On orbit sets generated by semigroups of one-dimensional affine functions

A common problem in inventory planning is the uncertainty of the demand. One technique for determining the demand approximation value is the fractal interpolation. The aim of this study is to develop a fractal interpolation technique with an Fractal Interpolated Function constructed by the affine function that forms the Box Fractal shape. The development results are applied to interpolate rice demand data based on prices at a rice milling factory. Mean Absolute Percentage Error (MAPE) is used to measure the accuracy of interpolation results. For the nth iteration, the number of boxes formed are 5n and 4×5n pairs of points. Based on the rice demand data at one of the factories, the best MAPE was obtained at the 6th Iteration, which is 7.1596% within very good category. Based on the data used, the affine function that forms the Box Fractal as an Fractal Interpolated Function can be used in the fractal interpolation technique.

Ribozymes for site-specific RNA modification provide an elegant approach for the installation of diverse functional groups, fluorophores, affinity tags, or crosslinkers at defined positions within an RNA of interest. There is increasing interest in expanding the ribozyme toolbox, since recently reported in vitro selected ribozymes have been mostly limited to labeling at adenosine sites, either by alkylation of the nucleobase or phosphodiester formation at the 2'-OH group. Here we report a cytidine-specific alkyltransferase ribozyme (CSAR) that uses O6-benzylguanines as alkyl group donors. CSAR is the first ribozyme that catalyzes direct alkylation of the exocyclic amino group of a nucleobase and generates N4-alkylated cytidine in a defined sequence context of a short RNA hairpin loop. In combination with tuning the electronic parameters of the transferred benzyl group, CSAR enables highly efficient cytidine alkylation for the installation of bioorthogonal functional groups.

In multivariate time series forecasting, series decomposition architectures that decouple trend and residual components have become a mainstream solution for handling data non-stationarity. However, existing methods are limited by the "component independence assumption," modeling these components independently, thereby neglecting the intrinsic constraints macro-trends impose on micro-fluctuations. Furthermore, trend modeling faces a dilemma between efficiency and expressiveness: global attention-based methods are prone to introducing non-causal noise and disrupt trend continuity, whereas simple linear mappings lack dynamic modeling capabilities. To address these challenges, we propose the Causal Trend Evolution and Adaptive Modulation Network (CTMNet), a coupled decomposition architecture that employs a modeling strategy balancing differentiation and interaction. First, we design a Causal Trend Encoder (CTE), which utilizes patch-level causal convolution and gating mechanisms to introduce a strict temporal causal inductive bias, accurately characterizing the unidirectional evolution of trends with linear complexity. Second, for the residual component, we innovatively propose an Adaptive Trend Modulation Interaction (ATMI) mechanism. This mechanism uses the causal trend state extracted by the CTE as a contextual prior to dynamically generate affine transformation parameters, to hierarchically calibrate residual features. This design not only maintains the physical consistency of trend modeling but also restores the deep coupling between trend and residual components. Extensive experiments on 10 real-world benchmark datasets, covering both long- and short-term forecasting, demonstrate that CTMNet achieves competitive or leading performance in terms of prediction accuracy and robustness compared to 7 state-of-the-art (SOTA) models.

Drug combinations are crucial for overcoming resistance in cancer therapy. Although deep learning has achieved strong performance in synergy prediction, existing models often treat cell-specific features and paired drugs as a static background and fail to capture how the specific cell-drug environment dynamically modulates drug representations, thereby hindering the modeling of environment-specific synergistic effects. We propose Env-Syn, a framework for modeling drug-drug-cell interactions through Environment-Conditioned Feature Modulation, which incorporates a Residual Feature-wise Linear Modulation (R-FiLM) module to perform precise affine transformations on drug representations conditioned on paired drugs and cellular environments. Benchmark evaluations show that Env-Syn consistently outperforms state-of-the-art methods. Notably, the model exhibits exceptional generalization performance in rigorous inductive scenarios. It maintains high predictive accuracy for unseen drugs with AUROC and AUPRC exceeding 0.81 in the Leave-drug-out setting, and further demonstrates strong cross-dataset reliability by surpassing a recall of 0.7 on independent test set. Furthermore, among 15 novel predicted drug combinations, eight are directly supported by literature evidence. These results demonstrate that Env-Syn is an effective computational tool for drug synergy discovery. The source code is available at https://github.com/AnQi-87/Env-Syn. Supplementary data is available at Bioinformatics online.

We propose a spatial affordance-aware affine transformation method between heterogeneous spaces for continuous multi-object matching in shared Mixed Reality (MR) spaces. While previous redirection and spatial mapping approaches utilize physical objects and walkable areas, a critical gap remains in enabling continuous mapping between dissimilar physical environments that supports both precise object alignment and seamless locomotion in a shared space. Our method structurally segments heterogeneous spaces into interaction zones and constructs affine patches based on object adjacency and facing configuration, enabling continuous correspondence. We evaluate our method using a dataset of paired dissimilar spaces and demonstrate that, unlike conventional grid-based methods, our approach achieves broader spatial alignment and richer object matching. The results show that our method can serve as an effective mapping framework for shared environments requiring semantic continuity and structural coherence across diverse real-world spaces.

To address the problems of high cost, low efficiency, and high rates of missed and incorrect detections in the production of metal can lid printing products, an online inspection system for metal can lids was designed based on machine vision. Firstly, threshold segmentation was performed using the maximum inter-class variance method, and the detection area of the can lid was extracted through feature extraction and intersection operations. For surface printing detection, a printing defect detection method based on constructing a difference model was proposed. The Sobel operator was used to extract the edge information of the image to create a difference model, and template matching and the detection area were used to process the tested image using similarity measurement, affine transformation, and scaling of gray values, etc. Finally, the obtained images were input into the difference model for the final defect detection. Experiments were conducted by detecting a large number of tested images with different defects to verify the effectiveness of the scheme.

Selective metal ion affinity binding as a simple and renewable enzyme immobilization was investigated using the same affinity function on various supports. Phenylalanine ammonia-lyase from parsley (PcPAL) and an amine transaminase from Vibrio fluvialis (VfTA) with His-tag were used as model enzymes. Metal ion chelating groups on the surface of six enzyme carriers were created from the surface-alkylamino moieties by treatment with ethylenediaminetetraacetic dianhydride and subsequent complexation with cobalt(II) ions. Three porous polymer beads, two silica-based supports, and a silica-coated magnetic nanoparticle (MNP) were investigated as carriers. The most effective PcPAL biocatalyst forms were tested in kinetic resolution and ammonia addition reactions with substrates containing phenyl and thiophen-2-yl rings. In the selective ammonia addition reaction onto the (hetero)arylacrylates needing a harsh medium of a 6 M ammonia solution, the biocatalysts exhibited excellent stability and led to l-amino acids in high yield and excellent enantiomeric excess. The recharging of the MNP supports was investigated by five subsequent cycles of reactions-after elution with 5% diethylenetriamine and reloading with fresh PcPAL or VfTA-retaining over 80% of the relative activities until the third cycle. The repurposing of the supports was also investigated by changing one enzyme to the other on the MNP-immobilized metal ion affinity chromatography support.

A quantifier-reversal approximation paradigm for recurrent neural networks.

Fractional calculus modifies the geometric roughness of functions and alters global fractal dimensions in a monotonic manner. However, a comprehensive description of how fractional operators transform full scaling structures and multifractal spectra remains incomplete. In this paper, we establish a unified scaling-law theory describing the action of Riemann- Liouville and Weyl-Marchaud fractional operators on local regularity, structure functions, and multifractal spectra. We prove that fractional differentiation of order [Formula: see text] induces a translation of local Hölder exponents by [Formula: see text], yielding an exact shift law for the multifractal spectrum. Furthermore, we derive an affine transformation rule for structure-function scaling exponents, showing that fractional operators generate linear deformations of scaling laws across statistical moments. An AI-assisted identification framework is introduced to recover fractional order directly from observed fractal signals. Numerical experiments on synthetic multifractal processes confirm the theoretical predictions and demonstrate the robustness of the proposed method. These results provide a geometric and scaling interpretation of fractional calculus and establish a unified framework connecting fractal geometry, scaling laws, and artificial intelligence.

Abstract— Stroke is a serious medical condition caused by the interruption or reduction of blood flow to the brain, often resulting in facial weakness or disability. Early detection of stroke symptoms, particularly facial asymmetry, enables timely medical intervention and improves patient outcomes. This paper proposes an artificial intelligence-based approach that utilizes a limited set of neutral and smiling facial images to detect stroke-related facial weakness. To address data scarcity, a hybrid dataset is developed by combining real images with synthetic data generated using FaceGAN and deepfake-based augmentation techniques. Facial regions are segmented into left and right halves using landmark detection, followed by affine transformations based on Delaunay triangulation for geometric alignment. A deep learning architecture integrating a ConvNeXt encoder with a lightweight convolutional neural network (CNN) decoder is employed for feature extraction and classification. The model demonstrates strong robustness and achieves an accuracy of 98.9% using four- fold cross-validation. The results highlight the potential of AI- assisted facial analysis for rapid and accessible stroke screening in clinical and resource-limited environments. Keywords— Stroke detection, Facial weakness, Artificial intelligence, Deep learning, FaceGAN, Deepfake, Lightweight CNN, ConvNeXt

Abstract In classical credibility theory, estimation is typically limited to the hypothetical mean, restricting its use for premium principles that depend on higher-order moments. To address this, we develop a credibility-based framework for estimating the process variance under both known and unknown hypothetical means and apply these estimators to a broad class of variance-related premium principles, including the expected value, variance, standard deviation, and modified-variance principles. The estimators are derived via constrained linear projection techniques, minimizing the mean squared error between the estimator and the true process variance. Explicit formulas are obtained that are optimal among affine transformations of the data. The proposed estimators exhibit desirable statistical properties, including conditional unbiasedness, consistency, mean squared error convergence, and asymptotic normality. Numerical studies demonstrate their favorable convergence behavior, and an empirical analysis with real insurance data highlights their practical relevance. This framework extends Bühlmann’s classical credibility theory to second-moment estimation while remaining computationally tractable and requiring only mild moment conditions, without specifying the population or prior distributions.

Rock masses naturally exhibit significant anisotropy, however, majority of the analytic solution of a half-plane with a hole are based on the isotropic assumption, which would result in the larger difference from the real scenario. Hence, the purpose of present study is to derive the general form of the stress functions in an anisotropic medium because it can be easily used to solve the problem of the unbalanced forces by tunnel excavation. Since the affine transformation is used, the computing model may become asymmetrical and conventional mapping functions are difficult to be obtained. Without loss of generality, decoupling conformal mapping functions are introduced. By adopting Discrete Fourier Transform, all coefficients of the stress function can be determined. Compared with the numerical results, the analytical solution of stress around the unlined tunnel is higher precision. In the present study, the effects of the depth, the tectonic stress and the anisotropic parameters are discussed on the stress field and the displacement field. When compared to the isotropic case, it is unfavorable for the safety and stability of tunnel if the problem is solved under the isotropic condition.

Accurate alignment of real-world object poses with their virtual counterparts using sensors, e.g. cameras, is essential for consistent interaction in mixed-reality systems. However, objects can undergo abrupt, untracked movements during periods when a tracking system is inactive, e.g., overnight, causing stored pose records to become inconsistent with the real scene and breaking user interaction in the virtual environment. Off-the-shelf 3D reconstruction networks such as MASt3R (Matching and Stereo 3D Reconstruction) method provide metrically scaled 3D point maps and pixel correspondences, but they are trained on static scenes and therefore fail to produce reliable object correspondences when the object has moved. We propose a robust pipeline that combines MASt3R's metrically scaled 3D outputs with a background-based alignment strategy to recover and apply the true pose change of moved objects. Our method first segments foreground and background and extracts 3D background point sets for a reference day and a current day. An affine transformation between these background point sets is estimated via a standard registration technique and used to express the current-day object 3D coordinates in the reference coordinate frame. Within that unified frame we compute the object pose change and apply the resulting transform to the virtual object, restoring real-virtual consistency. Experiments on real scenes demonstrate that the proposed approach reliably corrects pose misalignments introduced during inactive periods and substantially improves over applying MASt3R alone, thereby enabling restored and consistent user interaction in the virtual environment.

Discovering governing equations from data is a central challenge in scientific machine learning, particularly when observations are high-dimensional and the underlying state variables are not directly accessible. In this work, we introduce a framework for data-driven discovery of partial differential equations (PDEs) from indirect high-dimensional observations. The proposed approach combines nonlinear representation learning through an autoencoder with sparse identification of governing equations in the latent space, enabling simultaneous model reduction and PDE discovery while preserving spatial structure. Unlike existing methods that either operate on observable variables or discover latent ordinary differential equations, our framework identifies PDEs directly in the learned latent coordinates. We validate the approach on high-dimensional observations generated from Burgers and Korteweg–de Vries (KdV) systems, where the true state variables are intentionally hidden. In both cases, the method successfully recovers the correct dynamical operators, including diffusion, nonlinear advection, and dispersive terms. Although the recovered coefficients differ due to latent coordinate transformations, we show both theoretically and empirically that the discovered equations are dynamically equivalent to the ground-truth systems up to an affine transformation. These results demonstrate that governing PDEs can be recovered from indirect, high-dimensional data without access to the physical state variables, providing a foundation for interpretable model discovery in realistic measurement settings.

Introduction: Long-term time series forecasting (LTSF) has gained significant attention in recent years. While various specialized designs exist for capturing temporal dependency, recent studies have shown that even a single linear layer can achieve competitive performance. This paper investigates the intrinsic effectiveness of recent LTSF approaches and reveals the critical role of affine mapping. Materials and methods: We conduct comprehensive experiments on both simulated and real-world datasets to analyze the components of state-of-the-art models. A theoretical analysis is provided to explain the working mechanisms of affine mapping in periodic signal forecasting. We evaluate the impact of reversible normalization and input horizon extension on model robustness. Results: We find that (1) affine mapping dominates forecasting performance across commonly utilized benchmarks, with models learning similar transition matrices from input to output; (2) affine mapping effectively captures periodic patterns but struggles with non-periodic signals or time series with varying periods across channels; (3) reversible normalization significantly enhances trend forecasting by transforming non-periodic trends into periodic-like patterns; (4) increasing input horizon improves performance on multi-channel data with different periods. Conclusions: Our findings provide theoretical and experimental insights into the working mechanisms of LTSF models, highlighting both the strengths and limitations of linear approaches. The results suggest that future model development should focus on handling cross-channel period variations and non-periodic components.

Acoustic-optical joint underwater object detection with multi-modality correlation features matching network.

The paper addresses the problem of phase synthesis of apertures with assigned amplitude. Applying the method of stationary phase it will be shown that the asymptotic solution satisfies a Monge–Ampère partial differential equation (PDE) with appropriate boundary value conditions. In agreement Chu’s energy mapping principle for reflector shaping, the Monge–Ampère PDE can solved identifying an irrotational transport map from the source aperture to the target beam. After a description of the general theory, the paper focuses on irrotational linear maps associated to quadratic phase solutions demonstrating the possibility of obtaining beams of the same shape of the source aperture, a result only observed for circular and square apertures. Exploiting a polar decomposition of the affine transformation matrix, it will be also demonstrated the possibility of rotating the beam, a result reported (to the best knowledge of the authors) for the first time. In a companion paper, the general problem of finding a solution to the Monge–Ampère PDE via irrotational transport maps will be addressed by mean of the theory of “optimal transport”.

ViSymRe: Vision multimodal symbolic regression.

Gravity matching navigation algorithm with affine transformation based on particle swarm optimization and validation