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As space becomes increasingly crowded and contested, robust autonomous capabilities for multi-agent environments are gaining critical importance. Current autonomous systems in space primarily rely on optimization-based path planning or long-range orbital maneuvers, which have not yet proven effective in adversarial scenarios where one satellite is actively pursuing another. We introduce Divergent Adversarial Reinforcement Learning (DARL), a two-stage Multi-Agent Reinforcement Learning (MARL) approach designed to train autonomous evasion strategies for satellites engaged with multiple adversarial spacecraft. Our method enhances exploration during training by promoting diverse adversarial strategies, leading to more robust and adaptable evader models. We validate DARL through a cat-and-mouse satellite scenario, modeled as a partially observable multi-agent capture the flag game where two adversarial `cat' spacecraft pursue a single `mouse' evader. DARL's performance is compared against several benchmarks, including an optimization-based satellite path planner, demonstrating its ability to produce highly robust models for adversarial multi-agent space environments.

We establish an analogue of the fundamental theorem of algebra for polynomial matrix equations, in which the matrices-coefficients and unknown matrix are assumed to be circulant matrices., Comment: 5 pages, to appear in the American Mathematical Monthly in 2025

We propose a new approach to extending the notion of commutator and Lie algebra to algebras with ternary multiplication laws. Our approach is based on ternary associativity of the first and second kind. We propose a ternary commutator, which is a linear combination of six (all permutations of three elements) triple products. The coefficients of this linear combination are the cube roots of unity. We find an identity for the ternary commutator that holds due to ternary associativity of the first or second kind. The form of the found identity is determined by the permutations of the general affine group GA(1,5). We consider the found identity as an analogue of the Jacobi identity in the ternary case. We introduce the concept of a ternary Lie algebra at the cubic root of unity and give examples of such an algebra constructed using ternary multiplications of rectangular and three-dimensional matrices. We point out the connection between the structure constants of a ternary Lie algebra with three generators and an irreducible representation of the rotation group., Comment: 17 pages

Embedding models play a crucial role in Natural Language Processing (NLP) by creating text embeddings used in various tasks such as information retrieval and assessing semantic text similarity. This paper focuses on research related to embedding models in the Russian language. It introduces a new Russian-focused embedding model called ru-en-RoSBERTa and the ruMTEB benchmark, the Russian version extending the Massive Text Embedding Benchmark (MTEB). Our benchmark includes seven categories of tasks, such as semantic textual similarity, text classification, reranking, and retrieval. The research also assesses a representative set of Russian and multilingual models on the proposed benchmark. The findings indicate that the new model achieves results that are on par with state-of-the-art models in Russian. We release the model ru-en-RoSBERTa, and the ruMTEB framework comes with open-source code, integration into the original framework and a public leaderboard.

In this paper we study ternary algebras of third-order hypermatrices. By hypermatrix we mean a complex-valued variable with three indices, which is also called a three-dimensional matrix or spatial matrix. We assume that a hypermatrix is defined in three-dimensional Euclidean space and when this space is rotated, it transforms as a SO(3)-tensor. We consider two ternary multiplications of hypermatrices, which have the property of generalized associativity. We explore the geometric meaning of two independent SO(3)-invariants of hypermatrices and show that one of them defines a Hermitian metric. We study the 10-dimensional subspace of hypermatrices, known in the theory of representations of the rotation group, as the space of the weight 2 tensor representation of the rotation group. It is proved that the elements of this subspace that satisfy the regularity condition are right biunits of the ternary algebra of hypermatrices. The motivation for studying biunits of ternary algebra of hypermatrices was a ternary generalization of the Pauli exclusion principle.

Building a scalable universal high-performance quantum processor is a formidable challenge. In particular, the problem of realizing fast high-perfomance two-qubit gates of high-fidelity remains needful. Here we propose a unitary cell for a scalable quantum processor consisting of two transmons and a tunable three-mode coupler allowing for a ZZ interaction control. We experimentally demonstrate the native CZ gate with the pulse duration of 60~ns achieving the two-qubit gate fidelity above 98%, limited mostly by qubit coherence time. Numerical simulations show that by optimizing the gate duration the fidelity can be pushed over 99.97%., Comment: 13 pages, 9 figures, 3 tables

In our recent works, we proposed a theory of turbulence creation via the mean field effect of an intermolecular potential, which in part relies on the empirically observed "equilibrated" behavior of the pressure variable in a low Mach, high Reynolds number flow -- that is, while the density and temperature may exhibit considerable variations, the pressure is (nearly) constant. At the same time, conventional kinetic theory does not offer satisfactory explanation for such a behavior of the pressure variable, instead leading to an isentropic flow in the form of the usual compressible Euler or Navier-Stokes equations. In the current work, we introduce a novel correction term into the pair correlation function in the closure of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy in the deterministic, Vlasov-type collision integral. This term adjusts the density of incident and recedent pairs of particles to the macroscopic compression or expansion rate of the gas. Remarkably, the novel term does not affect the mass and momentum transport equations, and manifests solely in the pressure transport equation. Moreover, its effect on the pressure dynamics matches the observed behavior -- that is, it tends to attenuate the acoustic waves and smooth out the pressure solution. We also find that the novel correction term fails to produce such an effect in a stochastic, Boltzmann-type collision integral. This suggests that simplifying potential interactions via instantaneous collisions may lead to the loss of observable macroscopic effects in solutions of the fluid mechanics equations., Comment: 34 pages

The Spin Physics Detector collaboration proposes to install a universal detector in the second interaction point of the NICA collider under construction (JINR, Dubna) to study the spin structure of the proton and deuteron and other spin-related phenomena using a unique possibility to operate with polarized proton and deuteron beams at a collision energy up to 27 GeV and a luminosity up to $10^{32}$ cm$^{-2}$ s$^{-1}$. As the main goal, the experiment aims to provide access to the gluon TMD PDFs in the proton and deuteron, as well as the gluon transversity distribution and tensor PDFs in the deuteron, via the measurement of specific single and double spin asymmetries using different complementary probes such as charmonia, open charm, and prompt photon production processes. Other polarized and unpolarized physics is possible, especially at the first stage of NICA operation with reduced luminosity and collision energy of the proton and ion beams. This document is dedicated exclusively to technical issues of the SPD setup construction.

There are reasons to suggest that a number of mental disorders may be related to alteration in the neural complexity (NC). Thus, quantitative analysis of NC could be helpful in classifying mental and understanding conditions. Here, focusing on a methodological procedure, we have worked with young individuals, typical and with attention-deficit/hyperactivity disorder (ADHD) whose NC was assessed using q-statistics applied to the electroencephalogram (EEG). The EEG was recorded while subjects performed the visual Attention Network Test (ANT) and during a short pretask period of resting state. Time intervals of the EEG amplitudes that passed a threshold were collected from task and pretask signals from each subject. The data were satisfactorily fitted with a stretched $q$-exponential including a power-law prefactor(characterized by the exponent c), thus determining the best $(c, q)$ for each subject, indicative of their individual complexity. We found larger values of $q$ and $c$ in ADHD subjects as compared with the typical subjects both at task and pretask periods, the task values for both groups being larger than at rest. The $c$ parameter was highly specific in relation to DSM diagnosis for inattention, where well-defined clusters were observed. The parameter values were organized in four well-defined clusters in $(c, q)$-space. As expected, the tasks apparently induced greater complexity in neural functional states with likely greater amount of internal information processing. The results suggest that complexity is higher in ADHD subjects than in typical pairs. The distribution of values in the $(c, q)$-space derived from $q$-statistics seems to be a promising biomarker for ADHD diagnosis., Comment: 12 pages,5 figures

For a class of irreducible Markov chains with an infinitely countable set of states, we establish a new verifiable necessary and sufficient condition for recurrence and transience. We show that if one of the basic assumptions is not satisfied, then the statement of the theorem becomes invalid., Comment: 15 pages in the journal format. Initial title is changed. This is a substation revision and the final version that is accepted for publication in "Theory of Probability and Mathematical Statistics."

Most modern Integrated Development Environments (IDEs) and code editors have a feature to search across available functionality and items in an open project. In JetBrains IDEs, this feature is called Search Everywhere: it allows users to search for files, actions, classes, symbols, settings, and anything from VCS history from a single entry point. However, it works with the candidates obtained by algorithms that don't account for semantics, e.g., synonyms, complex word permutations, part of the speech modifications, and typos. In this work, we describe the machine learning approach we implemented to improve the discoverability of search items. We also share the obstacles encountered during this process and how we overcame them.

The present paper extends the earlier results obtained by Abramov [`Conditions for recurrence and transience for time-inhomogeneous birth-and-death processes' \emph{Bull. Aust. Math. Soc.} \textbf{109} (2024), 393--402] for the case of time-inhomogeneous random walks, the increments of which take values in $\mathbb{R}$. By this, we give a full solution of the open problem formulated by Menshikov and Volkov [`Urn-related random walk with drift $\rho x^\alpha/t^\beta$' \emph{Electron. J. Probab.}, \textbf{13} (2008), paper No. 31, 944--960] that was partially solved in the aforementioned paper by Abramov., Comment: 10 pages of one and half spaced, bibl. 15, this substantial revision addresses the comments of the anonymous referee

In this paper we propose the notion of a transposed Poisson superalgebra. We prove that a transposed Poisson superalgebra can be constructed by means of a commutative associative superalgebra and an even degree derivation of this algebra. Making use of this we construct two examples of transposed Poisson superalgebra. One of them is the graded differential algebra of differential forms on a smooth finite dimensional manifold, where we use the Lie derivative as an even degree derivation. The second example is the commutative superalgebra of basic fields of the quantum Yang-Mills theory, where we use the BRST-supersymmetry as an even degree derivation to define a graded Lie bracket. We show that a transposed Poisson superalgebra has six identities that play an important role in the study of the structure of this algebra.

We propose a notion of a ternary skew-symmetric covariant tensor of 3rd order, consider it as a 3-dimensional matrix and study a ten-dimensional complex space of these tensors. We split this space into a direct sum of two five-dimensional subspaces and in each subspace there is an irreducible representation of the rotation group SO(3) -> SO(5). We find two independent SO(3)-invariants of ternary skew-symmetric tensors, where one of them is the Hermitian metric and the other is the quadratic form. We find the stabilizer of this quadratic form and its invariant properties. Making use of these invariant properties we define a SO(3)-irreducible geometric structure on a five-dimensional complex Hermitian manifold. We study a connection on a five-dimensional complex Hermitian manifold with a SO(3)-irreducible geometric structure, find its curvature and torsion. The structures proposed in this paper and their study are motivated by a ternary generalization of the Pauli's principle proposed by R. Kerner., Comment: 20 pages

For a linear difference equation with the coefficients being computable sequences, we establish algorithmic undecidability of the problem of determining the dimension of the solution space including the case when some additional prior information on the dimension is available., Comment: In memory of Marko Petkov\v{s}ek

The notion of lacunary infinite numerical sequence is introduced. It is shown that for an arbitrary linear difference operator L with coefficients belonging to the set R of infinite numerical sequences, a criterion (i.e., a necessary and sufficient condition) for the infinite dimensionality of its space $V_L$ of solutions belonging to R is the presence of a lacunary sequence in $V_L$., Comment: In memory of Marko Petkov\v{s}ek

Scalable quantum computers hold the promise to solve hard computational problems, such as prime factorization, combinatorial optimization, simulation of many-body physics, and quantum chemistry. While being key to understanding many real-world phenomena, simulation of non-conservative quantum dynamics presents a challenge for unitary quantum computation. In this work, we focus on simulating non-unitary parity-time symmetric systems, which exhibit a distinctive symmetry-breaking phase transition as well as other unique features that have no counterpart in closed systems. We show that a qutrit, a three-level quantum system, is capable of realizing this non-equilibrium phase transition. By using two physical platforms -- an array of trapped ions and a superconducting transmon -- and by controlling their three energy levels in a digital manner, we experimentally simulate the parity-time symmetry-breaking phase transition. Our results indicate the potential advantage of multi-level (qudit) processors in simulating physical effects, where additional accessible levels can play the role of a controlled environment., Comment: 20 pages, 10 figures

Xsuite is a newly developed modular simulation package combining in a single flexible and modern framework the capabilities of different tools developed at CERN in the past decades, notably Sixtrack, Sixtracklib, COMBI and PyHEADTAIL. The suite consists of a set of Python modules (Xobjects, Xpart, Xtrack, Xcoll, Xfields, Xdeps) that can be flexibly combined together and with other accelerator-specific and general-purpose python tools to study complex simulation scenarios. The code allows for symplectic modeling of the particle dynamics, combined with the effect of synchrotron radiation, impedances, feedbacks, space charge, electron cloud, beam-beam, beamstrahlung, and electron lenses. For collimation studies, beam-matter interaction is simulated using the K2 scattering model or interfacing Xsuite with the BDSIM/Geant4 library. Tools are available to compute the accelerator optics functions from the tracking model and to generate particle distributions matched to the optics. Different computing platforms are supported, including conventional CPUs, as well as GPUs from different vendors.

Transformer language models (LMs) are fundamental to NLP research methodologies and applications in various languages. However, developing such models specifically for the Russian language has received little attention. This paper introduces a collection of 13 Russian Transformer LMs, which spans encoder (ruBERT, ruRoBERTa, ruELECTRA), decoder (ruGPT-3), and encoder-decoder (ruT5, FRED-T5) architectures. We provide a report on the model architecture design and pretraining, and the results of evaluating their generalization abilities on Russian language understanding and generation datasets and benchmarks. By pretraining and releasing these specialized Transformer LMs, we aim to broaden the scope of the NLP research directions and enable the development of industrial solutions for the Russian language., Comment: LREC-COLING-2024

Modern large language models demonstrate impressive capabilities in text generation and generalization. However, they often struggle with solving text editing tasks, particularly when it comes to correcting spelling errors and mistypings. In this paper, we present a methodology for generative spelling correction (SC), which was tested on English and Russian languages and potentially can be extended to any language with minor changes. Our research mainly focuses on exploring natural spelling errors and mistypings in texts and studying the ways those errors can be emulated in correct sentences to effectively enrich generative models' pre-train procedure. We investigate the impact of such emulations and the models' abilities across different text domains. In this work, we investigate two spelling corruption techniques: 1) first one mimics human behavior when making a mistake through leveraging statistics of errors from particular dataset and 2) second adds the most common spelling errors, keyboard miss clicks, and some heuristics within the texts. We conducted experiments employing various corruption strategies, models' architectures and sizes on the pre-training and fine-tuning stages and evaluated the models using single-domain and multi-domain test sets. As a practical outcome of our work, we introduce SAGE(Spell checking via Augmentation and Generative distribution Emulation). It is a library for automatic generative SC that includes a family of pre-trained generative models and built-in augmentation algorithms., Comment: to appear in EACL 2024