Discrete Transform Research Articles

Quantification of the Anterior-Centripetal Movement of the Ciliary Muscle During Accommodation Using Dynamic OCT Imaging.

Although the lens undoubtedly plays a major role in presbyopia, altered lens function could be in part secondary to age-related changes of the ciliary muscle. Ciliary muscle changes with accommodation have been quantified using optical coherence tomography, but so far these studies have been limited to quantifying changes in ciliary muscle thickness, mostly at static accommodative states. Quantifying ciliary muscle thickness changes does not effectively capture the dynamic anterior-centripetal movement of the ciliary muscle during accommodation. To address this issue, we present a method to quantify the movement of the ciliary muscle during accommodation using trans-scleral optical coherence tomography images obtained dynamically. An image processing framework including distortion correction, geometric transformation, and Procrustes analysis, was used to quantify the anterior-centripetal movement of the ciliary muscle apex and centroid during accommodation. The method was applied in a preliminary study to quantify ciliary muscle displacement and its relation to lens thickness change with accommodation on two young adults and two prepresbyopes. The magnitude and the direction relative to the pupil plane of the apex/centroid displacement in response to a two diopters (2D) stimulus were 0.16/0.20 mm at 11.3°/30.5° and 0.26/0.34 mm at 6.6°/33.2° for the young adults and 0.20/0.20 mm at 29.7°/40.6° and 0.24/0.40 mm at 33.0°/31.7° for the prepresbyopes, respectively. This study demonstrates the feasibility of quantifying dynamic anterior-centripetal movement of the ciliary muscle during accommodation using optical coherence tomography. The method better captures the functional response of the muscle than the quantification of thickness changes. We provide a method that holds potential to better understand the age-related changes of the ciliary muscle on presbyopia.

Development of Career Centers of Russian Universities: Challenges and Opportunities

Placement training of students for employment is a serious challenge for modern Russian universities. University graduates are faced with solving the problem of employment in the face of continuous transformation of the labor market. As a result, the issue of training highly professional specialists capable of adapting to the dynamically changing requirements of employers and willing to build a successful career throughout their lives is on the agenda. As the university practice of career centers shows, the job search assistance and employment support is usually carried out within its framework. Meanwhile, the issue of training students for career development should become a key one in the philosophy of university education. In modern conditions, universities are designed to prepare a student who is potentially capable of acting independently to develop his career to meet the challenges of the labor market and his own vision of an individual educational trajectory and professional interests. Thus, university training programs for specialists in a context of ever-changing technologies in the professional sphere need to be adjusted accordingly. It assumes restructuring the system of relations between all the subjects of the educational process, when it is necessary to take into account the importance of readiness for employability and building a career of a university graduate and his life self-determination. Despite the importance of the employability problem and career development readiness to achieve the sustainable development of the Russian economy, this topic has been little studied by domestic scientists. At the same time, Russia's higher education development agenda began to see the problem of graduate employment as a special one especially during the pandemic. In particular, the topic on developing career centers of universities has gained momentum in the large-scale program of the Ministry of Science and Higher Education of the Russian Federation on the development of Russian universities Priority-2030. Thus, this study will be useful to the stakeholders of systemic changes in processes related to building employment conditions for students and graduates. Also, this study can contribute to analytical basis development for the expansion of career centers of Russian universities.

Efficient Data Augmentation Methods for Crop Disease Recognition in Sustainable Environmental Systems

Crop diseases significantly threaten agricultural productivity, leading to unstable food supply and economic losses. The current approaches to automated crop disease recognition face challenges such as limited datasets, restricted coverage of disease types, and inefficient feature extraction, which hinder their generalization across diverse crops and disease patterns. To address these challenges, we propose an efficient data augmentation method to enhance the performance of deep learning models for crop disease recognition. By constructing a new large-scale dataset comprising 24 different classes, including both fruit and leaf samples, we intend to handle a variety of disease patterns and improve model generalization capabilities. Geometric transformations and color space augmentation techniques are applied to validate the efficiency of deep learning models, specifically convolution and transformer models, in recognizing multiple crop diseases. The experimental results show that these augmentation techniques improve classification accuracy, achieving F1 scores exceeding 98%. Feature map analysis further confirms that the models effectively capture key disease characteristics. This study underscores the importance of data augmentation in developing automated, energy-efficient, and environmentally sustainable crop disease detection solutions, contributing to more sustainable agricultural practices.

Impact of Structural Subtleties on Chirality Induction and Amplification in Trizinc(II)Porphyrin Trimers.

Herein, we report the precise control of molecular to supramolecular chirality induction at the single-molecule level just upon subtle modification in an achiral 'nano-size' trizinc(II) porphyrin trimer. A slight variation in the projection of the substituent at the periphery of the central porphyrin unit in a porphyrin trimer (host) resulted in pronounced changes in the interchromophoric arrangement, leading to distinct 'open' and 'closed' conformations. While 'open' form generates 'monomeric' complex with low CD amplitude, 'closed' form produces exclusive 'polymer' with large, amplified CD signal with opposite sign due to stronger intermolecular excitonic coupling. Also, the sign of the CD couplets is just opposite between R and S substrates for both polymer and monomer which suggest that the chirality is predominantly governed by the stereogenic projection of the chiral center. X-ray structures of the host and polymer have been reported here. Crystallographic characterization offers a detailed perspective on the structural and geometrical transformations in the polymer, enabling a systematic understanding of its optical properties. DFT and TD-DFT calculations strongly corroborate with the experimental findings.

Discrete Wavelet Transform-Based Detection Transformer for Battery Weld Defect Detection

Discrete Wavelet Transform-Based Detection Transformer for Battery Weld Defect Detection

A MODIFIED NUMERICAL METHOD OF DETERMINING HYDRAULIC SYSTEM PARAMETERS FOR THE DEVELOPMENT OF MATHEMATICAL MODELS AND INFORMATION COMPLEXES OF COMPUTER SIMULATION MODELS FOR INDUSTRIAL CHEMICAL PRODUCTION

The paper introduces a modified numerical method for determining the parameters of hydraulic systems used in mathematical modeling and simulation-based computer systems for industrial chemical production. It explores the dynamics of fluids, gases, and their mixtures as they traverse pipelines equipped with valves, compressors, and other complex components. Traditional methods for solving nonlinear equation systems often face limitations, including sensitivity to initial approximations and the need for relaxation coefficient adjustments, which complicate simulation processes. The proposed method converts nonlinear equations into an optimization problem, us- ing the Nelder-Mead algorithm to minimize deviations between initial estimates and comput- ed parameters. This derivative-free approach employs a simplex geometric transformation, overcoming issues associated with iterative methods and delivering high accuracy, stable convergence, and computational efficiency. Its adaptability makes it suitable for handling in- tricate hydraulic systems. To validate the method, a practical example involving a pipeline system with multiple restricting devices is analyzed. The mathematical model includes equations for pressures and flow rates, supplemented by material balance constraints at branching points. Numerical ex- periments evaluate how input pressure influences system parameters, demonstrating the mod- el's robustness and precision. The results confirm that the method accurately simulates system parameters under steady-state conditions and identifies critical optimization points. This innovative approach offers significant advantages for designing and managing industrial chemical facilities. By simplifying model construction, enhancing reliability, and accelerating simulation processes, the method provides a powerful tool for optimizing the op- eration and control of complex technological systems.

Pengembangan Multimedia Interaktif untuk Membantu Peserta Didik dalam Memahami Konsep Matematika pada Materi Transformasi Geometri Kelas XI MIPA SMA Negeri Benlutu

During the learning of mathematics in SMA Negeri Benlutu, especially in class XI, teacher use WhatsApp group to send materials in .pdf format to students. Meanwhile, there is no sufficient learning media to support learning in the classroom. Therefore, the purpose of this study is to create interactive learning media, to help students understand valid, practical, and effective mathematical concepts about geometric transformation material in class XI MIPA SMA Negeri Benlutu. This research uses the research and development (R&D) method with the ADDIE development model consisting of five stages: analysis, design, development, implementation, and evaluation. The instruments used are interviews, questionnaires, and concept understanding tests. The results showed that the ThransForMath application met the three criteria of learning media feasibility: valid, practical, and effective. Valid criteria were obtained from the average validity of three material and media experts, which reached 4,7, or in the "valid" category. Practical criteria are obtained from the average practicality of all students in small and large classes, which reached 4,74 and 4,83, respectively, or in the "practical" category. Effective criteria are obtained from the results of students' concept understanding tests in small and large class trials of 100% and 88%, respectively, or in the "effective" category.

Towards a Unitary Formulation of Quantum Field Theory in Curved Spacetime: The Case of de Sitter Spacetime

Before we ask what the quantum gravity theory is, there is a legitimate quest to formulate a robust quantum field theory in curved spacetime (QFTCS). Several conceptual problems, especially unitarity loss (pure states evolving into mixed states), have raised concerns over several decades. In this paper, acknowledging the fact that time is a parameter in quantum theory, which is different from its status in the context of General Relativity (GR), we start with a “quantum first approach” and propose a new formulation for QFTCS based on the discrete spacetime transformations which offer a way to achieve unitarity. We rewrite the QFT in Minkowski spacetime with a direct-sum Fock space structure based on the discrete spacetime transformations and geometric superselection rules. Applying this framework to QFTCS, in the context of de Sitter (dS) spacetime, we elucidate how this approach to quantization complies with unitarity and the observer complementarity principle. We then comment on understanding the scattering of states in de Sitter spacetime. Furthermore, we discuss briefly the implications of our QFTCS approach to future research in quantum gravity.

A signal processing tool adapted to the periodic biphasic phenomena: the Dynalet transform.

The linear functional analysis, historically founded by Fourier and Legendre (Fourier's supervisor), has provided an original vision of the mathematical transformations between functional vector spaces. Fourier, and later Laplace and Wavelet transforms, respectively defined using the simple and damped pendulum, have been successfully applied in numerous applications in Physics and engineering problems. However the classical pendulum basis may not be the most appropriate in several problems, such as biological ones, where the modelling approach is not linked to the pendulum. Efficient functional transforms can be proposed by analysing the links between the physical or biological problem and the orthogonal (or not) basis used to express a linear combination of elementary functions approximating the observed signals. In this study, an extension of the Fourier point of view called Dynalet transform, is described. The approach provides robust approximated results in the case of relaxation signals of periodic biphasic organs in human physiology.

Investigating robustness dynamics of shallow machine learning techniques: beyond basic natural variations in image classification

Despite the widespread adoption of deep learning models, shallow machine learning (SML) algorithms are still used for image classification due to simplicity, interpretability and efficiency. This study aims to bridge this gap by investigating the robustness dynamics of SML techniques under more complex scenarios, such as adversarial perturbations and geometric transformation. Five popular classification algorithms, including k-nearest neighbour and support vector machines, were employed to build classification models. Methodology involves investigating the robustness of proposed methods, first, on original and corrupted data by utilising benchmark datasets across several image domains. To strengthen the investigation, the models were trained using a new low-rank representation (LRR) strategy. This hybrid model simultaneously addresses two key limitations in classical LRR models: overcoming the sequential learning process and effectively capturing both local and global data structures. By introducing a dual regularisation mechanism, it integrates a k-nearest neighbour graph to preserve local consistency, while a global low-rank constraint ensures coherent data representation. Experimental results reveal significant drops in accuracy of most SML methods, especially under adversarial attacks and geometric transformations, but LRR approach mitigates these effects to a notable extent, boosting performance across data variations. The results also show that the proposed method outperforms state-of-the-art LRR techniques in most experiments.

High-Frequency Workpiece Image Recognition Model Based on Hybrid Attention Mechanism

High-frequency workpieces are specialized items characterized by complex internal textures and minimal variance in properties. Under intricate lighting conditions, existing mainstream image recognition models struggle with low precision when applied to the identification of high-frequency workpiece images. This paper introduces a high-frequency workpiece image recognition model based on a hybrid attention mechanism, HAEN. Initially, the high-frequency workpiece dataset is enhanced through geometric transformations, random noise, and random lighting adjustments to augment the model’s generalization capabilities. Subsequently, lightweight convolution, including one-dimensional and dilated convolutions, is employed to enhance convolutional attention and reduce the model’s parameter count, extracting original image features with robustness to strong lighting and mitigating the impact of lighting conditions on recognition outcomes. Finally, lightweight re-estimation attention modules are integrated at various model levels to reassess spatial information in feature maps and enhance the model’s representation of depth channel features. Experimental results demonstrate that the proposed model effectively extracts features from high-frequency workpiece images under complex lighting, outperforming existing models in image classification tasks with a precision of 97.23%.

Analysis of the Effects of Different Spectral Transformation Methods on the Estimation of Chlorophyll Content of Reclaimed Vegetation in Rare Earth Mining Areas

Ion adsorption rare earths are an important strategic resource, but their leach mining causes post-mining wastelands and tailings to suffer from soil sanding, acidification, and heavy metal contamination. This makes natural vegetation recovery difficult, relying mainly on artificial reclamation; however, the reclaimed vegetation grows poorly due to environmental stress. Hyperspectral remote sensing technology, with its high efficiency, non-destructive nature, and wide-range monitoring capability, can accurately estimate the physiological parameters of reclaimed vegetation. This provides support for environmental regulation in mining areas. In this study, three typical types of reclaimed vegetation in the Lingbei Rare Earth Mining Area, Dingnan County, Ganzhou City, were analyzed. Hyperspectral data and the corresponding chlorophyll content were collected to compare the spectral differences between reclaimed and normal vegetation. The spectral data were processed using mathematical transformation, fractional order differentiation, discrete wavelet transform, and continuous wavelet transform. Sensitive bands were extracted, and multispectral transformed feature bands were integrated. Linear and machine learning regression models were used to estimate chlorophyll content. The effects of different spectral processing methods on chlorophyll estimation were then analyzed. The results showed that reclaimed vegetation had higher spectral reflectance than normal vegetation, with the red valley shifting towards the long-wave direction and a steeper red edge slope. Different spectral transformation methods impact the accuracy of chlorophyll content estimation. Using appropriate methods can improve estimation accuracy. Fusing multi-spectral transformation features can achieve relatively good results. Among the models, the random forest regression model provides the best performance in estimating the chlorophyll content of reclaimed vegetation. This study provides a scientific basis for rapid and accurate monitoring of reclaimed vegetation growth in rare earth mining areas, supporting environmental management and decision-making and contributing to ecological restoration.

Leveraging Non-formal Action Research to Enhance Teacher Research Activity at a Pedagogical University in Republic of Kazakhstan

The study was conducted with the aim of identifying the possibilities for implementing the informal research method of Action Research into the educational process of a pedagogical university as a tool for enhancing the research activity of university teachers in Kazakhstan. The significance of mastering this method by pedagogical university faculty is grounded in their ability to disseminate their experience, involving students—future teachers—in a cyclical process of continuous research and transformation of their pedagogical practices. As a result of the literature review, the advantages of Action Research were highlighted, particularly in terms of activating personal, professional, and environmental resources that were previously underutilized in traditional formal research formats. The relevance of the study lies in the necessity to examine global experiences with informal research methods, focusing on the feasibility of their implementation with consideration of the specific context of Kazakhstan. The article describes the process of conceptualizing the informal method of Action Research, diagnosing awareness and demand for this method among young pedagogical university faculty, developing and testing a program for its implementation, evaluating its effectiveness, ensuring post-course support, and determining the prospects for integrating the method on a national scale. Methods such as surveys, pilot studies, formative experiments, and Action Research tools were applied. A pilot implementation of Action Research was conducted to develop the research activity of young faculty members at Abai University, considering their needs within the framework of a modular professional development program titled “Action Research – the Foundation for Developing a Pedagogue-Researcher Model.” Analysis of the results confirmed the effectiveness of implementing the method in enhancing the research activity of teachers and transforming them into researcher-teachers. Based on the review and feedback analysis, the prospects for the expanded integration of informal research methods into the practice of education in Kazakhstan were identified.

Students' Visual-Spatial Thinking Ability in Solving Geometry Transformation Problems Based on Jombangan Ethnomathematics in Junior High Schools

Students must have visual-spatial thinking ability in order to understand geometric transformation material which is abstract in nature and requires imagination. This research aims to analyze students' visual-spatial thinking abilities in solving geometric transformation problems based on Jombangan ethnomathematics in junior high schools. This research uses a qualitative approach with a descriptive type. The subjects of this research were class VIII students at MTs Negeri 3 Jombang who were determined using purposive sampling. Data collection techniques were carried out using tests in the context of Jombangan ethnomathematics, semi-structured interviews, observation, and documentation. The data analysis technique uses three steps, namely data reduction, data display, and conclusion/verification. The credibility test is carried out by triangulating methods and increasing persistence. The results of this research show that students at MTs Negeri 3 Jombang achieve the indicators of pattern searching and imagining more dominantly, while the indicators of problem solving and conceptualization are still lacking.

Perception of Symmetry and Spatial Reasoning in 11–12-Year-Old Pupils

Visual perception and visualization are crucial in mathematical thinking and, more importantly, in geometric thinking. Our research study aimed to follow the link of geometric transformations, mental rotation, spatial ability, and visualisation in geometric thinking. During a longitudinal study, we examined the spatial ability-related geometric competencies of 11–12-year-old students from three lower secondary schools. We analysed their test results from axial symmetry and its application in practical problems, orientation in spatial labyrinths, and building spatial constructions with three views. During a detailed analysis of the written results, a grounded theory hypothesis arose that there was a possible relationship between symmetry perception and spatial thinking. This hypothesis was tested with CHIC statistical analysis. The analysis, however, did not show any deeper connection between symmetry perception and spatial thinking from the given data. We can conclude that this connection occurs in individual cases but not in general.

Longitudinal determination of seroprevalence and immune response to SARS-CoV-2 in a population of food and retail workers through decentralized testing and transformation of ELISA datasets.

Since the onset of the global COVID-19 pandemic in early 2020, numerous studies have been conducted worldwide to understand our immune response to the virus and to vaccination. This study investigates the humoral response elicited by SARS-CoV-2 infection and by vaccination in the poorly studied population of food and retail workers. These occupations were classified as essential by the Public Health Agency of Canada, potentially placing this population at greater risk of infection. Such a risk requires access to reliable and adaptable serological assays that can be rapidly deployed to guide public health strategies. Here we investigate the benefits and limitations of applying adaptable, decentralized tests for population-level immune surveillance in response to a pandemic, even before centralized testing is available. The 1.5-year study period spans from early 2021, when vaccination became available in this region, to mid-2022, following the emergence of the first Omicron variants. The cohort of 304 food and retail workers was recruited in the Québec City area. Participants attended five evenly spaced visits, providing blood samples as well as information on SARS-CoV-2 symptoms or risk factors, prior antigen or PCR test results and vaccination status, as well as work-related risk factors and protective measures. Parallel COVID-19 serological assays were performed using both a standardized chemiluminescent ELISA assay at the centralized platform operated in partnership with the Public Health Agency of Canada, and a semi-automated in-house colorimetric ELISA assay developed at our decentralized site. The YES/NO determination of SARS-CoV-2 vaccine seroconversion and/or infection events using the SARS-CoV-2 ancestral spike protein and nucleocapsid protein validated coherence of the centralized and decentralized assays. The flexibility of the decentralized assays allowed broadening the study to determine cross-reactivity of IgG directed against the spike protein of the SARS-CoV-2 Delta and Omicron VOCs, and IgM directed against the ancestral spike and nucleocapsid proteins. The nature of the data obtained in the decentralized assays allowed treatment with a recently developed mathematical transformation to obtain normal distribution, enabling ANOVA-Welsh statistical analysis. Although no significant differences were observed in humoral response as related to BMI, age, level of education, or chronic illnesses in this cohort of workers, statistically higher levels of vaccine-induced antibodies were observed for restaurant workers and hardware store workers in the early stages of the study, compared to workers in bars and grocery stores and in non-smokers versus smokers. This work highlights the importance of developing adaptable, decentralized tests for population-level immune surveillance in response to a pandemic, even before centralized testing is available. To our knowledge, no other study has reported such an extensive longitudinal investigation during key periods of the COVID-19 pandemic in a cohort of food and retail workers to analyze two types of immunoglobulin, three epitopes and antigens to three VOC. This study will inform strategies and measures to be implemented in the event of a future pandemic.

Few‐shot real scenes convolutional anchor clustering twin network for hyperspectral image classification

AbstractIn order to improve the performance of hyperspectral open set recognition processing with insufficient sample size, the authors propose a new supervised contrastive learning (SCL) framework (FSSCL‐OSC) that can achieve open‐set classification of hyperspectral images in scenarios with very few sample sizes, which consists of three steps. First, supervised contrastive learning (SCL) with geometric transformations is designed, which uses rotated labels as supervision to obtain lower‐level characteristics that more accurately capture various orientations and then makes use of a spectral‐spatial characteristic extraction network to maximize the utilization of HSI's spectrum and spatial information. Next, a class anchor open‐set classification module based on a twin clustering network is designed, which uses SCL and FSL to extract more specific personal information by mining the category‐invariant characteristics present in the known versus unknown class data. Finally, multiple convolution and open‐set recognition (OSC) is performed on the feature blocks. Experimental results on three classical HSI datasets show that FSSCL‐OSC provides a significant improvement over existing methods, under a sample size of only 10%, the overall accuracy reached 82.38%, 90.76% and 84.70%, respectively.

Multifunctional Integrated Biosensors Based on Two-Dimensional Field-Effect Transistors.

In recent years, field-effect transistor (FET) sensing technology has attracted significant attention owing to its noninvasive, label-free, real-time, and user-friendly detection capabilities. Owing to the large specific surface area, high flexibility, and excellent conductivity of two-dimensional (2D) materials, FET biosensors based on 2D materials have demonstrated unique potential in biomarker analysis and healthcare applications, driving continuous innovation and transformation in the field. Here, we review recent trends in the development of 2D FET biosensors based on key performance metrics and main characteristics, and we also discuss structural designs and modification strategies for biosensing devices utilizing graphene, transition metal dichalcogenides, black phosphorus, and other 2D materials to enhance key performance metrics. Finally, we offer insights into future directions for biosensor advancements, discuss potential improvements, and present new recommendations for practical clinical applications.

Geometric rigidity of sections in the form of in torsion

This article is a generalization of known solutions to the problem of determining the reduced geometric stiffness of sections of elastic prismatic beams using geometric arguments: the shape coefficient and the ratio of conformal radii (internal to external). Analytical dependences are constructed for all considered sections (regular polygons, ellipses, rectangles, isosceles and right triangles): reduced geometric stiffness is the coefficient of shape and reduced geometric stiffness is the ratio of conformal radii. Formulas in the form of polynomials for determining the ratio of conformal radii are also constructed for these sections. An analysis of the changes in both arguments under various geometric transformations showed that the ratio of conformal radii has similar isoperimetric properties as the shape coefficient. This allows to determine the geometric torsional stiffness of the sections by interpolation.

Geometric transformations in school geometry

The study delves into the learning progression for school geometry based on transformations proposed by Hung-Hsi Wu. Plane transformations – translations, reflections, rotations, and dilations – are considered. Criteria for the triangle congruence and for triangle similarity, as well as the properties of the graphs of a quadratic function, are proved with their help. Axioms of school geometry used to justify the system of concepts are formulated. The study was motivated by the geometry topic presented in the mathematics curriculum as of 2022 and in the textbooks published.