Search Results (43)

While the quantum emergence of spacetime is becoming a major research topic in physics, the quantum emergence of intelligence has not been widely researched in quantum information science (QIS). Following causal-logical quantum gravity theory, bipolar entropy vs. entropy and negative entropy (or negentropy) are reviewed and distinguished for quantum emergence/submergence of quantum agent (QA) and quantum intelligence (QI) in algebraic terms. This work refers to QA as an entangled bipolar string/superstring in bipolar dynamic equilibrium (BDE) and QI being centered on logically definable causality in regularity, mind-light-matter unity, and brain-universe similarity. ER = EPR is extended to ER ≥≥ EPR for the mathematical scalability of bipolar strings and their collective entanglement. The extension leads to a number of conjectures, testable predictions, and theorems. The term “equilibraton” is proposed as a type of EPR or bipolar generic string to serve as an entropic stitch to collectively hold the universe together as a quantum entanglement in BDE with ubiquitous, regulated local emergence and submergence of QA&QI. Equilibraton leads to the concept of bipolar entropy square—a complete entropic solution to the background issue in quantum gravity. With complete background independence, energy/information conservational bipolar entropy, energy/information invariance, bipolar entropy non-additivity, and equilibrium-based plateau concavity are introduced. The nature of the one-dimensional arrow of time is conjectured. As a unification of order and disorder for equilibrium-based regulation, bipolar entropy bridges QA&QI to agentic AI, where quantum-bio-economics can be viewed as a topological intervention of a natural dynamic equilibrium in a social or natural world. Use cases are reviewed to illustrate the practical and theoretical aspects of bipolar entropy in business management, quantum-bio-economics, quantum cryptography, physics, and biology. Eddington–Einstein’s comments on entropy are revisited. It is expected that bipolar entropy will bring quantum emergence/submergence to agentic AI&QI for entangled machine thinking and imagination as a naturally scalable and testable foundation of real-world quantum gravity, quantum information science (QIS), quantum cognition, and quantum biology (QCQB) to enhance Large Language AI Models (LLMs) and machine intelligence. Full article

Topic modeling of large news streams is widely used to reconstruct economic and political narratives, which requires coherent topics with low lexical overlap while remaining interpretable to domain experts. We propose TF-SYN-NER-Rel, a structural–semantic term weighting scheme that extends classical TF-IDF by integrating positional, syntactic, factual, and named-entity coefficients derived from morphosyntactic and dependency parses of Russian news texts. The method is embedded into a standard Latent Dirichlet Allocation (LDA) pipeline and evaluated on a large Russian-language news corpus from the online archive of Moskovsky Komsomolets (over 600,000 documents), with political, financial, and sports subsets obtained via dictionary-based expert labeling. For each subset, TF-SYN-NER-Rel is compared with standard TF-IDF under identical LDA settings, and topic quality is assessed using the C_v coherence metric. To assess robustness, we repeat model training across multiple random initializations and report aggregate coherence statistics. Quantitative results show that TF-SYN-NER-Rel improves coherence and yields smoother, more stable coherence curves across the number of topics. Qualitative analysis indicates reduced lexical overlap between topics and clearer separation of event-centered and institutional themes, especially in political and financial news. Overall, the proposed pipeline relies on CPU-based NLP tools and sparse linear algebra, providing a computationally lightweight and interpretable complement to embedding- and LLM-based topic modeling in large-scale news monitoring. Full article

In this paper we present the development of an energy and power system modelling, simulation, and analysis (ePowerSim.jl) package in Julia programming language. ePowerSim.jl is designed to present a uniform data interface for static, quasi-static, dynamic analysis, as well as network operation optimisation. It provides a co-simulation framework for the further development and experimentation of various types of models of electric power systems components or abstract entities that have mathematical formalism or data representation. ePowerSim.jl makes extensive use of cutting edge packages such as DifferentialEquations.jl, Dataframes.jl, NamedTupleTools.jl, Helics.jl, ForwardDiff.jl, JuMP.jl, and BifurcationKit just to mention a few in the Julia ecosystem. Models of synchronous generator, synchronous condenser, excitation systems, and governors developed in the package were used to model IEEE 9 bus and IEEE 14 bus test networks and subsequently validated by a real-time digital simulator of electric power systems (RTDS). The results obtains for static and dynamic models simulation in ePowerSim.jl show a close match with a simulation of the same system in RTDS. A maximum error of $0.00001$ pu and $0.0001$ pu were obtained for steady states and transient state respectively. Similarly, a maximum deviation of $0.0001$ pu was obtained during validation for voltage magnitude during transient state at buses in the network. Full article

Tarski’s first-order axiom system ${\mathcal{E}}_2$ for Euclidean geometry is notable for its completeness and decidability. However, the Pythagorean theorem—either in its modern algebraic form $a^2+b^2=c^2$ or in Euclid’s Elements—cannot be directly expressed in ${\mathcal{E}}_2$, since neither distance nor area is a primitive notion in the language of ${\mathcal{E}}_2$. In this paper, we introduce an alternative axiom system ${\mathcal{E}}_d$ in a two-sorted language, which takes a two-place distance function d as the only geometric primitive. We also present a conservative extension ${\mathcal{E}}_{da}$ of it, which also incorporates a three-place angle function a, both formulated strictly within first-order logic. The system ${\mathcal{E}}_d$ has two distinctive features: it is simple (with a single geometric primitive) and it is quantitative. Numerical distance can be directly expressed in this language. The Axiom of Similarity plays a central role in ${\mathcal{E}}_d$, effectively killing two birds with one stone: it provides a rigorous foundation for the theory of proportion and similarity, and it implies Euclid’s Parallel Postulate (EPP). The Axiom of Similarity can be viewed as a quantitative formulation of EPP. The Pythagorean theorem and other quantitative results from similarity theory can be directly expressed in the languages of ${\mathcal{E}}_d$ and ${\mathcal{E}}_{da}$, motivating the name Quantitative Euclidean Geometry. The traditional analytic geometry can be united under synthetic geometry in ${\mathcal{E}}_d$. Namely, analytic geometry is not treated as a model of ${\mathcal{E}}_d$, but rather, its statements can be expressed as first-order formal sentences in the language of ${\mathcal{E}}_d$. The system ${\mathcal{E}}_d$ is shown to be consistent, complete, and decidable. Finally, we extend the theories to hyperbolic geometry and Euclidean geometry in higher dimensions. Full article

The classical fiber product in algebraic geometry provides a powerful tool for studying loci where two morphisms to a base scheme, $\varphi :X\to S$ and $\psi :Y\to S$, coincide exactly. This condition of strict equality, however, is insufficient for describing many real-world applications, such as the geometric structure of semantic spaces in modern large language models whose foundational architecture is the Transformer neural network: The token spaces of these models are fundamentally approximate, and recent work has revealed complex geometric singularities, challenging the classical manifold hypothesis. This paper develops a new framework to study and quantify the nature of approximate alignment between morphisms in the context of arithmetic geometry, using the tools of étale homotopy theory. We introduce the central object of our work, the étale mismatch torsor, which is a sheaf of torsors over the product scheme $X{\times }_{S}Y$. The structure of this sheaf serves as a rich, intrinsic, and purely algebraic object amenable to both qualitative classification and quantitative analysis of the global relationship between the two morphisms. Our main results are twofold. First, we provide a complete classification of these structures, establishing a bijection between their isomorphism classes and the first étale cohomology group $H_{ét}^1(X{\times }_{S}Y,\underline{{\pi }_1^{ét}(S)})$. Second, we construct a canonical filtration on this classifying cohomology group based on the theory of infinitesimal neighborhoods. This filtration induces a new invariant, which we term the order of mismatch, providing a hierarchical, algebraic measure for the degree of approximation between the morphisms. We apply this framework to the concrete case of generalized Howe curves over finite fields, demonstrating how both the characteristic class and its order reveal subtle arithmetic properties. Full article

Building a causal-loop diagram (CLD) is central to system-dynamics modeling but demands domain insight, the mastery of CLD notation, and the ability to juggle AI, mathematical, and execution tools. Pipeline Algebra (PA) reduces that burden by treating each step—LLM prompting, symbolic or numeric computation, algorithmic transforms, and cloud execution—as a typed, idempotent operator in one algebraic expression. Operators are intrinsically idempotent (implemented through memoization), so every intermediate result is re-used verbatim, yielding bit-level reproducibility even when individual components are stochastic. Unlike DAG (directed acyclic graph) frameworks such as Airflow or Snakemake, which force analysts to wire heterogeneous APIs together with glue code, PA’s compact notation lets them think in the problem space, rather than in workflow plumbing—echoing Iverson’s dictum that “notation is a tool of thought.” We demonstrated PA on a peer-reviewed study of novel-energy commercialization. Starting only from the article’s abstract, an AI-extracted problem statement, and an AI-assisted web search, PA produced an initial CLD. A senior system-dynamics practitioner identified two shortcomings: missing best-practice patterns and lingering dependence on the problem statement. A one-hour rewrite that embedded best-practice rules, used iterative prompting, and removed the problem statement yielded a diagram that conformed to accepted conventions and better captured the system. The results suggest that earlier gaps were implementation artifacts, not flaws in PA’s design; quantitative validation will be the subject of future work. Full article

This work presents a system developed to determine changes in the impedance of an eddy current probe placed above a conductive disc containing two layers of different diameters. In the first step, an analytical model was derived with an employment of the truncated region eigenfunction expansion (TREE) method. The final formula for the probe impedance change was presented in a closed form, which makes it possible to implement it in any programming language or computer algebra system. The mathematical model was implemented in MATLAB and used to design probes and to determine the optimal test parameters. In the next step, two eddy current probes with a single coil with different geometric dimensions were constructed. Impedance measurements were carried out using an LCR meter for three sets of double-layer discs. The tested discs were made of materials with different electrical conductivities. The upper and lower layers of the disc also differed in terms of the geometric dimensions, i.e., the diameter and thickness. The tests were performed for the operating frequency of the probe ranging from 1 kHz to 10 kHz. In all cases, a very good agreement was obtained between the measurement and the calculation results. Both the error in the changes in resistance and the error in the changes in reactance did not exceed 3.5%. Full article

In multitasking systems, concurrent execution leads to an exponential growth of the state space, posing significant challenges for formal verification. This complexity is further exacerbated in hybrid systems that integrate discrete and continuous dynamics. To address these challenges, we propose to model multitasking hybrid systems and systematically verify system properties through formal verification methods, using synergistic formal verification of model checking and theorem proving to ensure rigorous correctness analysis. We, therefore, introduce a transformation framework that converts behavioral specifications into rewrite specifications, enabling the integration of verification techniques from both approaches. To demonstrate the effectiveness of our approach, we model self-driving car group control systems as Multitask Hybrid Observational Transition Systems (MHOTS), a framework extending Observational Transition Systems (OTS) to support hybrid and multitask behaviors, specify their safety properties in theorem proving via CafeOBJ, in model checking via real-time Maude, and verify that the system remains safe regardless of the number of processes involved. The approach leverages specification translation between CafeOBJ and Real-Time Maude to exploit the complementary strengths of theorem proving and model checking. CafeOBJ is an algebraic specification language that provides a rigorous mathematical foundation for theorem proving, enabling the verification of system properties through logical deductions, while Real-Time Maude facilitates model checking, thereby enhancing the safety and reliability of autonomous vehicle systems. This methodology not only confirms the safety properties of the control system but also establishes a robust framework for the future development and validation of autonomous driving technologies. The integration of these formal verification techniques provides a rigorous and systematic approach to ensuring the desired properties of Multitask Hybrid Observational Transition systems, contributing to the advancement of safe and reliable autonomous driving solutions. Full article

Marcolli, Chomsky, and Berwick described the minimalist program, proposed by Chomsky in generative linguistics, as an algebra of binary trees in an analogy of quantum physics on Feynman diagrams. In this paper, we proposed another model of the minimalist program based on simplicial Hodge theory by taking the relevant brain neural network into account. We focused on a long directed pathway connecting distant areas in the brain, and took the (abstract) simplex spanning the locations on the terminal area, which the signals going through the pathway can reach. The identity of each signal is represented by the symmetry of the corresponding face, consisting of locations receiving the signal simultaneously. Then, we showed that this model fits the minimalist program. Further, we calculated the spectrum and eigenspaces of the Hodge Laplacian in important cases and found their surprising rationality. According to this rationality, we could draw pictures of syntactic relations based only on the calculation without using linguistic knowledge. In addition, though word order depends on what language is used, and thus has nothing to do with the minimalist program, planar word arrangements are still possible and within the scope of our model. Full article

Graph query languages such as Cypher are widely adopted to match and retrieve data in a graph representation, due to their ability to retrieve and transform information. Even though the most natural way to match and transform information is through rewriting rules, those are scarcely or partially adopted in graph query languages. Their inability to do so has a major impact on the subsequent way the information is structured, as it might then appear more natural to provide major constraints over the data representation to fix the way the information should be represented. On the other hand, recent works are starting to move towards the opposite direction, as the provision of a truly general semistructured model (GSM) allows to both represent all the available data formats (Network-Based, Relational, and Semistructured) as well as support a holistic query language expressing all major queries in such languages. In this paper, we show that the usage of GSM enables the definition of a general rewriting mechanism which can be expressed in current graph query languages only at the cost of adhering the query to the specificity of the underlying data representation. We formalise the proposed query language in terms declarative graph rewriting mechanisms described as a set of production rules $L\to R$ while both providing restriction to the characterisation of L, and extending it to support structural graph nesting operations, useful to aggregate similar information around an entry-point of interest. We further achieve our declarative requirements by determining the order in which the data should be rewritten and multiple rules should be applied while ensuring the application of such updates on the GSM database is persisted in subsequent rewriting calls. We discuss how GSM, by fully supporting index-based data representation, allows for a better physical model implementation leveraging the benefits of columnar database storage. Preliminary benchmarks show the scalability of this proposed implementation in comparison with state-of-the-art implementations. Full article

This paper explores the performance of ChatGPT and GeoGebra Discovery when dealing with automatic geometric reasoning and discovery. The emergence of Large Language Models has attracted considerable attention in mathematics, among other fields where intelligence should be present. We revisit a couple of elementary Euclidean geometry theorems discussed in the birth of Artificial Intelligence and a non-trivial inequality concerning triangles. GeoGebra succeeds in proving all these selected examples, while ChatGPT fails in one case. Our thesis is that both GeoGebra and ChatGPT could be used as complementary systems, where the natural language abilities of ChatGPT and the certified computer algebra methods in GeoGebra Discovery can cooperate in order to obtain sound and—more relevant—interesting results. Full article

Generative AI applications have played an increasingly significant role in real-time tracking applications in many domains including, for example, healthcare, consultancy, dialog boxes (common types of window in a graphical user interface of operating systems), monitoring systems, and emergency response. This paper considers generative AI and presents an approach which combines hedge algebra and a multilingual large language model to find hidden rules in big data for ChatGPT. We present a novel method for extracting natural language knowledge from large datasets by leveraging fuzzy sets and hedge algebra to extract these rules, presented in meta data for ChatGPT and generative AI applications. The proposed model has been developed to minimize the computational and staff costs for medium-sized enterprises which are typically resource and time limited. The proposed model has been designed to automate question–response interactions for rules extracted from large data in a multiplicity of domains. The experimental results show that the proposed model performs well using datasets associated with specific domains in healthcare to validate the effectiveness of the proposed model. The ChatGPT application in case studies of healthcare is tested using datasets for English and Vietnamese languages. In comparative experimental testing, the proposed model outperformed the state of the art, achieving in the range of 96.70–97.50% performance using a heart dataset. Full article

The application of contemporary artificial intelligence techniques to address geometric problems and automated deductive proofs has always been a grand challenge to the interdisciplinary field of mathematics and artificial intelligence. This is the fourth article in a series of our works, in our previous work, we established a geometric formalized system known as FormalGeo. Moreover, we annotated approximately 7000 geometric problems, forming the FormalGeo7k dataset. Despite the fact that FGPS (Formal Geometry Problem Solver) can achieve interpretable algebraic equation solving and human-like deductive reasoning, it often experiences timeouts due to the complexity of the search strategy. In this paper, we introduced FGeo-TP (theorem predictor), which utilizes the language model to predict the theorem sequences for solving geometry problems. The encoder and decoder components in the transformer architecture naturally establish a mapping between the sequences and embedding vectors, exhibiting inherent symmetry. We compare the effectiveness of various transformer architectures, such as BART or T5, in theorem prediction, and implement pruning in the search process of FGPS, thereby improving its performance when solving geometry problems. Our results demonstrate a significant increase in the problem-solving rate of the language model-enhanced FGeo-TP on the FormalGeo7k dataset, rising from 39.7% to 80.86%. Furthermore, FGeo-TP exhibits notable reductions in solution times and search steps across problems of varying difficulty levels. Full article

It is important to establish solid mathematical knowledge throughout the education period. Matrices are important mathematical objects commonly used in many diverse disciplines, including mathematics, engineering, and science. Most problems encountered in such disciplines are represented by mathematical models with various types of matrices, and solved through some applications of matrix algebra. Although simple or advanced operations of matrices can be performed by using modern programming languages, it usually results in a large fragment of code with a low level of readability due to a complicated sequence of control statements. On the other hand, special-purpose languages handle these operations via library functions, presenting poor integration with other programming environments, and less programming flexibility and practice. This paper addresses the design and development of a programming language, called MxPL, which supports matrix-related mathematics with the provision of some basic structures and functions. Firstly, a grammar that is compatible with the usual notations of matrices is constructed and the parser is produced. Then, the code verifier and interpreter for MxPL programs are implemented. Some code examples are presented to illustrate the performance of several sophisticated matrix operations. The comparative analysis of MxPL is conducted with modern programming languages based on language features. Full article

Optimal operation of petroleum production is important in a transition from energy systems based on fossil fuel to sustainable systems. One sub-process in petroleum production deals with transport from the (subsea) well-bore to a topside separator. Good control design for such operation requires a dynamic model of the petroleum flow from the well-bore to the separator. Here, such a dynamic model is considered for liquid production (oil/water) using an electric submersible pump (ESP) to aid in counteracting gravity and friction forces. Based on an existing model used for industrial control design, one goal is to report a complete dynamic model in a single paper. Emphasis is put on dimensionless equipment models for the simple change of units, and the model is developed from physical laws for easy replacement of sub-models, if needed. All the necessary information (equations, parameters) for model implementation is provided, and two candidate equation-based modeling languages are selected and compared: Modelica and ModelingToolkit [MTK] for Julia. The simulation results are virtually identical for the two languages and make sense from physics; however, there is a minor discrepancy in one plot—likely caused by slight differences in accuracy in handling initialization in the implicit algebraic equations. The implementation structures of the model in Modelica and MTK are similar. Modelica is a mature and excellent modeling tool, handles large-scale models, and has tools for producing C code and integration with other tools. MTK is still in rapid development, supports more model types than Modelica, and is integrated in an eco-system with excellent support for control design, optimization, model fitting, and more. To illustrate the suitability of using the developed model for control design, a simple PI controller is designed within the eco-system of MTK/Julia. Full article