To obtain more accurate model parameters and improve prediction accuracy, we proposed a regularized Kriging model that penalizes the hyperparameter theta in the Gaussian stochastic process, termed the Theta-regularized Kriging. We derived the optimization problem for this model from a maximum likelihood perspective. Additionally, we presented specific implementation details for the iterative process, including the regularized optimization algorithm and the geometric search cross-validation tuning algorithm. Three distinct penalty methods, Lasso, Ridge, and Elastic-net regularization, were meticulously considered. Meanwhile, the proposed Theta-regularized Kriging models were tested on nine common numerical functions and two practical engineering examples. The results demonstrate that, compared with other penalized Kriging models, the proposed model performs better in terms of accuracy and stability.

We show that the matrix perspective function, which is jointly convex in the Cartesian product of a standard Euclidean vector space and a conformal space of symmetric matrices, has a proximity operator in an almost closed form.

In the era of Large Language Models (LLMs), Retrieval-Augmented Generation (RAG) architectures are gaining significant attention for their ability to ground language generation in reliable knowledge sources. Despite their impressive effectiveness in many areas, RAG systems based solely on semantic similarity often fail to ensure factual accuracy in specialized domains, where terminological ambiguity can affect retrieval relevance. This study proposes an enhanced RAG architecture that integrates a factual signal derived from Entity Linking to improve the accuracy of educational question-answering systems in Italian. The system includes a Wikidata-based Entity Linking module and implements three re-ranking strategies to combine semantic and entity-based information: a hybrid score weighting model, reciprocal rank fusion, and a cross-encoder re-ranker. Experiments were conducted on two benchmarks: a custom academic dataset and the standard SQuAD-it dataset. Results show that, in domain-specific contexts, the hybrid schema based on reciprocal rank fusion significantly outperforms both the baseline and the cross-encoder approach, while the cross-encoder achieves the best results on the general-domain dataset. These findings confirm the presence of an effect of domain mismatch and highlight the importance of domain adaptation and hybrid ranking strategies to enhance factual precision and reliability in retrieval-augmented generation. They also demonstrate the potential of entity-aware RAG systems in educational environments, fostering adaptive and reliable AI-based tutoring tools.

Nowadays, formal theorem provers have made monumental progress on high-school and competition-level mathematics, but few of them generalize to more advanced mathematics. In this paper, we present REAL-Prover, a new open-source stepwise theorem prover for Lean 4 to push this boundary. This prover, based on our fine-tuned large language model (REAL-Prover-v1) and integrated with a retrieval system (Leansearch-PS), notably boosts performance on solving college-level mathematics problems. To train REAL-Prover-v1, we developed HERALD-AF, a data extraction pipeline that converts natural language math problems into formal statements, and a new open-source Lean 4 interactive environment (Jixia-interactive) to facilitate synthesis data collection. In our experiments, our prover using only supervised fine-tune achieves competitive results with a 23.7% success rate (Pass@64) on the ProofNet dataset-comparable to state-of-the-art (SOTA) models. To further evaluate our approach, we introduce FATE-M, a new benchmark focused on algebraic problems, where our prover achieves a SOTA success rate of 56.7% (Pass@64).

Insect species subject to infection, predation, and anisotropic environmental conditions may exhibit preferential movement patterns. Given the innate stochasticity of exogenous factors driving these patterns over short timescales, individual insect trajectories typically obey overdamped stochastic dynamics. In practice, data-driven modeling approaches designed to learn the underlying Fokker-Planck equations from observed insect distributions serve as ideal tools for understanding and predicting such behavior. Understanding dispersal dynamics of crop and silvicultural pests can lead to a better forecasting of outbreak intensity and location, which can result in better pest management. In this work, we extend weak-form equation learning techniques, coupled with kernel density estimation, to learn effective models for lepidopteran larval population movement from highly sparse experimental data. Galerkin methods such as the Weak form Sparse Identification of Nonlinear Dynamics (WSINDy) algorithm have recently proven useful for learning governing equations in several scientific contexts. We demonstrate the utility of the method on a sparse dataset of position measurements of fall armyworms (Spodoptera frugiperda) obtained in simulated agricultural conditions with varied plant resources and infection status.

This perspective paper explores the future potential of "conversational intelligence" by examining how Large Language Models (LLMs) could be combined with GRAPHYP's network system to better understand human conversations and preferences. Using recent research and case studies, we propose a conceptual framework that could make AI rea-soning transparent and traceable, allowing humans to see and understand how AI reaches its conclusions. We present the conceptual perspective of "Matching Game Preferences through Dialogical Large Language Models (D-LLMs)," a proposed system that would allow multiple users to share their different preferences through structured conversations. This approach envisions personalizing LLMs by embedding individual user preferences directly into how the model makes decisions. The proposed D-LLM framework would require three main components: (1) reasoning processes that could analyze different search experiences and guide performance, (2) classification systems that would identify user preference patterns, and (3) dialogue approaches that could help humans resolve conflicting information. This perspective framework aims to create an interpretable AI system where users could examine, understand, and combine the different human preferences that influence AI responses, detected through GRAPHYP's search experience networks. The goal of this perspective is to envision AI systems that would not only provide answers but also show users how those answers were reached, making artificial intelligence more transparent and trustworthy for human decision-making.

We present a machine-learning guided approach to predict saturation magnetization (MS) and coercivity (HC) in Fe-rich soft magnetic alloys, particularly Fe-Si-B systems. ML models trained on experimental data reveals that increasing Si and B content reduces MS from 1.81T (DFT~2.04 T) to ~1.54 T (DFT~1.56T) in Fe-Si-B, which is attributed to decreased magnetic density and structural modifications. Experimental validation of ML predicted magnetic saturation on Fe-1Si-1B (2.09T), Fe-5Si-5B (2.01T) and Fe-10Si-10B (1.54T) alloy compositions further support our findings. These trends are consistent with density functional theory (DFT) predictions, which link increased electronic disorder and band broadening to lower MS values. Experimental validation on selected alloys confirms the predictive accuracy of the ML model, with good agreement across compositions. Beyond predictive accuracy, detailed uncertainty quantification and model interpretability including through feature importance and partial dependence analysis reveals that MS is governed by a nonlinear interplay between Fe content, early transition metal ratios, and annealing temperature, while HC is more sensitive to processing conditions such as ribbon thickness and thermal treatment windows. The ML framework was further applied to Fe-Si-B/Cr/Cu/Zr/Nb alloys in a pseudo-quaternary compositional space, which shows comparable magnetic properties to NANOMET (Fe84.8Si0.5B9.4Cu0.8 P3.5C1), FINEMET (Fe73.5Si13.5B9 Cu1Nb3), NANOPERM (Fe88Zr7B4Cu1), and HITPERM (Fe44Co44Zr7B4Cu1. Our fundings demonstrate the potential of ML framework for accelerated search of high-performance, Co- and Ni-free, soft magnetic materials.

Deepfake technology utilizes deep learning based face manipulation techniques to seamlessly replace faces in videos creating highly realistic but artificially generated content. Although this technology has beneficial applications in media and entertainment misuse of its capabilities may lead to serious risks including identity theft cyberbullying and false information. The integration of DL with visual cognition has resulted in important technological improvements particularly in addressing privacy risks caused by artificially generated deepfake images on digital media platforms. In this study we propose an efficient and lightweight method for detecting deepfake images and videos making it suitable for devices with limited computational resources. In order to reduce the computational burden usually associated with DL models our method integrates machine learning classifiers in combination with keyframing approaches and texture analysis. Moreover the features extracted with a histogram of oriented gradients (HOG) local binary pattern (LBP) and KAZE bands were integrated to evaluate using random forest extreme gradient boosting extra trees and support vector classifier algorithms. Our findings show a feature-level fusion of HOG LBP and KAZE features improves accuracy to 92% and 96% on FaceForensics++ and Celeb-DFv2 respectively.

Pollution that originates from automobiles is a concern in the current world, not only because of global warming, but also due to the harmful effects on people's health and lives. Despite regulations on exhaust gas emissions being applied, minimizing unsuitable driving habits that cause elevated fuel consumption and emissions would achieve further reductions. For that reason, this work proposes a self-organized map (SOM)-based intelligent system in order to provide drivers with eco-driving-intended driving style (DS) recommendations. The development of the DS advisor uses driving data from the Uyanik instrumented car. The system classifies drivers regarding the underlying causes of non-optimal DSs from the eco-driving viewpoint. When compared with other solutions, the main advantage of this approach is the personalization of the recommendations that are provided to motorists, comprising the handling of the pedals and the gearbox, with potential improvements in both fuel consumption and emissions ranging from the 9.5\% to the 31.5\%, or even higher for drivers that are strongly engaged with the system. It was successfully implemented using a field-programmable gate array (FPGA) device of the Xilinx ZynQ programmable system-on-a-chip (PSoC) family. This SOM-based system allows for real-time implementation, state-of-the-art timing performances, and low power consumption, which are suitable for developing advanced driving assistance systems (ADASs).

Advanced driving assistance systems (ADAS) are primarily designed to increase driving safety and reduce traffic congestion without paying too much attention to passenger comfort or motion sickness. However, in view of autonomous cars, and taking into account that the lack of comfort and motion sickness increase in passengers, analysis from a comfort perspective is essential in the future car investigation. The aim of this work is to study in detail how passenger's comfort evaluation parameters vary depending on the driving style, car or road. The database used has been developed by compiling the accelerations suffered by passengers when three drivers cruise two different vehicles on different types of routes. In order to evaluate both comfort and motion sickness, first, the numerical values of the main comfort evaluation variables reported in the literature have been analyzed. Moreover, a complementary statistical analysis of probability density and a power spectral analysis are performed. Finally, quantitative results are compared with passenger qualitative feedback. The results show the high dependence of comfort evaluation variables' value with the road type. In addition, it has been demonstrated that the driving style and vehicle dynamics amplify or attenuate those values. Additionally, it has been demonstrated that contributions from longitudinal and lateral accelerations have a much greater effect in the lack of comfort than vertical ones. Finally, based on the concrete results obtained, a new experimental campaign is proposed.