuss axiomatization and…

Differrential Graded Lie Algebra Dg was previously introduced in the context of current algebras. We show that under some conditions, the problem of constructing equivariantly closed form from closed invariant form is reduces to…

Latent Dirichlet Allocation (LDA) is a foundational model for discovering latent thematic structure in discrete data, but its Dirichlet prior cannot represent the rich correlations and hierarchical relationships often present among topics.…

A Dyson map explicitly determines the appropriate basis of electromagnetic fields which yields a unitary representation of the Maxwell equations in an inhomogeneous medium. A qubit lattice algorithm (QLA) is then developed perturbatively to…