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arXiv 2024年

作者： Russkikh, Ivan Volkov, Boris Pechen, Alexander Department of Mathematical Methods for Quantum Technologies Steklov Mathematical Institute of Russian Academy of Sciences 8 Gubkina Str. Moscow119991 Russia University of Science and Technology MISIS 4 Leninsky Prosp. Moscow119049 Russia Ivannikov Institute for System Programming The Russian Academy of Sciences Alexandra Solzhenitsyna str. 25 Moscow109004 Russia

Most general dynamics of an open quantum system is commonly represented by a quantum channel, which is a completely positive trace-preserving map (CPTP or Kraus map). Well-known are the representations of quantum channels by Choi matrices and by Kraus operator-sum representation (OSR). As was shown before, one can use Kraus OSR to parameterize quantum channels by points of a suitable quotient under the action of the unitary group of some complex Stiefel manifold. In this work, we establish a continuity relation (homeomorphism) between the topological space of quantum channels and the quotient of the complex Stiefel manifold. Then the metric on the set of quantum channels induced by the Riemannian metric on the Stiefel manifold is defined. The established relation can be applied to various quantum optimization problems. As an example, we apply it to the analysis of extrema points for a wide variety of quantum control objective functionals defined on the complex Stiefel manifolds, including mean value, generation of quantum gates, thermodynamic quantities involving entropy, *** Codes 81Q93 Copyright © 2024, The Authors. All rights reserved.

关键词： Quantum channel

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Epistemic Multiagent Reasoning with Collaborative Robots 37

Epistemic Multiagent Reasoning with Collaborative Robots

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37th Italian Conference on Computational Logic, CILC 2022

作者： Soldà, Davide Fabiano, Francesco Dovier, Agostino Constraint and Logic Programming Lab University of Udine Udine33100 Italy Embedding System Unit of Fondazione Bruno Kessler Trento38123 Italy Department of Mathematical Physical and Computer Sciences University of Parma Parma43124 Italy Department of Mathematics Computer Science and Physics University of Udine Udine33100 Italy

Over the last few years, the fields of Artificial Intelligence, Robotics and IoT have gained a lot of attention. This increasing interest has brought, among other things, to the development of autonomous multi-agent systems where robotic entities may interact with each other. As for all the other autonomous settings, also these systems require arbitration. Our work tries to address this problem by presenting a framework that embeds both a classical and a multi-agent epistemic (epistemic, for brevity) planner in a robotic control architecture. The idea is to combine the (i) classical and the (ii) epistemic solvers to model efficiently the interaction with: the (i) physical world and the (ii) information flows, respectively. In particular, the presented architecture starts by planning on the "epistemic level" refining then single-agent world-altering actions thanks to the classical planner. To further optimize the solving process, we also introduce the concept of macros in epistemic planning. Macros, in fact, have been successfully employed in classical planning as they allow for opportune aggregations of actions that may lead to a reduction of plans' length. Finally, the overall framework is exemplified and validated with two Franka Emika manipulators. This allowed us to empirically justify how the combination of the two planning approaches (classical and epistemic), and the introduction of macros, reduce the computational time required by the orchestrating phase. © 2022 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0)

关键词： Robot programming

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On the symbol calculus for multidimensional Hausdorff operators

arXiv

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arXiv 2023年

作者： Liflyand, E. Mirotin, A. Department of Mathematics Bar-Ilan University Ramat-Gan52900 Israel Department of Mathematics and Programming Technologies Francisk Skorina Gomel State University Gomel Belarus Regional Mathematical Center Southern Federal University Rostov-on-Don Russia

The aim of this work is to derive a symbol calculus on L2(n) for multidimensional Hausdorff operators. Two aspects of this activity result in two almost independent parts. While throughout the perturbation matrices are supposed to be self-adjoint and form a commuting family, in the second part they are additionally assumed to be positive definite. What relates these two parts is the powerful method of diagonalization of a normal Hausdorff operator elaborated earlier by the second named *** Codes 47B38 (Primary) 42B10 (Secondary) © 2023, CC BY.

关键词： Matrix algebra

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On greedy approximation in complex Banach spaces

arXiv

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arXiv 2024年

作者： Gasnikov, A. Temlyakov, V. Ivannikov institute for System Programming Russian Academy of Sciences Moscow Russia Steklov Mathematical Institute Russian Academy of Sciences Moscow Russia Innopolis University Tatarstan Russia University of South Carolina United States Lomonosov Moscow State University Russia Moscow Center of Fundamental and Applied Mathematics Russia

The general theory of greedy approximation with respect to arbitrary dictionaries is well developed in the case of real Banach spaces. Recently, some of results proved for the Weak Chebyshev Greedy Algorithm (WCGA) in the case of real Banach spaces were extended to the case of complex Banach spaces. In this paper we extend some of known in the real case results for other than WCGA greedy algorithms to the case of complex Banach spaces. Copyright © 2024, The Authors. All rights reserved.

关键词： Banach spaces

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An Artificial Neural Network Based Ensemble Model for Predicting Antigenic Variants: Application of Reduced Amino Acid Alphabets and Word2Vec

An Artificial Neural Network Based Ensemble Model for Predic...

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International Conference of Signal Processing and Intelligent Systems (ICSPIS)

作者： Majid Forghani Michael Khachay Artyom Firstkov Edward Ramsay Math. Programming Lab Krasovskii Institute of Math. & Mechanics Yekaterinburg Russia Combinatorial Algebra Lab Institute of Natural Sciences & Mathematics Ural Federal University Yekaterinburg Russia Mathematical Programming Lab Krasovskii Institute of Mathematics & Mechanics Yekaterinburg Russia Department of Scientific Productivity Saint Petersburg Pasteur Institute Saint Petersburg Russia

ISBN: (纸本)9781665476249

Assessment of antigenic similarity between strains of the influenza virus is a crucial factor when planning vaccine compositions. To perform this, a gold-standard laboratory procedure, hemagglutination inhibition assay, is conventionally used. Despite its theoretical importance and accuracy, this procedure suffers from several shortcomings, including high time consumption. Therefore, various computer-aided and mathematical methods have been developed to acquire earlier knowledge on the antigenic characteristics of currently circulating viruses. In this paper, we introduce a state-of-the-art ensemble artificial neural network model based on features derived from multi-representation of antigenicity. Generally, each feature is generated from an optimized convolutional neural network whose input describes the genetic difference between viruses in a specific numerical space. The space is determined based on embedding of the genetic sequence by a reduced amino acid alphabet and the Word2Vec framework. Our experiments indicated that the proposed model outperformed approaches from the literature by achieving an accuracy level of 0.933 for the HINI subtype. This implies possible application of our model as a promising exploratory tool in practical tasks of virus control.

关键词： Computer viruses Computational modeling Biological system modeling Influenza Predictive models Amino acids Genetics

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Evaluating Keyphrase Extraction Methods for Clustering Influenza-Related Scientific Papers

Evaluating Keyphrase Extraction Methods for Clustering Influ...

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International Conference of Signal Processing and Intelligent Systems (ICSPIS)

作者： Majid Forghani Artyom Firstkov Mohammad. M. AlyanNezhadi Kazem Forghani Mathematical Programming Lab. Krasovskii Institute of Mathematics & Mechanics Yekaterinburg Russia Department of Science University of Science and Technology of Mazandaran Behshahr Iran Computer Science Department Iran University of Science and Technology Tehran Iran

ISBN: (纸本)9781665476249

The number of annual scientific publications is growing year by year, which has led to the accumulation and formation of large databases. This increases the complexity of the search for relevant articles. Modern search engines leverage keyphrases to improve the performance of search results. Keyphrases (or keywords) are a set of single or multi-word expressions which provide a very compact summary of contents and describe the overall topic of a document. Implementation of keyphrase extraction can be varied for specific-domain databases. This motivated us to evaluate these methods on a database of influenza scientific literature. In this work, we considered 9 well known methods for extracting keyphrases. Our preliminary results show txhat graph-based methods which employ topics outperform others using our database. We also determined that influenza-related papers can be grouped into three general topics: public health & medical care; molecular biology & immunology; and phylogenetic & epidemiological studies.

关键词： Databases Immunology Biological system modeling Influenza Search engines Phylogeny Molecular biology

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Object recognition method based on logical correcting functions

Object recognition method based on logical correcting functi...

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2020 International Conference on Information Science and Communications Technologies, ICISCT 2020

作者： Kabulov, Anvar Urunboev, Erkin Saymanov, Islambek National University of Uzbekistan Named after Mirzo Ulugbek Dept. of Information Security Tashkent Uzbekistan Samarkand State University Dept. of Mathematical Modeling and Complex Programming Samarkand Uzbekistan

ISBN: (纸本)9781728199696

The article discusses the logical method of object recognition and the construction of corrective functions. To construct a logical method for classifying objects, the method for constructing the optimal continuation of logical correcting functions is used. An algorithm for the optimal continuation of logical correcting functions is constructed and an estimate of the complexity of the constructed algorithm is calculated. A theorem is proved that the search algorithm for the minimum upper zero of a Boolean monotone function mu_F(y_1, y_2, ldots, y_n) is in one-to-one correspondence with the problem of finding a minimal set of variables that is essential for a function F(x_1, x_2, ldots, x_n) that is not defined everywhere. © 2020 IEEE.

关键词： Object recognition

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Profit Maximization in a Gas Field Model 14

Profit Maximization in a Gas Field Model

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14th International Conference Management of Large-Scale System Development, MLSD 2021

作者： Skiba, Alexander Skiba, Nadezhda Federal Research Center 'Computer Science and Control' Russian Academy of Sciences Department of Mathematical Methods of Regional Programming Moscow Russia Kuban State Technological University Institute of Oil Gas and Energy Ministry of Science and Higher Education Department of Oil and Gas Business Named after Prof Vartumyan G. T. Krasnodar Russia

ISBN: (纸本)9781665412308

We consider a dynamic continuous gas production at a deposit. We set and solve the optimization control problem for maximum profit, taking into account the discount factor. The problem posed relates to some optimal control problems with a mixed constraint with a fixed time and an unbounded right endpoint. We use the principle of Pontryagin maximum in the Arrow form. © 2021 IEEE.

关键词： Deposits

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Finite groups whose n-maximal subgroups are σ-subnormal

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Science China Mathematics 2019年第7期62卷 1355-1372页

作者： Wenbin Guo Alexander N. Skiba School of Mathematical Sciences University of Science and Technology of China Hefei 230026 China Department of Mathematics and Technologies of Programming Francisk Skorina Gomel State University Gomel 246019 Belarus

Let σ={σi | i ∈ I} be some partition of the set of all primes P. A set H of subgroups of G is said to be a complete Hall σ-set of G if every member ≠ 1 of H is a Hall σi-subgroup of G, for some i ∈ I, and H contains exactly one Hall σi-subgroup of G for every σi ∈σ(G). A subgroup H of G is said to be:σ-permutable or σ-quasinormal in G if G possesses a complete Hall σ-set H such that HAx= AxH for all A ∈ H and x ∈ G:σ-subnormal in G if there is a subgroup chain A = A0≤A1≤···≤ At = G such that either Ai-1■Ai or Ai/(Ai-1)Ai is a finite σi-group for some σi ∈σ for all i = 1,..., *** Mn < Mn-1 <···< M1 < M0 = G, where Mi is a maximal subgroup of Mi-1, i = 1, 2,..., n, then Mn is said to be an n-maximal subgroup of G. If each n-maximal subgroup of G is σ-subnormal(σ-quasinormal,respectively) in G but, in the case n > 1, some(n-1)-maximal subgroup is not σ-subnormal(not σ-quasinormal,respectively) in G, we write mσ(G)= n(mσq(G)= n, respectively).In this paper, we show that the parameters mσ(G) and mσq(G) make possible to bound the σ-nilpotent length lσ(G)(see below the definitions of the terms employed), the rank r(G) and the number |π(G)| of all distinct primes dividing the order |G| of a finite soluble group G. We also give the conditions under which a finite group is σ-soluble or σ-nilpotent, and describe the structure of a finite soluble group G in the case when mσ(G)=|π(G)|. Some known results are generalized.

关键词： finite group n-maximal subgroup σ-subnormal subgroup σ-quasinormal subgroup σ-soluble group σ-nilpotent group

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Optimal control of solutions to showalter–sidorov problem for a high order sobolev type equation with additive "noise" 3rd

Optimal control of solutions to showalter–sidorov problem f...

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3rd Semigroups of Operators: Theory and Applications Conference, SOTA 2018

作者： Zamyshlyaeva, Alyona A. Tsyplenkova, Olga N. Department of Applied Mathematics and Programming South Ural State University 76 Lenin ave Chelyabinsk454080 Russia Department of Mathematical Physics Equations South Ural State University 76 Lenin ave Chelyabinsk454080 Russia

ISBN: (纸本)9783030460785

In this paper, the problem of optimal control of solutions to the Showalter–Sidorov problem for a high-order Sobolev type equation with additive "noise" is investigated. The existence and uniqueness of a strong solution to the Showalter–Sidorov problem for this equation are proved. Sufficient conditions for the existence and uniqueness of an optimal control of such solutions are obtained. For this, we built the space of "noises". For the differentiation of additive "noise", we use the derivative of a stochastic process in the sense of Nelson–Gliklikh. © Springer Nature Switzerland AG 2020.

关键词： Stochastic systems

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