Search Results (33)

Background/Objectives: Malnutrition among older adults remains a significant healthcare issue, yet existing questionnaires primarily measure knowledge and attitudes rather than actual behaviors. This study aimed to develop the Nursing Nutritional Care Behaviors Scale (B-NNC Scale) in its original Italian version, translate it into German, and evaluate its psychometric properties in registered nurses and nurse assistants in Austria. Methods: This study followed a two-phase, multi-method design. In Phase 1 (Development Phase), the scale was developed in Italian through a scoping review, expert focus group, and content validation involving 18 clinical nutrition experts using the Content Validity Ratio (CVR). In Phase 2 (Validation Phase), the scale was translated into German through a cross-cultural adaptation process, pilot-tested, and psychometrically validated in a sample of 1072 nurses and nurse assistants working in Austrian hospitals across various clinical settings. Exploratory and confirmatory factor analyses (EFA and CFA) were performed to assess construct validity, measurement invariance between professional roles was tested, and internal consistency was measured using McDonald’s Omega. Results: Content validity was confirmed with a mean CVR of 0.634. EFA suggested a three-factor solution—(1) Nutritional Assessment and Calculation Skills, (2) Nutritional Evaluation and Care Planning, and (3) Nutritional Support and Care Implementation—leading to the retention of 19 items. CFA supported this structure, and McDonald’s Omega indicated high internal consistency across subgroups. Partial measurement invariance revealed some differences in response patterns between registered nurses and nurse assistants. Conclusions: The B-NNC Scale demonstrated robust validity and reliability in measuring self-reported nursing behaviors related to nutritional care in older adults. It addresses a notable gap in existing instruments and may serve as a valuable tool for research and practice to improve malnutrition management. Full article

Factorial invariance is critical for ensuring consistent relationships between measured variables and latent constructs across groups or time, enabling valid comparisons in social science research. Detecting factorial invariance becomes challenging when varying degrees of heterogeneity are present in the distribution of latent factors. This simulation study examined how changes in latent means and variances between groups influence the detection of noninvariance, comparing Bayesian and maximum likelihood fit measures. The design factors included sample size, noninvariance levels, and latent factor distributions. Results indicated that differences in factor variance have a stronger impact on measurement invariance than differences in factor means, with heterogeneity in latent variances more strongly affecting scalar invariance testing than metric invariance testing. Among model selection methods, goodness-of-fit indices generally exhibited lower power compared to likelihood ratio tests (LRTs), information criteria (ICs; except BIC), and leave-one-out cross-validation (LOO), which achieved a good balance between false and true positive rates. Full article

The radiative/scattering properties of cyanobacterial aggregates are crucial for understanding microalgal cultivation. This study analyzed the scattering matrix elements and cross-sections of cyanobacterial aggregates using the discrete dipole approximation (DDA) method. A stochastic random walk approach was adopted to generate a force-biased packing model for multicellular filamentous cyanobacterial aggregates. The effects of the shape and size of multicellular cyanobacterial aggregates on their scattering properties were investigated in this work. The possibility of invariance in the scattering properties of cyanobacterial aggregates was explored. The invariance interpretation intuitively represented the radiative property characteristics of the aggregates. The presented results show that the ratios of the matrix elements of cyanobacterial aggregates are nearly shape-, size-, and wavelength-invariant. The extinction and absorption cross-sections (EACSs) per unit volume exhibited shape and approximate size invariance for cyanobacterial aggregates, respectively. The absorption cross-section of aggregates is not merely a volumetric phenomenon for aggregates that exceed a certain size. Furthermore, the absorption cross-sections per unit volume are independent of the volumetric distribution of the microalgae cells. The invariance interpretation presents crucial characteristics of the scattering properties of cyanobacterial aggregates. The existence of invariance greatly improves our understanding of the scattering properties of microalgal aggregates. The scattering properties of microalgal aggregates are the most critical aspects of light propagation in the design, optimization, and operation of photobioreactors. Full article

An inverse-square probability mass function (PMF) is at the Newcomb–Benford law (NBL)’s root and ultimately at the origin of positional notation and conformality. $Pr\left(Z\right)={\left(2Z\right)}^{-2}$, where $Z\in {\mathbb{Z}}^{+}$. Under its tail, we find information as harmonic likelihood $\mathcal{L}\left(\left[s,t\right)\right)=H_{t-1}-H_{s-1}$, where $H_n$ is the nth harmonic number. The global $\mathbb{Q}$-NBL is $Pr\left(b,q\right)={\displaystyle \raisebox{1ex}{$\mathcal{L}\left(\left[q,q+1\right)\right)$}\!\left/ \!\raisebox{-1ex}{$\mathcal{L}\left(\left[1,b\right)\right)$}\right.}={\left(q{H}_{b-1}\right)}^{-1}$, where b is the base and q is a quantum ($1\le q<b$). Under its tail, we find information as logarithmic likelihood $\ell \left(\left[i,j\right)\right)=ln{\displaystyle \raisebox{1ex}{$j$}\!\left/ \!\raisebox{-1ex}{$i$}\right.}$. The fiducial $\mathbb{R}$-NBL is $Pr\left(r,d\right)={\displaystyle \raisebox{1ex}{$\ell \left(\left[d,d+1\right)\right)$}\!\left/ \!\raisebox{-1ex}{$\ell \left(\left[1,r\right)\right)$}\right.}={log}_r\left(1+{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$d$}\right.}\right)$, where $r\ll b$ is the radix of a local complex system. The global Bayesian rule multiplies the correlation between two numbers, s and t, by a likelihood ratio that is the NBL probability of bucket $\left[s,t\right)$ relative to b’s support. To encode the odds of quantum j against i locally, we multiply the prior odds ${\displaystyle \raisebox{1ex}{$Pr\left(b,j\right)$}\!\left/ \!\raisebox{-1ex}{$Pr\left(b,i\right)$}\right.}$ by a likelihood ratio, which is the NBL probability of bin $\left[i,j\right)$ relative to r’s support; the local Bayesian coding rule is $\tilde{o}\left(j:i|r\right)={\displaystyle \raisebox{1ex}{$i$}\!\left/ \!\raisebox{-1ex}{$j$}\right.}{log}_r{\displaystyle \raisebox{1ex}{$j$}\!\left/ \!\raisebox{-1ex}{$i$}\right.}$. The Bayesian rule to recode local data is $\tilde{o}\left(j:i|r^{\prime }\right)=\tilde{o}\left(j:i|r\right){\displaystyle \raisebox{1ex}{$lnr$}\!\left/ \!\raisebox{-1ex}{$ln{r}^{\prime }$}\right.}$. Global and local Bayesian data are elements of the algebraic field of “gap ratios”, ${\displaystyle \frac{A-B}{C-D}}$. The cross-ratio, the central tool in conformal geometry, is a subclass of gap ratio. A one-dimensional coding source reflects the global Bayesian data of the harmonic external world, the annulus $\left\{x\in \mathbb{Q}|1\le \left|x\right|<b\right\}$, into the local Bayesian data of its logarithmic coding space, the ball $\left\{x\in \mathbb{Q}|\left|x\right|<1-{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$b$}\right.}\right\}$. The source’s conformal encoding function is $y={log}_r\left(2x-1\right)$, where x is the observed Euclidean distance to an object’s position. The conformal decoding function is $x={\displaystyle \frac{1}{2}}\left(1+r^y\right)$. Both functions, unique under basic requirements, enable information- and granularity-invariant recursion to model the multiscale reality. Full article

We introduce a special class of cubic curves whose defining parameter satisfies a linear or quadratic equation provided by the values of a cross ratio. There are only seven such cubics and several properties of the real cubics in this class (some of them being elliptic curves) are discussed. Using the Möbius transformation, we extend this self-duality and obtain new families of remarkable complex cubics. In addition, we study (from the differential geometric viewpoint) the surface parameterized by all real cubic curves and we derive its curvature functions. As a by-product, we find a new classification of real Möbius transformations and some estimates for the number of vertices of real cubic curves. Full article

This research presents a novel algorithmic implementation to improve the analysis of visually controlled interception and accompanying motor action through the computational application of harmonic ratios and stimulation invariants. Unlike traditional models that focus mainly on psychological aspects, our approach integrates the relevant constructs into a practical mathematical framework. This allows for dynamic prediction of interception points with improved accuracy and real-time perception–action capabilities, essential for applications in neurorehabilitation and virtual reality. Our methodology uses stimulation invariants as key parameters within a mathematical model to quantitatively predict and improve interception outcomes. The results demonstrate the superior performance of our algorithms over conventional methods, confirming their potential for advancing robotic vision systems and adaptive virtual environments. By translating complex theories of visual perception into algorithmic solutions, this study provides innovative ways to improve motion perception and interactive systems. This study aims to articulate the complex interplay of geometry, perception, and technology in understanding and utilizing cross ratios at infinity, emphasizing their practical applications in virtual and augmented reality settings. Full article

Transformer has recently become widely adopted in point cloud registration. Nevertheless, Transformer is unsuitable for handling dense point clouds due to resource constraints and the sheer volume of data. We propose a method for directly regressing the rigid relative transformation of dense point cloud pairs. Specifically, we divide the dense point clouds into blocks according to the down-sampled superpoints. During training, we randomly select point cloud blocks with varying overlap ratios, and during testing, we introduce the overlap-aware Rotation-Invariant Geometric Transformer Cross-Encoder (RIG-Transformer), which predicts superpoints situated within the common area of the point cloud pairs. The dense points corresponding to the superpoints are inputted into the Transformer Cross-Encoder to estimate their correspondences. Through the fusion of our RIG-Transformer and Transformer Cross-Encoder, we propose Transformer-to-Transformer Regression (TTReg), which leverages dense point clouds from overlapping regions for both training and testing phases, calculating the relative transformation of the dense points by using the predicted correspondences without random sample consensus (RANSAC). We have evaluated our method on challenging benchmark datasets, including 3DMatch, 3DLoMatch, ModelNet, and ModelLoNet, demonstrating up to a $7.2\%$ improvement in registration recall. The improvements are attributed to our RIG-Transformer module and regression mechanism, which makes the features of superpoints more discriminative. Full article

Understanding pedestrian dynamics at bottlenecks and how pedestrians interact with their environment—particularly how they use and move in the space available to them—is of safety importance, since bottlenecks are a key point for pedestrian flow. We performed a series of experiments in which participants walked through a bottleneck individually for varying combinations of approaching angle, bottleneck width and walking speed, to investigate the dependence of the movement on safety-relevant influencing factors. Trajectories as well as 3D motion data were recorded for every participant. This paper shows that (1) the maximum amplitude of shoulder rotation is mainly determined by the ratio of the bottleneck width to the shoulder width of the participant, while the direction is determined by the starting angle and the foot position; (2) the ‘critical point’ is not invariant to the starting angle and walking speed; (3) differences between the maximum and minimum speed values arise mainly from the distribution of deceleration patterns; and (4) the position of crossing shifts by 1.75 cm/10 cm, increasing the bottleneck width in the direction of origin. Full article

The teacher–student framework is widely employed for cross-domain object detection. However, it suffers from two problems. One is that large distribution discrepancies will cause critical performance drops. The other is that the samples that deviate from the overall distributions of both domains will greatly mislead the model. To solve these problems, we propose a style-guided adversarial teacher (SGAT) method for domain adaptation. Specifically, on the domain level, we generate target-like images based on source images to effectively narrow the gaps between domains. On the sample level, we denoise samples by estimating the probability density ratio of the ‘target-style’ and target distributions, which could filter out the unrelated samples and highlight the related ones. In this way, we could guarantee reliable samples. With these reliable samples, we learn the domain-invariant features through teacher–student mutual learning and adversarial learning. Extensive experiments verify the effectiveness of our method. In particular, we achieve 52.9% mAP on Clipart1k and 42.7% on Comic2k, which are 6.4% and 5.0% higher than the compared baselines. Full article

A concentric circle target is commonly used in the vision measurement system for its detection accuracy and robustness. To enhance the camera calibration accuracy, this paper proposes an improved calibration method that utilizes concentric circle grids as the calibration target. The method involves accurately locating the imaged center and optimizing camera parameters. The imaged concentric circle center obtained by cross-ratio invariance is not affected by perspective projection, which ensures the location accuracy of the feature point. Subsequently, the impact of lens distortion on camera calibration is comprehensively investigated. The sub-pixel coordinates of imaged centers are taken into the iterative calibration method, and camera parameters are updated. Through simulations and real experiments, the proposed method effectively reduces the residual error and improves the accuracy of camera parameters. Full article

Recently, historians have discussed the relevance of the nineteenth-century mathematical discipline of projective geometry for early modern classical logic in relation to possible solutions to semantic problems facing it. In this paper, I consider Hegel’s Science of Logic as an attempt to provide a projective geometrical alternative to the implicit Euclidean underpinnings of Aristotle’s syllogistic logic. While this proceeds via Hegel’s acceptance of the role of the three means of Pythagorean music theory in Plato’s cosmology, the relevance of this can be separated from any fanciful “music of the spheres” approach by the fact that common mathematical structures underpin both music theory and projective geometry, as suggested in the name of projective geometry’s principal invariant, the “harmonic cross-ratio”. Here, I demonstrate this common structure in terms of the phenomenon of “inverse foreshortening”. As with recent suggestions concerning the relevance of projective geometry for logic, Hegel’s modifications of Aristotle respond to semantic problems of his logic. Full article

Machinery degradation assessment can offer meaningful prognosis and health management information. Although numerous machine prediction models based on artificial intelligence have emerged in recent years, they still face a series of challenges: (1) Many models continue to rely on manual feature extraction. (2) Deep learning models still struggle with long sequence prediction tasks. (3) Health indicators are inefficient for remaining useful life (RUL) prediction with cross-operational environments when dealing with high-dimensional datasets as inputs. This research proposes a health indicator construction methodology based on a transformer self-attention transfer network (TSTN). This methodology can directly deal with the high-dimensional raw dataset and keep all the information without missing when the signals are taken as the input of the diagnosis and prognosis model. First, we design an encoder with a long-term and short-term self-attention mechanism to capture crucial time-varying information from a high-dimensional dataset. Second, we propose an estimator that can map the embedding from the encoder output to the estimated degradation trends. Then, we present a domain discriminator to extract invariant features from different machine operating conditions. Case studies were carried out using the FEMTO-ST bearing dataset, and the Monte Carlo method was employed for RUL prediction during the degradation process. When compared to other established techniques such as the RNN-based RUL prediction method, convolutional LSTM network, Bi-directional LSTM network with attention mechanism, and the traditional RUL prediction method based on vibration frequency anomaly detection and survival time ratio, our proposed TSTN method demonstrates superior RUL prediction accuracy with a notable SCORE of 0.4017. These results underscore the significant advantages and potential of the TSTN approach over other state-of-the-art techniques. Full article

Spherical images have the advantage of recording full scenes using only one camera exposure and have been becoming an important data source for 3D reconstruction. However, geometric distortions inevitably exist due to the spherical camera imaging model. Thus, this study proposes a reliable feature matching algorithm for spherical images via the combination of local geometric rectification and CNN (convolutional neural network) learned descriptor. First, image patches around keypoints are reprojected to their corresponding tangent planes based on a spherical camera imaging model, which uses scale and orientation data from the keypoints to achieve both rotation and scale invariance. Second, feature descriptors are then calculated from the rectified image patches by using a pre-trained separate detector and descriptor learning network, which improves the discriminability by exploiting the high representation learning ability of the CNN. Finally, after classical feature matching with the ratio test and cross check, refined matches are obtained based on an essential matrix-based epipolar geometry constraint for outlier removal. By using three real spherical images and an incremental structure from motion (SfM) engine, the proposed algorithm is verified and compared in terms of feature matching and image orientation. The experiment results demonstrate that the geometric distortions can be efficiently reduced from rectified image patches, and the increased ratio of the match numbers ranges from 26.8% to 73.9%. For SfM-based spherical image orientation, the proposed algorithm provides reliable feature matches to achieve complete reconstruction with comparative accuracy. Full article

Measuring surface deformation is crucial for a better understanding of spatial-temporal evolution and the mechanism of mining-induced deformation, thus effectively assessing the mining-related geohazards, such as landslides or damage to surface infrastructures. This study proposes a method of retrieving surface deformation by combining multi-temporal digital surface models (DSMs) with image homonymous features using China’s ZY-3 satellite stereo imagery. DSM is generated from three-line-array images of ZY-3 satellite using a rational function model (RFM) as the imaging geometric model. Then, elevation changes in deformation are extracted using the difference of DSMs acquired at different times, while planar displacements of deformation are calculated using image homonymous features extracted from multi-temporal digital orthographic maps (DOMs). Scale invariant feature transform (SIFT) points and line band descriptor (LBD) lines are selected as two kinds of salient features for image homonymous features generation. Cross profiles are also extracted for deformation in typical regions. Four sets of stereo imagery acquired in 2012 to 2022 are used for deformation extraction and analysis in the Fushun coalfield of China, where surface deformation is quite distinct and coupled with rising and descending elevation together. The results show that 21.60% of the surface in the study area was deformed from 2012 to 2017, while a decline from 2017 to 2022 meant that 17.19% of the surface was deformed with a 95% confidence interval. Moreover, the ratio of descending area was reduced to 6.44% between 2017 and 2022, which is lower than the ratios in other years. The slip deformation area in the west open pit mine is about 1.22 km² and the displacement on the south slope is large, reaching an average of 26.89 m and sliding from south to north to the bottom of the pit between 2012 and 2017, but elevations are increased by an average of about 16.35 m, involving an area of about 0.86 km² between 2017 and 2022 due to the restoration of the open pit. The results demonstrate that more quantitative features and specific surface deformation can be retrieved in mining areas by combining image features with DSMs derived from ZY-3 satellite stereo imagery. Full article

Within the framework of dispersion theory, we study the the processes $e^{+}{e}^{-}\to \varphi \left(2170\right)\to \varphi \pi \pi \left(K\overline{K}\right)$. The strong pion–pion final-state interactions, especially the $K\overline{K}$ coupled channel in the S wave, are taken into account in a model-independent way using the Omnès function solution. Through fitting the experimental data of the $\pi \pi$ and $\varphi \pi$ invariant mass distributions of the $e^{+}{e}^{-}\to \varphi \left(2170\right)\to \varphi {\pi }^{+}{\pi }^{-}$ process, the low-energy constants in the chiral Lagrangian are determined. The theoretical prediction for the cross sections’ ratio $\sigma (e^{+}{e}^{-}\to \varphi \left(2170\right)\to \varphi K^{+}{K}^{-})/\sigma (e^{+}{e}^{-}\to \varphi \left(2170\right)\to$$\varphi {\pi }^{+}{\pi }^{-})$ is given, which could be useful for selecting the physical solution, when the fit to the $e^{+}{e}^{-}\to \varphi K^{+}{K}^{-}$ cross-section distribution is available in the future. Our results suggest that above the kinematical threshold of $\varphi K\overline{K}$, the mechanism $e^{+}{e}^{-}\to \varphi K^{+}{K}^{-}$, with the kaons rescattering to a pion pair, plays an important role in the $e^{+}{e}^{-}\to \varphi {\pi }^{+}{\pi }^{-}$ transition. Full article