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As significant vehicles for applying fuzzy set theories, fuzzy inference systems (FISs) have been widely utilized in artificial intelligence. However, challenges such as computational complexity and subjective design persist in FIS implementation. To address these issues, this paper introduces the fuzzy inference system based on axiomatic fuzzy sets (FIS-AFSs), which includes a fuzzy rule base and a fuzzy inference engine. This system eliminates the need for subjective decisions in the selection of fuzzification and defuzzification methods. The theoretical foundation of the approach involves defining the multi-dimensional vague partition (VP) of the multi-dimensional universe using an overlap function to aggregate one-dimensional VPs. Additionally, an axiomatic fuzzy set (AFS) on the multi-dimensional universe is defined. Building on this foundation, algorithms for single-input single-output (SISO) and multi-input single-output (MISO) fuzzy inference are developed using AFSs, eliminating the need for subjective fuzzy implication operators. The FIS-AFSs, with its universal approximation property and theoretical approximation precision, are then analyzed. Experimental tests are conducted to evaluate the approximation capabilities of the FIS-AFSs. Results from both theoretical analysis and experimental testing demonstrate that FIS-AFSs can achieve high approximation precision. [ABSTRACT FROM AUTHOR]

In our daily life, players may reduce their cooperation levels for various reasons. This paper studies how to evaluate and allocate the cooperation payoff when the players cooperate partially. Different from previous research that directly uses the cooperation level to calculate the payoffs of fuzzy coalitions, we introduce the concept of dual fuzzy cooperative games, where the payoffs of fuzzy coalitions equal the difference between the original payoff and the lost payoff caused by the decline of the cooperation level. Meanwhile, the dual Shapley value is introduced, and its axiomatic systems are studied. Further, a special kind of dual fuzzy cooperative game with Choquet integral form is presented. Finally, we provide an application of dual fuzzy cooperative games in the manufacturer–retailer supply chain to allocate the payoff for vertical co-op advertising. [ABSTRACT FROM AUTHOR]

This document provides a comprehensive review of the classification and structure of finite-dimensional simple right-alternative superalgebras. It explores the application of superalgebras in ring theory and the construction of a meaningful structural theory. The document covers various types of superalgebras, including associative superalgebras, commutative alternative superalgebras, and Abelian superalgebras, providing definitions, examples, and classifications. It also discusses the properties and decomposition of different types of superalgebras based on their even parts, as well as the structure of singular superalgebras. The document includes mathematical proofs, examples, and open questions for further research. [Extracted from the article]

This article explores the automorphisms of a Chevalley group of type G2 over a commutative ring R. The authors demonstrate that every automorphism of this group, when R is generated by the invertible elements and the ideal 2R, can be expressed as a combination of ring and inner automorphisms. The paper offers a historical overview of the study of automorphisms of classical groups and Chevalley groups, as well as the methods employed in previous research. The authors introduce definitions and main theorems related to Chevalley groups and their automorphisms. The text focuses on automorphisms of the group Gad(G2, R) and their properties, defining ring automorphisms and inner automorphisms, and establishing standard automorphisms as compositions of these two types. The primary objective is to prove that any automorphism of the group Gad(G2, R) is standard. The text also covers definitions and theorems concerning the localization of rings and modules, isomorphisms of Chevalley groups over fields, and the characteristic subgroup Ead(G2, R) in Gad(G2, R). The main theorem's proof is outlined in several steps, including the embedding of the ring R into a product of its localizations and the mapping of elements under conjugation by an element of Gad(G2, S). Additionally, a lemma is proven that demonstrates the mapping of matrices under conjugation by an element of Gad(G2, S) [Extracted from the article]

The article titled "Evald Ilyenkov: 'On the State of Philosophy [Letter to the Central Committee of the Party]'" provides an analysis of the current state of philosophy and its role in the communist transformation of the world. The author argues that philosophy's influence is diminishing, with other schools and concepts gaining more prominence. They criticize the dominance of neopositivism in the natural sciences and the rise of anthropological and existential approaches in the humanities. The author also highlights the confusion surrounding the understanding of philosophy as a distinct science and calls for the development of a theory of dialectics before philosophers can intervene in other sciences. The text also discusses the training of philosophical cadres at Moscow State University, criticizing the lack of clarity and neglect of dialectical materialism in current philosophical education. [Extracted from the article]

In this essay, I critically analyze Wittgenstein's dispensation with " = " in a correct concept-script. I argue inter alia (a) that in the Tractatus the alleged pseudo-character of sentences containing " = " or = -sentences remains largely unexplained and propose how it could be explained; (b) that at least in some cases of replacing = -sentences with equivalent identity-sign free sentences the use of the notion of a translation seems inappropiate; (c) that in the Tractatus it remains unclear how identity of the object as that which is expressed by identity of the sign should be understood specifically; (d) that there are = -sentences which have no obvious equivalent in Wittgenstein's novel notation; (e) that Wittgenstein's adherence to (non-relational) identity, although he dispenses with " = ", is probably motivated by his desire to ensure that the expressive power of an identity-sign free concept-script of first-order is on a par with standard first-order logic containing " = ". In the concluding section, I critically discuss some claims in Lampert and Säbel (The Review of Symbolic Logic, 14, 1–21, 2021) and defend Wehmeier's account of pseudo-sentences in the Tractatus (2012) against the objections they raise. [ABSTRACT FROM AUTHOR]

Rough sets (RSs) and fuzzy sets (FSs) are designed to tackle the uncertainty in the data. By taking into account the control or reference parameters, the linear Diophantine fuzzy set (LD-FS) is a novel approach to decision making (DM), broadens the previously dominant theories of the intuitionistic fuzzy set (IFS), Pythagorean fuzzy set (PyFS), and q-rung orthopair fuzzy set (q-ROFS), and allows for a more flexible representation of uncertain data. A promising avenue for RS theory is to investigate RSs within the context of LD-FS, where LD-FSs are approximated by an intuitionistic fuzzy relation (IFR). The major goal of this article is to create a novel method of roughness for LD-FSs employing an IFR over dual universes. The notions of lower and upper approximations of an LD-FS are established by using an IFR, and some axiomatic systems are carefully investigated in detail. Moreover, a link between LD-FRSs and linear Diophantine fuzzy topology (LDF-topology) has been established. Eventually, based on lower and upper approximations of an LD-FS, several similarity relations are investigated. Meanwhile, we apply the recommended model of LD-FRSs over dual universes for solving the DM problem. Furthermore, a real-life case study is given to demonstrate the practicality and feasibility of our designed approach. Finally, we conduct a detailed comparative analysis with certain existing methods to explore the effectiveness and superiority of the established technique. [ABSTRACT FROM AUTHOR]

This paper proposes a robust image encryption algorithm that utilizes a Novel three-dimensional (3D) Chaotic map and an Enhanced Logistic Sine System (ELSS). We leverage the unpredictability of 3D chaotic dynamics alongside the complexity of ELSS and DNA Sequence to forge a formidable image encryption scheme. Firstly, the image pixels are converted from decimal to hexadecimal notation and sorted in a 1D pixel array carrying a unique sequence of three channels of the RGB image. Secondly, the secret key is appended to XOR, the values with that 1-D pixels array. Thirdly, values are sorted by performing the binary right shift operation and encoded into DNA. Fourthly, a novel chaotic map is used to perform scrambling operations. Lastly, a novel enormous keyspace ELSS is used to perform efficient Border and Cross-Border (B &CB) pixel exchange, further enhancing the encryption quality of the proposed algorithm. Comprehensive security analysis proved that the proposed algorithm exhibits remarkable resilience against powerful known and chosen plaintext attacks and other prevalent cryptanalysis attacks, including differential attacks and exhaustive key search attacks. Henceforth, the proposed algorithm's superior security and low computational cost make it an ideal choice for real-time secure image communication across various platforms, including satellite, multimedia, and military communications. [ABSTRACT FROM AUTHOR]

The semiconductor industry has encountered the physical constraints of current semiconductor materials and the impending end of Moore's forecast. The recent edition of the International Roadmap for Devices and Systems reveals that the semiconductor industry is now combining More Moore, More than Moore and Beyond CMOS to explore the possibilities towards emerging nanotechnologies like Quantum Cellular Automata (QCA). The fast-working speed, extremely low energy and high packing density make QCA incredibly appealing. In this work, machine learning-based models are developed to predict the energy dissipation of LT universal logic gates in advance with single-cell displacement defect (SCDD) and cell polarisation. Firstly, the cell-wise energy components of the universal logic gates realised by Layered T (LT) and Majority voter (MV) and logic reduction methodologies are estimated utilising the coherence vector (watt/energy) simulation engine of QCADesigner-E. Then, SCDD is introduced at the output LT universal gates in the horizontal and vertical directions, and consequent deviation in output cell polarisation and energy dissipation are examined. A dataset, namely scdd_polarisation_energy (SPE), is created. In particular, K-Nearest Neighbour, Random Forest and Polynomial Regression-based machine learning (ML) models are found to be competent to anticipate the energy dissipation of LT universal logic gates. In ML models, the SCDD at the output cell and output polarisation are used as estimators, and energy dissipation (in electron Volt) is utilised as a response. These models offer less-complex and ease the energy estimation process in the QCA layout. The models are assessed based on r2-score, mean absolute error (MAE), mean squared error (MSE), and root mean squared error (RMSE). [ABSTRACT FROM AUTHOR]

Realizability notions in mathematical logic have a long history, which can be traced back to the work of Stephen Kleene in the 1940s, aimed at exploring the foundations of intuitionistic logic. Kleene's initial realizability laid the ground for more sophisticated notions such as Kreisel's modified realizability and various modern approaches. In this context, our work aligns with the lineage of realizability strategies that emphasize the accumulation, rather than the propagation of precise witnesses. In this paper, we introduce a new notion of realizability, namely herbrandized modified realizability. This novel form of (cumulative) realizability, presented within the framework of semi-intuitionistic logic is based on a recently developed star combinatory calculus, which enables the gathering of witnesses into nonempty finite sets. We also show that the previous analysis can be extended from logic to (Heyting) arithmetic. [ABSTRACT FROM AUTHOR]

Today, almost all information processing is performed using electronic logic circuits operating at several gigahertz frequency. All-optical logic holds the promise to allow for up to three orders of magnitude higher speed. Whereas essential all-optical transistor functionalities were demonstrated across a range of platforms, utilising them to implement a complete Boolean logic gate set and in particular negation, i.e. switching off an optical signal with another, weaker, optical signal, poses a major challenge. Here, we realize a cascadable NOT gate by introducing the concept of non-ground-state polariton amplification in organic semiconductor microcavities under non-resonant optical excitation. We unravel the importance of vibron-mediated stimulated scattering in room temperature operation of the inverter. Moreover, we extend the concept to a multi-input universal NOR logic gate, where in the presence of any of the input signals non-ground-state amplification supersedes spontaneous ground-state condensation, resulting in a NOR gate with ~1 ps switching time. The realisation of an ultrafast universal logic gate constitutes an essential step for more complex optical circuitry that could boost information processing applications. A cascadable all-optical NOT gate is a requirement for full-logic in optical computing. By introducing the concept of non-ground-state polariton amplification in organic semiconductor microcavities, the authors realized the operation of an all-optical cascadable universal gate. [ABSTRACT FROM AUTHOR]

This paper continues the research on the circuit synthesis problem for a multiplexer function of logic algebra, which is a component of many integrated circuits and is also used in theoretical study. The exact value of the depth of a multiplexer with select lines in the standard basis is found under the assumption that the conjunction and disjunction gates are of depth 1 and the negation gate is of depth 0; the depth equals if . Thus, it follows from previous results that the exact depth value equals for all positive integers such that either or . Moreover, for , this value equals 2, and for , it equals either or . Similar results are also obtained for a basis consisting of all elementary conjunctions and elementary disjunctions of two variables. [ABSTRACT FROM AUTHOR]

"The Bedrock of Logical Thought" was a television show produced in 1957 by NBC and ETRC with the goal of promoting interest in mathematics among young people. The show featured mathematicians Clifton Fadiman and John Wilder discussing the axiomatic method and its applications. Recently, the script for the show was discovered in the Archives of American Mathematics, providing insight into the history of mathematics on television in the 1950s. The show was well-received by viewers, including teachers, students, and families, who appreciated the opportunity to learn about mathematics in an engaging and accessible way. This article emphasizes the significance of educational television in reaching a broad audience and fostering interest in mathematics. [Extracted from the article]

This text explores the relationship between mathematicians Georg Cantor and Richard Dedekind and their differing perspectives on set theory. Cantor saw sets as vast and infinite, while Dedekind viewed them as closed and finite. Cantor sought Dedekind's support for his ideas on inconsistent sets, but Dedekind was not interested. Cantor's mental health declined, and he sought a position outside of academia. Despite their differences, both mathematicians made important contributions to the field of set theory. [Extracted from the article]

This paper examines the logic of conditional obligation, which originates from the works of Hansson, Lewis, and others. Some weakened forms of transitivity of the betterness relation are studied. These are quasi-transitivity, Suzumura consistency, acyclicity and the interval order condition. The first three do not change the logic. The axiomatic system is the same whether or not they are introduced. This holds true under a rule of interpretation in terms of maximality and strong maximality. The interval order condition gives rise to a new axiom. Depending on the rule of interpretation, this one changes. With the rule of maximality, one obtains the principle known as disjunctive rationality. With the rule of strong maximality, one obtains the Spohn axiom (also known as the principle of rational monotony, or Lewis' axiom CV). A completeness theorem further substantiates these observations. For interval order, this yields the finite model property and decidability of the calculus. [ABSTRACT FROM AUTHOR]

Although the subjective expected utility (SEU) theory is more than 60 years old, it was recently discovered by Hartmann (Econometrica 88(1):203–205, 2020, https://doi.org/10.3982/ECTA17428) that one of the original seven postulates is redundant, i.e., it is implied by the other six postulates. In this brief communication, we show that this redundant axiom is the only one that is implied by the other axioms, thereby establishing that the remaining six postulates form an independent axiomatic system. This result further streamlines the preference assumptions underlying the SEU theory. [ABSTRACT FROM AUTHOR]

Efim Zelmanov is a Russian-American mathematician who has made significant contributions to the field of algebra. He received his PhD from Novosibirsk State University and has held positions at various universities in the United States, Korea, and China. Zelmanov specializes in combinatorial problems of nonassociative algebra and group theory and was awarded the Fields Medal in 1994 for his solution of the restricted Burnside problem. He has been a member of prestigious scientific academies and has had influential mentors throughout his career. Zelmanov has also been involved in outreach activities to promote mathematics and is currently based in China. [Extracted from the article]

Medical images contain very sensitive and confidential information about the patient and are huge in terms of size. Therefore, there is a need to develop encryption schemes that reduce computational time without compromising the security level. Selective image encryption is one such technique that can reduce time and complexity. In this paper, we propose a selective image encryption scheme that can be used to encrypt medical images. The medical image is first decomposed into non-overlapping blocks, and then the variance of each block is calculated and compared to a preset threshold value. The blocks for which variance is greater than the threshold value are considered significant and encrypted. The pixels within each significant block are permutated with a hybrid sequence (which is different for each block) obtained from Logistic maps. The diffusion operation is performed using a different hybrid sequence obtained from a 1-D Logistic map and a 3-D Lorenz map, which also is different for every block. Finally, the cipher image is formed by concatenating the encrypted significant and insignificant blocks. The proposed encryption scheme has been tested on several grayscale and color medical images to validate its performance in terms of security provided and computational time. It has been found resilient to differential cryptanalysis, as the NPCR and UACI values are greater than 99.60% and 33.20%, respectively besides having a large key space of the order of 10 108. The PSNR values for all encrypted images are less than 12 dB even though the images are selectively encrypted, and the entropy of the Region of Interest (ROI), i.e., encrypted blocks, is nearly equal to 8, which signifies a better security of our system. The computational time required to encrypt an image of sizes 225 × 225 and 512 × 512 is 0.06 and 0.10 s respectively making it suitable for real time applications. The experimental results show that the proposed encryption scheme provides high security with less complexity and computational time. [ABSTRACT FROM AUTHOR]

Soft rough based on covering S R C theory has become a useful and well-known area of research in theories of uncertainty. The present work follows up on this flourishing research topic. We introduce a new model of S R C in a fusion of soft set theory S S T and rough set depending on covering C R S . We put forth a definition of soft rough covering approximation space S C A S via neighborhood concept. Some axiomatic systems of our model of S R C are discussed. We study the relationship between our model of S R C and three other S R C -models. An algorithm for reduction of the attributes of the information systems using S C A S is established. Based on the theoretical discussion, we set forth some applications of our model which will be helpful in decision making process via S R C theory. [ABSTRACT FROM AUTHOR]

For the design of the public-key exchange protocol, a chaos-based Triple-Layer Tree Parity Machine (TLTPM) directed group neural synchronization is presented in this study. For neural synchronization, a particular neural network structure called Tree Parity Machine (TPM) is utilized. Two TPMs take the same input but have distinct weight vectors, and update the weights using the neural learning algorithm by swapping output. It leads to perfect synchronization in certain phases, with the weights of the two TPMs becoming identical. The secret key is made up of these similar weights. However, there has not been much research on the randomness of the common input vector utilized in the synchronization process. A logistic chaotic system based on TLTPM is proposed in this paper. This proposed TLTPM model has several advantages like (1) leverages logistic chaos produced random common input vector for quicker synchronization. (2) With the same input, output, and hidden neurons, the suggested TLTPM model is quicker and more secure than TPM. (3) A binary tree framework considers each neural network as a node. (4) When the binary tree's i-th and j-th nodes are synchronized, one of these two nodes is chosen as the leader. (5) This leader node will now coordinate with the other branch's leader. After this procedure is completed, the coordinated weight has now become the cluster's session key. (6) And no need to synchronize each neural network in the group; rather, by coordinating between the elected leader nodes with just logarithmic synchronization steps, the whole group may share the same secret key. A variety of parametric tests have been performed on the suggested approach. The results were compared to some more contemporary methods. The suggested technique's findings have proven that it has both effective and resilient potential. [ABSTRACT FROM AUTHOR]

The article discusses the marginalization of philosopher Charles Peirce in the mainstream philosophy of science and the history of philosophy of science. The author reviews T.L. Short's book, "Charles Peirce and Modern Science," which aims to reintroduce Peirce as a philosopher of science. Short argues that Peirce wrote philosophy as a scientist, not a traditional philosopher, and emphasizes the centrality of science in Peirce's philosophy. The article also examines Peirce's conception of science as a restless spirit of inquiry and explores his views on system building and the pragmatic maxim. However, the author raises concerns about Short's defense of science and its implications for moral guidance. [Extracted from the article]

The biennial "Computer Sciences and Information Technologies" conference in Yerevan in September of 2023 was the 14th in this series. This event is of regional interest, provide a networking ecosystem to scientists in areas such as the Mathematical Logic and Logical Reasoning, Discrete Mathematics, Pattern Recognition and Cognitive Sciences, and Applications. 17 selected papers of this conference, included in Special Issue of PRIA journal provide up to date research results and research topics that make a sensitive input to the field known as "Logic Combinatorial Pattern Recognition". Results from Algebra and Mathematical Logic help in structural and semantic areas of pattern recognition, graph theoretical investigations help with clustering and image analysis, other selected papers and results are devoted directly to semantic pattern recognition, to cognitive sciences in general, or they provide application platforms where different artificial intelligence technologies are converging. [ABSTRACT FROM AUTHOR]

There is a well-known gap between metamathematical theorems and their philosophical interpretations. Take Tarski's Theorem. According to its prevalent interpretation, the collection of all arithmetical truths is not arithmetically definable. However, the underlying metamathematical theorem merely establishes the arithmetical undefinability of a set of specific Gödel codes of certain artefactual entities, such as infix strings, which are true in the standard model. That is, as opposed to its philosophical reading, the metamathematical theorem is formulated (and proved) relative to a specific choice of the Gödel numbering and the notation system. A similar observation applies to Gödel's and Church's theorems, which are commonly taken to impose severe limitations on what can be proved and computed using the resources of certain formalisms. The philosophical force of these limitative results heavily relies on the belief that these theorems do not depend on contingencies regarding the underlying formalisation choices. The main aim of this paper is to provide metamathematical facts which support this belief. While employing a fixed notation system, I showed in previous work (Review of Symbolic Logic, 2021, 14(1):51–84) how to abstract away from the choice of the Gödel numbering. In the present paper, I extend this work by establishing versions of Tarski's, Gödel's and Church's theorems which are invariant regarding both the notation system and the numbering. This paper thus provides a further step towards absolute versions of metamathematical results which do not rely on contingent formalisation choices. [ABSTRACT FROM AUTHOR]

This paper investigates the implicative conditional, a connective intended to describe the logical behavior of an empirically defined class of natural language conditionals, also named implicative conditionals, which excludes concessive and some other conditionals. The implicative conditional strengthens the strict conditional with the possibility of the antecedent and of the contradictory of the consequent. p ⇒ q is thus defined as ¬ ◊ (p ∧ ¬ q) ∧ ◊ p ∧ ◊ ¬ q . We explore the logical properties of this conditional in a reflexive normal Kripke semantics, provide an axiomatic system and prove it to be sound and complete for our semantics. The implicative conditional validates transitivity and contraposition, which we take to be integral parts of reasoning and communication. But it only validates restricted versions of strengthening the antecedent, right weakening, simplification, and rational monotonicity. Apparent counterexamples to some of these properties are explained as due to contextual factors. Finally, the implicative conditional avoids the paradoxes of material and strict implication, and validates some connexive principles such as Aristotle's theses and weak Boethius' thesis, as well as some highly entrenched principles of conditionals, such as conjunction of consequents, disjunction of antecedents, modus ponens, cautious monotonicity and cut. [ABSTRACT FROM AUTHOR]

A nonlinear integral equation arising from a parametric closure of the third spatial moment in the single-species model of logistic dynamics of U. Dieckmann and R. Law is analyzed. The case of piecewise constant kernels is studied, which is important for further computer modeling. Sufficient conditions are found that guarantee the existence of a nontrivial solution to the equilibrium equation. The use of constant kernels makes it possible to obtain more accurate results compared to earlier works, in particular, more accurate estimates for the L1 norm of the solution and for the closure parameter are obtained. [ABSTRACT FROM AUTHOR]

Image denoising techniques are very important in modern digital image processing. Many classical denoising algorithms have evolved over the years, such as Butterworth filter, Mean filter, Median filter, Laplacian filter, Multidimensional filter, Gaussian filter and Wiener filter. In this paper, a new method of removing high density salt and pepper noise is proposed via using Lukasicwicz algebra with square root (MV-algebra) and fuzzy logic function for digital images. In the proposed method, a new constructed fuzzy logic function in MV-algebra is used to remove the salt and pepper noise in contaminated images. The proposed method is called LASRNM, which has a strong mathematical foundation and strong robustness in removing salt and pepper noise. Therefore, experiments on five datasets illustrate that our proposed LASRNM method works the best in high density salt and pepper noise situation in terms of the peak signal noise ratio (PSNR), signal to noise ratio (SNR) and structural similarity (SSIM). [ABSTRACT FROM AUTHOR]

Maxwell's verbal statement of Coulomb's experimental verification of his hypothesis, concerning force between two electrified bodies, is suggestive of a modification of the respective computable expression on logical grounds. This modification is in tandem with the completeness condition for a physical theory, that was stated by Einstein, Podolsky and Rosen in their seminal work. Working with such a modification, I show that the first Maxwell's equation, symbolically identifiable as ∇ · E = ρ / ϵ 0 from the standard literature, is unprovable. This renders Poynting's theorem to be unprovable as well. Therefore, the explanation of 'light' as 'propagation of electromagnetic energy' comes into question on theoretical grounds. [ABSTRACT FROM AUTHOR]

Floating-point arithmetic is a well-known and extremely efficient way of performing approximate computations over the real numbers. Although it requires some careful considerations, floating-point numbers are nowadays routinely used to prove mathematical theorems. Numerical computations have been applied in the context of formal proofs too, as illustrated by the CoqInterval library. But these computations do not benefit from the powerful floating-point units available in modern processors, since they are emulated inside the logic of the formal system. This paper experiments with the use of hardware floating-point numbers for numerically intensive proofs verified by the Coq proof assistant. This gives rise to various questions regarding the formalization, the implementation, the usability, and the level of trust. This approach has been applied to the CoqInterval and ValidSDP libraries, which demonstrates a speedup of at least one order of magnitude. [ABSTRACT FROM AUTHOR]

Interpretation is commonly used in mathematical logic to compare different theories and identify cases where two theories are for almost all intents and purposes the same. Similar techniques are used in the comparison between alternative logics although the links between these approaches are not transparent. This paper generalizes theoretical comparison techniques to the case of logical comparison using an extremely general approach to semantics that provides a very generous playing field upon which to make our comparisons. In particular, we aim to develop the useful idea that interpretations should determine inner models. [ABSTRACT FROM AUTHOR]

The review presents the history of the creation and work of the Scientific Council "Cybernetics" (SCC)—the center for development of cybernetics in the USSR and Russia. The Council's activity is covered as a structure that coordinates scientific and technical activity in cybernetics in the country via a system of sections: about 16 public and professional bodies involving thousands of specialists. Brief information about the sections is given. The chronology of development of the SCC is discussed, in particular, information about its chairmen, starting with the renowned organizer of research and development, Academician and Admiral Axel Ivanovich Berg and the following academicians: B.N. Petrov, O.M. Belotserkovsky, A.P. Ershov, E.P. Velikhov, B.V. Bunkin, and Yu.I. Zhuravlev. The SCC's publishing activity is briefly reviewed. The second function, built into the SCC from its onset, is as a research institute conducting its own research on the most pressing scientific problems insufficiently covered by existing structures. Several main areas of research by the SCC itself and its successor, the Axel Berg Institute of Cybernetics and Educational Computing of the Federal Research Center "Computer Science and Control" of the RAS: coding and transmission of information, economic cybernetics, aircraft control, supercomputers, digital technologies in education, mathematical logic and the theory of algorithms, pattern recognition and image analysis, mathematical methods of image analysis, theoretical physics, biomedical cybernetics, and ultrasound imaging. Another function of the SCC is considered: as an incubator of new academic industrially oriented structures and the fate of one of them—the Institute of Cybernetics Problems—is traced. [ABSTRACT FROM AUTHOR]

Background: Approximately 90% of the global human population have access to a supply of electrical energy. Existing national electrical energy supply systems possess good technical availability but with significant system-inherent risks. The latter show their effects in the systems' operational behaviour, their impact on the national economy and on the global climate. National electrical energy supply systems in their current state can therefore not be considered sustainable. This invites the question, "can there be a national electrical energy supply system that is simultaneously technologically, economically and environmentally sustainable?". Main text: The contents of this article are of a fundamental nature. They start from a newly established axiomatic system for multiple-sustainable electric energy systems. The axioms contain no dependencies on individual users, nation states or technologies. For the transition into a sustainable energy system, core challenges faced by existing systems are synthesized, the fulfillment of which determines the feasibility of future systems. We state that anthropogenically generated electrical energy is a product possessing a cultural-technical significance. In this article, the possibilities arising from the physical fundamentals are considered. In addition, a new control system is developed that integrates user impact, quality assurance and cost developments in order to show a means to multiple-sustainable energy supply systems. An essential component of the control system is a unified view of energy production and energy transport. This also includes a transition from the previous, technology-dominated energy supply system into a new system for which the relevant social concerns are primary. One axiom deals with the economic concerns of management organizations of national electrical energy systems. At first, only the monetary working hypothesis is formulated, whereby organizations within the energy economy must be decoupled from basic business principles. Detailed discussions will be dealt with in a further article. Conclusions: Through the transition from a technology-defined to a user-defined electrical energy supply system, the system-immanent risks in the operational behaviour, the national economy and the climate can be avoided simultaneously in an ideal complementary combination. Building upon the physical solution space, the quality-assured control process, which contains a systematic cost-reversal and a central focus upon the cultural-technical product of electrical energy, ensures such a transition is achievable by means of fulfillment of the core challenges. For these fundamental statements, which refer to the transformation into a future system, detailed explanations of organizational units are not yet necessary since they are not subject to any natural-scientific restrictions. However, they are essential for the post-transformation process. [ABSTRACT FROM AUTHOR]

As finance minister, Hibbert accompanied President Vincent to a meeting in 1934 in Washington, D.C., with the American president Franklin Delano Roosevelt to negotiate the end of the United States' nineteen-year occupation of Haiti and to plan for its fiscal and economic policies post occupation. Hibbert delivered a paper, I La Connaissance et les Mathématiques i (Knowledge and Mathematics) [[26]], on the philosophy of mathematics and particularly on the nature of mathematics. While Hibbert was rector of the University of Haiti, although not involved in major mathematical research, he remained connected with Arnaud Denjoy (one of those whom he acknowledged in his thesis), who was invited to Haiti in 1948 as an official guest of the government. Back in Haiti, Hibbert returned to teaching: physics at the school of medicine, mathematics at the school of applied sciences, and statistics at the law school [[41]]. [Extracted from the article]

Digital data plays a paramount part in various fields of life, in which multimedia data represent the majority of transferred digital data via communication networks. Consequently, cryptographers and researchers have paid attention to the security of multimedia. Chaotic models are utilised intensely with optimisation techniques for designing modern multimedia cryptosystems, but the role of optimisation approaches is to improve experimental outcomes rather than complex computations in designing cryptosystems. Amidst the rapid evolution of quantum resources, current multimedia cryptosystems may be cracked because their construction relies on mathematical paradigms. This paper introduces a robust image cryptosystem that leverages bit-level permutation, particle swarm optimization, the 3D logistic system, and quantum walk. In the presented cryptosystem, the probability distribution generated by quantum walk and the chaotic sequences produced by the 3D logistic function are utilized as inputs for a customized particle swarm optimization algorithm. The resulting keystreams are then employed in both the permutation phase (at the pixel and bit levels) and substitution phase of the image cryptosystem. Experimental results indicate that the suggested cryptosystem has high-security contra different raids such as differential, statistical, and occlusion attacks. The average outcome for local entropy, global entropy, NPCR (Number of Pixel Change Rate), UACI (Unified Average Changed Intensity), Chi-square, and encryption speed are measured at 7.9025, 7.99985, 99.61306%, 33.4657%, 256.960725, and 1.7081 megabits per second, respectively. [ABSTRACT FROM AUTHOR]

Uncertainty theory is an area in axiomatic mathematics recently proposed by Professor Baoding Liu and aiming to deal with belief degrees. Retrieving 1004 journal articles from the Web of Science database between 2008 and 2019, and utilizing CiteSpace and Pajek software, we analyze the publications per year and by geographical distribution, productive scholars and their cooperation, key journals, highly cited articles and main paths of the field. In this way, seven key sub-fields of uncertainty theory and their research potential are derived. The results show the following: (1) The literature on uncertainty theory follows a linear growth trend, involves an extensive network of 1000 scholars worldwide and is published in 300 journals, indicating thus that uncertainty theory has become increasingly attractive, and its academic influence is gradually expanding. (2) Seven key sub-fields of uncertainty theory have clearly been identified, including the axiomatic system, uncertain programming, uncertain sets, uncertain logic, uncertain differential equations, uncertain risk analysis, and uncertain processes. Among them, uncertain differential equations and programming are the two main sub-fields with the largest numbers of published papers. Furthermore, for evaluating the research potential of sub-fields, maturity and recent attention indicators are calculated using the citations, total number of publications, quantity of most cited literature and half-life. Based on these indicators, uncertain processes shows the greatest development potential, and has remained a hot topic in recent years, being mainly concentrated on the uncertain renewal reward process, optimal control of discrete-time uncertain systems, and uncertain linear quadratic optimal control. Additionally, uncertain risk analysis is ranked second, and focuses on the analysis of expected losses, investment risk, and structural reliability of uncertain systems. [ABSTRACT FROM AUTHOR]

Representationalist accounts of mental content face the threat of the homunculus fallacy. In collapsing the distinction between the conscious state and the conscious subject, self-representational accounts of consciousness possess the means to deal with this objection. We analyze a particular sort of self-representational theory, built on the work of John von Neumann on self-reproduction, using tools from mathematical logic. We provide an explicit theory of the emergence of referential beliefs by means of modal fixed points, grounded in intrinsic properties yielding the subjective aspects of experience. Furthermore, we study complications introduced by allowing for the modification of such symbolic content by environmental influences. [ABSTRACT FROM AUTHOR]

The article discusses the concept of faithful representations of finite conformal Lie algebras. It explores the question of whether every finite conformal Lie algebra, freely generated as an H-module, has a faithful representation on a finitely generated free H-module. The article presents theorems and proofs related to this question, as well as the relationship between the Ado theorem and the structure of universal enveloping associative algebras. It also discusses the radical splitting problem in finite-dimensional Lie algebras and its adaptation to the conformal case. The article concludes with a classification theorem for semisimple associative conformal algebras with finite faithful representation. [Extracted from the article]

We prove that for every natural number n, there exists a natural number N (n) such that every multilinear skew-symmetric polynomial in N (n) or more variables which vanishes in the free associative algebra also vanishes in any n-generated alternative algebra over a field of characteristic 0. Previously, a similar result was proved only for a series of skew-symmetric polynomials constructed by I. P. Shestakov in [Algebra and Logic, 16, No. 2, 153-166 (1977)]. [ABSTRACT FROM AUTHOR]

This article explores the concepts of pretabularity and interpolation in various logics, including propositional modal and positive logics, as well as J-logics. It discusses the decidable nature of the tabularity problem in intuitionistic logic, minimal logic, and modal logics. The article also examines Craig's interpolation property in different logics, providing descriptions and decidable results for superintuitionistic, positive, and modal logics. The text utilizes algebraic semantics to establish correspondences between logics and algebraic structures. While the tabularity and pretabularity problems are decidable in certain logics, there are still open questions regarding the interpolation problem in the class of extensions of minimal logic J and modal logic K. The decidability of the interpolation property over J and the exact number of extensions of S4 with the interpolation property remain unknown. [Extracted from the article]

Globally known about the drivers through which farmers are instigated to uphold and use Hail Canon Technology (HCT) is lacking. Therefore, this article intended to examine the drivers of forecasting the behavioral intention and acceptance behavior of the HCT, 249 apple farmers from northwestern Iran were recruited, including adopters (n1 = 114) and non-adopters (n2 = 135). The conceptual foundation included demographic theory, resource-based theory, theory of planned behavior, innovation diffusion model, and institutional support model. We also used the system dynamics model (SDM) in the Netlogo to assess the results of the conventional statistical approach (i.e., the logistic model). Authenticated the fitness of conceptual model with the data, logistic model manifests that the most outstanding determinants of the acceptance of HCT entail age, experience, total land size, income, attitude, compatibility, visibility, relative advantage, and financial support. Using the SDM, it was also shown that the results of the logistic model are confirmed by the SDM. In conclusion, management implications are available for the university extension to eliminate the adoption obstacles and stir up farmers to join in applying HCT, furthermore, researchers would avail themselves of remarks for future research. [ABSTRACT FROM AUTHOR]

Some cooperative games may have some players whose marginal contribution is zero but are indispensable to forming the coalition. However, the marginalism-based index allocates such players with zero payoffs. It is unreasonable and inconsistent with practical cases because the rest players cannot cooperate to make more payoffs without the participation of the players with no marginal contribution. This paper studies one such type of cooperative game called games with communication structure and introduces the α-Egalitarian Myerson value. This payoff index consolidates the Myerson value and the Equal Component Division value, which not only considers the marginal contribution of players but also regards egalitarianism. The main feature of this payoff index is to protect all players' payoffs. Three axiomatic systems are provided to show the rationality of the α-Egalitarian Myerson value. An application of the theoretical results in pharmaceutical supply chain management is offered to show the efficiency of the new payoff index. [ABSTRACT FROM AUTHOR]

In a recent work, Pizzi proposes a notion of dyadic non-contingency, and then gives an axiomatic system of dyadic non-contingency named KD Δ 2 , which is shown to be translationally equivalent to the deontic system KD and has the minimal system K Δ of monadic contingency as a fragment. However, the reason why he defines dyadic non-contingency like that is unclear. In this article, inspired by the notion of relativized knowing-value in the literature, we give a plausible explanation for this. We also show that KD Δ 2 is not sound with respect to the class of serial frames, and then correct a mistake in the previous-mentioned Pizzi's work. [ABSTRACT FROM AUTHOR]

Biological computation is becoming a viable and fast-growing alternative to traditional electronic computing. Here we present a biocomputing technology called Trumpet: Transcriptional RNA Universal Multi-Purpose GatE PlaTform. Trumpet combines the simplicity and robustness of the simplest in vitro biocomputing methods, adding signal amplification and programmability, while avoiding common shortcomings of live cell-based biocomputing solutions. We have demonstrated the use of Trumpet to build all universal Boolean logic gates. We have also built a web-based platform for designing Trumpet gates and created a primitive processor by networking several gates as a proof-of-principle for future development. The Trumpet offers a change of paradigm in biocomputing, providing an efficient and easily programmable biological logic gate operating system. Biological computation is becoming a viable and fast-growing alternative to traditional electronic computing. Here the authors present Trumpet, which uses DNA and enzymes to build logic gate circuits with amplified fluorescent readout. [ABSTRACT FROM AUTHOR]

This paper establishes a sound and complete semantics for the impure logic of ground. Fine (Review of Symbolic Logic, 5(1), 1–25, 2012a) sets out a system for the pure logic of ground, one in which the formulas between which ground-theoretic claims hold have no internal logical complexity; and it provides a sound and complete semantics for the system. Fine (2012b) [§§6-8] sets out a system for an impure logic of ground, one that extends the rules of the original pure system with rules for the truth-functional connectives, the first-order quantifiers, and λ-abstraction. However, no semantics has yet been provided for this system. The present paper partly fills this lacuna by providing a sound and complete semantics for a system GG containing the truth-functional operators that is closely related to the truth-functional part of the system of Fine (2012b). [ABSTRACT FROM AUTHOR]

Set theory faces two difficulties: formal definitions of sets/subsets are incapable of assessing biophysical issues; formal axiomatic systems are complete/inconsistent or incomplete/consistent. To overtake these problems reminiscent of the old-fashioned principle of individuation, we provide formal treatment/validation/operationalization of a methodological weapon termed "outer approach" (OA). The observer's attention shifts from the system under evaluation to its surroundings, so that objects are investigated from outside. Subsets become just "holes" devoid of information inside larger sets. Sets are no longer passive containers, rather active structures enabling their content's examination. Consequences/applications of OA include: a) operationalization of paraconsistent logics, anticipated by unexpected forerunners, in terms of advanced truth theories of natural language; b) assessment of embryonic craniocaudal migration in terms of Turing's spots; c) evaluation of hominids' social behaviors in terms of evolutionary modifications of facial expression's musculature; d) treatment of cortical action potentials in terms of collective movements of extracellular currents, leaving apart what happens inside the neurons; e) a critique of Shannon's information in terms of the Arabic thinkers' active/potential intellects. Also, OA provides an outer view of a) humanistic issues such as the enigmatic Celestino of Verona's letter, Dante Alighieri's "Hell" and the puzzling Voynich manuscript; b) historical issues such as Aldo Moro's death. Summarizing, we suggest that the safest methodology to quantify phenomena is to remove them from our observation and tackle an outer view, since mathematical/logical issues such as selective information deletion and set complement rescue incompleteness/inconsistency of biophysical systems. [ABSTRACT FROM AUTHOR]

But to what extent did Skolem have a complete and coherent view of the foundation of mathematics? Skolem 1920 One hundred years ago, the Norwegian mathematician Thoralf Albert Skolem published the first of a series of remarkable papers on logic and the foundations of mathematics [[33]]. Davies is in no doubt about what mathematics is: "Mathematics is an aspect of human culture, just as are language, law, music, and architecture" [[6], p. 101]. But we note that the "grand view" of mathematics toward which these developments aim stands in stark contrast to Skolem's skepticism and his insistence on the primacy of specific structures and doable algorithms. [Extracted from the article]

It is shown for the first time in this paper, that Kleinberg's (2002) (self-contradictory) axiomatic system for distance-based clustering fails (that is one of the data transforming axioms, consistency axiom, turns out to be identity transformation) in fixed-dimensional Euclidean space due to the consistency axiom limitations and that its replacement with inner-consistency or outer consistency does not help if continuous data transformations are required. Therefore we formulate a new, sound axiomatic framework for cluster analysis in the fixed dimensional Euclidean space, suitable for k-means like algorithms. The system incorporates centric consistency axiom and motion consistency axiom which induce clustering preserving transformations useful e.g. for deriving new labelled sets for testing clustering procedures. It is suitable for continuous data transformations so that labelled data with small perturbations can be derived. Unlike Kleinberg's consistency, the new axioms do not lead the data outside of Euclidean space nor cause increase in data dimensionality. Our cluster preserving transformations have linear complexity in data transformation and checking. They are in practice less restrictive, less rigid than Kleinberg's consistency as they do not enforce inter-cluster distance increase and inner cluster distance decrease when performing clustering preserving transformation. [ABSTRACT FROM AUTHOR]

This paper is devoted to investigating a haptotactic cross-diffusion system with generalized logistic source in two-dimensional domain, which describes the interaction among uninfected and infected cancer cells, extracellular matrix and oncolytic virus particles. It is mainly concerned with the global boundedness of classical solutions. Indeed, we rigorously proved that an associated spatially two-dimensional initial-boundary value problem has a unique global bounded classical solution under some suitably conditions. Our work generalizes and improves the partial of the results in the literature. [ABSTRACT FROM AUTHOR]

Specialization of configurable heterogeneous ICs for specific customer proposals requires the flexibility of design and technological solutions. This, in turn, leads to the necessity of the automatic adjustment of CAD, including software placement tools, on the changes made. The development of efficient methods and tuning algorithms is impossible without relying on the appropriate mathematical apparatus. This study presents a set-theoretic mathematical model of a hierarchical project and formalizes a hierarchical approach to the netlist using the apparatus of set theory, mathematical logic, and graph theory. To ensure quick configuration of clustering and placement software tools, taking into account the changes made to the basic design, the correspondence between the elements of the basic FPGA design and user-designed circuits from the end user is formalized. The obtained results can serve as a base for the development of the efficient methods and algorithms for the automatic tuning of software clustering and placement tools. [ABSTRACT FROM AUTHOR]

Did Turing Stand on Gödel's Shoulders? After all, by 1935, Gödel's incompleteness paper was well known to mathematical logicians - including Turing's mentor, Max Newman - and Turing cited and discussed the paper in OCN. Kleene's Remarks According to the Standard Story, Turing's work was founded on, and was a development of, Gödel's: Turing, it is said, "recast" Gödel's findings "in the guise of the Halting Problem" [[14], p. 133]. Moreover, Kleene's claim that Turing's thought was "unalloyed by any input from Gödel" certainly fits with what Turing said, and didn't say, in his précis. The text of OCN contains nothing at all to indicate that Gödel's work was the foundation for Turing's, or that Turing used concepts or techniques drawn from Gödel's 1931 paper. [Extracted from the article]

Barrio et al. (Journal of Philosophical Logic, 49(1), 93–120, 2020) and Pailos (Review of Symbolic Logic, 2020(2), 249–268, 2020) develop an approach to define various metainferential hierarchies on strong Kleene models by transferring the idea of distinct standards for premises and conclusions from inferences to metainferences. In particular, they focus on a hierarchy named the S T -hierarchy where the inferential logic at the bottom of the hierarchy is the non-transitive logic ST but where each subsequent metainferential logic 'says' about the former logic that it is transitive. While Barrio et al. (2020) suggests that this hierarchy is such that each subsequent level 'in some intuitive sense, more classical than' the previous level, Pailos (2020) proposes an extension of the hierarchy through which a 'fully classical' metainferential logic can be defined. Both Barrio et al. (2020) and Pailos (2020) explore the hierarchy in terms of semantic definitions and every proof proceeds by a rather cumbersome reasoning about those semantic definitions. The aim of this paper is to present and illustrate the virtues of a proof-theoretic tool for reasoning about the S T -hierarchy and the other metainferential hierarchies definable on strong Kleene models. Using the tool, this paper argues that each level in the S T -hierarchy is non-classical to an equal extent and that the 'fully classical' metainferential logic is actually just the original non-transitive logic ST 'in disguise'. The paper concludes with some remarks about how the various results about the S T -hierarchy could be seen as a guide to help us imagine what a non-transitive metalogic for ST would tell us about ST. In particular, it teaches us that ST is from the perspective of ST as metatheory not only non-transitive but also transitive. [ABSTRACT FROM AUTHOR]