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32 pages, 4589 KB  
Article
Tactule: A Multilayer-Bimorph Piezoelectric Tactile Display Module—System Architecture, Load-Dependent Frequency Response, and Receptor-Level Response Predictions
by Takahiro Miura, Ken-ichiro Yabu, Atsushi Katagiri, Masaki Matsuo, Naoyuki Okochi, Keiichi Yasu, Masatsugu Sakajiri and Tohru Ifukube
J. Sens. Actuator Netw. 2026, 15(4), 69; https://doi.org/10.3390/jsan15040069 - 18 Aug 2026
Abstract
We developed Tactule, a compact tactile display module that can be attached to host hardware ranging from PCs to game controllers, and characterized its frequency response under controlled, finger-pad-like loading. Tactule uses a 6×6 matrix of multilayer-bimorph piezoelectric pins (with [...] Read more.
We developed Tactule, a compact tactile display module that can be attached to host hardware ranging from PCs to game controllers, and characterized its frequency response under controlled, finger-pad-like loading. Tactule uses a 6×6 matrix of multilayer-bimorph piezoelectric pins (with the four corner pins removed; 32 channels at 2 mm pitch), together with an 8×8 variant, that delivers more than 60 μm of free displacement at AC 5 V, a regime accessible from a standard USB power supply. We measured per-pin peak-to-peak rear-face displacement at 50–800 Hz across a graded series of five silicone loads (Shore A 10 to 90) and an unloaded reference, using sinusoidal and rectangular driving signals. The unloaded response peaks at 600 Hz; Shore A 10 loading shifts the peak to 750 Hz; and above 700 Hz, the Shore A 10 amplitude exceeds the unloaded amplitude. Coupling the measured waveforms to published models of the tactile periphery shows that the module drives the Pacinian channel with a wide margin throughout the band while reaching the non-Pacinian channels only at its low-frequency edge, providing engineering knowledge for designing receptor-specific stimulation patterns in assistive applications. Full article
(This article belongs to the Section Actuators, Sensors and Devices)
22 pages, 541 KB  
Article
FINGERTRAP: A Self-Defending Cryptographic Protocol for Network Communications
by Victoria Mellor, Mo Adda and Fahad Ahmad
Electronics 2026, 15(16), 3690; https://doi.org/10.3390/electronics15163690 - 18 Aug 2026
Abstract
FINGERTRAP is a network encryption and authentication protocol that extends the X3DH
and Double Ratchet frameworks with three novel mechanisms inspired by the Chinese
finger trap (zh˘ı w˘ang): a friction ratchet that exponentially increases computational cost
for each failed authentication attempt; a recursive [...] Read more.
FINGERTRAP is a network encryption and authentication protocol that extends the X3DH
and Double Ratchet frameworks with three novel mechanisms inspired by the Chinese
finger trap (zh˘ı w˘ang): a friction ratchet that exponentially increases computational cost
for each failed authentication attempt; a recursive annihilation protocol that irreversibly
destroys all cryptographic state after a configurable failure threshold; and a committhen-
challenge handshake that requires a counterintuitive “inward” action for legitimate
authentication. A bidirectional weave hash extends the Double Ratchet’s transcript binding
to cover every message in both directions. Together, these mechanisms provide permessage
forward secrecy, post-compromise security (self-healing), clock-free operation,
and a self-destruct capability. The individual ingredients-client puzzles, key erasure, and
ratcheting-each build on established lines of work; their combination into a single stateful
protocol, in which failed authentication attempts cryptographically tighten the session
state and ultimately destroy it, is not to our knowledge offered by deployed transport
protocols such as TLS 1.3, Signal, or WireGuard. The design targets deployments in which
interception or capture of a device implies endpoint compromise, such as Unmanned Aerial
Vehicle (UAV) telemetry links and body-worn sensors, where denial of exploitation requires
guaranteed loss of past and future session material. We describe the full protocol, provide
game-based security arguments under an explicit adversarial model, give analytic cost
estimates for the friction mechanism, analyse the denial-of-service surface and a two-layer
mitigation strategy, and specify a post-quantum extension using hybrid X25519/ML-KEM-
768 ratcheting. Full article
(This article belongs to the Special Issue Computer Networking Security and Privacy)
27 pages, 13812 KB  
Article
Multimodal Data Fusion for a Self-Adaptive, Smart, Serious-Game Ecosystem Under Development
by Xiya Tao, Peng Chen and Martina Eckert
Sensors 2026, 26(16), 5132; https://doi.org/10.3390/s26165132 - 13 Aug 2026
Viewed by 209
Abstract
This article presents the implementation and technical feasibility evaluation of the multimodal sensing and feature-level fusion layer of BLEXER v3, a broader serious-game ecosystem under development for upper-limb rehabilitation. The implemented framework integrates Kinect-based motion tracking, Polar H10 and Bangle.js physiological sensing, wearable [...] Read more.
This article presents the implementation and technical feasibility evaluation of the multimodal sensing and feature-level fusion layer of BLEXER v3, a broader serious-game ecosystem under development for upper-limb rehabilitation. The implemented framework integrates Kinect-based motion tracking, Polar H10 and Bangle.js physiological sensing, wearable accelerometer data, and facial affective cues within a middleware-based architecture. Heterogeneous sensor streams are locally preprocessed, temporally aligned, and transformed into a common quality-aware multimodal feature representation containing motion, heart-rate and heart-rate-variability-related descriptors, affective information, availability indicators, signal-quality metadata, and freshness descriptors. The fused representation is additionally mapped, using predefined rules, to heuristic operational descriptors, including low demand, moderate stable, active engagement, physical load, affective activation, high demand, and uncertain. These descriptors are not intended as clinical diagnoses, independently validated user states, or final adaptation decisions. An exploratory K-means analysis of 12,675 complete multimodal windows reveals partial correspondence between the data-driven cluster structure and the predefined operational descriptors. Some descriptors show comparatively concentrated cluster patterns, whereas others exhibit overlap and internal heterogeneity. The results demonstrate the technical feasibility of generating structured multimodal representations that can provide input for subsequent context-aware reasoning. Independent validation of the operational descriptors, completion and evaluation of the whole system, and clinical validation with rehabilitation patients remain future work. Full article
(This article belongs to the Special Issue Smart Sensing System for Intelligent Human–Computer Interaction)
42 pages, 3602 KB  
Review
A Comprehensive Review of Sequence and Generative Models in Motor Imagery (MI) Classification for Brain–Computer Interfaces (BCIs)
by Muhammad Ahmed Abbasi, Hafza Faiza Abbasi, Muhammad Arsalan, Danish Khan, Andres Annuk and Xiaojun Yu
Sensors 2026, 26(16), 5097; https://doi.org/10.3390/s26165097 - 11 Aug 2026
Viewed by 316
Abstract
Motor imagery (MI) classification serves as the backbone to brain–computer interfaces (BCIs) by strengthening the communication bridge between the human brain and external peripheral devices. The past two decades have witnessed unprecedented success in MI-BCIs, with applications not only in medical fields but [...] Read more.
Motor imagery (MI) classification serves as the backbone to brain–computer interfaces (BCIs) by strengthening the communication bridge between the human brain and external peripheral devices. The past two decades have witnessed unprecedented success in MI-BCIs, with applications not only in medical fields but also in several other domains, such as gaming and robotic control. Initially, MI classification primarily relied on classical signal processing techniques that were heavily impacted by signal variations; however, recent trends in deep learning (DL), specifically in sequence-oriented, attention-based, hybrid, and generative architectures such as recurrent neural networks (RNNs), variational autoencoders (VAEs), generative adversarial networks (GANs), and transformers have significantly improved the efficiency and robustness of MI classification. This study presents a comprehensive review of these sequence-oriented, attention-based, hybrid, and generative architectures including RNNs, VAEs, GANs, and transformers, comparing their robustness across various public MI datasets, highlighting their challenges, such as inter-subject variation, low signal-to-noise ratio (SNR), and the obstacles in real-time signal classification. We perform an in-depth analysis on the strengths and limitations of traditional models such as RNNs and LSTMs as well as emergent models such as VAEs and transformers, which have demonstrated superior performance in extracting the intricate patterns of the EEG data with low latency. Moreover, we critically examine the future potential of such models in overcoming current bottlenecks, such as weak generalization on unseen data and high computational load. This study aims to assist researchers in attaining significant insights into the state-of-the-art sequence, attention-based, hybrid, and generative models used in MI classification, thus offering a direction for future innovation. Full article
(This article belongs to the Section Biomedical Sensors)
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29 pages, 5204 KB  
Article
Spatio-Temporal-Frequency Graph Decoupling and Mamba-WKAN Knowledge Distillation for Anomaly Prediction and Early Warning of Power Distribution IoT Devices
by Chen Yang, Xiaofeng Dong, Junhua Hao and Ren Gu
Algorithms 2026, 19(8), 662; https://doi.org/10.3390/a19080662 - 10 Aug 2026
Viewed by 208
Abstract
Power IoT acts as the final frontier of the modern grid, where the reliability of energy supply hinges on precise monitoring. However, current systems often suffer from delayed responses, poor feature separation, and a computational wall when dealing with high-frequency data on the [...] Read more.
Power IoT acts as the final frontier of the modern grid, where the reliability of energy supply hinges on precise monitoring. However, current systems often suffer from delayed responses, poor feature separation, and a computational wall when dealing with high-frequency data on the edge. We move past the traditional reactive detection mindset and propose STF-MKD, a framework built on spatio-temporal-frequency graph decoupling and Mamba-WKAN knowledge distillation. Our goal is to shift the operational focus from responding to failures to forecasting them. The first part of the system is the STF-Extractor. It uses dynamic graph attention to map the connections between nodes and a masking game to pull structural features out of the background noise. Following this, we address the wild nonlinear nature of equipment failure with the Mamba-WKAN backbone. By embedding Mexican Hat wavelets and B-splines into the Mamba architecture, the model maintains efficiency while splitting the work: splines track the daily cycles and wavelets lock onto sudden transients. To prevent the model from smoothing away rare anomaly signals, we introduce the TGAR (Teacher-Guided Anomaly-focused Reconstruction) distillation scheme. This one-teacher-two-students setup uses a teacher model with a global view to guide the student predictor. In doing so, the system triggers early warnings based on faint structural shifts before a fault fully develops. Tests on six major datasets, including ETTh/m and WADI, show that STF-MKD outperforms mainstream methods. Full article
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31 pages, 11673 KB  
Article
Feasibility, Usability, and Preliminary Kinematic Outcomes of a Hand-Tracking Virtual Reality Rehabilitation System Delivered as an Adjunct to Conventional Therapy in Individuals with Stroke: A Single-Arm Pilot Study
by Hayati Türe, Eren Kalfa, Osman Topçu, Köksal Sarıhan, Erhan Özdemir and Buket Özdemir Işık
Healthcare 2026, 14(15), 2373; https://doi.org/10.3390/healthcare14152373 - 3 Aug 2026
Viewed by 331
Abstract
Purpose: Upper extremity motor impairments following stroke substantially limit independence in daily living. Hand-tracking virtual reality (VR) rehabilitation systems may support intensive task-oriented practice while enhancing motivation; however, evidence integrating objective kinematic indicators with usability and patient-reported outcomes for controller-free consumer-grade VR remains [...] Read more.
Purpose: Upper extremity motor impairments following stroke substantially limit independence in daily living. Hand-tracking virtual reality (VR) rehabilitation systems may support intensive task-oriented practice while enhancing motivation; however, evidence integrating objective kinematic indicators with usability and patient-reported outcomes for controller-free consumer-grade VR remains limited. The primary aim of this single-arm pilot study was to evaluate the feasibility, safety (tolerability), and usability of a hand-tracking VR rehabilitation system delivered as an adjunct to conventional physiotherapy in individuals with stroke; describing its preliminary in-game kinematic profile and exploring participants’ experiences through open-ended feedback were secondary aims. The study was explicitly not designed or powered to test clinical efficacy. Materials and Methods: Ten individuals with stroke completed a 20-session (8-week) single-arm pilot intervention; all participants concurrently received standard hospital-based physiotherapy (median 3 sessions/week, ∼45 min/session). Early-phase (sessions 1–5) and late-phase (sessions 16–20) within-subject performance were compared using the Wilcoxon signed-rank test with Holm–Bonferroni correction across four pre-specified primary outcomes. Movement smoothness was assessed using the Spectral Arc Length (SPARC), usability was evaluated using the System Usability Scale (SUS), and cybersickness was monitored with the Simulator Sickness Questionnaire (SSQ). Results: Sixteen patients were screened, of whom fourteen started the intervention and ten completed the 8-week per-protocol program (intervention completion rate, 10/14 = 71.4%; per-protocol session adherence among the ten completers, 200/200 = 100%; no SSQ-defined adverse events). Within-subject comparisons showed a +10.6-point increase in success rate (adjusted p=0.020), a +0.10 m/s increase in mean movement speed (adjusted p=0.020), a 341 ms reduction in pause duration (adjusted p=0.022), and a +27.0-point Hodges–Lehmann median-difference increase in SS-QOL (95% CI 14.041.0; participant-level median Δ+18.5; adjusted p=0.020). The mean SUS score was 78.5±5.4, indicating “good” usability. Thematic analysis of post-intervention open-ended feedback identified three themes—motivation and engagement, the value of feedback, and design and comfort suggestions—that converged with the high adherence and good usability ratings. Correlations between VR-derived kinematic change and clinical change were non-significant trends (p0.12). Conclusions: A controller-free hand-tracking VR system was found to be feasible, well tolerated, and rated as having good usability when delivered as an adjunct to conventional therapy. Because the study used a single-arm design, included only ten participants, and did not control for the confounding effect of concurrent conventional physiotherapy or natural recovery, the observed within-subject changes cannot be causally attributed to the VR intervention and should be interpreted as exploratory feasibility signals. Adequately powered randomized controlled trials with stroke-specific clinical scales (e.g., FMA-UE, ARAT) are required before clinical efficacy can be claimed. Full article
(This article belongs to the Special Issue Physical and Rehabilitation Medicine—2nd Edition)
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36 pages, 4717 KB  
Article
SEAL-MAC: Symmetry-Equivariant Lyapunov Actor–Critic for Queue-Stable MEC Offloading
by Mingchuan Wu, Jian Lu and Yulin Li
Symmetry 2026, 18(8), 1311; https://doi.org/10.3390/sym18081311 - 3 Aug 2026
Viewed by 229
Abstract
Mobile edge computing (MEC) must serve rapidly growing populations of latency-critical and energy-constrained devices, yet distributed offloading faces two coupled problems: learned multi-agent policies depend on the arbitrary numerical ordering of edge servers, which wastes training samples and treats physically equivalent configurations inconsistently, [...] Read more.
Mobile edge computing (MEC) must serve rapidly growing populations of latency-critical and energy-constrained devices, yet distributed offloading faces two coupled problems: learned multi-agent policies depend on the arbitrary numerical ordering of edge servers, which wastes training samples and treats physically equivalent configurations inconsistently, while short-horizon cost minimization overloads attractive servers and destabilizes their queues. This paper presents SEAL-MAC (Symmetry-Equivariant Lyapunov Multi-Agent Actor–Critic), a distributed learning framework that addresses both problems jointly. First, a symmetric resource-set actor with a mirror consistency regularizer enforces server relabeling equivariance of each user’s policy and invariance of its value and Lyapunov critics. Second, a load-symmetric Lyapunov–potential shaping mechanism augments drift-plus-penalty rewards with normalized load-balance signals, coupling queue stability, fairness, and strategic alignment. The shaped interaction is analyzed as a Lyapunov-shaped Markov potential game: exact under orthogonal congestion-separable conditions, and a Markov α-potential game under heterogeneity or interference, yielding conditional finite-time (ϵ+α)-Nash convergence and mean-square queue stability. Each device learns from local observations and O(M) queue broadcasts without exchanging gradients or policies. In simulations with up to 200 users, SEAL-MAC reduces average delay by 9.0%, 95th-percentile delay by 11.8%, energy consumption by 10.6%, and the deadline-violation rate from 3.1% to 1.8% relative to the strongest Lyapunov baseline, halves the empirical one-step deviation gain of an identically shaped Ly-PPO agent (0.048 versus 0.098), and raises the Jain fairness index from 0.88 to 0.94. Full article
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19 pages, 1922 KB  
Article
The Perceptual Game-Theoretic Transform (PGTT): Axiomatizing Signal Compression via the Fourier–Shapley Isomorphism
by Adnan H. Abdulwahid
Foundations 2026, 6(3), 29; https://doi.org/10.3390/foundations6030029 - 3 Aug 2026
Viewed by 165
Abstract
The mathematical representation of discrete signals is classically governed by linear basis transforms, such as the Discrete Fourier Transform (DFT), which treat spectral projection as a rigid, deterministic geometric operation. Under this paradigm, signal compression and thresholding rely on heuristic error metrics like [...] Read more.
The mathematical representation of discrete signals is classically governed by linear basis transforms, such as the Discrete Fourier Transform (DFT), which treat spectral projection as a rigid, deterministic geometric operation. Under this paradigm, signal compression and thresholding rely on heuristic error metrics like the Minimum Mean Squared Error (MMSE). To mathematically axiomatize these fundamental operations, this paper reformulates computational basis transforms through the lens of Cooperative Game Theory. By defining discrete signal reconstruction as a Grand Coalition of orthogonal frequency players, we establish a strict mathematical isomorphism between functional analysis and cooperative game theory. We prove that the spectral energy assigned to each frequency coefficient is exactly its Shapley Value and that classical MMSE minimization is mathematically equivalent to maximizing the retained Shapley payout. Furthermore, we extend this framework to physical hardware and linear shift-invariant (LSI) systems, modeling 8-bit quantization and the Modulation Transfer Function (MTF) as sub-additive “economic taxes” on the coalition. Finally, by intentionally violating the Shapley Symmetry Axiom to mimic the Contrast Sensitivity Function (CSF) of the human visual system, we propose a fundamentally new mathematical basis: the Perceptual Game-Theoretic Transform (PGTT). Unlike classical methods that rely on post hoc quantization for signal compression, the PGTT acts as an inherently efficient transform that structurally guarantees sub-Nyquist computational complexity and dynamic range reallocation prior to physical hardware saturation. Full article
(This article belongs to the Section Mathematical Sciences)
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43 pages, 4035 KB  
Article
A Bi-Level Operation Strategy for Home Energy Management System Integrating the Goals of Residential Users with Distribution Network Operator
by Wu Yitong, Shitikantha Dash and Dipti Srinivasan
Sustainability 2026, 18(15), 7823; https://doi.org/10.3390/su18157823 - 3 Aug 2026
Viewed by 302
Abstract
With the advancement of net-zero targets and the large-scale deployment of distributed photovoltaic (PV) systems, battery energy storage systems (BESS), and electric vehicles (EVs) in residential sectors, home energy management systems (HEMS) have become central to improving end-use energy efficiency. However, reliance on [...] Read more.
With the advancement of net-zero targets and the large-scale deployment of distributed photovoltaic (PV) systems, battery energy storage systems (BESS), and electric vehicles (EVs) in residential sectors, home energy management systems (HEMS) have become central to improving end-use energy efficiency. However, reliance on synthetic data, simplified and homogeneous load modeling, and lack of coordination between dynamic pricing mechanisms and multi-device scheduling, make them practically inefficient. Furthermore, most studies address only unilateral user-side optimization while neglecting the distribution network operational constraints and omitting rigorous anti-arbitrage mechanisms to preclude speculative user behavior. To address these gaps, this paper proposes a data-driven coordinated scheduling framework for residential PV-BESS and multi-device systems formulated within bi-level game-theoretic architecture. The upper-level employs particle swarm optimization (PSO) to determine dynamic additional price signals for peak shaving and distribution network security, with explicit constraints on distribution transformer capacity, node voltage deviation, and load ramp rate adapted to three-user scenarios. The lower-level formulates a mixed-integer quadratic programming (MIQP) model to achieve multi-objective optimization of user electricity cost, thermal comfort, device usage preference, battery cycle degradation, and end-of-cycle energy balance. Simulation results for representative summer and winter days indicate that the proposed framework reduces user-side electricity cost by around 30%, elevates PV self-consumption rate to over 70%, and achieves about 20% peak load reduction with around 15% peak-valley difference narrowing on the grid side. All distribution network security constraints and anti-arbitrage rules are strictly satisfied. The framework effectively reconciles the objectives of both residential users and the distribution grid. Full article
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34 pages, 3362 KB  
Article
Fault Diagnosis of Ship Chilled Water Units Based on a Hybrid Attention Domain-Adaptive Network
by Qiaolian Feng, Yanfei Li, Yongbao Liu, Xiao Liang, Mingyang Liu, Duo Qu and Yue Cen
Entropy 2026, 28(8), 840; https://doi.org/10.3390/e28080840 - 28 Jul 2026
Viewed by 260
Abstract
When marine chillers operate under complex marine conditions, they suffer from severe cross-equipment feature distribution shifts, scarce labeled fault samples in the target domain, industrial vibration noise mixed in sensor signals, and difficulties in accurately identifying subtle faults with varying severity levels. To [...] Read more.
When marine chillers operate under complex marine conditions, they suffer from severe cross-equipment feature distribution shifts, scarce labeled fault samples in the target domain, industrial vibration noise mixed in sensor signals, and difficulties in accurately identifying subtle faults with varying severity levels. To tackle these issues, this paper improves upon the domain difference perception network (DDPN) and proposes a dual-hybrid attention feature discriminant domain-Adversarial network (DAFDAN) to realize intelligent fault diagnosis across different equipment and working conditions under few-shot scenarios. The proposed method constructs a dual-branch feature encoder consisting of a source domain compressor and a target domain extender to accommodate the distinct sensor dimensions of two heterogeneous chiller types. A hybrid attention module is formed by integrating squeeze-and-excitation efficient channel attention (SE-ECA, a module for screening channel-wise features) and spatial attention, which adaptively amplifies time-series features sensitive to faults and suppresses irrelevant noise. Residual connections (shortcut paths in deep neural networks to mitigate the vanishing gradient problem during deep-layer training) are introduced to optimize feature transmission. A dual-layer domain alignment framework is built with gradient reversal layers and maximum mean discrepancy (MMD). Combined with adversarial training (a training paradigm that learns domain-agnostic features through a game between a feature extractor and a domain discriminator), the framework achieves joint optimization of implicit feature confusion and explicit distance constraints. Meanwhile, a five-stage progressive training strategy is designed, which activates multiple loss functions, including weighted cross-entropy, mean square error (MSE), binary cross-entropy (BCE), and Kullback–Leibler (KL) divergence stage by stage. Class weighting and early stopping strategies are adopted to alleviate sample imbalance and model overfitting. In this paper, the public ASHRAE RP-1043 centrifugal chiller dataset is used as the source domain, and time-series measurement data collected from a self-developed laboratory marine screw chiller serves as the target domain. Verification experiments are carried out covering one normal steady-state operating condition and 15 gradient faults falling into five major categories with different severity degrees. Results from ablation experiments (controlled-variable comparative experiments that quantify the independent contribution of each component by comparing model performance with or without a specific module/loss), multi-algorithm comparisons, and confusion matrix visualization demonstrate that the cross-domain fault diagnosis accuracy of the proposed DAFDAN approaches is 100%, outperforming mainstream transfer learning algorithms such as support vector machine (SVM), deep neural network (DNN), MMD, correlation alignment (CORAL), and domain-adversarial neural network (DANN). Multiple ablation experiments verify that the three core components—hybrid attention, adversarial training, and semi-supervised learning—jointly boost the model’s diagnosis accuracy and operational stability. The loss curves of the complete five-stage training process converge smoothly. The confusion matrix reveals zero misjudgments and zero false alarms across all 16 refined operating states, enabling precise identification of subtle incipient faults of all severity levels. This study proves that DAFDAN can effectively address the pain points of few-shot cross-equipment fault diagnosis for marine chillers and provides a reliable algorithmic reference for the intelligent operation and maintenance of ship refrigeration equipment. Full article
(This article belongs to the Section Multidisciplinary Applications)
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37 pages, 1563 KB  
Article
In Pursuit of the Emergence Point: Extracting Phase Transitions in Multi-Agent Communication
by Alexander Chernyavskiy, Ivan Tomilov, Natalia Gusarova and Aleksandra Vatian
Technologies 2026, 14(7), 432; https://doi.org/10.3390/technologies14070432 - 14 Jul 2026
Viewed by 370
Abstract
Modern multi-agent deep reinforcement learning algorithms have demonstrated empirical success in communication games, yet their black box nature precludes the analytical identification of the transition from random babbling to coordinated signalling. This study introduces an explicitly parameterised, interpretable surrogate model of belief evolution [...] Read more.
Modern multi-agent deep reinforcement learning algorithms have demonstrated empirical success in communication games, yet their black box nature precludes the analytical identification of the transition from random babbling to coordinated signalling. This study introduces an explicitly parameterised, interpretable surrogate model of belief evolution in Lewis signalling games. The proposed ordinary differential equation retains the strategic structure of cheap talk while permitting the closed-form computation of the Jacobian spectrum at the uniform babbling equilibrium. It was proven that the onset of communication corresponded to a supercritical pitchfork bifurcation with a critical threshold determined by the dissipation and sensitivity parameters. Consequently, the leading eigenvalue of the dynamics serves as a detector of the emergence point. The analytical predictions were validated through iterative simulations of Lewis signalling games, illustrating how the critical threshold dictates the consistent and stable transition from stochastic babbling to separating equilibrium. Moreover, a phenomenological experiment demonstrates a possible path toward extending spectral diagnostics to policies parameterised by neural networks in a low-dimensional setting, serving as a bridge towards potential method adaptation for general deep reinforcement learning policies, without fully validating the theoretical framework. Full article
(This article belongs to the Section Information and Communication Technologies)
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22 pages, 3549 KB  
Article
EvoGame-CAKNet: Integrating Evolutionary Game Theory and Multi-Head Contextual Attention Augmented Kolmogorov Arnold Networks for Accurate Carbon Price Forecasting
by Yufei Xi, Jiangzhang Zhu, Peng Wang and Mingfang He
Mathematics 2026, 14(14), 2487; https://doi.org/10.3390/math14142487 - 10 Jul 2026
Viewed by 249
Abstract
Accurate carbon price for ecasting is crucial for the management of emission trading schemes and the formulation of low-carbon policies. However, existing models face three intertwined challenges: the interdependent multi-agent strategies among market participants, the long-term time dependence of high-dimensional environmental and economic [...] Read more.
Accurate carbon price for ecasting is crucial for the management of emission trading schemes and the formulation of low-carbon policies. However, existing models face three intertwined challenges: the interdependent multi-agent strategies among market participants, the long-term time dependence of high-dimensional environmental and economic covariates, and the severe nonlinearity under the constraint of small samples. This paper proposes the novel hybrid framework EvoGame-CAKNet. Firstly, an evolutionary game theory (EGT) is proposed to simulate the evolution of dynamic strategies of different market participants (enterprises, regulatory agencies, financial institutions), and policy effect signals are embedded as structured prior information. Secondly, a knowledge network (CAKNet) combining multi-head context attention is designed for adaptive long-distance feature aggregation across climate, macroeconomy, and policy dimensions. Finally, a Kolmogorov–Arnold network (KAN) is proposed to replace the traditional multi-layer perceptron decoder, using learnable unary activation functions to achieve better nonlinear fitting under data scarcity conditions. Experiments on four major carbon markets in Beijing, Shanghai, Hubei, and Guangdong from 2014 to 2023 show that EvoGame-CAKNet achieves the most advanced performance, with an average absolute percentage error (MAPE) reduced by 18.3% to 31.6% compared to the best base model. Abandonment studies confirm that each component works collaboratively, with the prior knowledge of EGT having the most significant impact during the regulatory transition period. CAKNet not only provides theoretical progress in multi-agent market modeling but also offers practical decision support for stakeholders in the carbon market. Full article
(This article belongs to the Section C: Mathematical Analysis)
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31 pages, 6499 KB  
Article
A Frequency-Aware Dual-Stream Deep Learning Framework for Athlete Workload Monitoring and Injury Risk Assessment: A Multi-Dataset Validation Study in Professional Team Sports
by Jinnian Tong and Peng Gao
Sensors 2026, 26(13), 4228; https://doi.org/10.3390/s26134228 - 3 Jul 2026
Viewed by 681
Abstract
The accumulation of training and competition loads represents a critical determinant of musculoskeletal injury risk in professional team sports, yet contemporary monitoring systems remain limited by their reliance on single-domain temporal analysis that overlooks the multi-scale rhythmic patterns inherent in athletic workload signals. [...] Read more.
The accumulation of training and competition loads represents a critical determinant of musculoskeletal injury risk in professional team sports, yet contemporary monitoring systems remain limited by their reliance on single-domain temporal analysis that overlooks the multi-scale rhythmic patterns inherent in athletic workload signals. This study introduces FDTM (frequency-aware dual-stream temporal model), a deep learning framework that jointly encodes time-domain dependencies and frequency-domain spectral signatures from digital athlete monitoring streams to predict individual injury risk over a forward-looking seven-game horizon. The framework integrates a stacked bidirectional long short-term memory branch augmented with temporal self-attention pooling, a spectral encoding branch employing discrete Fourier transform decomposition across high-frequency (weekly), mid-frequency (bi-weekly), and low-frequency (seasonal) bands, and a cross-modal gated attention fusion module that adaptively balances temporal and spectral representations conditioned on player context. We evaluate FDTM on three heterogeneous public sports datasets spanning basketball (NBA game-log corpus 2013–2023), Australian rules football (AFL Player Workload Dataset), and soccer (SoccerMon open monitoring corpus), comprising 612 athletes and 247,830 player-game observations across ten competitive seasons. FDTM achieves AUC-ROC values of 0.858, 0.833, and 0.821 on the three datasets respectively, outperforming the strongest deep-learning baseline (FEDformer) by 2.0 to 3.3 percentage points and the strongest non-spectral baseline (TCN) by 3.2 to 4.5 percentage points while maintaining a Brier score below 0.04. Ablation studies confirm that the spectral branch contributes 5.1 percent to overall discriminative performance. SHAP attribution analyses identify high-frequency weekly components as the dominant injury-relevant signal, followed by low-frequency seasonal trends and the cumulative acute-to-chronic workload temporal feature, with gating-weight visualizations revealing dynamic modality contributions consistent with established sports science theory. Direct spectral analysis of the raw workload signal confirms that injury-preceding windows exhibit significantly elevated weekly-band power across all three datasets (Mann–Whitney U test, p < 1 × 10−7), and the architectural advantage is shown to be robust across 30 independent training seeds. These findings suggest that frequency-aware modeling may serve as a transferable methodology for sports engineering applications in injury prevention, return-to-play planning, and individualized rehabilitation, pending further external validation in female athletes and additional team sports. Full article
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34 pages, 6647 KB  
Article
Engineered Misunderstanding Under Psychological Warfare: A Bayesian Signaling Game of Felt-Understanding Collapse in the German Atomausstieg
by Ryanne R. L. Fairchild
Games 2026, 17(4), 36; https://doi.org/10.3390/g17040036 - 2 Jul 2026
Viewed by 515
Abstract
Russian state-sponsored disinformation has been described in policy and the operational literature, but it is less often formalized in game-theoretic terms. Here, a two-layered formal model is developed showing how adversarial perturbation of a communication channel can collapse cross-group felt understanding—the third-order intentional [...] Read more.
Russian state-sponsored disinformation has been described in policy and the operational literature, but it is less often formalized in game-theoretic terms. Here, a two-layered formal model is developed showing how adversarial perturbation of a communication channel can collapse cross-group felt understanding—the third-order intentional state/belief structure, established empirically by Livingstone, in which one group believes its perspectives are recognized and accepted as valid by another. The Analytical Model is a static Bayesian signaling game with binary types and a noisy channel parameterized by perturbation rate π. The Analytical Model shows that when recognition benefits exceed signaling costs, there exists a perturbation threshold π* = 1 − cR/(uR · p) above which mutual misrecognition becomes the unique Perfect Bayesian Equilibrium outcome. The Computational Model embeds this logic in an agent-based simulation on a homophilic stochastic block model and scale-free networks with continuous recognition capacity. Four substantive findings emerge: the closed-form analytical threshold from the Analytical Model predicts the boundary of collapse in the dynamic networked simulation; high network homophily protects cooperative behavior below π* but provides no rescue above it; bridge seeding—the placement of recognition-capable agents at structurally central cross-group positions—is the most effective of three policy interventions tested, rescuing cooperation even above π*; and uniform adversarial volume is approximately as damaging as strategically targeted adversarial precision across both small dense and large scale-free topologies, qualifying the operational claim that targeted disinformation should strictly outperform volume-based approaches. The model is illustrated with the German Atomausstieg (nuclear phase-out) case, and implications for clinical psychology, public policy, and intergroup recognition under psychological warfare are discussed. Full article
(This article belongs to the Special Issue Games with Incomplete Information)
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Article
Beyond Interaction Volume: Platform Visibility and Engagement Quality in Digital Game Consumption
by Kai Liu, Zhibin Xing and Haizhang Chen
J. Theor. Appl. Electron. Commer. Res. 2026, 21(7), 205; https://doi.org/10.3390/jtaer21070205 - 29 Jun 2026
Viewed by 551
Abstract
Digital game consumption increasingly unfolds across video platforms, comment sections, and community discussions, where platform visibility, creator-mediated information, interaction metrics, and commercialization signals shape users’ expectations. In platform-mediated digital commerce, visible interaction may indicate information use, cultural resonance, payment concern, or consumption-related complaint [...] Read more.
Digital game consumption increasingly unfolds across video platforms, comment sections, and community discussions, where platform visibility, creator-mediated information, interaction metrics, and commercialization signals shape users’ expectations. In platform-mediated digital commerce, visible interaction may indicate information use, cultural resonance, payment concern, or consumption-related complaint rather than uniformly positive engagement. Using self-determination theory as a motivational lens within a platform-mediated consumer-behavior framework, this study examines whether platform content cues, public comment responses, and user perceptions provide convergent evidence on differentiated engagement meanings. The empirical setting is Bilibili content related to the Chinese wuxia role-playing game Where Winds Meet. The analysis combines 1164 public videos, 19,919 hot comments, and a content-exposure-anchored survey of 564 valid respondents. The results show differentiated patterns: functional information cues correspond to saving-oriented engagement and useful responses; cultural-aesthetic cues correspond to supportive interaction and cultural responses; and payment-mechanism and experience-problem cues correspond to payment concerns and complaints. The survey further shows that perceived information value, cultural/experiential connection, perceived monetization fairness, consumer autonomy in spending decisions, and perceived monetization risk are associated with continued engagement intention. These findings suggest that engagement quality should be interpreted through platform-mediated consumer relationships rather than interaction volume alone, while recognizing that hot-comment evidence reflects a platform-visible layer of user response rather than the full distribution of comments or player attitudes. Full article
(This article belongs to the Special Issue Emerging Technologies on Digital Platforms)
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