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A new notion of an optimal algebra for a first order coordinate differential was introduced in \cite{BKO}. Some relevant examples are indicated. Quadratic identities in the optimal algebras and calculi on quadratic algebras are studied.…
In this paper we are interested in the studying coarse-graining in field theories using the language of quantum open systems. Motivated by the ideas of Calzetta and Hu on correlation histories we employ the Zwanzig projection technique to…
Knowledge graphs (KGs) have emerged as a powerful paradigm for structuring and leveraging diverse real-world knowledge, which serve as a fundamental technology for enabling cognitive intelligence systems with advanced understanding and…
Knowledge graphs (KGs) are widely acknowledged as incomplete, and new entities are constantly emerging in the real world. Inductive KG reasoning aims to predict missing facts for these new entities. Among existing models, graph neural…
Kullback--Leibler (KL) divergence is a fundamental measure of the dissimilarity between two probability distributions, but it can become unstable in high-dimensional settings due to its sensitivity to mismatches in distributional support.…
Multiview clustering (MC) aims to group samples using consistent and complementary information across various views. The subspace clustering, as a fundamental technique of MC, has attracted significant attention. In this paper, we propose a…
Inspired by the concept of coherent frozen waves, this paper introduces one possible theoretical framework of its partially coherent version, a frozen spatial coherence, in which a desired two-point correlation structure of an optical field…
Knowledge graph alignment is the task of matching equivalent entities (that is, instances and classes) and relations across two knowledge graphs. Most existing methods focus on pure entity-level alignment, computing the similarity of…
We report the investigation of spatial distribution of quasars using two different methods: the statistical study by means of 2-point correlation function and direct search for structures such as previously reported Large Quasar Groups.…
We consider one-dimensional reaction-diffusion equations for a large class of spatially periodic nonlinearities (including multistable ones) and study the asymptotic behavior of solutions with Heaviside type initial data. Our analysis…
We consider the task of distributed inner product estimation when allowed limited quantum communication. Here, Alice and Bob are given $k$ copies of an unknown $n$-qubit quantum states $\vert \psi \rangle,\vert \phi \rangle$ respectively.…
Quadratic constraints (QCs) are widely used to characterize nonlinearities and uncertainties, but generic analytical characterizations can be conservative on bounded domains. This paper develops a framework for constructing verified…
Language models contain ranking-based knowledge and are powerful solvers of in-context ranking tasks. For instance, they may have parametric knowledge about the ordering of countries by size or may be able to rank product reviews by…
In the framework of analytic approach to QCD the nonperturbative contributions in running coupling of strong interaction up to 4-loop order are obtained in an explicit form. For all $Q>\Lambda$ they are shown to be represented in the form…
Quantum machine learning is emerging as a promising application of quantum computing due to its distinct way of encoding and processing data. It is believed that large-scale quantum machine learning demonstrates substantial advantages over…
The notion of the Jacob's ladders, reversely iterated integrals and the $\zeta$-factorization is used in this paper in order to obtain new results in study of the function $\arg\zf$. Namely, we obtain new formulae for non-local and…
Traditional multi-agent reinforcement learning (MARL) algorithms, such as independent Q-learning, struggle when presented with partially observable scenarios, and where agents are required to develop delicate action sequences. This is often…
The complete knowledge of a theory is encoded in its correlation functions. Thus non-perturbative effects, like confinement in QCD, is necessarily contained in these correlation functions. As a consequence, a number of confinement scenarios…
Effective general-purpose search strategies are an important component in Constraint Programming. We introduce a new idea, namely, using correlations between variables to guide search. Variable correlations are measured and maintained by…
Quantum entanglement is a key resource for quantum technologies, including emerging ground-to-satellite quantum communication. In such a scenario, an important challenge to be overcome is to consider entanglement between two or more quantum…