Search Results (49)

3D Gaussian splatting (3DGS) has recently emerged as an efficient and scalable method for high-fidelity 3D scene reconstruction, representation, and real-time rendering. In addition to geometric reconstruction, increasing research attention focuses on enriching 3D Gaussian primitives with semantic information, which can be related to an arbitrary application or domain, as well as common knowledge. However, the existing approaches to semantic 3DGS significantly differ in how semantics are represented, learned, and accessed, which makes systematic analysis difficult. This paper provides a review on semantic extensions to 3DGS. We introduce a unified multi-axis taxonomy that enables us to classify the available methods in terms of five complementary categories: semantic vocabulary space, representation form, functional role, knowledge source, and query mechanism. The analysis reveals key design trade-offs related to the flexibility, efficiency, and semantic expressiveness of the methods. Furthermore, we review datasets, benchmarks, and evaluation metrics used in the field, indicating the diversity of approaches and the lack of common evaluation frameworks. Based on this analysis, we also identify open challenges and possible future research directions. The presented survey is relevant to advances in games and immersive technologies, where semantically enriched real-time 3D representations are essential for interactive environments, AR/VR, and intelligent scene understanding. The systematic analysis presented in this survey aims to facilitate a deeper understanding of semantic 3DGS and support the development of more general, efficient, and task-aware 3D scene understanding systems. Full article

Mobile edge computing (MEC) must serve rapidly growing populations of latency-critical and energy-constrained devices, yet distributed offloading faces two coupled problems: learned multi-agent policies depend on the arbitrary numerical ordering of edge servers, which wastes training samples and treats physically equivalent configurations inconsistently, while short-horizon cost minimization overloads attractive servers and destabilizes their queues. This paper presents SEAL-MAC (Symmetry-Equivariant Lyapunov Multi-Agent Actor–Critic), a distributed learning framework that addresses both problems jointly. First, a symmetric resource-set actor with a mirror consistency regularizer enforces server relabeling equivariance of each user’s policy and invariance of its value and Lyapunov critics. Second, a load-symmetric Lyapunov–potential shaping mechanism augments drift-plus-penalty rewards with normalized load-balance signals, coupling queue stability, fairness, and strategic alignment. The shaped interaction is analyzed as a Lyapunov-shaped Markov potential game: exact under orthogonal congestion-separable conditions, and a Markov $\alpha$-potential game under heterogeneity or interference, yielding conditional finite-time $(ϵ+\alpha )$-Nash convergence and mean-square queue stability. Each device learns from local observations and $O\left(M\right)$ queue broadcasts without exchanging gradients or policies. In simulations with up to 200 users, SEAL-MAC reduces average delay by 9.0%, 95th-percentile delay by 11.8%, energy consumption by 10.6%, and the deadline-violation rate from 3.1% to 1.8% relative to the strongest Lyapunov baseline, halves the empirical one-step deviation gain of an identically shaped Ly-PPO agent (0.048 versus 0.098), and raises the Jain fairness index from 0.88 to 0.94. Full article

We study convergence in multi-agent reinforcement learning (MARL) through the lens of sufficient conditions, using a single-point-of-failure analysis applied to multi-agent policy iteration integrated with linear programming (MAPI-LP), where results are proven for pure coordination games, and extension to broader settings is conjectured. We identify two sufficient conditions for convergence to Markov Perfect Equilibrium (MPE). The first is stability in best-response space that emerges from value monotonicity. The second, monotonic best-response space shrinking (MBRSS), is a novel condition requiring that each agent’s best-response space contracts monotonically across iterations until it collapses to a stable space. Furthermore, we show that MBRSS does not necessarily imply monotonic improvement in this setting. However, value monotonicity and stability in best-response space imply each other when a complementary condition is applied. Building on this hierarchical relationship, we propose conjectures on sufficient condition relationships in both serial and parallel MARL. In addition, we propose conjectures on generalized MBRSS to arbitrary finite repeated games and validation of stability in best-response space. We further discuss connections between MBRSS and existing related frameworks, and outline directions toward a taxonomy of sufficient conditions for MARL convergence. Full article

This paper describes the development of several software-based games using a high-level programming language (C in our case), designed so that they can be ported to a Field-Programmable Gate Array (FPGA). It also outlines the mathematical foundations underlying these games. Making executables portable in this way can simplify running applications on FPGA platforms. Porting a game to an FPGA serves as evidence that arbitrary executables can be migrated to such hardware. The complete workflow for creating the game, along with the final game outcomes, is detailed in this paper. In addition, statistical analyses of these games were conducted. The proposed approach relies on graphics and character-handling libraries typically available in advanced programming languages. The background of this work is that a microcontroller architecture which can easily be run on a Spartan-6 FPGA was needed. The innovative point of this paper is that it created the cross-compilation toolchain on an uncommon microcontroller architecture, like the OpenRISC. Full article

In this paper we investigate the chaos of a generalized perturbed Lotka–Volterra model based on considerations by other studies used in the literature. The model, containing N number of free parameters, could be of interest to specialists working in the fields of biological applications, chemistry, reaction kinetics, biostatistics, games theory, etc. With a specially developed software product, we generate the Melnikov equation $M(t)=0$ and examine all its zeros. This opens up an opportunity for the researcher to correctly understand and formulate the classical Melnikov criterion for the possible occurrence of chaos in the dynamical system. Several simulations are composed. We also demonstrate some specialized modules for investigating the dynamics of the proposed model. We further develop our model using the exponential form of the sine function. Thus, the perturbation can be interpreted as a term dependent on the characteristic function of a probability distribution. Although the original formulation leads to a distribution stated on a discrete domain, we can easily generalize the results for arbitrary distributions. Some particular examples are provided. Full article

Peter Lombard’s First Book of the Sentences presents formidable questions concerning the principle of the Son’s generation. Addressing a gap in contemporary scholarship, this article examines Lombard’s foundational exposition of the Father’s power and will to generate. Placing Lombard in dialogue with Thomas Aquinas, this study traces the development of this doctrine across Aquinas’s career, from his commentary on the Sentences to De potentia and the Summa theologiae. Our analysis adopts Aquinas’s own framework to investigate a series of questions: whether generation is an act of nature or will; whether the power to generate is part of omnipotence; whether it is essential or relational; and whether the Son possesses this power. This study finds that Aquinas’s conclusions often converge with Lombard’s intuitions. Both affirm that generation is by nature while simultaneously accompanied by a concomitant will, and that the generative power is rooted in the divine essence. Aquinas’s analysis, however, represents a significant metaphysical development. A key evolution is traced in Aquinas’s understanding of the power to generate, which shifts from being a quasi-natural power distinct from omnipotence to a form of paternal omnipotence. His characterization of this power also matures from being a middle ground between the essential and the relational to being principally essential, signifying the relation of paternity only obliquely. This trajectory toward a firmer grounding in the divine essence is supported by an increasingly refined set of arguments for the Son’s unicity, with principles like the determination of nature and divine simplicity becoming more prominent in his later works. By charting these developments, this article demonstrates how Aquinas builds upon Lombard’s foundational intuitions to construct a more systematic and robust Trinitarian theology. Ultimately, our analysis illuminates the intellectual journey from sound doctrinal intuition to profound metaphysical articulation, where the tenets of faith are secured by a cogent intellectual framework. Our analysis also offers a counter-narrative to contemporary assumptions, challenging modern conceptions of power as a zero-sum game and of freedom as mere arbitrary choice. Full article

This paper investigates the leader–follower consensus problem for a class of second-order multi-agent systems. These systems are composed of both discrete-time and continuous-time subsystems and are governed by switching dynamics. Within the framework of a fixed directed topology involving multiple leaders, two control strategies are formulated. One applies separate control protocols to the continuous and discrete subsystems, while the other adopts an unified sampled-data control protocol. First, a multi-player game model is established based on the analysis and simulation of conflict behaviors among agents, and the existence of a unique Nash equilibrium(NE) for the system is proven. Then, based on the Nash equilibrium, a continuous–discrete-time game-based switching control system is formulated. Furthermore, the results confirm that the proposed system achieves consensus under both control strategies, even under arbitrary switching patterns. Finally, the performance of the approach is verified through numerical simulations. Full article

This study presents a novel game-theoretical framework designed to support epidemic management, with a specific focus on the allocation of limited resources across competing public health objectives and intervention strategies. Recognizing the varied roles and capacities of participatory agents, we model their involvement as occurring at multiple levels, reflecting the complex decision-making processes encountered in real-world situations. To account for the unequal influence or priority of different agents and strategies, we further propose a suite of weighted allocation measures grounded in well-established theoretical principles. In response to ongoing concerns over the arbitrariness of externally assigned weights, we also construct a refined metric based on endogenous marginal intervention effects, offering a more organically derived representation of participator impact. A series of illustrative examples demonstrates the practical relevance of these models, revealing how they can capture key dynamics such as behavioral diversity, the coexistence of overlapping policies, and logical independence under distinct weighting perspectives. Collectively, these contributions aim to provide epidemic response teams with a set of interpretable and adaptable tools tailored to the complexity of real-world public health crises. Full article

Recent studies have proposed methods for extracting latent sharp frames from a single blurred image. However, these methods still suffer from limitations in restoring satisfactory images. In addition, most existing methods are limited to decomposing a blurred image into sharp frames with a fixed frame rate. To address these problems, we present an Arbitrary Time Blur Decomposition Triple Generative Adversarial Network (ABDGAN) that restores sharp frames with flexible frame rates. Our framework plays a min–max game consisting of a generator, a discriminator, and a time-code predictor. The generator serves as a time-conditional deblurring network, while the discriminator and the label predictor provide feedback to the generator on producing realistic and sharp image depending on given time code. To provide adequate feedback for the generator, we propose a critic-guided (CG) loss by collaboration of the discriminator and time-code predictor. We also propose a pairwise order-consistency (POC) loss to ensure that each pixel in a predicted image consistently corresponds to the same ground-truth frame. Extensive experiments show that our method outperforms previously reported methods in both qualitative and quantitative evaluations. Compared to the best competitor, the proposed ABDGAN improves PSNR, SSIM, and LPIPS on the GoPro test set by $16.67\%$, $9.16\%$, and $36.61\%$, respectively. For the B-Aist++ test set, our method shows improvements of $6.99\%$, $2.38\%$, and $17.05\%$ in PSNR, SSIM, and LPIPS, respectively, compared to the best competitive method. Full article

Slicing 3D polygonal meshes is a fundamental operation in various applications such as virtual surgery, garment simulation, and game development. Existing methods primarily slice meshes using either a single line or a set of line segments approximating a smooth curve. This paper introduces a novel approach to freely slice a triangle mesh using a freeform curve without discretizing it into line segments. The user draws a stroke on the screen, defining the desired cutting trajectory. Subsequently, a freeform curve approximating this stroke is generated and extended into a ruled surface in the user’s viewing direction. To efficiently compute intersections between the ruled surface and a triangle mesh, the Line–Surface Intersection (LSI) problem is broken down into two subproblems: Plane–Curve Intersection (PCI) followed by Line–Line Intersection (LLI). Intersection points are then connected to form polylines, effectively cutting the mesh into multiple submeshes. To ensure the solidity of the submeshes, cross-sections are generated by trimming the ruled surface along the polylines and merged with the corresponding submeshes. Our method empowers users to slice triangle meshes along arbitrary trajectories encompassing both straight and freely curved paths while preserving efficiency and accuracy. The effectiveness of the proposed approach is demonstrated through experimental results showing various examples of mesh slicing. Full article

Little is discussed regarding the meaning of “definition” in primary school, where children often memorize definitions. In geometry, students frequently confuse “definition” with the “description” of a geometric object. The aim of this study is to verify whether a new hybrid methodology between storytelling and game-based learning called Geometrikoland exercises skills that fall within what we understand as “definitory thinking”, which the set of competencies and meta-competencies is associated with acquiring a true mastery of definitions in geometry. This goal can be achieved because the dynamics of Geometrikoland alter the approach to definitions. The methodology applied is a hybrid of storytelling and adventure game-based learning applied to a “engine” of quadrilateral theory. The experiment took place in a fifth-grade class in an Italian school. The analysis of some data based on the accuracy of geometry actions during workshops and qualitative analysis based on the analysis of oral arguments produced during the labs lead to the conclusion that, on average, children have gained a greater awareness of what it means to define a geometric object and a better understanding of the relationships between various subsets of the set of quadrilaterals, previously seen as separate sets. Further confirmation has been provided by comparing the results of two mini-tests (a placement test and an exit test), which are useful for assessing the skills associated with the criterion of arbitrariness, the criterion of uniqueness, and classificatory thinking. Full article

Edge computing brings computation and storage resources to the edge of the mobile network to solve the problems of low latency and high real-time demand. However, edge computing is more vulnerable to malicious attacks due to its open and dynamic environments. In this article, we investigate security defense strategies in edge computing systems, focusing on scenarios with one attacker and multiple defenders to determine optimal defense strategies with minimal resource allocation. Firstly, we formulate the interactions between the defenders and the attackers as the mean-field Stackelberg game model, where the state and the objective functions of the defenders are coupled through the mean-field term, and are strongly influenced by the strategy of the attacker. Then, we analyze the local optimal strategies of the defenders given an arbitrary strategy of the attackers. We demonstrate the Nash equilibrium and the mean-field equilibrium for both the defenders and the attackers. Finally, simulation analysis will illustrate the dynamic evolution of the defense strategy of the defenders and the trajectory of the attackers based on the proposed Stackelberg game model. Full article

Developing efficient path-planning algorithms is an essential topic in modern robotics and control theory. Autonomous rovers and wheeled and tracked robots require path generators that can efficiently cover the explorable space with minimal redundancy. In this paper, we present a new path-planning algorithm based on the chaotic behavior of the Courbage–Nekorkin neuron model with a coverage control parameter. Our study aims to reduce the number of iterations required to cover the chosen investigated area, which is a typical efficiency criterion for this class of algorithms. To achieve this goal, we implemented a pseudorandom bit generator (PRBG) based on a Courbage–Nekorkin chaotic map, which demonstrates chaotic behavior and successfully passes all statistical tests for randomness. The proposed PRBG generates a bit sequence that can be used to move the tracked robot in four or eight directions in an operation area of arbitrary size. Several statistical metrics were applied to evaluate the algorithm’s performance, including the percentage of coverage of the study area and the uniformity of coverage. The performance of several competing path-planning algorithms was analyzed using the chosen metrics when exploring two test areas of the sizes 50 × 50 cells and 100 × 100 cells, respectively, in four and eight directions. The experimental results indicate that the proposed algorithm is superior compared to known chaotic path-planning methods, providing more rapid and uniform coverage with the possibility of controlling the covered area using tunable parameters. In addition, this study revealed the high dependence of the coverage rate on the starting point. To investigate how the coverage rate depends on the choice of chaotic map, we implemented six different PRBGs using various chaotic maps. The obtained results can be efficiently used for solving path-planning tasks in both real-life and virtual (e.g., video games) applications. Full article

Two recent studies addressed the problem of reducing transitional turbulence in applications developed in C# on .NET. The first study investigated this problem in desktop and Web GUI applications and the second in virtual and augmented reality applications using the Unity3D game engine. The studies used similar solution approaches, but both were somewhat embedded in the details of their applications and implementation platforms. This paper examines these two families of applications and seeks to extract the common aspects of their problem definitions and solution approaches and codify the problem-solution pair as a new software design pattern. To do so, the paper adopts Wellhausen and Fiesser’s writer’s path methodology and follows it systematically to discover and write the pattern, recording the reasoning at each step. To evaluate the pattern, the paper applies it to an arbitrary C#/.NET GUI application. The resulting design pattern is named Dynamically Coalescing Reactive Chains (DCRC). It enables the approach to transitional turbulence reduction to be reused across a range of related applications, languages, and user interface technologies. The detailed example of the writer’s path can assist future pattern writers in navigating through the complications and subtleties of the pattern-writing process. Full article

The Global Malmquist Productivity Index (GMPI) stands as an evolution of the Malmquist Productivity Index (MPI), emphasizing global technology to incorporate all-time versions of Decision-Making Units (DMUs). This paper introduces a novel approach, integrating the Nash Bargaining Game model with GMPI to establish a Cross-Productivity Index. Our primary objective is to develop a comprehensive framework utilizing the Nash Bargaining Game model to derive equitable common weights for different time versions of DMUs. These weights serve as a fundamental component for cross-evaluation based on GMPI, facilitating a holistic assessment of DMU performance over varying time periods. The proposed index is designed with essential properties: feasibility, non-arbitrariness concerning the base time period, technological consistency across periods, and weight uniformity for GMPI calculations between two-time versions of a unit. This research amalgamates cross-evaluation and global technology while employing geometric averages to derive a conclusive cross-productivity index. The core motivation behind this methodology is to establish a reliable and fair means of evaluating DMU performance, integrating insights from Nash Bargaining Game principles and GMPI. This paper elucidates the rationale behind merging the Nash Bargaining Game model with GMPI and outlines the objectives to provide a comprehensive Cross-Productivity Index, aiming to enhance the robustness and reliability of productivity assessments across varied time frames. Full article