This paper investigates the problem of merging word embedding sets from various pre-trained models. Since direct vector space alignment faces computational challenges and local minima issues, it is proposed to transition to ordinal aggregation methods. The absence of cycles in individual ordinal matrices of pairwise distance comparisons is proven, which guarantees the equivalence of the Kemeny and Copeland algorithms in this case. For aggregated matrices where the Condorcet paradox is possible, Copeland’s algorithm serves as an efficient heuristic. The Borda count method, which does not require building tournament graphs, is also considered. Experiments were conducted on 10 models and 3 datasets (WordSim-353, MEN, SimLex-999). It is shown that ordinal methods can identify optimal model combinations (triples, quads, and quints) that outperform individual models in Spearman correlation, with minimal difference between the Borda and Kemeny/Copeland methods.

The paper studies the computational complexity of detecting limit cycles of fixed length \(k\) in Boolean networks with local functions restricted to Post classes. It is proven that the problem is NP-complete for expressive classes \(D_2\) (monotone self-dual functions), \(F_6^\infty\), and \(F_2^\infty\), while polynomial-time solvable for linear functions \(L_1\). Explicit polynomial reductions from 3-SAT preserving limit cycles of length \(k\) are constructed.

In this paper, operations on cellular automata with locators are proposed. These operations allow us to describe some cellular automaton with locators in the form of formulas over other cellular automaton with locators. As an example, a formula is constructed that defines a cellular automaton with locators equivalent to a cellular automaton with locators that performs multiplication of natural numbers in \(2n+2\) cycles.

Previously, the problems of existence and cardinality estimation of the domain of universal functions for various classes of functions in Boolean and \(k\)-valued logics were investigated. For the universal function for pairs of linear functions, existence was proven starting from seven variables. We obtained an upper linear bound on the cardinality of the domain of the universal function for pairs of linear functions by applying generalizations of the gradient method.

We study the problem of \(K\)-finite generation for precomplete classes of linear automata over the field \(E_2\). It is proved that the classes not belonging to the \(A\)-criterial system are not \(K\)-finitely generated. In addition, a countable series of \(K\)-closed classes that are \(K\)-finitely generated is found. It is also shown that any \(K\)-precomplete class which is not \(K\)-finitely generated is \(A\)-complete.

We study the coboundary expansion property of product codes called product expansion, which played a key role in all recent constructions of good qLDPC codes. It was shown before that this property is equivalent to robust testability and agreement testability for products of two codes with linear distance. First, we show that robust testability for the product of many codes with linear distance is equivalent to agreement testability. Second, we provide an example of the product of three codes with linear distance that is robustly testable but not product expanding.

This paper studies the completeness problem under superposition in the class of linear definite automata over the finite field with two elements. Its main result is a completeness criterion for arbitrary subsets of linear definite automata, stated in terms of a family of closed classes. This criterion extends earlier results that applied only to finitely generated subsets containing the zero constant. As a consequence, the paper proves that completeness is decidable for finite subsets of the class of linear definite automata.

We study the clone of all functions on four elements that can be represented as polynomials modulo 4. We show that any such function is uniquely determined by a set of Boolean functions of the same arity. The main result of the paper is a description of a maximal clone within the clone of polynomial functions that contains all unary polynomials, and which is analogous to the Słupecky maximal clone.

This paper proposes the concept of a human-centric architectural information system — the Language Radical Service Platform for Analysis and Synthesis (YARSPAS) of Automated Multi-Agent Artificial Intelligence Systems (AMASII). In the context of the growth of autonomous intelligent modules and the increasing complexity of digital spaces, the need arises for a formalized mechanism for their independence, adaptive configuration, and centralized control. A conceptual model of YARSPAS is proposed, considered as a distributed environment created by modules with controlled activation and redundancy states, interacting through an event-oriented communication bus and a conducting knowledge area. The necessary and sufficient requirements for the YARSPAS platform for the construction and maintenance of mass-scale smart systems like AMASII for various purposes are substantiated. Methods of radical, mathematical, information, language, neural network, and digital modeling, as well as system and ultra-system analysis and synthesis are used. Basic requirements for YARSPAS and AMASII are formulated and substantiated. A new type of neural network transformers is developed.