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29 pages, 9057 KB  
Article
TSIE: Robust Blind Locomotion Learning for Bipedal Robots via Terrain and State Implicit-Explicit Estimation
by Zhiyuan Liang, Jie Xue, Haiming Mou, Qingdu Li and Jianwei Zhang
Biomimetics 2026, 11(9), 615; https://doi.org/10.3390/biomimetics11090615 - 1 Sep 2026
Viewed by 180
Abstract
Robust blind locomotion over complex unstructured terrains relies on accurate estimation of robot states and surrounding terrain geometry. However, under real-world deployment conditions without exteroceptive perception, it remains challenging to accurately estimate robot states and infer surrounding terrain structures solely from noisy proprioceptive [...] Read more.
Robust blind locomotion over complex unstructured terrains relies on accurate estimation of robot states and surrounding terrain geometry. However, under real-world deployment conditions without exteroceptive perception, it remains challenging to accurately estimate robot states and infer surrounding terrain structures solely from noisy proprioceptive observations. Existing methods commonly learn single-scale implicit terrain representations from historical proprioceptive observations and explicitly estimate robot states. However, they lack explicit terrain estimation and may lose critical geometric details. Moreover, single-scale terrain information is insufficient to capture both local geometric structures and global terrain trends. To address these issues, we propose a Terrain and State Implicit-Explicit Estimation (TSIE) framework to improve the locomotion capability of bipedal robots over complex terrains. TSIE encodes long-horizon proprioceptive observations using a Long Short-Term Memory (LSTM) network and introduces a dual-branch architecture consisting of a Terrain Implicit-Explicit Estimator (Terrain-IE) and a State Implicit-Explicit Estimator (State-IE). Terrain-IE performs multi-scale terrain implicit-explicit estimation by explicitly estimating a local high-resolution height map and implicitly reconstructing a global low-resolution height map. By preserving gradient connections between the two terrain branches, Terrain-IE enables joint implicit-explicit training of multi-scale terrain representations, improving terrain understanding and estimation accuracy. State-IE explicitly estimates the base linear velocity and foot-centered height map, while implicitly reconstructing future proprioceptive states to further improve tracking performance and locomotion robustness. We validate TSIE through simulation and real-world experiments on a full-sized bipedal robot platform with a height of 170cm and a mass of 35kg. Experimental results show that TSIE outperforms baseline methods in complex-terrain traversal capability, terrain and state estimation accuracy, and velocity-tracking stability. Real-world deployment further demonstrates the robustness of TSIE across indoor and outdoor complex terrains, achieving a 95% success rate in continuous stair ascent and descent tasks. Full article
(This article belongs to the Section Locomotion and Bioinspired Robotics)
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19 pages, 473 KB  
Article
The Contributions of Statistical Learning to L2 Morphosyntax Processing Across Visual and Auditory Modalities in Chinese Adolescent Learners
by Kaiyue Song, Weijia Yan, Guoying Yang, Yueyan Huang, Hui Yu and Li Li
Behav. Sci. 2026, 16(8), 1452; https://doi.org/10.3390/bs16081452 - 21 Aug 2026
Viewed by 298
Abstract
Individual differences in statistical learning (SL) constitute an important cognitive mechanism that supports second language (L2) syntactic processing. However, existing research has primarily focused on adult populations, while potential differences across input modalities remain understudied. This study investigated the associations between SL and [...] Read more.
Individual differences in statistical learning (SL) constitute an important cognitive mechanism that supports second language (L2) syntactic processing. However, existing research has primarily focused on adult populations, while potential differences across input modalities remain understudied. This study investigated the associations between SL and implicit L2 morphosyntactic processing among Chinese adolescent English learners, comparing results across visual and auditory modalities. Participants completed visual and auditory SL tasks, self-paced reading (SPR), self-paced listening (SPL), as well as working memory (WM) and attention tasks. L2 morphosyntactic processing ability was measured via grammatical sensitivity indicators extracted from SPR and SPL data. Mixed-effects analyses did not detect statistically reliable group-level grammaticality effects in either task, though SPR exhibited a descriptive pattern where ungrammatical sentences elicited longer reading times at the third word. Participants achieved higher accuracy on the visual SL task than the auditory one. In exploratory regression analyses, visual SL accuracy was found to positively predict grammatical sensitivity measured at Word 3 in SPR. Still, this association was not confirmed in a follow-up sensitivity analysis. No corresponding significant association was observed between auditory SL and SPL sensitivity, and neither working memory nor attention showed consistent independent contributions to the outcome. These findings extend individual-differences research on this topic to adolescent classroom L2 learners and underscore the potentially important role of visual regularity learning in online L2 reading processing. Full article
(This article belongs to the Section Cognition)
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16 pages, 459 KB  
Article
A Game-Based Eye-Tracking Task for Inclusive Educational Assessment in Children with Autism Spectrum Disorder and Dyslexia: An Exploratory Study
by Gülce Alev-Savtak, Şükrü Torun and Aşena Karamete
Educ. Sci. 2026, 16(8), 1315; https://doi.org/10.3390/educsci16081315 - 17 Aug 2026
Viewed by 280
Abstract
Background: Inclusive educational assessment requires tools that capture how learners with diverse cognitive profiles engage with tasks. This study examines whether a game-based, gaze-contingent eye-tracking task can generate relevant indicators for inclusive assessment of autistic children and children with dyslexia. Methods: Forty-five children [...] Read more.
Background: Inclusive educational assessment requires tools that capture how learners with diverse cognitive profiles engage with tasks. This study examines whether a game-based, gaze-contingent eye-tracking task can generate relevant indicators for inclusive assessment of autistic children and children with dyslexia. Methods: Forty-five children (15 autistic, 15 with dyslexia, 15 neurotypical) completed a Unity 3D eye-tracking task assessing implicit joint attention, inhibitory control, and task engagement. Six gaze-based metrics were analyzed alongside standardized measures of joint attention, theory of mind, working memory, and processing speed. Group differences in the eye-tracking metrics were examined using permutation-based analysis of covariance controlling for chronological age and Full-Scale IQ, and associations with clinical measures were examined using a small set of pre-specified, Holm-corrected Spearman correlations. Results: Significant group differences were observed for five of the six metrics (partial η2 = 0.33–0.81). The autistic group showed the highest values on difficulty-related metrics and differed significantly from both the neurotypical and dyslexia groups on nearly every measure, while the neurotypical and dyslexia groups did not differ significantly from each other. One correlation remained significant after correction for multiple comparisons: task efficiency in the autistic group was linked to a behavioral correlate of theory of mind. Conclusions: Gaze-based indicators within a game-based task can differentiate autistic children from neurotypical and dyslexic peers and show a preliminary behavioral correlate of theory of mind in autism specifically. These findings offer narrow, preliminary support for the value of process-oriented tools for inclusive educational assessment. Future research should examine feasibility, validity, and psychometric stability in larger, matched samples and in authentic school contexts. Full article
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19 pages, 753 KB  
Article
Breaking the Sign Symmetry of Attention: A Conflict-Aware Vision–Language Fusion Framework for Privacy-Sensitive Information Detection
by Ming Lian, Yuanyuan Li and Teng Li
Symmetry 2026, 18(8), 1352; https://doi.org/10.3390/sym18081352 - 11 Aug 2026
Viewed by 309
Abstract
As image data are shared ever more openly, they increasingly leak privacy-sensitive information, yet existing detectors seldom model how the text embedded in an image relates to its visual content and tend to fail precisely when the two modalities disagree. We note that [...] Read more.
As image data are shared ever more openly, they increasingly leak privacy-sensitive information, yet existing detectors seldom model how the text embedded in an image relates to its visual content and tend to fail precisely when the two modalities disagree. We note that the conventional softmax attention used for multimodal fusion carries an implicit sign symmetry: Every source token contributes only additively, so conflicting evidence is averaged away rather than resolved. We propose a symmetric dual-source fusion framework whose decoder deliberately breaks this sign symmetry. Image and text are first encoded by a Swin Transformer and a policy knowledge-enhanced BERT (KL-BERT) and projected into a common space to form a permutation-symmetric dual-source memory. A Signed Cross-attention Auto-compressing Decoder (SCAD) then fuses the two sources through an attention map that factorizes into a sign-symmetric (even) magnitude term and a sign-antisymmetric (odd) polarity term, allowing the model to either reinforce or actively subtract cross-modal evidence. Experiments on a self-constructed privacy-sensitive image dataset show that the proposed method attains an accuracy of 97.69% and an F1-score of 96.70%, with its largest gains on the face category, the most conflict-prone class in our data, suggesting that controlled symmetry breaking is an effective principle for cross-modal fusion. Full article
(This article belongs to the Special Issue Symmetry in Fault Diagnosis: Methods, Models, and Applications)
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23 pages, 1133 KB  
Review
Prenatal Stress, Enteric Nervous System Development, and the Microbiota–Gut–Brain Axis: A Hypothesis-Generating Framework for Irritable Bowel Syndrome and Fibromyalgia
by Noemi Császár-Nagy and István Bókkon
Int. J. Mol. Sci. 2026, 27(16), 7177; https://doi.org/10.3390/ijms27167177 - 11 Aug 2026
Viewed by 768
Abstract
The enteric nervous system (ENS) can function semi-autonomously from the central nervous system (CNS) in regulating complex gastrointestinal processes and exhibits substantial developmental, epigenetic, neuroimmune, and adaptive plasticity. We propose the concept of Stress-Induced Long-term Epigenetic Implicit Memory (SLEIM) as a hypothesis-generating theoretical [...] Read more.
The enteric nervous system (ENS) can function semi-autonomously from the central nervous system (CNS) in regulating complex gastrointestinal processes and exhibits substantial developmental, epigenetic, neuroimmune, and adaptive plasticity. We propose the concept of Stress-Induced Long-term Epigenetic Implicit Memory (SLEIM) as a hypothesis-generating theoretical framework suggesting that prenatal maternal stress may contribute to persistent biological alterations within ENS-related pathways through interacting epigenetic, neuroimmune, neuronal, glial, and microbiota-associated mechanisms. The precise biological substrates and mechanisms underlying this proposed framework remain unknown. Through the microbiota–gut–brain axis (MGBA), such stress-related biological alterations may influence physiological communication between the ENS and CNS and in turn affect stress-response systems, including HPA axis activity, immune signalling, cortisol regulation, mast-cell activation, and cytokine balance. The frequent comorbidity of fibromyalgia (FM) and irritable bowel syndrome (IBS) suggests the existence of shared pathogenic mechanisms involving central sensitisation, neuroimmune processes, and MGBA dysfunction. In this study, we therefore also address dependency-related characteristics and autonomy vulnerabilities reported in some patients with FM and consider how developmental, psychological, neurobiological, and illness-related factors may contribute to these patterns. Within the proposed SLEIM framework, prenatal stress-related biological influences may represent a potential developmental pathway that contributes to vulnerability to IBS, FM, and related functional disorders later in life. However, these relationships remain hypothetical and require future empirical investigation. Full article
(This article belongs to the Section Molecular Biology)
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16 pages, 2197 KB  
Article
IA-3DGS Identity-Anchored Dynamic Gaussian Splatting for Long-Term Facial Detail Preservation
by Ze Zhao, Lili Yin, Shuaijie Wang and Jie Gao
Sensors 2026, 26(15), 4947; https://doi.org/10.3390/s26154947 - 5 Aug 2026
Viewed by 324
Abstract
Dynamic 3D Gaussian Splatting (3DGS) enables efficient facial-avatar rendering but may suffer from cumulative geometric drift and degradation of identity-specific details when applied to long monocular sequences. To address this problem, we propose IA-3DGS, an identity-anchored dynamic Gaussian framework for long-term facial animation. [...] Read more.
Dynamic 3D Gaussian Splatting (3DGS) enables efficient facial-avatar rendering but may suffer from cumulative geometric drift and degradation of identity-specific details when applied to long monocular sequences. To address this problem, we propose IA-3DGS, an identity-anchored dynamic Gaussian framework for long-term facial animation. The proposed framework contains three main components. First, a 3D morphable model-guided semantic initialization strategy associates Gaussian primitives with anatomically meaningful facial regions. Second, a region-weighted Jacobian rigidity regularizer suppresses non-physical shear and anisotropic stretching in quasi-rigid facial regions while preserving sufficient flexibility in expression-sensitive regions. Third, a cyclic memory correction mechanism periodically aligns the current identity representation with a frozen reference representation and applies exponential moving average smoothing to reduce correction-induced temporal discontinuities. Experiments were conducted on the NeRSemble and NHA datasets and on a self-collected Custom-5K dataset containing continuous monocular facial sequences longer than 5000 frames. IA-3DGS achieved a PSNR of 31.85 dB, an SSIM of 0.942, and an LPIPS of 0.038 on standard-length sequences. At frame 5000, the method obtained an L-LPIPS of 0.046 and a landmark mean error of 1.3 mm, compared with 0.245 and 6.8 mm, respectively, for the purely implicit dynamic 3DGS baseline. The system rendered 1920 × 1080 images at approximately 48 frames per second on a single NVIDIA RTX 4090. These results indicate that the proposed semantic, geometric, and temporal constraints improve long-sequence identity consistency under the evaluated subject-specific monocular setting. Full article
(This article belongs to the Section Sensing and Imaging)
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56 pages, 1197 KB  
Article
Well-Posedness of Nonlinear Implicit ψ-Hilfer Fractional Problems of Complex Order with Applications to an Oscillator with Saturating Feedback
by Jakgrit Sompong, Ekkarath Thailert, Samten Choden and Sotiris K. Ntouyas
Mathematics 2026, 14(15), 2765; https://doi.org/10.3390/math14152765 - 3 Aug 2026
Viewed by 231
Abstract
This paper investigates the well-posedness of a class of nonlinear implicit fractional differential equations involving the ψ-Hilfer fractional derivative of complex order α with (α)(n1,n) for nN, under [...] Read more.
This paper investigates the well-posedness of a class of nonlinear implicit fractional differential equations involving the ψ-Hilfer fractional derivative of complex order α with (α)(n1,n) for nN, under general initial conditions in weighted spaces. The implicit nature of the problem, where the highest-order derivative appears nonlinearly on both sides of the equation, presents significant analytical challenges. By transforming the fractional Cauchy problem into an equivalent Volterra integral equation, we employ fixed-point theory to establish existence via Schaefer’s fixed-point theorem and uniqueness via Banach’s fixed-point theorem under suitable Lipschitz-type conditions. A generalized Gronwall inequality with singular kernels is developed to handle the nonlocal memory effects inherent to fractional operators. We further investigate four types of Ulam stability, namely Ulam–Hyers stability, generalized Ulam–Hyers stability, Ulam–Hyers–Rassias stability, and generalized Ulam–Hyers–Rassias stability, demonstrating that small perturbations in the equation yield correspondingly small changes in the solution. Continuous dependence on initial conditions is also established. The theoretical framework is applied to a physically motivated fractional nonlinear oscillator with saturating acceleration-dependent feedback, where explicit verification of the hypotheses is provided. Full article
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32 pages, 5046 KB  
Article
Scalable Machine Learning on IoT Edge Devices Through Adaptive Coreset Selection with Differentiable Greedy Sampling
by Fatema A. Albalooshi and M. R. Qader
Technologies 2026, 14(8), 476; https://doi.org/10.3390/technologies14080476 - 2 Aug 2026
Viewed by 354
Abstract
The rapid growth of Internet of Things (IoT) devices generates high-dimensional, high-velocity data streams that demand real-time machine learning (ML) inference under strict hardware constraints. We propose the Adaptivecoreset Selection Engine (ACS-Engine), a unified framework for adaptive, differentiable, and resource-aware coreset selection on [...] Read more.
The rapid growth of Internet of Things (IoT) devices generates high-dimensional, high-velocity data streams that demand real-time machine learning (ML) inference under strict hardware constraints. We propose the Adaptivecoreset Selection Engine (ACS-Engine), a unified framework for adaptive, differentiable, and resource-aware coreset selection on streaming IoT data. ACS-Engine introduces three tightly integrated innovations: (i) Differentiable Greedy Sampling (DGS), which relaxes discrete subset selection via Gumbel-Softmax reparameterization to enable end-to-end gradient-based optimization; (ii) Entropy-Aware Regularization (EAR), which promotes coreset diversity and provides implicit concept drift detection through a self-calibrating entropy threshold; and (iii) Resource-Aware Memory Management (RAMM), which dynamically adjusts the target coreset size based on real-time hardware telemetry—available memory, CPU utilization, remaining energy, and sampling frequency. Evaluated on eight real-world IoT datasets spanning three heterogeneous edge platforms, ACS-Engine achieves 15× memory reduction and a 20% energy efficiency improvement while retaining 98% of full-dataset accuracy, with a per-sample latency of 2 ms that satisfies real-time edge deployment requirements. Full article
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22 pages, 464 KB  
Hypothesis
Territory, Memory and Archives: Toward a Theory of Implicit Territoriality
by Carlos Vladimir Zambrano
Culture 2026, 2(3), 20; https://doi.org/10.3390/culture2030020 - 28 Jul 2026
Viewed by 336
Abstract
Archive studies have traditionally conceptualized archives as documentary repositories and memory institutions, whereas territorial studies have examined territorialities as processes through which social groups produce, signify, and contest space. Although both fields address the social production of meaning, the constitutive relationship through which [...] Read more.
Archive studies have traditionally conceptualized archives as documentary repositories and memory institutions, whereas territorial studies have examined territorialities as processes through which social groups produce, signify, and contest space. Although both fields address the social production of meaning, the constitutive relationship through which archives participate in the political–cultural production of territoriality remains insufficiently theorized. This article advances the hypothesis that every archive possesses an Implicit Territoriality as a constitutive property and, by virtue of this condition, contributes to the political–cultural production of territory. To develop this hypothesis, it proposes a theoretical framework in which Implicit Territoriality constitutes the central analytical category. As a constitutive property of every archive, Implicit Territoriality becomes analytically observable through three interdependent constitutive dimensions: the Mode of Differential Documentation (collections), the Territorial System of Site (spatial infrastructures and locations), and the Condensed Informational Potential (contents). The interaction among these dimensions gives rise to the deployment of Implicit Territoriality through two complementary processes—Territorialized Subjectivity and the Regime of Expansibility—which explain how territorial meanings become socially embodied and projected across different spatial and social scales. Its empirical recognition is achieved through a system of Inference Devices, understood as analytical operators that establish the relationship between empirical evidence and its implicit territorial dimension. Together, these components provide an integrated explanatory framework for understanding how archives actively participate in the political–cultural production of territory. Beyond preserving documents, archives implicitly contribute to the production of territories. They organize, stabilize, circulate, legitimize, and project memories and territorial meanings across different social and spatial scales. By conceptualizing Implicit Territoriality as a constitutive property of every archive, this article situates archives within the dynamics of territorialization and provides a coherent framework for analyzing their territorial dimension. Full article
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19 pages, 5599 KB  
Review
Path-Dependent Constitutive Modeling for Superplastic Forming of Titanium Alloys: Memory-Architecture Perspective
by Ling Ding, Cik Suhana Hassan, Wei Hong Lim, Swee Pin Yeap, Ke Wei and Lu-Cui Chao
Materials 2026, 19(13), 2817; https://doi.org/10.3390/ma19132817 - 2 Jul 2026
Viewed by 409
Abstract
Superplastic forming (SPF) of titanium alloys exhibits strong deformation path dependence because microstructural evolution, damage development, and material response are influenced by prior loading history. However, constitutive models for SPF are often evaluated primarily by fitting accuracy rather than their ability to represent [...] Read more.
Superplastic forming (SPF) of titanium alloys exhibits strong deformation path dependence because microstructural evolution, damage development, and material response are influenced by prior loading history. However, constitutive models for SPF are often evaluated primarily by fitting accuracy rather than their ability to represent deformation history. This review examines path-dependent constitutive modeling from a memory-architecture perspective. The relevant literature was identified through a structured review of titanium-alloy SPF studies, which were supplemented by selected high-temperature forming studies from other metallic systems when they provided transferable constitutive frameworks. Existing constitutive models were classified into four categories according to how deformation history is retained and represented: stateless models, implicit or projected memory models, reduced-order memory models, and high-dimensional or explicit memory models. The analysis shows that many conventional formulations achieve acceptable accuracy within calibrated monotonic regimes by strongly compressing deformation history, thereby limiting their ability to distinguish complex loading paths. Internal-state-variable models provide a practical balance between path representation, interpretability, and implementation, whereas high-dimensional memory models offer stronger sequence sensitivity at the cost of greater data and calibration requirements. This memory-architecture framework clarifies the limitations and applicability of existing constitutive models and provides guidance for model selection in SPF process simulation. Full article
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33 pages, 6275 KB  
Article
IRC-Bench: Recognizing Entities from Contextual Cues in First-Person Reminiscences
by Yehudit Aperstein, Eden Moran and Alexander Apartsin
Mach. Learn. Knowl. Extr. 2026, 8(7), 186; https://doi.org/10.3390/make8070186 - 1 Jul 2026
Viewed by 366
Abstract
When people recount personal memories, they often refer to people, places, and events indirectly, relying on contextual cues rather than explicit names. Such implicit references are central to reminiscence narratives: first-person accounts of lived experience used in therapeutic, archival, and social settings. They [...] Read more.
When people recount personal memories, they often refer to people, places, and events indirectly, relying on contextual cues rather than explicit names. Such implicit references are central to reminiscence narratives: first-person accounts of lived experience used in therapeutic, archival, and social settings. They pose a difficult computational problem because the intended entity must be inferred from dispersed narrative evidence rather than from a local mention. We introduce IRC-Bench, the Implicit Reminiscence Context Benchmark, for evaluating implicit entity recognition in reminiscence transcripts. The benchmark targets non-locality: entity-identifying cues are distributed across multiple, non-contiguous clauses, unlike named entity recognition, entity linking, or coreference resolution. IRC-Bench comprises 25,136 samples constructed from 12,337 Wikidata-linked entities across 1994 transcripts spanning 11 thematic domains. Each sample pairs an Entity-Grounded Narrative, in which the target entity is explicitly mentioned, with an Entity-Elided Narrative, in which direct mentions are removed. We evaluate 19 configurations across LLM generation, dense retrieval, RAG, and fine-tuning. QLoRA-adapted Llama 3.1 8B performs best in the open-world setting (38.94% exact match; 51.59% Jaccard), while fine-tuned DPR leads in closed-world retrieval (35.38% Hit@1; 71.49% Hit@10). We release IRC-Bench with data, code, and evaluation tools. Full article
(This article belongs to the Special Issue Language Acquisition and Understanding)
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29 pages, 393 KB  
Article
The Theological Transformation of Tengrism from the Ancient Turkish Belief System to the Modern Era and Its Cultural Interactions
by Fuzuli Bayat and Haktan Kaplan
Religions 2026, 17(6), 693; https://doi.org/10.3390/rel17060693 - 9 Jun 2026
Viewed by 1853
Abstract
This study examines the theological structure of Tengrism, understood here as a heuristic term for the broader Tengri-centered early Turkic belief system, its historical transformation, and its continuity in post-Islamic Turkic culture and folklore from an interdisciplinary perspective. Although the continuity of pre-Islamic [...] Read more.
This study examines the theological structure of Tengrism, understood here as a heuristic term for the broader Tengri-centered early Turkic belief system, its historical transformation, and its continuity in post-Islamic Turkic culture and folklore from an interdisciplinary perspective. Although the continuity of pre-Islamic Turkic beliefs in later Turkish folk culture has been noted in previous scholarship, the specific mechanisms through which Tengri-centered concepts survived as implicit theological structures within lived religion, folk belief, and Alevi-Bektashi ritual–poetic traditions have not been sufficiently systematized. The research argues that Tengrism should not be understood merely as an archaic remnant of belief but as a comprehensive theological paradigm shaping cosmology, political legitimacy, ethical order, and the perception of sacredness in early Turkic societies. In this context, epic and mythological texts such as the Orkhon Inscriptions, the Epic of Oghuz Khan, the Book of Dede Korkut, and the Epic of Manas constitute the primary textual sources of the study. The research is based on a qualitative design and employs phenomenological and hermeneutic approaches. The phenomenological perspective seeks to understand the theological principles of Tengrism and the perception of sacredness within their own cultural and symbolic universe, while hermeneutic analysis interprets the continuity of symbolic and mythological elements preserved in folkloric narratives. The findings indicate that the Tengri-centered and cosmologically structured character of early Turkic religiosity did not disappear after the adoption of Islam; rather, it persisted through folkloric narratives, popular beliefs, ritual practices, and the Alevi-Bektashi tradition. These findings demonstrate that Tengrism continues to function as a dynamic theological paradigm within Turkish cultural memory and popular religiosity. Full article
(This article belongs to the Section Religions and Humanities/Philosophies)
24 pages, 475 KB  
Article
Memory-Kernel Damping in Wave Propagation from a Variational Reservoir Model: Dispersion, Stability, and Fractional Regimes
by Derik W. Gryczak, Gabriel G. da Rocha, Aloisi Somer, Luiz R. Evangelista and Ervin K. Lenzi
Fractal Fract. 2026, 10(6), 390; https://doi.org/10.3390/fractalfract10060390 - 5 Jun 2026
Viewed by 440
Abstract
Hereditary damping and fractional attenuation are widely used to model wave propagation in complex media, but the variational and spectral origin of the corresponding nonlocal-in-time operators is often left implicit. In this work, we derive such operators from a minimal conservative field–reservoir model. [...] Read more.
Hereditary damping and fractional attenuation are widely used to model wave propagation in complex media, but the variational and spectral origin of the corresponding nonlocal-in-time operators is often left implicit. In this work, we derive such operators from a minimal conservative field–reservoir model. A real scalar field is coupled locally to a continuum of harmonic reservoir modes, which are then eliminated exactly. The resulting reduced dynamics is a causal wave equation with a memory-friction term acting on the field velocity. The memory kernel is generated by the reservoir coupling spectrum through a cosine-transform relation, establishing a direct spectrum-to-kernel correspondence. This relation provides both a physical interpretation of hereditary damping and a practical admissibility criterion: macroscopic attenuation and dispersion arise from the delayed back-action of unresolved internal modes, while physically admissible kernels are constrained by the non-negativity of the underlying spectral density. The framework unifies several standard damping regimes. A broadband reservoir recovers the Markovian locally damped wave equation, reservoirs with a finite characteristic time generate finite-memory relaxation and frequency-dependent dispersion, and scale-free reservoir spectra produce power-law memory kernels. In the latter case, the hereditary damping operator reduces to a Caputo-type fractional derivative, showing that fractional wave attenuation can emerge as an effective reduced dynamics rather than being postulated phenomenologically. We further analyze dispersion, attenuation, causality, stability, and admissibility conditions in terms of the reservoir spectrum. The main contribution of the work is therefore to provide a variational and spectral derivation of hereditary and fractional wave damping, linking the structure of unresolved reservoir modes to macroscopic nonlocal wave dynamics. Full article
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21 pages, 438 KB  
Article
A Fast Chebyshev Spectral Collocation Method for a Coupled System of Nonlinear Klein–Gordon Equations with Caputo Fractional Memory
by Yertay Kazez, Zhanars A. Abdiramanov, Nauryzbay Adil and Abdumauvlen S. Berdyshev
Axioms 2026, 15(6), 409; https://doi.org/10.3390/axioms15060409 - 30 May 2026
Viewed by 290
Abstract
We develop a fast Chebyshev spectral collocation method for a coupled system of nonlinear Klein–Gordon equations augmented by Caputo-type fractional memory integrals. The governing equations retain the classical second-order time derivative as the leading operator and incorporate weakly singular convolution integrals modelling viscoelastic [...] Read more.
We develop a fast Chebyshev spectral collocation method for a coupled system of nonlinear Klein–Gordon equations augmented by Caputo-type fractional memory integrals. The governing equations retain the classical second-order time derivative as the leading operator and incorporate weakly singular convolution integrals modelling viscoelastic memory damping. The spatial discretisation employs Chebyshev–Gauss–Lobatto collocation, while the temporal integration uses a Newmark scheme (βNM=1/4) combined with an implicit–explicit linearisation in which the linear spatial operator is treated implicitly and the nonlinear terms are treated explicitly through a second-order extrapolation. This linearisation eliminates the need for Newton–Raphson iterations at each time step. To overcome the dense memory bottleneck arising from two distinct fractional orders αβ, the convolution memory kernels are compressed by independent sum-of-exponentials approximations obtained from a double-exponential quadrature of the kernel’s integral representation, which significantly reduces the computational complexity of the history term. A rigorous stability estimate and a global convergence bound are established using a discrete Grönwall inequality. Numerical experiments confirm the theoretical temporal and spatial convergence rates and demonstrate the practical speed-up afforded by the sum-of-exponentials acceleration. A solitary wave collision scenario illustrates the method’s capability to capture asymmetric dispersive wakes generated by the fractional memory. Full article
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32 pages, 854 KB  
Article
A CUDA Performance Study of Global- and Shared-Memory Kernels for the Buckley–Leverett Polymer-Flooding Problem
by Yerlan Makhmut, Timur Imankulov, Sergei Gorlatch and Bazargul Matkerim
Appl. Sci. 2026, 16(11), 5449; https://doi.org/10.3390/app16115449 - 30 May 2026
Viewed by 556
Abstract
Polymer-augmented waterflooding is a key enhanced oil recovery technique whose simulation remains computationally demanding at a high spatial resolution. This paper presents a fully GPU-resident parallel solver for the one-dimensional Buckley–Leverett polymer-flooding problem within an Implicit-Pressure–Explicit-Saturation framework. The solver combines Jacobi iteration for [...] Read more.
Polymer-augmented waterflooding is a key enhanced oil recovery technique whose simulation remains computationally demanding at a high spatial resolution. This paper presents a fully GPU-resident parallel solver for the one-dimensional Buckley–Leverett polymer-flooding problem within an Implicit-Pressure–Explicit-Saturation framework. The solver combines Jacobi iteration for pressure, first-order upwind flux splitting for saturation, and a first-order upwind flux-splitting update for polymer mass with explicit concentration recovery inside a coupled Picard–IMPES iteration. Two CUDA implementations are compared: a global-memory baseline and a shared-memory variant that stages a per-block pressure tile with halo cells on chip. Both kernels were profiled on an NVIDIA GeForce RTX 2080 Ti over problem sizes from N=65,536 to N=67,108,864 and block sizes 128, 256, 512, and 1024. The two GPU implementations match the serial reference within 2×108, and peak speed-ups are 20.2× (global) and 20.1× (shared). Per-kernel Nsight Compute profiling classifies every kernel in both builds as compute-bound: SM throughput is 54–83% of peak and DRAM throughput 3–29% of peak. The bottleneck is the FP64 pipeline of consumer Turing hardware (FP64 throughput is one thirty-second of FP32); three FP64 divisions per cell, from inline polymer-modified mobility recomputation, saturate the FP64 unit. Shared-memory tiling cannot improve performance because it acts on memory traffic rather than on compute throughput. The result therefore characterizes a specific regime, namely FP64 one-dimensional, low-reuse transport stencils on consumer-class NVIDIA GPUs with reduced FP64 throughput, and is not a universal property of CUDA shared memory. Full article
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