Search Results (22,707)

The accurate inference of hidden states from non-stationary physiological signals remains a significant challenge in stochastic process modeling. This paper proposes an Adaptive Sticky Hidden Markov Model (Sticky-HMM) framework designed to enhance the robustness of state decoding in noisy environments. To address the “state-flickering” issue inherent in traditional HMMs, we incorporate a “Sticky” parameter into the transition matrix, imposing a temporal penalty on spurious state switching to maintain continuity. Furthermore, we introduce a Dynamic Prior Strategy that adaptively calibrates self-transition probabilities by mapping frequency-domain features of the observed sequence to the model’s parameter space. The proposed decoding process employs a two-pass refinement strategy and the Viterbi algorithm in the logarithmic domain to ensure numerical stability. The model’s efficacy was validated using a high-fidelity dataset of simulated apnea events. This work provides a computationally efficient and mathematically rigorous approach that demonstrates strong potential for long-term respiratory health monitoring. Full article

Non-dilute emulsions are emulsions where the concentration of the droplets is high enough for the neighbouring droplets to interact with each other hydrodynamically but is still smaller than the packed bed concentration where the droplets are packed and deformed against each other. Thus, they cover a broad range of droplet concentrations. Many emulsions encountered in industrial applications fall under this category. Non-dilute emulsions exhibit rich rheological behaviour, from a simple Newtonian fluid to a highly non-Newtonian fluid, reflecting shear-thinning, shear-thickening, yield stress, viscoelasticity, etc. In this article, the rheology of non-dilute emulsions is reviewed comprehensively. Emulsions of hard-sphere-type droplets and deformable droplets, with and without surfactants, are covered. The mathematical models describing the rheological behaviour of non-dilute emulsions are discussed. The influences of electric charge and interfacial rheology on the rheological behaviour of emulsions are covered in detail. The flocculation of droplets caused by different mechanisms, such as depletion and bridging induced by additives, and their effect on emulsion rheology are investigated thoroughly. Finally, the dynamic rheology of non-dilute emulsions is discussed, covering both pure oil–water interfaces and additive-laden interfaces. The mathematical models describing the dynamic rheological behaviour of non-dilute emulsions are described. Based on the existing theoretical and empirical models, it is possible to a priori predict the rheology of non-dilute emulsions. However, serious gaps in the existing knowledge on non-dilute emulsion rheology remain. This review identifies the gaps in existing knowledge and points out future directions in research related to non-dilute emulsion rheology. 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

In this paper, by means of a comprehensive analysis of the statutory and non-statutory documents that govern its preschool provision, we examine how early childhood education and care (ECEC), particularly in relation to mathematics, is conceptualised by the English educational authorities. Situated within international debates about economic (school-readiness, accountability-driven) versus social (holistic, play-based, rights-oriented) models of ECEC, the study explores how curriculum expectations, assessment practices and didactical guidance collectively frame young children’s learning opportunities. Drawing on a document-based analytic approach, and guided by six literature-derived questions, the analysis reveals significant inconsistencies both within and between documents, including conflicting messages about the purpose of preschool, an uneven emphasis on school readiness, and ambivalent statements regarding the role of play, instruction and practitioner agency, as well as contradictory and shifting expectations surrounding the scope, status and pedagogical treatment of early mathematics. While statutory materials frequently privilege school readiness and narrowly defined number outcomes, non-statutory guidance promotes broader mathematical thinking, exploratory play and child-initiated reasoning. Overall, the findings demonstrate limited coherence across the English authorities’ ECEC expectations and highlight the interpretive and professional challenges faced by practitioners expected to implement this fragmented early years mathematics policy landscape. Full article

Coal preparation tailings from the K18 seam of the Abayskaya mine were evaluated as a potential secondary source of critical rare earth elements (REEs). The study showed that REEs are predominantly associated with the mineral fraction of coal; therefore, during beneficiation, approximately 70% of their total content is transferred to flotation tailings. The concentrations of valuable elements in the tailings are as follows (g/t): Li—65; Sc—16; Y—17; Yb—2.5; V—135; and Ti—2293. These values significantly exceed the Clarke values and are comparable to those of some low-grade primary ores, indicating the potential of coal preparation wastes as a technogenic raw material for critical elements. To extract REEs from the resistant aluminosilicate matrix, a fluorine–ammonium sulfate thermochemical activation method was proposed. Using a probabilistic–deterministic experimental design approach, a mathematical model of the process was developed and optimal parameters were determined (400 °C, 120 min, (NH₄)₂SO₄ consumption—140% relative to Al, NH₄HF₂ consumption—110% relative to Si), providing a feed liberation degree (by Al extraction) of up to 94%. Under optimal conditions, high leaching efficiencies of key elements were achieved: Sc (95%), Y (100%), Yb (100%), and Li (100%). The results demonstrate the significant potential of coal preparation tailings as a secondary resource of rare earth elements and confirm the efficiency of fluorine–ammonium sulfate technology for processing this type of technogenic waste. Full article

Many physical systems contain elements with distributed and lumped parameters; this paper proposes modeling these systems using a bond graph approach. A junction structure is proposed in which the relationships between the distributed and lumped parameter elements are indicated; from this structure, the state space mathematical model of the system is obtained. Thus, a symmetry between the graphical model and the mathematical model is determined. Traditionally, the distributed parameters in the bond graph approach have been modeled by fields. However, when these fields may be subject to external disturbances or parametric uncertainties, their analysis is complicated to carry out because all the information is in a compact form. Therefore, this paper presents a methodology for changing a field in an element model; these fields can be storage fields in an integral or derivative causality assignment or dissipation fields in both cases for any number of field ports. Likewise, there is another symmetry in bond graph from a model with fields to a model with elements. As a case study, a wind turbine containing fields and elements in bond graph is modeled. The state space mathematical model of the turbine is obtained from the bond graph structure of the model with fields in bond graph. Another model of the turbine in bond graph with elements only, applying the field decomposition procedure to elements, is presented. Thus, an external disturbance is introduced into the turbine model with elements showing the objective of obtaining this symmetrical model of the turbine. Simulation results of bond graphs with fields and elements are obtained by checking the symmetry of the models. Likewise, the behavior under conditions of an external disturbance applied to the turbine is presented. Full article

Additive-manufactured (AM) 316L stainless steel, produced via direct metal laser sintering (DMLS) and characterised by a surface topography of high irregularities and tensile residual stresses with specific anisotropy, was subjected to milling and shot peening. The milling process caused a reduction in surface topography parameters, but tensile residual stresses increased significantly. The shot peening process was carried out according to the full factorial design 3² and technological parameters such as a shot diameter in the range of 1-3 mm and an air supply pressure between 0.2 and 0.6 MPa. As a result of the experiments and the analysis, reduced surface topography was achieved, and a favourable residual stress state was formed with compressive stresses. The mechanism of the changes was demonstrated via microstructure observation and statistical models obtained by mathematical analysis. Full article

In this paper, we clarify several issues concerning the abstract geometrical formulation of thermodynamics on non-compact symmetric spaces $\mathrm{U}/\mathrm{H}$ that are the mathematical model of hidden layers in the new paradigm of Cartan Neural Networks. We introduce a clear-cut distinction between the generalized thermodynamics associated with Integrable Dynamical Systems and the challenging proposal of Gibbs probability distributions on $\mathrm{U}/\mathrm{H}$ provided by generalized thermodynamics à la Souriau. Our main result is the proof that $\mathrm{U}/\mathrm{H}$.s supporting such Gibbs distributions are only the Kähler ones. Furthermore, for the latter, we solve the problem of determining the space of temperatures, namely, of Lie algebra elements for which the partition function converges. The space of generalized temperatures is the orbit under the adjoint action of $\mathrm{U}$ of a positivity domain in the Cartan subalgebra $C_c\subset \mathbb{H}$ of the maximal compact subalgebra $\mathbb{H}\subset \mathbb{U}$. We illustrate how our explicit constructions for the Poincaré and Siegel planes might be extended to the whole class of Calabi–Vesentini manifolds utilizing Paint Group symmetry. Furthermore, we claim that Rao’s, Chentsov’s, and Amari’s Information Geometry and the thermodynamical geometry of Ruppeiner and Lychagin are the very same thing. In particular, we provide an explicit study of thermodynamical geometry for the Poincaré plane. The key feature of the Gibbs probability distributions in this setup is their covariance under the entire group of symmetries U. The partition function is invariant against $\mathrm{U}$ transformations, and the set of its arguments, namely the generalized temperatures, can always be reduced to a minimal set whose cardinality is equal to the rank of the compact denominator group $\mathrm{H}\subset \mathrm{U}$. Full article

Background and Objectives: Determining the mechanical stability of osteosynthesis in pertrochanteric fractures remains a critical challenge in orthopedic biomechanics. The aim of this study was to develop a mathematical model for quantifying the stability of osteosynthesis and to establish criteria for its evaluation under physiological loading conditions. Materials and Methods: A mathematical model describing the biomechanical behavior of a proximal femur with a pertrochanteric fracture stabilized using a cephalomedullary nail (CMN) was developed. The model integrates force equilibrium, stress–strain relationships, and loading conditions representative of early functional rehabilitation. The theoretical framework was implemented in MATLAB/Simulink R2025b and complemented by finite element analysis to determine stress distribution, deformation patterns, and stability-related parameters of the bone–implant system. Results: The developed mathematical model enabled a quantitative assessment of osteosynthesis stability through the evaluation of key mechanical indicators, including displacement, stress distribution, and safety factor within the fixation system. Critical stress zones in the implant and surrounding bone were identified, allowing analysis of load transfer mechanisms. Finite element simulations showed that improved fixation mechanics reduced peak implant stresses, limited displacement at the fracture site, and increased the safety factor of the fixation construct, resulting in a more uniform load distribution in the surrounding bone and enhanced overall stability of the osteosynthesis system. Conclusions: The proposed mathematical model provides a systematic approach for determining the stability of osteosynthesis in pertrochanteric fractures. It offers a theoretical basis for optimizing implant design and fixation strategies, with potential applications in preclinical evaluation and surgical planning. Full article

This study stems from the need to investigate how GenAI tools, particularly ChatGPT-4o, can support the professional development of mathematics teachers. It explores how Blum’s modeling cycle can serve as a conceptual and operational framework for mathematics teachers’ instructional design when supported by ChatGPT-4o. Drawing on a qualitative case study within a teacher professional development program, the research analyzes how two upper secondary school teachers engaged with ChatGPT-4o to redesign a mathematical task involving probability and real-world contexts. Data include responses to three modeling-related tasks, teachers’ prompts and interactions with ChatGPT-4o, and the final mathematical activity they designed. These materials were analyzed qualitatively according to the modeling cycle and its sub-competencies. The results indicate that the modeling cycle provided teachers with a cognitive and methodological scaffold to guide their interaction with ChatGPT-4o, allowing them to structure, validate, and refine AI-generated ideas through all stages of modeling—from understanding and mathematizing to interpreting and validating. These findings suggest that the modeling cycle can be reinterpreted as a design-oriented framework for integrating ChatGPT-4o in mathematics teacher education. Implications for teacher professional development and future research directions are discussed. Full article

This paper presents an integrated mathematical model to improve the safety and operational efficiency of train traffic in centralised railway dispatching systems. The proposed approach combines the alternative graph model with a Mealy automaton to synchronously address route planning, delay minimisation, and strict compliance with safety requirements. Formal control theory based on finite-state automata is employed to describe routing logic and signal control through state transitions, while the alternative graph model represents scheduling constraints and resource conflicts. To enhance real-time adaptability, a tabu search algorithm is implemented for train schedule optimisation, enabling dynamic rescheduling under changing operational conditions. The mathematical formulation incorporates blocking time parameters, a system of discrete constraints, and automaton-based safety conditions governing train movements and route authorisation. The integrated model explicitly formalises the processes of block section occupation and release, ensuring consistency between control logic and scheduling decisions. Practical testing and computational experiments demonstrate that the proposed approach effectively reduces train delays, improves the reliability of dispatch control, and increases system resilience to dynamic disturbances. The results confirm that the developed model can be implemented within existing centralised dispatching infrastructures without requiring a complete system overhaul. Overall, the proposed framework expands the functional capabilities of centralised dispatch systems by enabling efficient schedule generation, minimising the propagation of delays, and ensuring reliable command exchange between central control posts and field-level railway infrastructure. Full article

Personalized instruction remains a major bottleneck in higher education, especially in large classes where timely, individualized feedback is difficult to achieve. Existing automation typically relies on rigid rule-based pipelines or computationally heavy deep learning models, making it difficult to simultaneously achieve interpretability, instructional usability, and scalable deployment. In this study, we present CalcTutor, a generative-AI-based assessment and feedback system designed to support open-ended handwritten calculus problem solving. The system organizes instructional support through three coordinated components: (1) a multi-agent large language model (LLM) mechanism that evaluates solution processes and produces diagnostic feedback, (2) a retrieval-augmented generation (RAG) pipeline that links diagnosed difficulties to aligned instructional materials, and (3) real-time learner analytics for both students and instructors, forming an integrated instructional support workflow rather than an automated answer-checking tool. In offline evaluation and a pilot classroom deployment, the multi-agent grader achieved a weighted agreement accuracy of 0.931 and an F1-score of 0.934 on 1055 handwritten solutions. Participant feedback and workflow testing indicated that CalcTutor can be stably integrated into routine classroom use and enables students to interpret and act upon the provided feedback. These results indicate that automated assessment, diagnostic feedback, and targeted review can operate coherently within a single instructional process that supports instructor-led assessment practices. Using undergraduate calculus as an application domain for open-ended handwritten mathematical assessment, the study demonstrates the operational feasibility of a closed-loop assessment–feedback–revision workflow and provides a deployable instructional infrastructure for formative instructional support in real classroom contexts. Full article

The control of surface residual stress is paramount for ensuring the mechanical performance and longevity of machined GH2132 superalloy bolts. However, direct measurement of residual stress remains challenging. This study introduces a novel, efficient approach by establishing a quantitative correlation between Vickers hardness and residual stress based on the energy indentation method. The core hypothesis leverages the principle that residual stress modifies the indentation work; the difference in energy dissipation between stressed and stress-free states provides a direct measure of residual stress. A mathematical model relating hardness (HV) to residual stress (σ) was derived. To validate the model and unravel the underlying microstructural mechanisms, orthogonal cutting experiments were conducted. Comprehensive microstructural characterization using SEM, XRD, and metallography revealed a synchronous relationship between hardness and residual stress. Both properties increased concurrently with greater grain refinement and higher volume fraction/distribution density of carbides and γ’ phases, which impede dislocation motion and introduce micro-strain. The model predictions showed excellent agreement (R² = 92.5%) with X-ray diffraction measurements, confirming its reliability. Furthermore, the influence of cutting parameters (speed V_c, feed f, depth of cut a_p) on residual stress was analyzed. Cutting depth was identified as the most significant factor. An optimal parameter combination (V_c = 20 m × min⁻¹, f = 1 mm × rev⁻¹, a_p = 1.2 mm) was identified to maximize beneficial compressive residual stress, corresponding to the most refined microstructure. This work presents a validated, hardness-based model for residual stress assessment in GH2132 and provides a microstructure-guided pathway for optimizing machining processes to enhance component life. Full article

This study addresses the problem of improving the efficiency of fine grinding of bulk materials in a spring-rotor mill. The objective is to determine technologically sound operating parameters based on mathematical modeling, design of experiments, and multi-objective optimization. The methodology relies on a full-factorial experimental design according to the Hartley plan, with five control factors: rotor rotational speed, material loading ratio, overlap of the working zones, grinding chamber clearance, and grinding duration. The analyzed responses include grinding fineness, throughput, power consumption, specific energy consumption, and specific metal intensity. Based on experimental data, adequate second-order polynomial regression models were obtained for all response variables using the least-squares method. Statistical analysis showed that grinding time and rotational speed had the most significant influence on the process. Multi-objective optimization using the weighted-sum method enabled the identification of optimal operating conditions that balance product quality, throughput, and energy consumption. Verification experiments confirmed the adequacy of the developed models. Practical implementation of the optimized regimes increases throughput by 15–20% while simultaneously reducing energy consumption by 8–12% compared with empirically selected operating conditions. The proposed models and recommendations provide a quantitative basis for tuning and controlling grinding equipment in processing industries. Full article

Background: Gestational diabetes mellitus (GDM) affects many pregnancies worldwide and is associated with adverse maternal and fetal outcomes. Current screening at 24–28 weeks limits opportunities for early intervention. We evaluated whether machine learning (ML) models using first-trimester clinical and dietary data can predict GDM risk before the standard oral glucose tolerance test. Methods: We analyzed data from 797 pregnant women enrolled in the BORN2020 prospective cohort study (Thessaloniki, Greece). Ten ML algorithms were evaluated across five class-imbalance handling strategies using stratified 5-fold cross-validation, with final evaluation on an independent 20% held-out test set. Features included maternal demographics, obstetric history, lifestyle factors, and 22 dietary micronutrient intakes from the pre-pregnancy period assessed by Food Frequency Questionnaire. Results: The best-performing model (Logistic Regression without resampling) achieved an AUC-ROC of 0.664 (95% CI: 0.542–0.777), with sensitivity of 0.783 and NPV of 0.932 at the pre-specified threshold. The high NPV should be interpreted in the context of the low GDM prevalence (14.7%), as NPV is mathematically dependent on disease prevalence. A reduced nine-feature model using only routine clinical and demographic variables achieved a numerically higher AUC of 0.712 (95% CI: 0.589–0.825), with overlapping confidence intervals, indicating that detailed FFQ-derived micronutrient data did not improve prediction. Maternal age and pre-pregnancy BMI were the strongest individual predictors by SHAP analysis. No model reached the AUC >0.80 threshold for good discrimination. Substantial miscalibration was observed (slope: 0.56; intercept: −1.83), limiting use for absolute risk estimation. Conclusions: This exploratory study demonstrates that first-trimester ML models achieve modest discriminative ability for early GDM prediction, with routine clinical variables performing comparably to models incorporating detailed dietary assessment. These findings should be interpreted with caution, as no external validation cohort was available and the low events-per-variable ratio (~3.8) constrains the reliability of individual model estimates. Substantial miscalibration further limits use for absolute risk estimation. Accordingly, these models should be regarded as exploratory risk-ranking tools only and require external validation and recalibration before any clinical implementation. Full article