Discrete Transform Research Articles

Improving deep learning-based automatic cranial defect reconstruction by heavy data augmentation: From image registration to latent diffusion models

Modeling and manufacturing of personalized cranial implants are important research areas that may decrease the waiting time for patients suffering from cranial damage. The modeling of personalized implants may be partially automated by the use of deep learning-based methods. However, this task suffers from difficulties with generalizability into data from previously unseen distributions that make it difficult to use the research outcomes in real clinical settings. Due to difficulties with acquiring ground-truth annotations, different techniques to improve the heterogeneity of datasets used for training the deep networks have to be considered and introduced. In this work, we present a large-scale study of several augmentation techniques, varying from classical geometric transformations, image registration, variational autoencoders, and generative adversarial networks, to the most recent advances in latent diffusion models. We show that the use of heavy data augmentation significantly increases both the quantitative and qualitative outcomes, resulting in an average Dice Score above 0.94 for the SkullBreak and above 0.96 for the SkullFix datasets. The results show that latent diffusion models combined with vector quantized variational autoencoder outperform other generative augmentation strategies. Moreover, we show that the synthetically augmented network successfully reconstructs real clinical defects, without the need to acquire costly and time-consuming annotations. The findings of the work will lead to easier, faster, and less expensive modeling of personalized cranial implants. This is beneficial to numerous people suffering from cranial injuries. The work constitutes a considerable contribution to the field of artificial intelligence in the automatic modeling of personalized cranial implants.

Shape-Memory Effect and the Topology of Minimal Surfaces

Martensitic transformations, viewed as continuous mappings between triply periodic minimal surfaces (TPMSs), as suggested by Hyde and Andersson (Z. Kristallogr. 1986, 174, 225–236), are extended to include paths between the initial and final phases. Reversible transformations, which correspond to shape-memory materials, occur only if lattice points remain at flat points on a TPMS throughout a continuous transformation. For the shape-memory material NiTi, the density functional calculations by Hatcher et al. [Phys. Rev. B2009, 80, 144203] yield irreversible and reversible paths with and without energy barriers, respectively, in agreement with our theory. Although there are TPMSs for face-centered and body-centered cubic crystals for iron, the deformation between them is not reversible, in agreement with the non-vanishing energy barriers obtained from the density functional calculations of Zhang et al. (RSC Advances2021, 11, 3043–3048).

Analyticity and the Unruh effect: a study of local modular flow

The Unruh effect can be formulated as the statement that the Minkowski vacuum in a Rindler wedge has a boost as its modular flow. In recent years, other examples of states with geometrically local modular flow have played important roles in understanding energy and entropy in quantum field theory and quantum gravity. Here I initiate a general study of the settings in which geometric modular flow can arise, showing (i) that any geometric modular flow must be a conformal symmetry of the background spacetime, and (ii) that in a well behaved class of “weakly analytic” states, geometric modular flow must be future-directed. I further argue that if a geometric transformation is conformal but not isometric, then it can only be realized as modular flow in a conformal field theory. Finally, I discuss a few settings in which converse results can be shown — i.e., settings in which a state can be constructed whose modular flow reproduces a given vector field.

Innovation in Local Digital Media: The Case of Sevilla Directo

The journalistic industry is undergoing a process of continuous transformation in response to an ongoing crisis. In this scenario, marked by disruptive technological changes and shifts in audience and advertiser behaviour, a new communication ecosystem is emerging that facilitates the rise of novel media outlets. Community social media, data journalism, and specialisation are some of the key features present in these emerging business models. This research aims to identify and understand the role of innovation in media adaptation to the current communication paradigm. Methodology: We employ a case study approach, analysing Sevilla Directo, a native digital medium in a city of approximately 700,000 inhabitants. Data collection techniques include observation, website analysis, in-depth interviews, focus groups with journalists, and analysis of sector reports and databases. Results and Discussion: Our findings indicate that technological advancements and the reach of social networks are fundamental to the growth of local media. However, we observe that adaptive changes predominate with little disruption and minimal focus on R&D&I. The organisation under study lacks a business model that guarantees its long-term sustainability and relies primarily on traditional income streams. Concurrently, social capital emerges as a key element in financing.

An Extended Application of the Fast Multi-Locus Ridge Regression Algorithm in Genome-Wide Association Studies of Categorical Phenotypes.

Categorical (either binary or ordinal) quantitative traits are widely observed to measure count and resistance in plants. Unlike continuous traits, categorical traits often provide less detailed insights into genetic variation and possess a more complex underlying genetic architecture, which presents additional challenges for their genome-wide association studies. Meanwhile, methods designed for binary or continuous phenotypes are commonly used to inappropriately analyze ordinal traits, which leads to the loss of original phenotype information and the detection power of quantitative trait nucleotides (QTN). To address these issues, fast multi-locus ridge regression (FastRR), which was originally designed for continuous traits, is used to directly analyze binary or ordinal traits in this study. FastRR includes three stages of continuous transformation, variable reduction, and parameter estimation, and it can computationally handle categorical phenotype data instead of link functions introduced or methods inappropriately used. A series of simulation studies demonstrate that, compared with four other continuous or binary or ordinal approaches, including logistic regression, FarmCPU, FaST-LMM, and POLMM, the FastRR method outperforms in the detection of small-effect QTN, accuracy of estimated effect, and computation speed. We applied FastRR to 14 binary or ordinal phenotypes in the Arabidopsis real dataset and identified 479 significant loci and 76 known genes, at least seven times as many as detected by other algorithms. These findings underscore the potential of FastRR as a very useful tool for genome-wide association studies and novel gene mining of binary and ordinal traits.

International Experience of Personnel Selection in the Conditions of the Digital Environment, War and Sustainable Development: Social and Corporate Responsibility of Employers for the Non-Transparent Hiring Process

The article represents an attempt to outline ad systematize peculiarities of landscape and practices of personnel selection in the conditions of BANI-environment with the influence of continuous digital transformation, war conflicts, and sustainable development. General scientific methods of analysis, synthesis and generalization constituted the methodological base of research. It was revealed that one of the most successful vectors of personnel selection within sustainable HRM today is talent marketplaces.

Uncountable group of continuous transformations of unit segment preserving tails of Q_2-representation of numbers

We consider two-base Q2-representation of numbers of segment [0;1] which is defined by two bases q0 ∈ (0;1), q1 = 1-q0 and alphabet A={0,1}, (αn) ∈ A × A × .... It is a generalization of classic binary representation q0=1/2. In the article we prove that the set of all continuous bijections of segment [0;1] preserving "tails" of Q2-representation of numbers forms an uncountable non-abelian group with respect to composition such that it is a subgroup of the group of continuous transformations preserving frequencies of digits of Q2-representation of numbers. Construction of such transformations (bijections) is based on the left and right shift operators for digits of Q2-representation of numbers.

Study of the readiness of university teachers and staff to participate in higher education development programs

Introduction. Currently, higher education is considered as one of the drivers of the socio-economic development of the country, in connection with which continuous transformations are taking place in the higher education system, management mechanisms are being formed that can ensure that the results of the activities of universities correspond to their goals, which consist not only in training highly qualified specialists, competitive in the labor market, but also in strengthening university science, including applied scientific research. Achieving these goals directly depends on the readiness of employees, primarily university teachers, to participate and actively contribute to the implementation of adopted development programs. Research aim: a study of the degree of involvement of university employees in the implementation of current trends in the development of higher education, as well as their readiness to contribute to ongoing programs within the framework of their activities. Materials and methods. A survey of university staff was conducted using a questionnaire developed by the author. The sample consisted of 100 people. The research base is the Federal State Budgetary Educational Institution of Higher Education, Moscow State Psychological and Pedagogical University. The questionnaire included 22 questions related to determining the involvement of university employees in the higher education development programs it implements, as well as identifying problems that reduce their willingness to participate in these programs. Results. The survey made it possible to note the need to improve the mechanisms of coordination and involvement of university staff in order to increase the efficiency of activities in achieving development targets determined by the state. Thus, 67% of respondents named the lack of a clear and understandable strategy as the main problem in the development of higher education, and 54% drew attention to the need to improve coordination and communication between levels of higher education management. At the same time, a fairly high degree of staff readiness to take part in the higher education development programs proposed by the university management was noted. Conclusion. Based on the conducted research, it is concluded that special attention should be paid to involving university staff in the development of their development strategies, stimulating their innovative activity and willingness to participate in the implementation of development programs.

RF-ULM: Ultrasound Localization Microscopy Learned From Radio-Frequency Wavefronts.

In Ultrasound Localization Microscopy (ULM), achieving high-resolution images relies on the precise localization of contrast agent particles across a series of beamformed frames. However, our study uncovers an enormous potential: The process of delay-and-sum beamforming leads to an irreversible reduction of Radio-Frequency (RF) channel data, while its implications for localization remain largely unexplored. The rich contextual information embedded within RF wavefronts, including their hyperbolic shape and phase, offers great promise for guiding Deep Neural Networks (DNNs) in challenging localization scenarios. To fully exploit this data, we propose to directly localize scatterers in RF channel data. Our approach involves a custom super-resolution DNN using learned feature channel shuffling, non-maximum suppression, and a semi-global convolutional block for reliable and accurate wavefront localization. Additionally, we introduce a geometric point transformation that facilitates seamless mapping to the B-mode coordinate space. To understand the impact of beamforming on ULM, we validate the effectiveness of our method by conducting an extensive comparison with State-Of-The-Art (SOTA) techniques. We present the inaugural in vivo results from a wavefront-localizing DNN, highlighting its real-world practicality. Our findings show that RF-ULM bridges the domain shift between synthetic and real datasets, offering a considerable advantage in terms of precision and complexity. To enable the broader research community to benefit from our findings, our code and the associated SOTA methods are made available at https://github.com/hahnec/rf-ulm.

Stückelberg-modified massive Abelian 3-form theory: Constraint analysis, conserved charges and BRST algebra

For the Stückelberg-modified massive Abelian 3-form theory in any arbitrary D-dimension of spacetime, we show that its classical gauge symmetry transformations are generated by the first-class constraints. We establish that the Noether conserved charge (corresponding to the local gauge symmetry transformations) is same as the standard form of the generator for the underlying local gauge symmetry transformations (expressed in terms of the first-class constraints). We promote these classical local, continuous and infinitesimal gauge symmetry transformations to their quantum counterparts Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST symmetry transformations which are respected by the coupled (but equivalent) Lagrangian densities. We derive the conserved (anti-)BRST charges by exploiting the theoretical potential of Noether’s theorem. However, these charges turn out to be non-nilpotent. Some of the highlights of our present investigation are (i) the derivation of the off-shell nilpotent versions of the (anti-)BRST charges from the standard non-nilpotent Noether conserved (anti-)BRST charges, (ii) the appearance of the operator forms of the first-class constraints at the quantum level through the physicality criteria with respect to the nilpotent versions of the (anti-)BRST charges, and (iii) the deduction of the Curci–Ferrari-type restrictions from the straightforward equality of the coupled (anti-)BRST invariant Lagrangian densities as well as from the requirement of the absolute anticommutativity of the off-shell nilpotent versions of the conserved (anti-)BRST charges.

Deep-UEO: Empowering medical image registration with hybrid strategy based on deep learning and united equilibrium optimizer

Traditional optimization methods encounter challenges in determining the optimal geometric transformation parameters and often lacking to achieve global optimum which leads to extended computational time required for convergence. To address this challenge, a dual-phase strategy is proposed for multimodal biomedical image registration by amalgamating the united equilibrium optimizer (UEO) with Visual Geometry Group (VGG-19). In first phase, the input images are aligned by identifying the optimal values of rigid transformation parameters through UEO, with mutual information (MI) maximization serving as an objective function. In second phase, VGG19 is employed to enhance the reliability of resulting registered image obtained through UEO optimization for extracting both the low- and high-level features of reference and target images. Following this, dynamic inlier selection is employed to refine the matching process, integrating expectation maximization for iterative updating of inlier selection, thus improving registration accuracy. Finally, thin plate spline interpolation is utilized to calculate the transformation matrix, ensuring precise alignment between reference and UEO registered image. Extensive experiments are conducted on multimodal medical images sourced from publicly available repositories and clinical(in-house) datasets to validate the reliability of the proposed scheme. These experiments showcase substantial improvements in RMSE from 22.21094 to 10.983654, SSIM from 0.7190832 to 0.8409321, PSNR from 30.176044 to 34.095471, and CC from 0.9304633 to 0.9809432, outperforming state-of-the-art methods.

의미 네트워크(Semantic Network)를 활용한 중국 독자의 한국 여성 서사 수용 연구: 최은영 『밝은 밤』의 정동(Affect)적 접근

This study analyzes Chinese readers' rating reviews of Eunyoung Choi's Bright Night using a semantic network to explore Chinese readers' acceptance of Korean female narratives in terms of affect. Eunyoung Choi's Bright Night was ranked second overall and first in the foreign fiction category in the 2023 annual book rankings on Douban, China's largest book rating site. The novel centers on the stories of four women: a great-grandmother, a grandmother, a mother, and a daughter. The relationship between the great-grandmother, aunt, and neighboring women who lived through the Japanese occupation and the Korean War, as well as the conflict and reconciliation between grandmother, mother, and me, are important narrative devices in the novel. Affect refers to the continuous transformation of potential states inherent in the body into reality through ‘encounter’. The bodies that are encountered are not only human bodies, but also literary works such as Bright Night. The idea transformed by the encounter between bodies is affect, and the actual state is objectified in language. The analysis showed that Chinese readers were most affected by the matriarchal narratives of the four women, and the women's painful lives and internal conflicts, and the friendship and solidarity of other women to help them overcome them. Cluster analysis of the reviewed texts to identify specific emotional patterns revealed four patterns: ‘empathizing with women's suffering and pain’, ‘emotions of healing and hope for female characters’ ‘friendship and reconciliation’, ‘literary emotions of female solidarity’, and ‘heart-to-heart encounters’. This study confirms that Korean women's narratives can reach readers with different national systems and social structures and cause emotional changes, which can be extended to East Asian women's narratives.

PENGEMBANGAN LEMBAR KERJA PESERTA DIDIK (LKPD) BERBASIS ETNOMATEMATIKA PADA MATERI TRANSFORMASI

This study aims to produce teaching materials in the form of ethnomathematics-based worksheets on Lampung batik motifs in understanding valid and practical geometric transformation concepts. The type of research used is Research and Development (R&D). This research produced a product in the form of ethnomathematics-based worksheets on transformation material at SMP PGRI Kesumadadi. The research procedure used is the Borg and Gall development model which goes through several stages including: potentials and problems, data collection, product design, design validation, design revision, product testing, and product revision. In the product trial stage, a limited trial was carried out involving 15 class IX students at SMP PGRI Kesumadadi. The research instruments used were material expert validation sheets, media expert validation sheets, and student response questionnaires. The results of this development research show that the assessment of the material expert validation obtained an average validation result of 88.12% with the validation criterion of "Very Valid". Furthermore, the results of the validation of media experts obtained an average validation result of 91.66% with the validation criterion of "Very Valid". The results of the analysis of the student response questionnaire at the limited trial stage obtained a percentage of 92.6% with the practicality criterion "Very Practical".

Nucleation Mechanism of Hexagonal Boron Nitride on Diamond (111) and Its Hydrogen-Terminated Surface: A DFT Study.

Hexagonal boron nitride (h-BN) has attracted significant attention due to its exceptional properties. Among various substrates used for h-BN growth, diamond emerges as a more promising substrate due to its high-temperature resistance and superior electrical properties. To reveal the nucleation mechanism of h-BN on the diamond (111) surface and the impact of hydrogenation treatment on this process, we explored the adsorption, diffusion, nucleation morphologies, and predicted nucleation pathways in this process using first-principles calculations based on density functional theory (DFT). Our results indicate that N positioned above the first layer of C and B positioned above the second layer of C enhance the stability of BN clusters. During the growth of BN clusters, there is a geometric transformation from chain-like structures to honeycomb-like structures. The proportion of unhybridized sp2 atoms within BN clusters and geometric symmetry significantly influence h-BN growth. Moreover, computational findings also suggest that to enhance the nucleation rate of h-BN it is essential to inhibit the formation of zigzag chain structures by BN clusters during the early stages of nucleation on a clean diamond surface. Additionally, hydrogenation treatment decreases the binding affinity of B and N on the substrate, facilitating atomic diffusion, and has been identified as an effective approach to facilitate nucleation. Furthermore, hydrogen-terminated diamond acts as an electron donor in the system, which profoundly affects the morphology of growing h-BN and the characteristics of the h-BN/diamond heterostructures. These conclusions are important to understanding and optimizing h-BN growth on diamond and provide a theoretical basis of the construction and application of the h-BN/diamond heterostructure.

Bohr chaoticity of number-conserving shifts

Let X be a compact metric space and T:X→X be a continuous transformation. A dynamical system (X,T) is called Bohr chaotic if for each weight sequence (wn)∈ℓ∞(N,R) there are f∈C(X) and x∈X such that (wn) is orthogonal to {f∘Tn(x)}. In this paper, we demonstrate that a number-conserving shift X is either finite or Bohr chaotic, uncovering the relationship between the topological behavior and the coefficients of X. Furthermore, a number-conserving shift is consisting of periodic points whenever it is finite.

On the Geometric Pattern Transformation (GPT) Properties of Unidimensional Signals

The Geometric Pattern Transformation (GPT) has several advantages of use concerning contemporary algorithms that have been duly studied in previous research. Regarding some of its properties, four different but complementary aspects of the GPT are presented in this work. After a brief review of the GPT concept, how tied data are manifested in data sets is shown, to obtain a symmetric representation of the GPT, a linear transformation is performed that regularizes the geometric representation of the GPT and the theoretical relationship between the GPT and the phase-state representation of 1D signals is analyzed and formalized, then the study of the forbidden pattern is easily revealed, obtaining a strong relationship with the stable and unstable fixed points of the logistic equation. Finally, the characterization of colored noises and the application in real world signals taken through experimental procedures is analyzed. With these results, in this work is proposed an advance in the potential applications of the GPT in an integral way in the processing and analysis of data series.

Clockwise vs anti-clockwise chiral metamaterials: Influence of base tessellation symmetry and rotational direction of chiralisation on mechanical properties

Chiral honeycombs are a class of auxetic metamaterials which are characterised by a lack of plane symmetry. Besides the traditional chiral honeycombs based on regular monohedral tessellations such as the hexachiral and tetrachiral honeycombs, a vast range of auxetic chiral metamaterials may be produced through the ‘chiralisation’ of Euclidean tessellations made from polyhedral tilings and/or irregular monohedral polygons. In this work, we show for the first time, how the direction of the geometric chiral transformation, i.e. clockwise vs anti-clockwise chiralisation, has an influence on the mechanical properties and deformation modes of the resultant chiral metamaterial systems. This influence, which is a result of the intrinsic absence of axial symmetry in the original base tessellation, can lead to the production of two unique and distinct chiral metamaterial configurations with completely different mechanical properties originating from a single base tessellation. In this work we demonstrate and quantify, through a wide range of numerical simulations and experimental tests on additively-manufactured prototypes, the effect of the direction of chiralisation on two tessellations: a Florent pentagonal system with hexagonal rotational symmetry and a hexagonal monohedral tessellation with trigonal rotational symmetry. The results obtained show that the clockwise and anti-clockwise chiral structures exhibit significantly different mechanical properties and deformation modes, highlighting the increased versatility of this relatively novel class of chiral metamaterials.

Optimization of structural reinforcement assessment for architectural heritage digital twins based on LiDAR and multi-source remote sensing

This study investigates the geometric modelling of architectural heritage digital twins constructed based on multi-source point cloud data and its effectiveness in structural reinforcement assessment. Particular emphasis has been placed on the use of static stiffness rules to identify areas of structural weakness in the geometric models of digital twins and the need for their reinforcement, in order to prevent potential structural problems and to ensure the long-term preservation of the built heritage. Taking Yingxian wooden pagoda as a study case, based on the collection of multi-source point cloud data, the digital twin geometric model is constructed through fine modelling, decoupling of digital models, and geometric transformation. This enhances the true reflection of the column-architrave structure morphology, providing a more accurate model for structural stress analysis. Based on verifying the accuracy of the digital twin geometric model, the instability conditions are identified through static stiffness rules and the deformation values at multiple points are analyzed, enabling precise identification of weak areas in the column-architrave structure. Two types of reinforcement measures are designed and simulated for the structural weak areas identified through the geometric modelling, and the optimal reinforcement scheme is obtained after detailed analysis, according to which specific adjustments and optimization strategies are proposed to enhance the overall stability and durability of the structure. The results showed that the maximum deformation value of 4.65 mm existed in column M2W23, which required reinforcement. Aluminum reinforcement reduced the deformation to 3.5 mm (24.7% reduction), while CFRP fabric reinforcement was more effective, reducing the deformation to 2.8 mm (39.7% reduction), showing high stability. The research results demonstrate the potential application of digital twin technology in architectural heritage preservation and restoration, providing methodological and empirical guidance for heritage preservation research.

A Novel Multi-Dimensional Joint Search Method for the Compression of Medical Image Segmentation Models.

Due to the excellent results achieved by transformers in computer vision, more and more scholars have introduced transformers into the field of medical image segmentation. However, the use of transformers will make the model's parameters very large, which occupies a large amount of the computer's resources, making them very time-consuming during training. In order to alleviate this disadvantage, this paper explores a flexible and efficient search strategy that can find the best subnet from a continuous transformer network. The method is based on a learnable and uniform L1 sparsity constraint, which contains factors that reflect the global importance of the continuous search space in different dimensions, while the search process is simple and efficient, containing a single round of training. At the same time, in order to compensate for the loss of accuracy caused by the search, a pixel classification module is introduced into the model to compensate for the loss of accuracy in the model search process. Our experiments show that the model in this paper compresses 30% of the parameters and FLOPs used, while also showing a slight increase in the accuracy of the model on the Automatic Cardiac Diagnosis Challenge (ACDC) dataset.

Fractal Geometry, Fibonacci Numbers, Golden Ratios, And Pascal Triangles as Designs

Fractal geometry is a part of mathematics that discusses the shape of fractals or any form that is self-similarity. A fractal can be broken down into parts that are all similar to the original fractal. Fractals have infinite detail and can have self-similar structures at different magnifications. In many cases, a fractal can be generated by repeating a pattern, which is usually in a recursive or iterative process. In mathematics and art, two values are considered to be a golden ratio relationship if the ratio between the sum of the two values to the large value is equal to the ratio between the large value to the small value. A Fibonacci sequence is a sequence of numbers that has a unique shape. The first term of this sequence of numbers is 1, then the second term is also 1, then for the third term it is determined by adding the two previous terms so that a sequence of numbers with a certain pattern is obtained. Pascal's triangle is a geometric rule of binomial coefficients in a triangle. Shapes that resemble fractal geometry, golden ratios and Fibonacci numbers are found in many places in this realm, for example the shapes of various plants, animals, as well as in humans themselves, even the universe. This fractal geometry can also be used to design batik motif creations, architectural design or musical art. This paper describes how a fractal object can be made with geometric transformations that can be used to develop batik motif creations. And also look at the relationship between fractal geometry, the golden ratio, Fibonacci numbers, and Pascal's triangles and the shapes of these shapes that exist in this nature.