Search Results (926)

Semantic communication has attracted considerable interest due to its potential to support emerging human-centric services, such as holographic communications, extended reality (XR), and human-machine interactions. Different from traditional communication systems that focus on minimizing the symbol-level distortion (e.g., bit error rate, signal-to-noise ratio, etc.), semantic communication targets at delivering the intended meaning at the destination user which is often quantified by various statistical divergences, often referred to as the semantic distances. Currently, there still lacks a unified framework to quantify the rate-distortion tradeoff for semantic communication with different task-specific semantic distance measures. To tackle this problem, we propose the task-specific rate-distortion theory for semantic communication where different task-specific statistic divergence metrics can be considered. To investigate the impact of different semantic distance measures on the achievable rate, we consider two popular tasks, classification and signal generation. We present the closed-form expressions of the semantic rate-distortion functions for these two different tasks and compare their performance under various scenarios. Extensive experimental results are presented to verify our theoretical results. Full article

Logics of Statements in Context have been proposed as a general framework to describe and relate, in a uniform and unifying way, a broad spectrum of logics and specification formalisms, which also comprise “open formulas”. In particular, it has been shown that we can define arbitrary first-order “open formulas” in arbitrary categories. At present, there are two deficiencies. In the general case, only signatures with predicate symbols are considered and institutions of statements in context are only defined for single signatures. In this paper, we elaborate the special case of traditional many-sorted first-order logic. We show that any many-sorted first-order signature $\mathrm{\Sigma }$ with predicates and (!) operation symbols gives rise to an institution ${\mathcal{FL}}_{\mathrm{\Sigma }}$ of $\mathrm{\Sigma }$-statements in context and that any signature morphism results in a comorphism between the corresponding institutions. We prove that we obtain a functor $\mathcal{FL}:\mathsf{Sig}\to co\mathbb{I}ns$ from the category of signatures into the category of institutions and comorphisms. We construct a corresponding Grothendieck institution ${\mathcal{FL}}^{♯}$ and prove that ${\mathcal{FL}}^{♯}$ is, indeed, an extension of the traditional institution of first-order logic, which only comprises “closed formulas”. We also investigate substitutions in detail and discuss (elementary) diagrams in the sense of traditional first-order logic. Full article

Let $\Sigma$ be a nonempty set of characters, called an alphabet. The run-length encoding $\left(\mathrm{RLE}\right)$ algorithm processes any nonempty string u over $\Sigma$ and produces two outputs: a k-tuple $(b_1,b_2,\dots ,b_k)$, where each $b_i$ is a character and $b_{i+1}\ne b_i$; and a corresponding k-tuple $(q_1,q_2,\dots ,q_k)$ of positive integers, so that the original string can be reconstructed as $u=b_1^{q_1}{b}_2^{q_2}\dots b_k^{q_k}$. The integer k is termed the run-length of u, and symbolized by $\rho \left(u\right)$. By convention, we let $\rho \left(\epsilon \right)=0$. In the Euclidean space $({\mathbb{R}}^n,\parallel ·{\parallel }_2)$, the volume of a sphere is determined solely by the dimension n and the radius, following well-established formulas. However, for spheres of strings under the edit metric, the situation is more complex, and no general formulas have been identified. This work intended to show that the volume of the sphere ${\mathbf{S}}_L(u,1)$, composed of all strings of Levenshtein distance 1 from u, is dependent on the specific structure of the “$\mathrm{RLE}$-decomposition” of u. Notably, this volume equals $(2\mathcal{l}\left(u\right)+1)s-\left(2\mathcal{l}\left(u\right)-\rho \left(u\right)\right)$, where $\rho \left(u\right)$ represents the run-length of u and $\mathcal{l}\left(u\right)$ denotes its length (i.e., the number of characters in u). Given an integer $p\ge 2$, we present a partial result concerning the computation of the volume $\left|{\mathbf{S}}_L(u,p)\right|$ in the specific case where the run-length $\rho \left(u\right)=1$. More precisely, for a fixed integer $n\ge 1$ and a character $a\in \Sigma$, we explicitly compute the volume of the Levenshtein sphere of radius p, centered at the string $u=a^n$. This case corresponds to the simplest run structure and serves as a foundational step toward understanding the general behavior of Levenshtein spheres. Full article

The Buades Gallery (1973–2003) was not merely a commercial space in Madrid. In the history of art in Spain, it served as a professional and political node for Spanish conceptualism, an art form which, due to its idiosyncrasies, required its own channels of distribution. This article seeks to examine the trajectory of Mercedes Buades in alignment with this movement, re-evaluating her role from a feminist perspective and highlighting the importance of certain agents who have traditionally been invisibilised. To this end, a theoretical approach is adopted, following the sociology of art and the social history of art, paying particular attention to the contributions of Enrico Castelnuovo, Pierre Bourdieu and Núria Peist. These frameworks enable an analysis of the role of the gallerist as a structuring agent within the artistic field, capable of generating symbolic capital and establishing dynamics of production, circulation and consumption in the context of post-Franco Spain, a country that lacked a consolidated museum infrastructure at the time. Even so, Mercedes Buades established a model of gallery practice that, beyond its commercial dimension, contributed decisively to the symbolic configuration of contemporary art in Spain and formed part of a network of artistic visibility that promoted experimental art. Full article

Physics-informed neural networks (PINNs) have emerged as a transformative methodology integrating deep learning with scientific computing. This review establishes a three-dimensional analytical framework to systematically decode PINNs’ development through methodological innovation, theoretical breakthroughs, and cross-disciplinary convergence. The contributions include threefold: First, identifying the co-evolutionary path of algorithmic architectures from adaptive optimization (neural tangent kernel-guided weighting achieving 230% convergence acceleration in Navier-Stokes solutions) to hybrid numerical-deep learning integration (5× speedup via domain decomposition) and second, constructing bidirectional theory-application mappings where convergence analysis (operator approximation theory) and generalization guarantees (Bayesian-physical hybrid frameworks) directly inform engineering implementations, as validated by $72\%$ cost reduction compared to FEM in high-dimensional spaces ($p<0.01,n=15$ benchmarks). Third, pioneering cross-domain knowledge transfer through application-specific architectures: TFE-PINN for turbulent flows ($5.12\pm 0.87\%$ error in NASA hypersonic tests), ReconPINN for medical imaging ($▵\mathrm{SSIM}=+0.18\pm 0.04$ on multi-institutional MRI), and SeisPINN for seismic systems ($0.52\pm 0.18$ km localization accuracy). We further present a technological roadmap highlighting three critical directions for PINN 2.0: neuro-symbolic, federated physics learning, and quantum-accelerated optimization. This work provides methodological guidelines and theoretical foundations for next-generation scientific machine learning systems. Full article

We present a pipeline for synthetic simplification of text in French that combines large language models with structured semantic guidance. Our approach enhances data generation by integrating contextual knowledge from Wikipedia and Vikidia articles and injecting symbolic control through lightweight knowledge graphs. To construct document-level representations, we implement a progressive summarization process that incrementally builds running summaries and extracts key ideas. Simplifications are generated iteratively and assessed using semantic comparisons between input and output graphs, enabling targeted regeneration when critical information is lost. Our system is implemented using LangChain’s orchestration framework, allowing modular and extensible coordination of LLM components. Evaluation shows that context-aware prompting and semantic feedback improve simplification quality across successive iterations. Full article

Tool wear modeling in CNC turning processes is critical for proactive maintenance and process optimization in intelligent manufacturing. However, traditional physics-based models lack adaptability, while machine learning approaches are often limited by poor interpretability. This study develops Kolmogorov–Arnold Networks (KANs) to address the trade-off between accuracy and interpretability in lathe tool wear modeling. Three KAN variants (KAN-A, KAN-B, and KAN-C) with varying complexities are proposed, using feed rate, depth of cut, and cutting speed as input variables to model flank wear. The proposed KAN-based framework generates interpretable mathematical expressions for tool wear, enabling transparent decision-making. To evaluate the performance of KANs, this research systematically compares prediction errors, topological evolutions, and mathematical interpretations of derived symbolic formulas. For benchmarking purposes, MLP-A, MLP-B, and MLP-C models are developed based on the architectures of their KAN counterparts. A comparative analysis between KAN and MLP frameworks is conducted to assess differences in modeling performance, with particular focus on the impact of network depth, width, and parameter configurations. Theoretical analyses, grounded in the Kolmogorov–Arnold representation theorem and Cybenko’s theorem, explain KANs’ ability to approximate complex functions with fewer nodes. The experimental results demonstrate that KANs exhibit two key advantages: (1) superior accuracy with fewer parameters compared to traditional MLPs, and (2) the ability to generate white-box mathematical expressions. Thus, this work bridges the gap between empirical models and black-box machine learning in manufacturing applications. KANs uniquely combine the adaptability of data-driven methods with the interpretability of physics-based models, offering actionable insights for researchers and practitioners. Full article

In his passion, Jesus Christ was a victim of the intentional violent acts of others, which were highly likely to have been traumatic for him and those around him. In the Eucharist, traumatizing acts and events are represented through symbolism, narrative and action. Although the body is a common doctrinal and eucharistic trope, particularly in Paul, the flesh, which is prominent in Johannine imagery, is a more distinctively Christian symbol as well as being more generative for a eucharistic theology of the victim. In the eucharistic elements of separated bread and wine, Christ the priest is presented as also the paradigmatic victim. His shed blood, which was not reassimilated into his flesh at his resurrection, indicates an abiding earthly humanity in solidarity with other victims. For traumatized victims, where space in the Eucharist is provided for the acknowledgement of suffering and other negativity, participation in it may be a pathway of transformation. Traumatized victims might themselves continue this priestly transformation in the world, bearing, like Christ, the sins and woundedness of others and contributing to Christian witness, instruction and healing. Full article

Digital predistortion and nonlinear behavioral modeling of power amplifiers (PA) have been the subject of intensive research in the time domain (TD), in contrast with the limited number of works conducted in the frequency domain (FD). However, the adoption of orthogonal frequency division multiplexing (OFDM) as a prevalent modulation scheme in current wireless communication standards provides a promising avenue for employing an FD approach. In this work, a procedure to model nonlinear distortion in wireless OFDM systems in the frequency domain is demonstrated for general model structures based on a sparse Bayesian learning (SBL) algorithm to identify a reduced set of regressors capable of an efficient and accurate prediction. The FD-SBL algorithm is proposed to first identify the active FD regressors and estimate the coefficients of the PA model using a given symbol, and then, the coefficients are employed to predict the distortion of successive OFDM symbols. The performance of this proposed FD-SBL with a validation NMSE of $-47$ dB for a signal of 30 MHz bandwidth is comparable to $-46.6$ dB of the previously proposed implementation of the TD-SBL. In terms of execution time, the TD-SBL fails due to excessive processing time and numerical problems for a 100 MHz bandwidth signal, whereas the FD-SBL yields an adequate validation NMSE of −38.6 dB. Full article

Machine predictive maintenance plays a critical role in reducing unplanned downtime, lowering maintenance costs, and improving operational reliability by enabling the early detection and classification of potential failures. Artificial intelligence (AI) enhances these capabilities through advanced algorithms that can analyze complex sensor data with high accuracy and adaptability. This study introduces an explainable AI framework for failure detection and classification using symbolic expressions (SEs) derived from a genetic programming symbolic classifier (GPSC). Due to the imbalanced nature and wide variable ranges in the original dataset, we applied scaling/normalization and oversampling techniques to generate multiple balanced dataset variations. Each variation was used to train the GPSC with five-fold cross-validation, and optimal hyperparameters were selected using a Random Hyperparameter Value Search (RHVS) method. However, as the initial Threshold-Based Voting Ensembles (TBVEs) built from SEs did not achieve a satisfactory performance for all classes, a meta-dataset was developed from the outputs of the obtained SEs. For each class, a meta-dataset was preprocessed, balanced, and used to train a Random Forest Classifier (RFC) with hyperparameter tuning via RandomizedSearchCV. For each class, a TBVE was then constructed from the saved RFC models. The resulting ensemble demonstrated a near-perfect performance for failure detection and classification in most classes (0, 1, 3, and 5), although Classes 2 and 4 achieved a lower performance, which could be attributed to an extremely low number of samples and a hard-to-detect type of failure. Overall, the proposed method presents a robust and explainable AI solution for predictive maintenance, combining symbolic learning with ensemble-based meta-modeling. Full article

This paper develops the argument that, in the application of AI to improve the system of governance for higher education, machine learning will be more effective in some areas than others. To make that assertion more systematic, a classificatory taxonomy of types of decisions is necessary. This paper draws upon the classification of decision processes as either symbolic or sub-symbolic. Symbolic approaches focus on whole system design and emphasise logical coherence across sub-systems, while sub-symbolic approaches emphasise localised decision making with distributed engagement, at the expense of overall coherence. AI, especially generative AI, is argued to be best suited to working at the sub-symbolic level, although there are exceptions when discriminative AI systems are designed symbolically. The paper then uses Beer’s Viable System Model to identify whether the decisions necessary for viability are best approached symbolically or sub-symbolically. The need for leadership to recognise when a sub-symbolic system is failing and requires symbolic intervention is a specific case where human intervention may be necessary to override the conclusions of an AI system. The paper presents an initial analysis of which types of AI would support which functions of governance best, and explains why ultimate control must always rest with human leaders. Full article

Quaternions are used in various applications, especially in those where it is necessary to model and represent rotational movements, both in the plane and in space, such as in the modeling of the movements of robots and mechanisms. In this article, a methodology to model the rigid rotations of coupled bodies by means of unit quaternions is presented. Two parallel robots were modeled: a planar RRR robot and a spatial motion PRRS robot using the proposed methodology. Inverse kinematic problems were formulated for both models. The planar RRR robot model generated a system of 21 nonlinear equations and 18 unknowns and a system of 36 nonlinear equations and 33 unknowns for the case of space robot PRRS; both systems of equations were of the polynomial algebraic type. The systems of equations were solved using the Broyden–Fletcher–Goldfarb–Shanno nonlinear programming algorithm and Mathematica V12 symbolic computation software. The modeling methodology and the algebra of unitary quaternions allowed the systematic study of the movements of both robots and the generation of mathematical models clearly and functionally. Full article

In the context of rapid global digitalization and evolving media ecologies, sustainable cultural communication has become central to both museum transformation and the theoretical renewal of iconology. Images, as vital carriers of cultural memory and identity, are shifting from static, linear presentations to generative, interactive, and participatory modes enabled by digital platforms. This shift calls for a new paradigm in image communication—one that integrates meaning construction with technological and user-centered logics. This study adopts a “technology–culture–user” framework, drawing on constructivism, cultural memory theory, and symbolic interactionism to construct a digital-era iconological system. Through comparative analysis of the Chinese Palace Museum and the National Museum of Korea, the research reveals complementary approaches: the former emphasizes structured, authoritative knowledge dissemination, while the latter prioritizes immersive, user-driven interaction. These differences provide a basis for cross-cultural cooperation. Accordingly, the paper proposes five collaborative strategies: integrating advanced technologies, building shared image resource systems, enhancing user engagement mechanisms, expanding East Asian visual symbol networks, and adapting institutional frameworks to diverse cultural contexts. These strategies aim to support both theoretical innovation in iconology and sustainable regional cultural communication in the digital age. Full article

In this study, we introduce Shannon entropy as a key metric for assessing concentration variability in diffusion processes. Shannon entropy quantifies the uncertainty or disorder in the spatial distribution of diffusing particles, providing a novel perspective on diffusion dynamics. This proposed approach enables a more comprehensive characterization of mixing efficiency, equilibrium states, and transient diffusion behavior. Numerical simulations performed using the finite difference method in the MAPLE 2025 symbolic computing environment illustrate how entropy evolution correlates with diffusion kinetics. The computational model used in this study is based on a previously developed framework from our earlier research, ensuring consistency and validation of the results. The findings suggest that Shannon entropy can serve as a robust descriptor of diffusion-driven mixing, with potential applications in engineering, environmental science, and biophysics. Full article

Archaeological mollusk shells, such as those of Littorina obtusata/fabalis, hold valuable information about past human behavior and cultural practices. However, the original coloration of these shells, crucial for understanding their symbolic significance, is often lost due to taphonomic processes. Raman spectroscopy is a powerful technique for non-destructive analysis of archaeological samples, enabling the identification of pigments and mineralogical components. In this study, we present a methodology to predict, using Raman spectroscopy and k-means clustering, the original coloration of archaeological L. obtusata/fabalis shells which have lost their original coloration. Raman spectra were acquired from both modern shells, exhibiting a range of natural colors, and archaeological shell samples from La Chora cave (Cantabria, northern Spain). Spectral data were preprocessed to remove noise and baseline effects, and k-means clustering was applied to group the spectra based on their inherent spectral similarities. By comparing the spectral signatures of the archaeological samples with those of the modern shells within the generated clusters, we inferred the likely original coloration of the archaeological specimens. This approach provides a quantitative framework for predicting archaeological shell colors. Full article