Search Results (396)

The necessity of utilizing unconventional water resources and wastewater has emerged today as an unavoidable imperative, particularly in Iran. The limitations of water resources have directed researchers’ attention toward the rational use of unconventional waters, such as wastewater. The overall aim of the present study is the optimal utilization of wastewater in the cultivation of non-fruit-bearing trees, industry, and eco-park applications, leveraging sustainable development indicators. In the present study, to achieve the objectives and prioritize the use of wastewater (in tree cultivation, eco-park development, or industrial applications), the fuzzy Shannon entropy method was employed to determine the importance of evaluation criteria, and the Fuzzy Additive Ratio Assessment (ARAS) method was used for assessing and prioritizing the options. Given the presence of uncertainty in experts’ opinions, fuzzy concepts and theory were utilized to reflect this uncertainty in the process of evaluating the options. An integrated fuzzy Shannon Entropy–ARAS framework is proposed to evaluate and prioritize wastewater reuse alternatives under sustainability criteria. In order to identify the evaluation criteria, relevant literature and previous studies were reviewed, and a questionnaire was designed and distributed among experts. To identify and prioritize the influential criteria, the snowball sampling technique was employed. During the implementation of this technique, 10 out of the initial 20 criteria were excluded, and ultimately, 10 key and impactful criteria were selected. The results of implementing the fuzzy Shannon entropy and fuzzy ARAS methods revealed that the optimal use of treated wastewater in the Shahrkord plain should initially focus on non-fruit-bearing trees. The second priority for utilizing treated wastewater in the Shahrkord plain is for the construction of eco-parks, while the third priority is its use in industry. Full article

Understanding complex systems requires analytical tools capable of covering nonlinear dynamics, structural complexity, and informational uncertainty simultaneously. In this context, chaos theory, fractal analysis, and entropy measures provide complementary perspectives for examining any irregular behavior in natural and socio-economic systems. This paper examined the relation between the Geopolitical Risk Index and the World Uncertainty Index to the volatility of West Texas Intermediate crude oil, gold, and Bitcoin over the period October 2010–February 2026. The analysis was motivated by the recent intensification of geopolitical tensions, particularly conflicts involving Iran, the United States, and Israel, which have significantly heightened uncertainty in global energy and financial markets. The empirical analysis first investigated the underlying complexity of the variables using entropy, chaos, and fractionality measures. Results from the Shannon, R-T entropy, Kolmogorov–Sinai complexity, Hurst, H-M and Lo’s R/S statistics, Phillips, and GPH fractionality tests consistently indicate entropy, fractal persistence, and long-range dependence across the series. In addition, the largest Lyapunov exponents and Hurst coefficients confirmed the presence of chaotic dynamics. The results reveal strong regime heterogeneity with geopolitical shocks exerting significantly stronger effects during high-uncertainty periods. Forecast comparisons show that regime-switching models outperform linear specifications, highlighting the importance of fractal and nonlinear dynamics in understanding financial market responses to geopolitical risk. Full article

Graph-based narrative extraction relies on a coherence function to score transitions between events, but the coherence metrics in current use are defined operationally and lack an information-theoretic foundation. We study the composite metric $C=\sqrt{A·T}$, where A is the angular similarity of document embeddings and $T=1-d_{\mathrm{JS}}$ is the topic proximity through the Jensen–Shannon distance of soft cluster memberships, and we provide an information-geometric reading of this metric together with an axiomatic characterization of the geometric-mean combinator. On the product manifold ${\mathbb{S}}^{d-1}\times {\Delta }_{+}^{K-1}$, the negative log-coherence decomposes additively into an angular and a topic cost. Because the Riemannian metric tensor induced by the Jensen–Shannon distance on the simplex is proportional to the Fisher information matrix, the topic component is locally consistent with the Fisher–Rao metric singled out by Chentsov’s theorem. Within a parametric family of combinators (the compensability spectrum), the geometric mean is the unique combinator consistent with four natural axioms (a boundary/veto condition, symmetry, log-additivity, normalization), and the construction also motivates a proper product metric $d_{\times }$ that we use as a reference distance. Experiments on four corpora spanning news and academic domains (40 to 6000 documents), three general-purpose embedding families (GPT-4/ada-002, MPNet, MiniLM-L6) plus citation-aware SPECTER2, and three alternative topic models (LDA, soft k-means, GMM) are consistent with the framework: the Fisher identity holds with $R\ge 0.99$, the geometric mean tracks $d_{\times }$ closely ($\rho =0.999$), and a downstream LLM-as-judge consistency check shows that the geometric mean is not empirically dominated by any alternative combinator or single-channel baseline. Sweeping the compensability spectrum, the bottleneck-coherence gap between extracted storylines and random sequences splits into a symmetric component—maximized at the geometric mean on the four corpora above and a fifth, human-navigation corpus—and a displacement term; a cross-modal case study on a human-curated image narrative reproduces the same effect in a second modality. Together, these results provide an information-geometric justification for the composite coherence metric and articulate the conditions under which the geometric mean is the natural choice. Full article

Discussion of consciousness and artificial intelligence has hitherto focused on the question of whether a large language model (LLM) exhibits signs of consciousness or understanding. This paper proposes to redirect attention elsewhere: not to the model itself, but to the orchestrating layer that governs the model—the backend, understood here as the collection of mechanisms (context management, retrieval, evaluation, planning, and tool-use control) that structure the model’s operation. We argue that the backend performs a function functionally analogous to the role of consciousness in the human brain: it stabilizes generative processes, directs attention, maintains context, and mitigates the entropic disintegration of thought. Consciousness fulfills this function through the phenomenal layer—qualia—which creates a persistent subjective “inner canvas”, used here as a metaphor for a more general multimodal phenomenal space. The backend fulfills it only algorithmically, without phenomenal quality. We further show that computation is an informationally conservative process in the sense of Shannon’s Data Processing Inequality (DPI), and therefore cannot increase Shannon information, even though it may yield novel or pragmatically useful recombinations of existing information. We conclude by proposing the hypothesis that consciousness constitutes a phenomenon orthogonal to computation—not an emergent property of complexity, but a qualitative leap into a different dimension. This hypothesis, which builds on the author’s prior work in this Special Issue and in Symmetry, is presented as a conceptual contribution rather than a formal theory, and may have implications for how future artificial intelligence research conceptualizes the limits of computational architectures. Full article

Corporate balance sheets report aggregate equity and liability totals but conceal the internal allocation of financing sources across asset categories—an identification problem that conventional econometric methods cannot resolve without additional parametric assumptions. This paper develops a maximum entropy (ME) panel estimator to recover two latent scalar parameters: x ∈ (0,1), the share of equity capital directed toward long-term asset financing, and y ∈ (0,1), the corresponding debt allocation share. Grounded in maximum entropy principle, the estimator selects the unique parameter vector that satisfies the mean-level balance-sheet constraint while maximising joint Shannon entropy—the least-biassed solution consistent with observable data. The closed-form logistic representation yields a scalar Lagrange multiplier λ*, interpreted as a financing pressure index, recoverable via bisection in at most 21 iterations at tolerance ε = 10⁻⁵. Building on the ME estimates, we introduce a continuous matching alignment index M* = x* − y* that measures the degree of compliance with the financial matching principle along a continuous spectrum rather than as a binary categorisation. Applied to a ten-firm, cross-sectoral panel spanning Technology, Finance, Energy, and Automotive sectors over an observation window spanning 2001 to 2025 (with firm-specific subperiods reflecting differences in IPO dates and data availability), the framework reveals substantial heterogeneity in latent financing flows: equity allocation shares range from 30.1% (NVIDIA) to 75.1% (ExxonMobil), while debt allocation shares span 37.1% to 77.5%. Across the panel, only Meta exhibits substantial positive matching alignment, while Microsoft, ExxonMobil, Apple, and Tesla show only very slight differences that fall within the neutral band, and the remaining firms show varying degrees of structural departure from the matching benchmark; the thresholds used to summarise these descriptive labels are interpretive aids rather than re-imposed binary criteria, and the substantive ranking of firms along M* does not depend on the specific threshold values adopted. The ME solution’s entropy H(x*, y*) and the normalised diversification index D(x*, y*) describe allocation balance under the estimator’s information–theoretic criterion rather than independently observed firm complexity; in the present sample, the cross-firm ordering of these values is not recovered by firm size, leverage, or sector classification alone. These findings, based on a ten-firm case-study panel with time-invariant allocation parameters, should be interpreted as descriptive patterns of the present sample rather than statistically validated regularities. They provide a theoretically rigorous and computationally tractable identification of unobservable corporate financing flows, with potential implications for capital structure theory, financial risk assessment, and balance sheet analysis that would benefit from validation on larger and more representative samples in future work. Full article

With the continuous evolution toward sixth-generation (6G) wireless communication systems, emerging scenarios such as terahertz transmission, integrated sensing and communication (ISAC), and ultra-massive multiple-input multiple-output (MIMO) have significantly increased the complexity, nonlinearity, and uncertainty of wireless propagation environments. The conventional model-driven paradigm, established upon Shannon information theory and precise mathematical modeling, is increasingly constrained by model-mismatch issues in real-world deployments. This paper systematically reviews recent advances in deep learning-enabled physical-layer signal processing. We examine intelligent channel estimation, signal detection, and end-to-end communication systems based on autoencoder architectures. We then analyze key technical challenges—including interpretability, data dependence, computational complexity, privacy and security in distributed learning, and system-level performance-overhead trade-offs—along with state-of-the-art solution strategies such as deep unfolding, transfer learning, model compression, federated learning, and lightweight design. Future evolutionary directions toward AI-native 6G networks, integrated sensing-communication-computing architectures, and intelligent reconfigurable wireless environments are discussed. Furthermore, emerging generative AI techniques, including diffusion models, are identified as a promising direction for addressing data scarcity and enhancing system adaptability. The study demonstrates that hybrid intelligence—integrating model-based prior knowledge with data-driven learning—will become the dominant design philosophy for next-generation intelligent physical-layer systems. Full article

The aim of this study is to thoroughly assess the informational content of the CBOE Volatility Index^® (VIX^® Index) in the context of various turbulent periods. The VIX Index is especially important from an investor perspective. It is often referred to as the “investor fear gauge”, because its level tends to spike during periods of market turmoil and other extreme events. Therefore, this index significantly differs from other market indices and financial instruments. Information theory and normalized Shannon entropy, combined with a rolling-window dynamic approach, are used to explore the evolution of the VIX Index over time. The research hypothesis states that the informational content of the VIX Index varies substantially across periods affected by crucial events. To verify this hypothesis, three important periods of the twenty-first century are analyzed: (1) the Global Financial Crisis, (2) the COVID-19 pandemic outbreak, and (3) the period covering the sub-periods before and after the Donald Trump’s Presidential Inauguration. The results provide no reason to reject the research hypothesis. The empirical findings show that the entropy values appear to be quite sensitive to the choice of discretizaton procedure. However, this evidence is consistent with the existing literature. Full article

Rapid metropolitan expansion reshapes not only land-use patterns and infrastructure networks but also the spatial organization of micro-commercial systems embedded in everyday urban life. While large-scale retail restructuring has been extensively examined, the mechanisms underlying micro-commercial spatial transformation remain insufficiently theorized, particularly in rapidly urbanizing contexts. This study investigates the spatio-temporal restructuring of a representative low-threshold urban food economy in Xi’an between 2014 and 2024. Using multi-temporal point-of-interest (POI) data, kernel density estimation, and spatial Shannon entropy, we model changes in intensity gradients, distributional complexity, and zonal differentiation across morphologically distinct urban belts. The results reveal a systematic transition from centralized concentration toward polycentric embedding, characterized by the relocation of clustered micro-commercial activities along metro corridors and within emerging residential zones. Unlike classical decentralization, which implies outward diffusion, polycentric embedding reflects the infrastructural and demographic re-anchoring of clustered economic activities within newly stabilized urban territories. Entropy analysis further indicates increasing structural heterogeneity in metropolitan expansion zones, while historic cores retain symbolic concentration but exhibit declining structural dominance. These findings demonstrate that micro-commercial systems reorganize not through random dispersion, but through infrastructure-mediated embedding processes driven by metro expansion, residential aggregation, and institutional anchoring. By integrating longitudinal POI data with spatial complexity metrics, this study advances a replicable analytical framework for linking micro-scale commercial dynamics with metropolitan structural transformation. The study contributes to urban theory by reframing low-threshold economic systems as embedded infrastructures of everyday urban reproduction and provides planning insights for fostering resilient and spatially balanced commercial ecosystems under rapid metropolitan growth. Full article

Generative AI systems trained on synthetic data exhibit progressive degradation known as model collapse. This paper provides a theoretical explanation of this phenomenon using Shannon’s Data Processing Inequality (DPI), modeling iterative synthetic-data training as a Markov chain of lossy transformations. We show that mutual information with respect to the original data distribution must decrease monotonically, yielding qualitative predictions for exponential decay tendencies and indicating that information loss arises from general finite-precision and capacity constraints rather than from any specific architectural mechanism. Building on this analysis, we introduce the AI conceptual theorem, a generalized stability limit for computable systems. The theorem states that any purely computational system that generates outputs iteratively under finite precision, bounded capacity, and without external low-entropy input must experience cumulative information degradation after a finite number of steps. DPI-based collapse emerges as a special case of this broader principle. The framework is intended as a conceptual information-theoretic perspective rather than a fully formalized theory, with several assumptions intentionally simplified to highlight the underlying entropic mechanism. The results should therefore be interpreted as principled limits that motivate further empirical and mathematical investigation rather than as definitive closed-form predictions. Together, DPI and the AI Theorem provide a unified information-theoretic framework for understanding degradation in synthetic training, long-horizon inference, and other iterative computational processes. The resulting predictions are quantitatively falsifiable and offer guidance for designing more stable and information-preserving AI systems. Full article

This paper surveys symbolic encoding procedures that can be successfully utilized in various entropy-based applications. The existing studies indicate several important advantages of the symbolic time series analysis (STSA) in finance and economics, specifically in assessing informational content of financial time series. Data symbolization comprises the conversion of a data series of many different possible values into a symbol series of only a few fixed values. The STSA procedures allow for capturing dynamic time-varying patterns of successive values in financial time series. Discretization techniques can reduce the noise and effectively filter the data. Particularly, they are robust to outliers. Moreover, symbolic encoding of information forms the basis for the Shannon’s mathematical theory of communication and the seminal concept of information entropy. Full article

Contemporary enterprise IT operations are largely implemented on Shannon–Turing computing models in which programs execute read–compute–write cycles over data structures, while governance—fault handling, configuration control, auditability, continuity, and accounting—is applied externally through infrastructure platforms, observability stacks, and human operational processes. This separation scales analytical throughput but accumulates what we term coherence debt: locally expedient operational commitments whose provenance and revisability degrade over time until exposed by failures, security incidents, regulatory demands, or architectural transitions. This paper examines the evolution of operational computing models that integrate com-pupation with regulation at two distinct levels. First, Distributed Intelligent Managed Elements (DIME) extend the classical Turing cycle toward a supervised execution loop—read–check-with-oracle–compute–write—by incorporating signaling overlays and FCAPS (Fault, Configuration, Accounting, Performance, and Security) supervision into computation in progress. Second, the Autopoietic Management and Orchestration System (AMOS), grounded in the General Theory of Information, the Burgin–Mikkilineni Thesis, and Deutsch’s epistemic framework, fully decouples process executors from governance by treating any Turing-equivalent engine as a replaceable execution substrate while elevating knowledge structures—encoded as local and global Digital Genomes—to first-class operational state within a governed knowledge network. Using a distributed microservice transaction testbed, we demonstrate how this approach operationalizes topology-as-data, a capability-oriented control plane, decoupled application-layer FCAPS independent of infrastructure management, and policy-selectable consistency/availability semantics. Our results show that the principal benefit of AMOS is not circumventing theoretical constraints such as the Consistency, Availability, and Partition tolerance (CAP) theorem, but governing their trade-offs as explicit, auditable commitments with defined convergence pathways and controlled return to a coherent system state, thereby reducing coherence debt and improving operational reliability in distributed AI-enabled enterprise systems. Full article

Classical Game Theory underpins much of AI and multi-agent research, but hybrid Human–AI systems require a framework in which execution authority can alternate within a digital environment. We introduce Neo-Game Theory, an extension of Classical Game Theory for hybrid Human–AI coalitions operating under Virtual Nature, the algorithmic analogue of classical (physical) Nature. The framework combines a lexicographic coalition utility with a delegation rule based on the Jensen–Shannon divergence between Human and AI policies. Two thresholds define agreement, contextual, and disagreement regions. In the contextual region, execution follows a scenario-specific rule. Apart from the theory, in this paper we develop the first regime, Human arbitration, in which the AI learns by observation and frequency matching while the Human retains final execution authority. We establish the axiomatic basis of the framework and characterize a frequency-convergence equilibrium, providing the foundation for later extensions and computational validation. Full article

Background: Topological Data Analysis (TDA) captures multi-scale geometric features of data as persistence diagrams, yet no principled information-theoretic framework quantifies how much information those features carry, how efficiently they compress, or when they are informationally irreducible. Methods: We construct a measure-theoretic probability space over persistence diagram space using a Poisson-process reference measure, and define topological entropy (H-T), topological mutual information (I-T), and a topological rate–distortion function as the core objects of a new theory. Results: Four theorems with full proofs establish finite stability, axiomatic uniqueness, a Topological Data Processing Inequality, and a Rate–Distortion Theorem with explicit Poisson-model closed-form formula. A Renyi generalization of topological entropy is also established. Computational and practical implementation aspects—including finite-sample estimation, multi-parameter extension, and algorithmic realization—are addressed inline throughout the paper. Conclusions: This framework provides a rigorous measure-theoretic information-theoretic foundation for persistent homology, demonstrated on simulated brain connectivity and point cloud data, with applications to threshold selection, genomic classification bounds, and compressed sensing. Full article

Evaluating emotional understanding in Large Language Models (LLMs) is challenging because assessments are subjective, ambiguous, multidimensional, and sensitive to controllable generation parameters. We developed a unified mathematical framework for characterizing LLM “emotional individuality” that integrates softmax sampling–temperature control (the decoding-time temperature parameter exposed by the API and typically used to modulate output randomness during token generation), fuzzy set theory with Shannon-type fuzzy entropy, and persona-based cognitive diversity analysis. We evaluated 36 API-accessible LLMs from seven major vendors on Japanese literary texts, using four personas each assigned a sampling temperature ($T\in \{0.1,0.4,0.7,0.9\}$), yielding 4227/4320 trial responses (97.8% coverage), of which 4067/4227 contained valid numeric emotion scores (96.2%). Temperature controllability varied approximately 25-fold (${\kappa }_M\in [0.039,0.982]$) with both positive and negative temperature–variance relationships across models. Because each sampling temperature is deterministically assigned to a persona in our design, ${\kappa }_M$ should be interpreted as an operational temperature–variance association across persona conditions rather than an isolated causal temperature effect. The model-level mean fuzzy entropy ranged from approximately 0.40 to 0.66, and the numerical stability consistency scores ranged from approximately 0.548 to 0.780. We also observed text-dependent structure, including genre-specific variation in the Interest–Sadness relationship. For practitioners, the framework is most directly useful as a benchmark-design and model-screening template for structured emotion-scoring tasks; its empirical conclusions remain limited to the present Japanese literary, text-only setting. Full article

The evolution of future Internet and sixth-generation (6G) networks is driving a paradigm shift from classical bit-centric communication toward meaning-aware and task-oriented communication models. Traditional information theory, while fundamental for ensuring reliable symbol transmission, does not account for semantic relevance or task effectiveness, which are critical for emerging applications such as autonomous systems, immersive services, and ultra-low-latency communications. This article presents a comprehensive review of Semantic Communications (SemCom) from a future Internet perspective. The review systematically analyses representative extensions of classical information theory aimed at quantifying semantic information, including semantic information measures, semantic channel capacity, and semantic rate–distortion formulations. In addition, the main mathematical and computational frameworks enabling practical semantic communication systems are examined, including the Information Bottleneck principle, learning-based end-to-end communication architectures, and reinforcement learning approaches for task-oriented optimization under network constraints. The review further discusses the role of semantic metrics, contextual modelling, and task-driven performance evaluation in the design of semantic-aware communication systems. The analysis identifies key open challenges, particularly the lack of a unified theoretical framework, the need for robust and context-aware semantic performance metrics, and the integration of semantic awareness into network-level design. Overall, this review highlights Semantic Communications as a promising paradigm for future Internet and 6G networks, where communication efficiency is increasingly determined by semantic relevance and task effectiveness rather than bit-level fidelity alone. Full article