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30 pages, 5684 KiB  
Article
Exploring Relationships Between Qualitative Student Evaluation Comments and Quantitative Instructor Ratings: A Structural Topic Modeling Framework
by Nina Zipser, Dmitry Kurochkin, Kwok Wah Yu and Lisa A. Mincieli
Educ. Sci. 2025, 15(8), 1011; https://doi.org/10.3390/educsci15081011 (registering DOI) - 6 Aug 2025
Abstract
This study demonstrates how Structural Topic Modeling (STM) can be used to analyze qualitative student comments in conjunction with quantitative student evaluation of teaching (SET) scores, providing a scalable framework for interpreting student evaluations of teaching. Drawing on 286,203 open-ended comments collected over [...] Read more.
This study demonstrates how Structural Topic Modeling (STM) can be used to analyze qualitative student comments in conjunction with quantitative student evaluation of teaching (SET) scores, providing a scalable framework for interpreting student evaluations of teaching. Drawing on 286,203 open-ended comments collected over fourteen years at a large U.S. research university, we identify eleven latent topics that characterize how students describe instructional experiences. Unlike traditional topic modeling methods, STM allows us to examine how topic prevalence varies with course and instructor attributes, including instructor gender, course discipline, enrollment size, and numeric SET scores. To illustrate the utility of the model, we show that topic prevalence aligns with SET ratings in expected ways and that students associate specific teaching attributes with instructor gender, though the effects are relatively small. Importantly, the direction and strength of topic–SET correlations are consistent across male and female instructors, suggesting shared student perceptions of effective teaching practices. Our findings underscore the potential of STM to contextualize qualitative feedback, support fairer teaching evaluations, inform institutional decision-making, and examine the relationship between qualitative student comments and numeric SET ratings. Full article
(This article belongs to the Special Issue Recent Advances in Measuring Teaching Quality)
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20 pages, 813 KiB  
Review
Exploring Design Thinking Methodologies: A Comprehensive Analysis of the Literature, Outstanding Practices, and Their Linkage to Sustainable Development Goals
by Matilde Martínez Casanovas
Sustainability 2025, 17(15), 7142; https://doi.org/10.3390/su17157142 - 6 Aug 2025
Abstract
Design Thinking (DT) has emerged as a relevant methodology for addressing global challenges aligned with the United Nations Sustainable Development Goals (SDGs). This study presents a systematic literature review, conducted following PRISMA 2020 guidelines, which analyzes 42 peer-reviewed publications from 2013 to 2023. [...] Read more.
Design Thinking (DT) has emerged as a relevant methodology for addressing global challenges aligned with the United Nations Sustainable Development Goals (SDGs). This study presents a systematic literature review, conducted following PRISMA 2020 guidelines, which analyzes 42 peer-reviewed publications from 2013 to 2023. Through inductive content analysis, 10 core DT principles—such as empathy, iteration, user-centeredness, and systems thinking—I identified and thematically mapped to specific SDGs, including goals related to health, education, innovation, and climate action. The study also presents five real-world cases from diverse sectors such as technology, healthcare, and urban planning, illustrating how DT has been applied to address practical challenges aligned with the SDGs. However, the review identifies persistent gaps in the field: the lack of standardized evaluation frameworks, limited integration across SDG domains, and weak adaptation of ethical and contextual considerations, particularly in vulnerable communities. As a response, this paper recommends the adoption of structured impact assessment tools (e.g., Cities2030, Responsible Design Thinking), integration of design justice principles, and the development of participatory, iterative ecosystems for innovation. By offering both conceptual synthesis and applied insights, this article positions Design Thinking as a strategic and systemic approach for driving sustainable transformation aligned with the 2030 Agenda. Full article
(This article belongs to the Section Sustainable Education and Approaches)
12 pages, 2316 KiB  
Article
Rubus magurensis (Rosaceae): A New Bramble Species from the Northern Carpathians (Poland)
by Mateusz Wolanin, Krystyna Musiał and Marcin Nobis
Forests 2025, 16(8), 1286; https://doi.org/10.3390/f16081286 - 6 Aug 2025
Abstract
Rubus magurensis Wolanin, M. Nobis & Oklej. (Rosaceae), a new species from the Northern Carpathians, described and illustrated here, is a tetraploid (2n = 28) belonging to the subgenus Rubus series Micantes. Among the most characteristic features of this species are first-year [...] Read more.
Rubus magurensis Wolanin, M. Nobis & Oklej. (Rosaceae), a new species from the Northern Carpathians, described and illustrated here, is a tetraploid (2n = 28) belonging to the subgenus Rubus series Micantes. Among the most characteristic features of this species are first-year stems that are almost glabrous, leaflets most often arched downward, and inflorescences leafy to the apex with a few simple oval leaves in the upper part, which make this species easy to recognise. This species resembles R. tabanimontanus Figert, from which it differs in having smaller primocane prickles, digitate to subpedate leaves, larger flowers, and inflorescences leafy to the apex. Rubus magurensis is currently known from 11 populations located in southeastern Poland (7 ATPOL 2 × 2 km units). Most of them were found in the central part of the Low Beskid Mts., with two populations located in the northwestern part of the Strzyżów Foothills. Full article
(This article belongs to the Section Forest Ecology and Management)
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21 pages, 944 KiB  
Article
An Early Investigation of the HHL Quantum Linear Solver for Scientific Applications
by Muqing Zheng, Chenxu Liu, Samuel Stein, Xiangyu Li, Johannes Mülmenstädt, Yousu Chen and Ang Li
Algorithms 2025, 18(8), 491; https://doi.org/10.3390/a18080491 - 6 Aug 2025
Abstract
In this paper, we explore using the Harrow–Hassidim–Lloyd (HHL) algorithm to address scientific and engineering problems through quantum computing, utilizing the NWQSim simulation package on a high-performance computing platform. Focusing on domains such as power-grid management and climate projection, we demonstrate the correlations [...] Read more.
In this paper, we explore using the Harrow–Hassidim–Lloyd (HHL) algorithm to address scientific and engineering problems through quantum computing, utilizing the NWQSim simulation package on a high-performance computing platform. Focusing on domains such as power-grid management and climate projection, we demonstrate the correlations of the accuracy of quantum phase estimation, along with various properties of coefficient matrices, on the final solution and quantum resource cost in iterative and non-iterative numerical methods such as the Newton–Raphson method and finite difference method, as well as their impacts on quantum error correction costs using the Microsoft Azure Quantum resource estimator. We summarize the exponential resource cost from quantum phase estimation before and after quantum error correction and illustrate a potential way to reduce the demands on physical qubits. This work lays down a preliminary step for future investigations, urging a closer examination of quantum algorithms’ scalability and efficiency in domain applications. Full article
39 pages, 5251 KiB  
Article
Metamodeling Approach to Sociotechnical Systems’ External Context Digital Twins Building: A Higher Education Case Study
by Ana Perisic, Ines Perisic, Marko Lazic and Branko Perisic
Appl. Sci. 2025, 15(15), 8708; https://doi.org/10.3390/app15158708 (registering DOI) - 6 Aug 2025
Abstract
Sociotechnical systems (STSs) are generally assumed to be systems that incorporate humans and technology, strongly depending on a sustainable equilibrium between the following nondeterministic social context ingredients: social structures, roles, and rights, as well as the designers’ Holy Grail, the deterministic nature of [...] Read more.
Sociotechnical systems (STSs) are generally assumed to be systems that incorporate humans and technology, strongly depending on a sustainable equilibrium between the following nondeterministic social context ingredients: social structures, roles, and rights, as well as the designers’ Holy Grail, the deterministic nature of the underlying technical system. The fact that the relevant social concepts are more mature than the supporting technologies qualifies the digital transformation of sociotechnical systems as a reengineering rather than an engineering endeavor. Preserving the social mission throughout the digital transformation process in varying social contexts is mandatory, making the digital twins (DT) methodology application a contemporary research hotspot. In this research, we combined continuous transformation STS theory principles, an observer-based system-of-sociotechnical-systems (SoSTS) architecture model, and digital twinning methods to address common STS context representation challenges. Additionally, based on model-driven systems engineering methodology and meta-object-facility principles, the research specifies the universal meta-concepts and meta-modeling templates, supporting the creation of arbitrary sociotechnical systems’ external context digital twins. Due to the inherent diversity, significantly influenced by geopolitical, economic, and cultural influencers, a higher education external context specialization illustrates the reusability potentials of the proposed universal meta-concepts. Substituting higher-education-related meta-concepts and meta-models with arbitrary domain-dependent specializations further fosters the proposed universal meta-concepts’ reusability. Full article
23 pages, 380 KiB  
Article
B Impact Assessment as a Driving Force for Sustainable Development: A Case Study in the Pulp and Paper Industry
by Yago de Zabala, Gerusa Giménez, Elsa Diez and Rodolfo de Castro
Reg. Sci. Environ. Econ. 2025, 2(3), 24; https://doi.org/10.3390/rsee2030024 - 6 Aug 2025
Abstract
This study evaluates the effectiveness of the B Impact Assessment (BIA) as a catalyst for integrating sustainability into industrial firms through a qualitative case study of LC Paper, the first B Corp-certified tissue manufacturer globally and a pioneer in applying BIA in the [...] Read more.
This study evaluates the effectiveness of the B Impact Assessment (BIA) as a catalyst for integrating sustainability into industrial firms through a qualitative case study of LC Paper, the first B Corp-certified tissue manufacturer globally and a pioneer in applying BIA in the pulp and paper sector. Based on semi-structured interviews, organizational documents, and direct observation, this study examines how BIA influences corporate governance, environmental practices, and stakeholder engagement. The findings show that BIA fosters structured goal setting and the implementation of measurable actions aligned with environmental stewardship, social responsibility, and economic resilience. Tangible outcomes include improved stakeholder trust, internal transparency, and employee development, while implementation challenges such as resource allocation and procedural complexity are also reported. Although the single-case design limits generalizability, this study identifies mechanisms transferable to other firms, particularly those in environmentally intensive sectors. The case studied also illustrates how leadership commitment, participatory governance, and data-driven tools facilitate the operationalization of sustainability. By integrating stakeholder and institutional theory, this study contributes conceptually to understanding certification frameworks as tools for embedding sustainability. This research offers both theoretical and practical insights into how firms can align strategy and impact, expanding the application of BIA beyond early adopters and into traditional industrial contexts. Full article
23 pages, 3031 KiB  
Article
Integrated Capuchin Search Algorithm-Optimized Multilayer Perceptron for Robust and Precise Prediction of Blast-Induced Airblast in a Blasting Mining Operation
by Kesalopa Gaopale, Takashi Sasaoka, Akihiro Hamanaka and Hideki Shimada
Geosciences 2025, 15(8), 306; https://doi.org/10.3390/geosciences15080306 - 6 Aug 2025
Abstract
Blast-induced airblast poses a significant environmental and operational issue for surface mining, affecting safety, regulatory adherence, and the well-being of surrounding communities. Despite advancements in machine learning methods for predicting airblast, present studies neglect essential geomechanical characteristics, specifically rock mass strength (RMS), which [...] Read more.
Blast-induced airblast poses a significant environmental and operational issue for surface mining, affecting safety, regulatory adherence, and the well-being of surrounding communities. Despite advancements in machine learning methods for predicting airblast, present studies neglect essential geomechanical characteristics, specifically rock mass strength (RMS), which is vital for energy transmission and pressure-wave attenuation. This paper presents a capuchin search algorithm-optimized multilayer perceptron (CapSA-MLP) that incorporates RMS, hole depth (HD), maximum charge per delay (MCPD), monitoring distance (D), total explosive mass (TEM), and number of holes (NH). Blast datasets from a granite quarry were utilized to train and test the model in comparison to benchmark approaches, such as particle swarm optimized artificial neural network (PSO-ANN), multivariate regression analysis (MVRA), and the United States Bureau of Mines (USBM) equation. CapSA-MLP outperformed PSO-ANN (RMSE = 1.120, R2 = 0.904 compared to RMSE = 1.284, R2 = 0.846), whereas MVRA and USBM exhibited lower accuracy. Sensitivity analysis indicated RMS as the main input factor. This study is the first to use CapSA-MLP with RMS for airblast prediction. The findings illustrate the significance of metaheuristic optimization in developing adaptable, generalizable models for various rock types, thereby improving blast design and environmental management in mining activities. Full article
(This article belongs to the Section Geomechanics)
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25 pages, 426 KiB  
Review
Survey on the Application of Robotics in Archaeology
by Panagiota Kyriakoulia, Anastasios Kazolias, Dimitrios Konidaris and Panagiotis Kokkinos
Sensors 2025, 25(15), 4836; https://doi.org/10.3390/s25154836 - 6 Aug 2025
Abstract
This work explores the application of robotic systems in archaeology, highlighting their transformative role in excavation, documentation, and the preservation of cultural heritage. By combining technologies such as LiDAR, GIS, 3D modeling, sonar, and other sensors with autonomous and semi-autonomous platforms, archaeologists can [...] Read more.
This work explores the application of robotic systems in archaeology, highlighting their transformative role in excavation, documentation, and the preservation of cultural heritage. By combining technologies such as LiDAR, GIS, 3D modeling, sonar, and other sensors with autonomous and semi-autonomous platforms, archaeologists can now reach inaccessible sites, automate artifact analysis, and reconstruct fragmented remains with greater precision. The study provides a systematic overview of underwater, aerial, terrestrial, and other robotic systems, drawing on scientific literature that showcases their innovative use in both fieldwork and museum settings. Selected examples illustrate how robotics is being applied to solve key archaeological challenges in new and effective ways. While the paper emphasizes the potential of these technologies, it also addresses their technical, economic, and ethical limitations, concluding that successful adoption depends on interdisciplinary collaboration, careful implementation, and a balanced respect for cultural integrity. Full article
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44 pages, 7941 KiB  
Article
A Numerical Investigation of Plastic Energy Dissipation Patterns of Circular and Non-Circular Metal Thin-Walled Rings Under Quasi-Static Lateral Crushing
by Shunsong Guo, Sunting Yan, Ping Tang, Chenfeng Guan and Wei Zhang
Mathematics 2025, 13(15), 2527; https://doi.org/10.3390/math13152527 - 6 Aug 2025
Abstract
This paper presents a combined theoretical, numerical, and experimental analysis to investigate the lateral plastic crushing behavior and energy absorption of circular and non-circular thin-walled rings between two rigid plates. Theoretical solutions incorporating both linear material hardening and power-law material hardening models are [...] Read more.
This paper presents a combined theoretical, numerical, and experimental analysis to investigate the lateral plastic crushing behavior and energy absorption of circular and non-circular thin-walled rings between two rigid plates. Theoretical solutions incorporating both linear material hardening and power-law material hardening models are solved via numerical shooting methods. The theoretically predicted force-denting displacement relations agree excellently with both FEA and experimental results. The FEA simulation clearly reveals the coexistence of an upper moving plastic region and a fixed bottom plastic region. A robust automatic extraction method of the fully plastic region at the bottom from FEA is proposed. A modified criterion considering the unloading effect based on the resultant moment of cross-section is proposed to allow accurate theoretical estimation of the fully plastic region length. The detailed study implies an abrupt and almost linear drop of the fully plastic region length after the maximum value by the proposed modified criterion, while the conventional fully plastic criterion leads to significant over-estimation of the length. Evolution patterns of the upper and lower plastic regions in FEA are clearly illustrated. Furthermore, the distribution of plastic energy dissipation is compared in the bottom and upper regions through FEA and theoretical results. Purely analytical solutions are formulated for linear hardening material case by elliptical integrals. A simple algebraic function solution is derived without necessity of solving differential equations for general power-law hardening material case by adopting a constant curvature assumption. Parametric analyses indicate the significant effect of ovality and hardening on plastic region evolution and crushing force. This paper should enhance the understanding of the crushing behavior of circular and non-circular rings applicable to the structural engineering and impact of the absorption domain. Full article
(This article belongs to the Special Issue Numerical Modeling and Applications in Mechanical Engineering)
24 pages, 759 KiB  
Article
The Mediating Role of the Firm Image in the Relationship Between Integrated Reporting and Firm Value in GCC Countries
by Mohammed Saleem Alatawi, Zaidi Mat Daud and Jalila Johari
J. Risk Financial Manag. 2025, 18(8), 438; https://doi.org/10.3390/jrfm18080438 - 6 Aug 2025
Abstract
In the context of the GCC, the adoption of integrated reporting (IR) remains limited, due in part to weak regulatory enforcement, a lack of awareness of the strategic benefits of IR, and a strong focus on short-term financial results. This limited reporting context [...] Read more.
In the context of the GCC, the adoption of integrated reporting (IR) remains limited, due in part to weak regulatory enforcement, a lack of awareness of the strategic benefits of IR, and a strong focus on short-term financial results. This limited reporting context presents a significant challenge for firms to credibly demonstrate their value to the market and attract potential investors, thus communicating long-term value. Given these limitations, this study considers how IR contributes to firm value, but also examines the mediating role that firm image (FI) plays in this relationship as a reputational construct representing stakeholder perspectives of a firm’s transparency and accountability. The research employs a quantitative methodology, analysing secondary data from corporate governance and integrated reports spanning 2017–2018 to 2022–2023. Findings indicate a positive and robust relationship between integrated reporting and the firm’s value, which was assessed using Tobin’s Q. The findings highlight the significant mediating role of firm image, illustrating how IR practices, via increased transparency, accountability, and sustainability, enhance firm value. This study provides significant insights for researchers, policymakers, and corporate managers, highlighting the strategic relevance of IR in the GCC region. The findings demonstrate that integrated reporting improves transparency, accountability, and sustainability, thereby assisting corporate managers in utilising IR to enhance firm image and facilitate value creation. Policymakers can utilise these insights to develop regulatory frameworks that promote integrated reporting practices, thereby enhancing transparency and sustainable growth within the corporate sector. Full article
(This article belongs to the Special Issue Emerging Trends and Innovations in Corporate Finance and Governance)
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23 pages, 311 KiB  
Article
Some Results on Maxima and Minima of Real Functions of Vector Variables: A New Perspective
by Bibiano Martin Cerna Maguiña, Dik Dani Lujerio Garcia, Victor Pocoy Yauri, Vladimir Giovanni Rodriguez Sabino and Ruben Mario Leiva Bernuy
Axioms 2025, 14(8), 611; https://doi.org/10.3390/axioms14080611 - 6 Aug 2025
Abstract
This article presents a method for proving several theorems that enable the determination of the maxima and minima of certain classes of real-valued functions with vector variables, without relying on the classical theory based on partial derivatives. However, the main objective of this [...] Read more.
This article presents a method for proving several theorems that enable the determination of the maxima and minima of certain classes of real-valued functions with vector variables, without relying on the classical theory based on partial derivatives. However, the main objective of this work is not to compare this approach with existing methods but, rather, to extend the study of extrema in real functions of vector variables that are not differentiable, as illustrated in Example 1. Each theorem is accompanied by various examples that demonstrate its applicability. The results are based on Theorems 1 and 2, as well as the selection of an appropriate connection between Theorem 2 and the functions to be optimized. Additionally, definitions related to the hierarchy between variables within a given domain are introduced, providing the theoretical framework necessary for the development of the proposed results. Full article
14 pages, 499 KiB  
Case Report
Advantages of FVIII-Extended Half-Life (Turoctocog Alfa Pegol) in the Management of Cardiac Surgery in a Patient with Mild Hemophilia A: A Case Report and Literature Review
by Angela Napolitano, Andrea Venturini, Mauro Ronzoni, Graziella Saggiorato, Paolo Simioni and Ezio Zanon
Hematol. Rep. 2025, 17(4), 41; https://doi.org/10.3390/hematolrep17040041 - 6 Aug 2025
Abstract
Background and Clinical Significance: Hemophilia A presents a considerable challenge in cardiac surgery due to the elevated risk of perioperative bleeding, particularly during procedures involving cardiopulmonary bypass. Standard management typically involves standard half-life (SHL) factor VIII (FVIII) concentrates, which require frequent dosing. Extended [...] Read more.
Background and Clinical Significance: Hemophilia A presents a considerable challenge in cardiac surgery due to the elevated risk of perioperative bleeding, particularly during procedures involving cardiopulmonary bypass. Standard management typically involves standard half-life (SHL) factor VIII (FVIII) concentrates, which require frequent dosing. Extended half-life (EHL) FVIII products offer theoretical advantages, including prolonged action and reduced infusion frequency, but their use in cardiac surgery remains largely undocumented. Case Presentation: We report the case of a 73-year-old male with mild Hemophilia A who underwent successful aortic valve replacement using a 25 mm Carpentier-Edwards Magna Ease biological prosthesis. The patient was managed perioperatively with an anti-hemorrhagic protocol based on EHL recombinant FVIII. The surgery and postoperative course were uneventful, with no bleeding complications or need for transfusion. Conclusions: This case illustrates the potential role of EHL FVIII in safely managing hemophilic patients undergoing major cardiac surgery. Given the lack of existing reports in the literature, further studies are warranted to evaluate the efficacy and safety of EHL FVIII in this setting and to potentially optimize perioperative care protocols for this patient population. Full article
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27 pages, 1062 KiB  
Article
Dynamic Supply Chain Decision-Making of Live E-Commerce Considering Netflix Marketing Under Different Power Structures
by Yawen Liu, Mohammed Gadafi Tamimu and Junwu Chai
J. Theor. Appl. Electron. Commer. Res. 2025, 20(3), 202; https://doi.org/10.3390/jtaer20030202 - 6 Aug 2025
Abstract
The rapid growth of live e-commerce, a sector valued at over USD 100 billion worldwide, demonstrates its transformative impact on the retail industry, especially in markets like China, where platforms such as Taobao Live and TikTok Shop have markedly altered consumer interaction. This [...] Read more.
The rapid growth of live e-commerce, a sector valued at over USD 100 billion worldwide, demonstrates its transformative impact on the retail industry, especially in markets like China, where platforms such as Taobao Live and TikTok Shop have markedly altered consumer interaction. This transition is further expedited by Netflix-like entertainment marketing methods, which have demonstrated the capacity to enhance consumer retention by as much as 40%. As organizations adjust to this evolving landscape, it is essential to optimize supply chain strategies to align with these dynamic, consumer-centric environments. This paper examines the complexity of decision-making in live e-commerce supply chains, specifically regarding Netflix-inspired marketing strategies. The primary aim of this study is to design a game-theoretic framework that examines the interactions between producers and online celebrity retailers (OCRs) across different power dynamics. As live commerce integrates digital retail with immersive experiences, businesses must optimize pricing, quality, and marketing strategies in real-time. We present engagement-driven marketing as a strategic variable and incorporate consumer regret and switching costs into the demand function. To illustrate practical trade-offs in strategy, we incorporate a multi-criteria decision-making (MCDM) layer with AHP-TOPSIS, assessing profit, consumer surplus, engagement score, and channel efficiency. The experiment results indicate that Netflix-style marketing markedly increases demand and profit in retailer-led frameworks, whereas centralized tactics enhance overall channel performance. TOPSIS analysis prioritizes high-effort, high-engagement methods, whereas the Stackelberg experiment underscores the influence of power dynamics on profit distribution. This study presents an innovative integrative decision-making methodology for enhancing live-streaming commerce tactics in data-driven and consumer-focused markets. Full article
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27 pages, 392 KiB  
Article
Pioneering Public Sector Innovation: The Case of Greece’s e-Government Team
by Athanasios Pantazis Deligiannis and Vassilios Peristeras
Adm. Sci. 2025, 15(8), 306; https://doi.org/10.3390/admsci15080306 - 6 Aug 2025
Abstract
This study offers the first systematic exploration of the Greek e-Government team, a public sector innovation unit that operated within the Office of the Prime Minister of Greece from 2009 to 2012—the sole example of such a unit in the country. It illustrates [...] Read more.
This study offers the first systematic exploration of the Greek e-Government team, a public sector innovation unit that operated within the Office of the Prime Minister of Greece from 2009 to 2012—the sole example of such a unit in the country. It illustrates how strategically positioned innovation units can function as change agents within government bureaucracies. The purpose of this work was to analyze how this distinctive unit functioned by bridging policy formulation, legislative drafting, and technological implementation at the highest government levels. The research involved thematic analysis of original interviews conducted with most core members of the team. The findings highlight successes, notably the Diavgeia transparency platform, which markedly improved administrative transparency, accountability, and citizen access to government decisions. Important challenges were also identified, particularly regarding the sustainability of the unit, issues of institutionalization, and meaningful citizen engagement. The experience of the Greek e-Government team suggests that public sector innovation (PSI) units are most effective when they combine high-level political access with multidisciplinary expertise and operational flexibility. The analysis also reveals inherent tensions between the need for centralized coordination and the benefits of decentralized implementation, as well as challenges in maintaining citizen participation throughout the policy development process. Full article
(This article belongs to the Special Issue Innovations, Projects, Challenges and Changes in A Digital World)
11 pages, 1039 KiB  
Article
A Random Riemann–Liouville Integral Operator
by Jorge Sanchez-Ortiz, Omar U. Lopez-Cresencio, Martin P. Arciga-Alejandre and Francisco J. Ariza-Hernandez
Mathematics 2025, 13(15), 2524; https://doi.org/10.3390/math13152524 - 6 Aug 2025
Abstract
In this work, we propose a definition of the random fractional Riemann–Liouville integral operator, where the order of integration is given by a random variable. Within the framework of random operator theory, we study this integral with a random kernel and establish results [...] Read more.
In this work, we propose a definition of the random fractional Riemann–Liouville integral operator, where the order of integration is given by a random variable. Within the framework of random operator theory, we study this integral with a random kernel and establish results on the measurability of the random Riemann–Liouville integral operator, which we show to be a random endomorphism of L1[a,b]. Additionally, we derive the semigroup property for these operators as a probabilistic version of the constant-order Riemann–Liouville integral. To illustrate the behavior of this operator, we present two examples involving different random variables acting on specific functions. The sample trajectories and estimated probability density functions of the resulting random integrals are then explored via Monte Carlo simulation. Full article
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