Search Results (18)

Recursive constructions derived from finite projective geometries generate scalable families of resolvable block designs exhibiting strong algebraic regularity and intrinsic symmetry. In this work, we investigate the structural optimization of recursion depth in such constructions and demonstrate that the combinatorial growth of recursive chains is governed by a quadratic scaling law originating from the asymptotic expansion of Gaussian binomial coefficients. We show that the resulting exponent is strictly concave, which guarantees the existence and uniqueness of an optimal recursion depth. This optimum occurs at the midpoint of the projective dimension and reflects the dual symmetry of the lattice of projective subspaces. To analyze this behavior, we introduce a normalized objective function that compares recursion depths and reveals a unique maximum corresponding to the midpoint of the projective dimension. Theoretical analysis is supported by exact enumeration and asymptotic validation, confirming that the optimal depth is robust to lower-order perturbations and remains invariant under the natural duality of projective geometry. The proposed framework establishes a direct connection between symmetry properties of discrete geometric structures and optimality in nonlinear discrete systems. These results provide a unified perspective on recursive design constructions, revealing that symmetry not only governs combinatorial structure but also induces a mathematically inevitable optimal configuration. The approach opens new directions for studying symmetry-induced optimality in combinatorial geometry, discrete optimization, and related nonlinear mathematical models. Full article

This paper proposes a recursive method for constructing intra-resolvable balanced incomplete block designs (BIBDs). The approach exploits the algebraic and geometric structure of finite projective geometries over Galois fields to generate resolvable designs with improved efficiency in terms of the number of blocks and treatment replications. The recursive procedure produces symmetric and uniform designs that are particularly suitable for high-dimensional settings. By systematically nesting resolvable blocks, we derive a new class of balanced n-ary designs that are both economical and scalable. These designs hold significant value for the statistical community, offering broad applicability in resource-constrained experimental environments such as precision agriculture, high-throughput drug screening, and computer-based simulation studies. We provide theoretical foundations through explicit constructions and comparative evaluations, demonstrating the advantages of our method over classical approaches. Full article

Theological engagement with artificial intelligence has largely focused on applied ethics, addressing bias, governance, and labor displacement. While indispensable, this framing often presumes that algorithmic systems operate as external instruments acting upon already constituted subjects. This article argues that contemporary predictive architectures intervene at a deeper anthropological level by structuring attention, expectation, and habituation prior to deliberative judgment. It introduces the concept of ordo extractionis to designate a technologically mediated regime of formation characterized by behavioral trace extraction, probabilistic modeling, and recursive projection of statistically inferred continuity. Drawing on Augustine’s account of ordered love and temporality and Aquinas’s doctrine of habitus and the invisible mission of the Spirit, the article distinguishes algorithmic projection from sanctification as divergent pedagogies of temporal formation. Predictive systems stabilize continuity by extrapolating from measurable past behavior; sanctification reorders desire teleologically toward a final end not deducible from prior pattern and grounded in non-competitive divine causality. Algorithmic mediation is therefore interpreted pedagogically rather than metaphysically: it does not rival divine agency but participates creaturely in shaping the ecology within which habituation unfolds. Engagement with contemporary AI research on recommender systems, reinforcement learning, and generative models situates the argument within technological realism and resists determinism. The digital twin is analyzed as a probabilistic representation that acquires institutional authority when operationalized in ranking, profiling, and evaluative systems, without constituting a metaphysical competitor to the imago Dei. In response to anticipatory closure, Eucharistic anamnesis and epiclesis are developed as practices that re-situate memory and expectation within eschatological promise. The article concludes that the central theological question posed by AI is not whether machines can think, but how formative sovereignty over desire is exercised within technologically mediated modernity. Full article

Recursion is often presented as a nice and illustrative technique, only to later conclude that it should (almost) never be used due to potential problems with call stack overflow. However, recursion can often be the technique of choice during algorithm development and testing, and even in final solutions. Therefore, a simple but effective technique is needed to overcome call stack limitations. We designed and implemented the Extendable Stack Library (ESL), which provides a simple and effective interface that enables deep recursion in C++. Its flexible usage model allows deep recursion to be used where needed, without requiring major project modifications or customization of development tools. The performance overhead is moderate and localized only to deep recursive functions using ESL. The library is designed to be flexible and cross-platform. It supports Linux on AMD64 and AArch64 processors and Windows on AMD64. It can be adapted to more platforms with relative ease. ESL has been tested through a series of unit tests, experiments, and practical applications. It has proven to be an effective solution for deep recursion. ESL has been successfully used in the implementation of the Wafl programming language interpreter. Full article

This study introduces a novel control strategy aimed at achieving projective synchronization in incommensurate fractional-order chaotic systems (IFOCS). The approach integrates the mathematical framework of fractional calculus with the recursive structure of the backstepping control technique. A key feature of the proposed method is the systematic use of the Mittag–Leffler function to verify stability at every step of the control design. By carefully constructing the error dynamics and proving their asymptotic convergence, the method guarantees the overall stability of the coupled system. In particular, stabilization of the error signals around the origin ensures perfect projective synchronization between the master and slave systems, even when these systems exhibit fundamentally different fractional-order chaotic behaviors. To illustrate the applicability of the method, the proposed fractional order backstepping control (FOBC) is implemented for the synchronization of two representative systems: the fractional-order Van der Pol oscillator and the fractional-order Rayleigh oscillator. These examples were deliberately chosen due to their structural differences, highlighting the robustness and versatility of the proposed approach. Extensive simulations are carried out under diverse initial conditions, confirming that the synchronization errors converge rapidly and remain stable in the presence of parameter variations and external disturbances. The results clearly demonstrate that the proposed FOBC strategy not only ensures precise synchronization but also provides resilience against uncertainties that typically challenge nonlinear chaotic systems. Overall, the work validates the effectiveness of FOBC as a powerful tool for managing complex dynamical behaviors in chaotic systems, opening the way for broader applications in engineering and science. Full article

Accurate forecasting of electricity production is crucial for the stability of the entire energy sector. However, predicting future renewable energy production and its value is difficult due to the complex processes that affect production using renewable energy sources. In this article, we examine the performance of basic deep learning models for electricity forecasting. We designed deep learning models, including recursive neural networks (RNNs), which are mainly based on long short-term memory (LSTM) networks; gated recurrent units (GRUs), convolutional neural networks (CNNs), temporal fusion transforms (TFTs), and combined architectures. In order to achieve this goal, we have created our benchmarks and used tools that automatically select network architectures and parameters. Data were obtained as part of the NCBR grant (the National Center for Research and Development, Poland). These data contain daily records of all the recorded parameters from individual solar and wind farms over the past three years. The experimental results indicate that the LSTM models significantly outperformed the other models in terms of forecasting. In this paper, multilayer deep neural network (DNN) architectures are described, and the results are provided for all the methods. This publication is based on the results obtained within the framework of the research and development project “POIR.01.01.01-00-0506/21”, realized in the years 2022–2023. The project was co-financed by the European Union under the Smart Growth Operational Programme 2014–2020. Full article

Dairy farm profitability in the European Union has become increasingly volatile following market deregulation, complicating farm operations and undermining food security amid geopolitical tensions. To address the need for a streamlined analytical tool, this study develops a simulation model of milk production profitability tailored to small, open economies, using Poland as a case study. The model defines a profitability coefficient as the ratio of sector-level milk revenues to feed costs and decomposes it into three dynamic components: production efficiency (milk yield per feed unit), the price spread between milk and feed, and the net effect of policy interventions on revenues and costs. Exogenous variables (milk prices, feed prices, and policy support indices) are projected under baseline, optimistic, and pessimistic scenarios, while endogenous variables (profitability, herd size, and yield) evolve recursively based on estimated lags reflecting biological and economic responses. Simulation results for 2023–2027 indicate that profitability trajectories hinge primarily on price spreads, with policy measures playing a stabilizing but secondary role. Optimistic scenarios yield significant increases in profitability, whereas pessimistic assumptions lead to significant declines. These findings highlight the need to balance key market drivers—such as the relationship between milk prices and feed costs—with appropriately designed support instruments for milk producers. The model provides policymakers with a tool to adjust interventions so that support instruments are effective but do not lead to excessive reliance on public assistance. Full article

This study integrates the 2017 United Nations ESD framework and UNESCO’s ESD priorities with the Sustainable Development Goal (SDG) of “quality education” and the CDIO (Conceive, Design, Implement, Operate) framework to propose an innovative programming teaching model. A central component is an automatic architecture diagram generation system that visualizes program code structures in real-time, reducing cognitive load and enhancing comprehension of abstract programming concepts such as recursion and data structures. Students complete a project-based assignment—developing a Scheme interpreter—to simulate real-world software development. This model emphasizes system thinking, modular design, and problem solving, aligning with CDIO’s structured learning progression. The experimental results show that students using the system significantly outperformed the control group in their final project scores, demonstrating improved practical programming ability. While cognitive load remained stable, learning motivation decreased slightly, indicating the need for additional affective design support. The findings confirm that the integration of visual learning tools and project-based pedagogy under the CDIO framework supports the development of critical competencies for sustainable development. This approach offers a transformative step forward in programming education, cultivating learners who are capable, innovative, and ready to meaningfully contribute to global sustainability. Full article

In this paper, a new consensus tracking control algorithm is proposed for discrete multi-agent systems under binary communication with noise and a time-varying reference state. Unlike previous studies, the leader’s reference state is time-varying and convergent. Each agent estimates its neighbors’ states using a recursive projection algorithm based on noisy binary-valued information. The controller design incorporates both the error between the current and estimated states and the rate of change of the estimated state, resulting in a proportional–derivative-like algorithm (PD-like algorithm). The algorithm achieves consensus tracking with a convergence rate of $O(1/t^{\epsilon })$ under certain conditions. Finally, numerical simulations demonstrate the algorithm’s effectiveness and validate the theoretical results. Full article

Accurately evaluating postgraduate education satisfaction is crucial for improving higher education quality and optimizing management practices. Traditional methods often fail to capture the complex behavioral interactions among influencing factors. In this study, an innovative satisfaction indicator system framework is proposed that integrates a two-stage feature optimization method and the Tree Augmented Naive Bayes (TAN) model. The framework is designed to assess key satisfaction drivers across seven dimensions: course quality, research projects, mentor guidance, mentor’s role, faculty management, academic enhancement, and quality development. Using data from 8903 valid responses, Confirmatory Factor Analysis (CFA) was conducted to validate the framework’s reliability. The two-stage feature optimization method, including statistical pre-screening and XGBoost-based recursive feature selection, refined 49 features to 29 core indicators. The TAN model was used to construct a causal network, revealing the dynamic relationships between factors shaping satisfaction. The model outperformed four common machine learning algorithms, achieving an AUC value of 91.01%. The Birnbaum importance metric was employed to quantify the contribution of each feature, revealing the critical roles of academic resilience, academic aspirations, dedication and service spirit, creative ability, academic standards, and independent academic research ability. This study offers management recommendations, including enhancing academic support, mentorship, and interdisciplinary learning. Its findings provide data-driven insights for optimizing key indicators and improving postgraduate education satisfaction, contributing to behavioral sciences by linking satisfaction to outcomes and practices. Full article

The application of BIM technology in building construction provides the possibility to realize design accuracy, to visualize the construction details, to optimize construction schemes, and to enhance cooperation among various professionals. The Yancheng Nanyang Airport terminal 2 project, with its large span of steel roof structure, complex installation in mechanical and electrical pipeline (MEP) engineering, and difficulty in construction organization, is taken as the engineering background. The whole process application of BIM technology in the construction process is introduced. In structural engineering construction, the application of BIM technology can provide guidance for plane layout of the construction site, and can also assist in deepening the designs of irregular steel components. In steel construction, the application of BIM technology gives a commendable visual demonstration of the construction process of the metal roof system and the single-layer reticulated shell. In MEP engineering, the application of BIM technology provides a great approach to establish a synthesis of pipeline drawings to further form pipeline section diagrams and operation drawings. By integrating the dimension of time, precision control, and deviation rectification, a recursive construction drawing can be built. With respect to synergistic management, the quality and safety management in the construction site can be implemented on the basis of BIM terminal equipment as well. This paper will give a great reference on the application of BIM technology in the airport terminal construction. Full article

Multistatic airborne SAR (MuA-SAR) benefits from the ability to flexibly adjust the positions of multiple transmitters and receivers in space, which can shorten the synthetic aperture time to achieve the required resolution. To ensure both imaging efficiency and quality of different system spatial configurations and trajectories, the fast factorized back projection (FFBP) algorithm is proposed. However, if the FFBP algorithm based on polar coordinates is directly applied to the MuA-SAR system, the interpolation in the recursive fusion process will bring the problem of redundant calculations and error accumulation, leading to a sharp decrease in imaging efficiency and quality. In this paper, a unified Cartesian fast factorized back projection (UCFFBP) algorithm with a multi-level regional attention strategy is proposed for MuA-SAR fast imaging. First, a global Cartesian coordinate system (GCCS) is established. Through designing the rotation mapping matrix and phase compensation factor, data from different bistatic radar pairs can be processed coherently and efficiently. In addition, a multi-level regional attention strategy based on maximally stable extremal regions (MSER) is proposed. In the recursive fusion process, only the suspected target regions are paid more attention and segmented for coherent fusion at each fusion level, which further improves efficiency. The proposed UCFFBP algorithm ensures both the quality and efficiency of MuA-SAR imaging. Simulation experiments verified the effectiveness of the proposed algorithm. Full article

Over the course of seven years during ten events, the author explored real-time interactive audiovisual projections, using ad hoc and portable projections and audio systems. This was done in the specific location of Cockatoo Island in the waters of a part of Sydney Harbour, Australia. The island offers a unique combination of the remnants of a shipyard industrial precinct, other buildings, and increasingly restored natural environment. The project explored real-time audiovisual responses through projected overlays reminiscing the rich history and past events, interactively resonating with the current landscape and built environment. This included the maritime industrial history, as well as other historical layers such as convict barracks, school, and the significance of the location for Australia’s original inhabitants before colonisation by the British started in 1788. But most prominently, the recent use of the island for large scale art projects (such as the Outpost street art festival in 2011, and over a decade of use as part of the Sydney Biennale of Art, and the use of the island for film sets). This was a rich source of image material collected by the author and used to extend and reflect on current realities. By using the projections, overlaying and extending the present reality with historical data in the form of sounds and video, dialogues were facilitated and a conflation of past and present explored. The main activity were the VideoWalks, where the author, using a custom built portable audiovisual projection system and a bank of audiovisual material was able to re-place sound and video of previous events in the present context, in some instances whilst delivering a performative lecture on the way. The explorations are part of the author’s Traces project, exploring traces and remnants of past events and how these can inform design approaches. The project over the years also developed an element of recursion, by using footage of an earlier projection into the current, the footage of which was then used in the next event, and so on—up to five layers of extended reality. Full article

The extended Kalman filter (EKF) has a wide range of applications (especially in power battery management systems) with a rapidly increasing market share. It aims to minimize the symmetric loss function (mean square error) and it has high accuracy and efficiency in battery state estimation. This study deals with the second-order extended Kalman filter-based process and the measurement white noise estimation problem for nonlinear continuous-discrete systems. The design of the white noise filter and smoother were, firstly, converted into a linear estimation problem by the second-order Taylor series expansion approximation and the function that makes the second-order term approximately equivalent to the estimation error variance. Secondly, based on the projection formula of the Kalman filtering (KF) theory and the Lemma of expectation for quadratic and quartic product traces of random vectors, the second-order EKF was derived. Then, to generate white noise estimators in the forms of filtering and smoothing, we derived a recursive solution, using an innovation method. Finally, a numerical example is given to show the effectiveness of the proposed method. Full article

Contemporary generative grammar assumes that syntactic structure is best described in terms of sets, and that locality conditions, as well as cross-linguistic variation, is determined at the level of designated functional heads. Syntactic operations (merge, MERGE, etc.) build a structure by deriving sets from lexical atoms and recursively (and monotonically) yielding sets of sets. Additional restrictions over the format of structural descriptions limit the number of elements involved in each operation to two at each derivational step, a head and a non-head. In this paper, we will explore an alternative direction for minimalist inquiry based on previous work, e.g., Frank (2002, 2006), albeit under novel assumptions. We propose a view of syntactic structure as a specification of relations in graphs, which correspond to the extended projection of lexical heads; these are elementary trees in Tree Adjoining Grammars. We present empirical motivation for a lexicalised approach to structure building, where the units of the grammar are elementary trees. Our proposal will be based on cross-linguistic evidence; we will consider the structure of elementary trees in Spanish, English and German. We will also explore the consequences of assuming that nodes in elementary trees are addresses for purposes of tree composition operations, substitution and adjunction. Full article