Abstract: Optical precision measurement is fundamental to space technology and physics. For over a century, the “ray-of-light” paradigm and the Equivalence Principle have underpinned both theoretical and applied optics. However, recent theoretical and experimental work demonstrates that these paradigms are fundamentally flawed when applied to photon-level phenomena. This manuscript synthesizes a trilogy of research—spanning theoretical falsification, experimental confirmation, and practical application—to show that photons do not inherit the velocity vector of their source, and that the Equivalence Principle does not hold for photon propagation. We introduce the Real Velocity Measuring Device (RVMD), a novel instrument enabling direct measurement of real velocity vectors in real space. The potential implications for spacecraft navigation and metrology (including our planet) are profound, necessitating a paradigm shift in optical science.

Abstract: This pilot study evaluates whether Wi-Fi Channel State Information (CSI)-derived micro-movements can reflect autonomic patterns associated with Heart Rate Variability (HRV). CSI-estimated inter-beat intervals were compared with smartwatch-derived HRV metrics during relaxation and mild stress tasks involving 14 volunteers. While absolute HRV values differed, CSI-derived LF/HF variations showed directional alignment with physiological state changes (r = 0.84, p < 0.001), with mean absolute error of 5.8 ms for SDNN and 4.1 ms for RMSSD. Results underscore potential for contactless autonomic monitoring and motivate further clinical investigation, avoiding any claim of diagnostic utility. The findings suggest CSI-based passive wireless analytics may complement existing wearable methods for stress monitoring and autonomic assessment in ecologically valid settings.

Abstract: Topography plays a crucial role in shaping local urban microclimates and can drive the formation of cold-air pools in valley bottoms. This study examines the Eiras Valley (Coimbra, Portugal), a rapidly growing peri-urban area, to identify the conditions under which cold-air pools form and to characterize their spatial and vertical dynamics. Field measurements were carried out using Tinytag Plus 2 data loggers at the surface (≈1.5 m above ground) and mounted on an unmanned aerial vehicle (UAV) for vertical profiles, complemented by high-resolution thermal mapping through Empirical Bayesian Kriging. The results show that a nocturnal cold-air pool develops within the valley under clear, anticyclonic winter conditions, persisting into the early morning hours and dissipating after sunrise due to solar heating. In contrast, under overcast or summer conditions, no cold-air pooling was observed. The temperature inversion capping the cold-air pool was found at approximately 275 m altitude, inhibiting vertical mixing and trapping pollutants near the ground. These findings underscore the importance of topoclimatology in urban and regional planning, with implications for thermal comfort, air quality, and public health. The study contributes to urban climate research by highlighting how local topography and seasonal atmospheric stability govern cold-air pool formation in valley environments, supporting the development of mitigation strategies aligned with urban sustainability goals.

Abstract: People in mid-life interact with several different environments during their daily life in-cluding employment, leisure, commuting, and various family responsibilities, a concept defined as activity space. However, little is known about how these activity spaces contrib-ute to individuals’ daily health behavior choices. The Everyday Environments and Expe-riences (E3) study was conducted to explore these relationships. In this paper, we provide a reproducible GPS processing workflow to generate time-weighted exposure measures (activity spaces) inferred from 21 days of continuous GPS monitoring among 340 mid-life adults in Cook County, Illinois (N=340) from the E3 study. Data from waist-mounted GPS devices that recorded one-minute location epochs were aggregated after excluding time spent within an 800-meter buffer around the home. For each epoch, we derived proximity and kernel density measures for eleven food and physical-activity-related location types (e.g., supermarkets, fitness facilities), along with twenty-six environmental context varia-bles (e.g., land use, crime, population density). Time-weighted averages characterized each participant’s typical non-home environmental exposure. After adjustment for envi-ronmental context, age and gender were generally unrelated to activity-space measures. However, Black and Hispanic participants (as compared to White participants) spent less time near both food and physical-activity resources, suggesting systemic inequities in ac-cess beyond neighborhood composition.

Abstract: Physical activity (PA) improves health and well-being, and helps prevent long-term conditions. Yet opportunities to be active are not evenly distributed, with social, economic, and environmental disadvantages constraining access to PA among populations who may benefit most. Since the extent to which PA interventions incorporate equity considerations remains insufficiently characterised, risking exacerbation of health inequity, this scoping review aims to synthesise trial evidence on interventions of PA to improve health outcomes in populations at risk of health inequity as defined by the PROGRESS-Plus and CORE20PLUS5 frameworks. PubMed, Web of Science, and Scopus were searched for randomised controlled trials of PA interventions with at-risk populations published between 2020 and 2025. Study characteristics, intervention design, and equity-relevant factors were extracted. Two reviewers independently screened and synthesised findings narratively. Results indicate that of 2,480 articles identified, 23 trials met eligibility criteria. Most reported positive effect of PA on health outcomes amongst at-risk populations, including weight loss, improved motor skills and gait speed, reduced anxiety and PTSD, and fewer fractures or hospital visits. Interventions commonly included strength and balance training, group exercise, stretching, and aerobic fitness. UK-based studies and subgroup analyses by e.g. sex or age were largely absent, and many populations at risk of health inequity were underrepresented. Explicit equity considerations throughout design, implementation, or evaluation were rare across trials and few assessed differential effects between social or economic groups. Integrating equity frameworks and engaging with at-risk populations is recommended in future physical activity interventions to mitigate exacerbation of health inequity.

Abstract: Head-mounted (“virtual reality”) perimeters (HMPs), based on standard consumer electronic hardware, are a cheaper alternative to standard automated perimetry. They have not been validated in patients with inherited retinal disease (IRDs), yet. We evaluated the Iowa-HMP in a first pilot study. It consists of a legacy smartphone, a headset, and freely available, open-source software. We used the 10-2 grid, the ZEST algorithm, and a background of 10 cd/m^2 to measure central visual fields in one normal subject, and in patients with occult macular dystrophy (n = 2), Stargardt’s disease (n=3) and retinitis pigmentosa (n = 6). Results were compared with those from an Octopus 900 perimeter. The typical patterns of visual field loss were clearly discernible, but head-mounted perimeters generally have a limited dynamic range. Within the dynamic range of the Iowa-HMP (14 to 30 dB Octopus sensitivity), the Limits of Agreement (Bland-Altman) were ±7.5 dB. The Iowa-HMP had a diagnostic sensitivity of 0.67 for detecting locations with low perimetric sensitivity (< 14 dB in the Octopus perimetry) with a diagnostic specificity of 0.95. Although the Iowa-HMP cannot be directly compared to standard perimetry in IRDs, open software greatly facilitates research in this area.

Abstract:

This population-based study aimed to analyze the annual incidence and case fatality trends, and the clinical-epidemiological profile of gastroschisis in the state of Paraná, Brazil, between 2013 and 2024. Specifically, temporal trends in annual incidence and mortality rates related to gastroschisis were examined. Maternal, gestational, and neonatal characteristics were analyzed. Data from the Live Birth Information System and the Mortality Information System were analyzed using polynomial regression modeling. During the study period, 1,798,727 live births were recorded, including 491 cases of gastroschisis and 179 related deaths. The mean incidence was 2.73 per 10,000 live births. A significant 39.5% decrease over the study period was observed (p < 0.001). The case fatality rate was 36.5%. The predominant profile included young mothers (< 25 years; 77%), low educational attainment (87.7%), and no partner (59.1%). High frequencies of cesarean deliveries (84.3%), prematurity (57.3%), low birth weight (63.7%), and low Apgar scores were also observed. Gastroschisis incidence in Paraná declined significantly from 2013 to 2024. While the annual incidence showed a decreasing trend, mortality fluctuated. The persistently high case fatality rate underscores the need for public policies focused on prenatal care and specialized neonatal management.

Abstract: Detecting coordinated inauthentic behavior on social media remains a critical challenge, as many existing methods rely on correlation-based heuristics, fixed configurations, and heavy manual annotation. From the perspective of symmetry and asymmetry, coordinated campaigns often exhibit repeatable temporal and structural invariances (e.g., synchronized bursts and stable influence motifs), whereas adversarial adaptation and noisy environments introduce symmetry breaking and context-dependent deviations. To address this issue, we propose Adaptive Causal Coordination Detection (ACCD), a three-stage progressive framework with memory-guided adaptation. In Stage 1, ACCD introduces an adaptive Convergent Cross Mapping (CCM) module that learns embedding parameters across scenarios to recover invariant causal dependencies. In Stage 2, ACCD integrates active learning with semi-supervised classification to reduce labeling effort while preserving robust discrimination under asymmetric user behaviors. In Stage 3, ACCD employs an experience-driven validation module to self-verify detection results and mitigate spurious correlations across varying contexts. We evaluate ACCD on real-world benchmarks, including the Twitter IRA dataset, Reddit coordination traces, and TwiBot-20. Experimental results show that ACCD achieves an F1-score of 87.3% on coordinated attack detection, outperforming the strongest baseline by 15.2%, while reducing manual annotation by 68% and delivering a 2.8× speedup via hierarchical clustering optimization. Overall, ACCD 19 provides an accurate and scalable end-to-end solution that explicitly leverages symmetry (invariant coordination signatures) and asymmetry (evolving adversarial behaviors) for practical coordination detection.

Abstract: We propose an algebraic framework constructed from a finite-dimensional 19-dimensional Z³-graded Lie superalgebra g = g₀ ⊕ g₁ ⊕ g₂ (dimensions 12+4+3), featuring exact closure of the graded Jacobi identities (verified symbolically in key sectors and numerically in a faithful matrix representation, with residuals ≲ 10⁻¹² across 10⁷ random combinations) and a unique (up to scale) invariant cubic form on the grade-2 sector, driving a triality symmetry on the vacuum sector. Interpreting the grade-2 sector as the physical vacuum state, we explore whether representation-theoretic invariants and contractions within this algebraic structure can account for observed Standard Model parameters—including fermion masses, mixing angles, and gauge couplings—as well as the magnitude of the cosmological constant, black-hole entropy scaling, and certain qualitative features of quantum entanglement. The framework yields twelve quantitative predictions amenable to experimental scrutiny at forthcoming facilities such as the High-Luminosity LHC, Hyper-Kamiokande, DARWIN/XLZD, and LiteBIRD.

Abstract: This work presents a strategy for implementing advanced control in a real Linear Low-Density PolyEthylene (LLDPE) production unit (“Sclairtech” technology) followed by a systematic evaluation of economic benefits in accordance with best international practices. Melt Index (MI), density and conversion were considered as controlled variables. The analysis considered two different situations (with and without hydrogen as process input) and comprised groups/ families of polyethylene (rotational molding, low-density injection, octene film and high-density injection). The proposed control strategy is capable of efficiently addressing two of the main problems associated with “Sclairtech” technology, namely, the generation of out-of-specification product during grade transitions and wide specification ranges. The benefits analysis involved using real process data, a statistical analysis of key variables to identify the dispersion and percentage of out-of-specification products, and the calculation of the net present value of financial indicators capable of validating the investment. An annual gain of US$ 791,812 was estimated, with US$ 494,883 coming from the reduction in catalyst consumption and US$ 296,929 from other sources (reduction in out-of-specification product and production losses associated with grade transitions).

Abstract: With the increasing demand for clean energy and the uncertainty surrounding the application of renewables, recent years have seen ammonia emerging as a viable way to store and transport hydrogen on a large scale. Its increasing importance in national hydrogen policies, as in the case of Brunei, highlights the need to look into technological readiness and global paths of innovation for this novel fuel. This study analyzes the global development of ammonia-based hydrogen production technologies from a methodological perspective and has shown that 708 granted patents to that were systematically screened, sorted and analyzed. A statistically sound retrieval method and screening process, following the PRISMA guidelines, have been employed to categorize the patents by synthesis processes, types of catalyst, and technological field. The results indicate that electrochemical, plasma-based, photocatalysis, and hybrid systems are becoming common paths as low-temperature alternatives, while thermal catalytic breakdown remains the most popular and well-known path to pursue. A range of reactor engineering, system integration, and catalyst design efforts have been undertaken, particularly in Asia. This indicates a high level of industrial and research interest in advancing ammonia-to-hydrogen technologies. These findings offer a clear overview of current technological maturity and emerging innovation trends, supporting long-term transitions toward cleaner hydrogen pathways.

Abstract: Over the last few years, we have attempted to develop an \( E_8 \times E_8 \) theory of unification to combine the standard model with general relativity. In the present new work, we give a self-contained construction in which the two extra \( SU(3) \) factors that appear in the maximal subgroup chain \( E_8\supset E_6\times SU(3) \) on each side of \( E_8\times \omega E_8 \) generate: (i) a six-dimensional base \( (M_6,g) \) of signature \( (3,3) \); (ii) two embedded Lorentzian 4D spacetimes; and (iii) per side, a canonical real 4-dimensional internal fibre naturally identified with the tangent of \( \mathbb{C}P^2=SU(3)/S(U(2)\times U(1)) \). The key algebraic ingredient is the octonionic split \( O=H\oplus H\varepsilon \) with \( \varepsilon\perp H \), by which the branch AdjSU(3) →\( \mathbf{3}_0\oplus \mathbf{2}_{+1}\oplus\overline{\mathbf{2}}_{-1}\oplus \mathbf{1}_0 \) is realised as ℑ\( H\oplus (H\varepsilon)_{\mathbb{R}}\oplus R \). The two \( U(1) \) factors play the role of Spin\( ^c \) connections on the \( \mathbb{C}P^2 \) fibres.

Abstract: It is posited that the two balanced ternary systems, (-1, 0, 1) and (-i, 0, i), are positioned on the line of real numbers and on the axis of complex numbers, respectively. In the event that the system is reduced to a single entity, the digits of the resulting system will be as follows: { -1, -i, 0, i, 1} The set (-1, -i, 0, i, 1) is transformed into a base five system. In this article and the following ones, I will outline the aforementioned relationship and its considerable potential for implementation in the domains of computer technology and a novel programming language. In addition to laying the groundwork for the trivalent system, which was clearly and brilliantly developed by Jan Łukasiewicz, we can expand beyond the {third middle defined by Aristotle in Chapter 9 of his treatise "De Interpretatione", which was written in opposition to the Stoics' determinism. This perspective enables us to extend the law of middles to the fourth, fifth, sixth, and so on, while adhering to the principles of polyvalent systems. This generates a proliferating field of probabilities where we can establish a chain of closely related probabilities, link by link, where each one is equally likely to be true or false. This allows us to approach or separate from the local truth or lie. I understand that the concepts of truth and falsehood, as developed by mathematical logic in a bivalent system, refer to a particular truth or lie. Thus, absolute truth is universal and impossible to know. However, it is not necessary to know absolute truth because what affects us in our daily lives is local truth or local falsehood. Then, it is appropriate to discern between a local truth universally accepted and a falsehood that can also be accepted as true, as well as the distinction between a true truth and a falsehood that could also be a true lie. In this article, we will analyze up to the third dimension (3D) which is composed by the following structures: i. A polyvalent system of "fifth truth degree", where the fifth middle is introduced. ii. A balanced system of base seven, in which seven coordinated points are introduced. iii. This balanced system operates within the Ternary Balanced system. iv. The Ternary base number defines the lowest and highest limits. v. Every volumetric body is founded on its complex plane, but empty space, between the volumetric bodies is a volume of its respective dimension. vi. Every mathematical operation can be developed directly as (ST110i0)(1T0S1) or (ST110i0)/(1T0S1) without requiring the complex polynomial form. A polyvalent system allows us to construct volumes of bodies, then surface of volumetric bodies, then volumes of volumetric bodies, then surface of volumes of volumetric bodies, and so forth. I briefly glance beyond the seventh base to the eleventh, thirteenth, and fifteenth bases.

Abstract: Background/Objectives: Type 2 diabetes (T2D) affects more than 38 million Americans and remains a leading public health challenge. Behavioral self-management is central to glycemic control but is often undermined by dysregulated and addictive-like eating. Continuous glucose monitoring (CGM) offers immediate feedback that may strengthen self-regulation, yet the psychological processes linking CGM use, food addiction (FA), and behavior change are poorly understood. This secondary mixed-methods study examined how CGM-supported group medical visits (GMVs) influence glycemic outcomes and FA symptoms in adults with diabetes. Methods: Adults with T2D participated in a 14-week GMV program integrating CGM review with education on nutrition, physical activity, sleep, stress, and intermittent fasting. Thirteen participants had paired CGM summaries and psychosocial data. Quantitative outcomes included mean glucose, glycemic variability, time-in-range (TIR) and symptoms of food addiction using the modified Yale Food Addiction Scale 2.0 (mYFAS 2.0). Qualitative data came from open-ended surveys analyzed using reflexive thematic analysis. Integration followed a convergent design, merging individual change trajectories with thematic interpretations and case vignettes. Results: Mean glucose decreased by 21 mg/dL and TIR improved by 9 percentage points. Among six participants with baseline FA symptoms, all showed improvement. Four moved from mild to no symptoms, one from moderate to no symptoms, and one from severe to no symptoms. Across the full sample, the mean change was a reduction of 1.2 in the mYFAS 2.0 symptom counts per participant. Thematic analysis identified four interrelated psychological mechanisms: enhanced awareness of food–glucose relationships, increased accountability through shared tracking, motivation via gamified self-monitoring, and relief from cognitive burden associated with dietary uncertainty. Conclusions: Integrating CGM feedback into GMVs may reduce addictive-like eating and promote glycemic improvement by enhancing awareness, accountability, and self-regulatory engagement. These findings position CGM as a behavioral intervention tool that complements its traditional monitoring role and highlight the value of combining real-time biofeedback with group-based support in diabetes care.

Abstract: Background: In triple-negative breast cancer (TNBC), the addition of immunotherapy has significantly improved outcomes. Immune-related adverse events (irAEs) can be accelerated in patients with pre-existing autoimmune (AI) conditions. The treatment-response standardised protocol used in clinical care raises concerns about the need for right-sizing strategies. As the use of immunotherapy expands, recognising toxicity from recurrence and optimising response-adapted approaches are essential to balance cure with quality of survival. Case Presentation: A 38-year-old pregnant woman with a distant history of uveitis and psoriasis was discovered to have pregnancy-associated TNBC. Postnatally, she was treated with neoadjuvant chemotherapy and pembrolizumab, followed by wire-guided left breast wide local excision and sentinel lymph node biopsy of left axilla. After surgery, residual cancer was noted. She continued adjuvant pembrolizumab and adjuvant radiotherapy 40.05Gy/15fr to the breast and nodes, followed by 13.35Gy/5fr. Despite a persistent residual tumour, pembrolizumab was continued as per protocol in a response-agnostic manner. At the end of one year of adjuvant pembrolizumab, she developed progressive numbness and weakness in the ipsilateral arm, initially raising suspicion for local recurrence. Comprehensive MRI and PET-CT imaging did not identify recurrent tumour or new metastatic disease. Electromyography confirmed a lower-trunk brachial plexopathy without a structural cause. An immune-mediated process was diagnosed by a process of elimination. Despite treatment with 1st-line high-dose corticosteroids and 2nd-line intravenous immunoglobulin (IVIG), improvement was limited. Therapeutic plasmapheresis, theoretically removing circulating immune complexes, cytokines, or checkpoint inhibitors, led to marked functional recovery and symptom resolution 20 months later. Discussion: Four main challenges are identified: (1) the diagnostic difficulty in identifying local recurrence or radiation injury from immune-related neuropathy; (2) the emerging therapeutic role of plasmapheresis in steroid-refractory irAEs; (3) the possible inconsistencies between rare toxicities observed in clinical trials vs clinical practice; and (4) the limitations in response in adjuvant therapy, particularly in patients with coexisting AI conditions. Conclusion: Although N-irAEs are rare, survival in early TNBC declines markedly when they occur during treatment. Early recognition and accurate distinction from tumour recurrence, as well as support for plasmapheresis as a potential option in steroid-refractory presentations, have been shown to improve patient survival and symptom reduction. With increasing use of immunotherapy, real-world toxicity data, predictive biomarkers, and personalised treatment strategies are urgently needed to balance cure with long-term functional outcomes.

Abstract: The advancement of autonomous driving technologies necessitates the development of sophisticated object detection systems capable of integrating heterogeneous sensor data to overcome the inherent limitations of unimodal approaches. While multi-modal fusion strategies offer promising solutions, they confront significant challenges including data alignment complexities in early fusion and computational burdens coupled with overfitting risks in deep fusion methodologies. We propose a Multi-modal Multi-class Late Fusion (MMLF) framework that operates at the decision level. This design preserves the architectural integrity of individual detectors and facilitates the flexible integration of diverse modalities. A key innovation of our approach is the incorporation of an evidence-theoretic uncertainty quantification mechanism, built upon Dempster-Shafer theory, which provides a mathematically grounded measure of confidence and significantly enhances the reliability and interpretability of the detection outcomes. Comprehensive experimental evaluation on the KITTI benchmark dataset demonstrates that our method achieves substantial performance improvements across multiple metrics, including 2D detection, 3D localization, and bird’s-eye view tasks. The framework reduces uncertainty estimates across different object categories. This work provides a versatile and scalable solution for multi-modal object detection that effectively addresses critical challenges in autonomous driving applications.

Abstract: To ensure the security and confidentiality of various data types (including text, images, audio, and video), this paper proposes a multi-wavelet figure-and-text hiding algorithm (MWFTHA) and its corresponding multi-wavelet figure-and-text restoration algorithm (MWFTRA). These algorithms facilitate the encoding and embedding of text and color images into a one-dimensional signal through multi-wavelet transforms. Text data is encoded using a character dataset, while color images are processed via a linear transformation before being integrated into the signal. Subsequently, the original text and image can be precisely retrieved from the synthesized signal using MWFTRA. An illustrative case demonstrates the efficacy of this approach. The efficiency of MWFTHA and MWFTRA is verified through 1,000 simulations. The results indicate rapid data hiding and recovery, as indicated by the mean execution time and standard deviation. The method's performance is evaluated using the structural similarity index measure (SSIM) and peak signal-to-noise ratio (PSNR), which indicate slight improvements in quality relative to traditional wavelet and integer wavelet transforms. Additionally, the system's security is analyzed, with a focus on private-key mechanisms and resistance to data tampering. This steganography technology provides a robust solution for the secure transmission and storage of sensitive data, thereby reducing the risk of information leakage.

Abstract: Safety management in the chemical process industry remains a critical challenge due to recurring high impact industrial accidents and the limited predictive capability of conventional threshold based safety systems. Traditional PLC–SCADA frameworks rely on static alarm limits and reactive shutdown logic, which often fail to detect early stage nonlinear deviations in complex, multivariate processes. This study presents ChemSafeAI+, a machine learning driven dynamic safety and optimization framework designed to augment existing industrial control architectures. The system integrates real-time anomaly detection using gradient-boosting models, predictive analytics, safety action processing, operator aware visualization dashboards, and traceable console logging within a unified, modular architecture. The framework is evaluated using a validated synthetic dataset derived from the Haber–Bosch ammonia synthesis process, capturing realistic thermodynamic, kinetic, and operational variability across 5000 operating scenarios. Experimental results demonstrate strong anomaly detection capability and consistent early warning behavior across multiple abnormal operating conditions. SHAP-based explainability provides both global and local interpretability, aligning model decisions with domain relevant process variables. By combining predictive intelligence with safety oriented decision logic and operator traceability, ChemSafeAI+ demonstrates the feasibility of ML driven supervisory safety systems for proactive risk mitigation and improved operational resilience in industrial chemical environments.

Abstract: As the threat landscape advances and pressure to reduce the energy footprint grows, it is crucial to understand how security mechanisms affect the power consumption of cloud-native platforms. Although several studies in this domain have investigated the performance impact of security practices or the energy characteristics of containerized applications, their combined effect remains largely underexplored. This study examines how common Kubernetes (K8s) safeguards influence cluster energy use across varying security configurations and workload conditions. By employing runtime and network monitoring, encryption, and vulnerability-scanning tools under diverse workloads (idle, stressed, realistic application), we compare the baseline system behavior against the energy consumption introduced by each security configuration. Our findings reveal that always-on security mechanisms impose a persistent baseline energy cost—occasionally making an idle protected cluster comparable to a heavily loaded unprotected one, while security under load results in substantial incremental overhead. In particular, service meshes and full-tunnel encryption show the largest sustained overhead, while eBPF telemetry, network security monitoring, and vulnerability scans add modest or short-lived costs. These findings provide useful security-energy insights and trade-offs for configuring K8s in resource-constrained settings, including IoT/smart city deployments.

Abstract: Shapley values are the most widely used point-valued solution concept for cooperative games and have recently garnered attention for their applicability in explainable machine learning. Due to the complexity of Shapley value computation, users mostly resort to Monte Carlo approximations for large problems. We take a detailed look at an approximation method grounded in multilinear extensions proposed by Okhrati and Lipani (2021) under the name Owen sampling. We point out why Owen sampling is biased and propose unbiased alternatives based on combining multilinear extensions with stratified sampling and importance sampling. Finally, we discuss empirical results of the presented algorithms for various cooperative games including real-world explainability scenarios.