Euclidean Method Research Articles

Morris method with improved sampling strategy and Sobol’ Variance-based method, as validation tool on Numerical Model of Richard’s Equation

Richard’s equation was approximated by finite-difference numerical scheme to model water infiltration profile in variably unsaturated soil. The published data of Philip’s semi-analytical solution was used to validate the simulated results from the numerical scheme. A discrepancy was found between the simulated and the published semi-analytical results. Morris method as a global sensitivity tool was used as an alternative to local sensitivity analysis to assess the results discrepancy. Morris method with different sampling strategies were tested, of which Manhattan distance method have resulted a better sensitivity measures and also a better scan of input space than Euclidean method. Moreover, Morris method at and Manhattan distance sampling strategy, with only 2 extra simulation runs than local sensitivity analysis, was able to produce reliable sensitivity measures ( , ). The sensitivity analysis results were cross-validated by Sobol’ variance-based method with 150,000 simulation runs. The global sensitivity tool has identified three important parameters, of which spatial discretization size was the sole reason of the discrepancy observed. In addition, a high proportion of total output variance contributed by parameters and is suggesting a greater significant digits is required to reduce its input uncertainty range.

Time series motifs discovery under DTW allows more robust discovery of conserved structure

In recent years, time series motif discovery has emerged as perhaps the most important primitive for many analytical tasks, including clustering, classification, rule discovery, segmentation, and summarization. In parallel, it has long been known that Dynamic Time Warping (DTW) is superior to other similarity measures such as Euclidean Distance under most settings. However, due to the computational complexity of both DTW and motif discovery, virtually no research efforts have been directed at combining these two ideas. The current best mechanisms to address their lethargy appear to be mutually incompatible. In this work, we present the first efficient, scalable and exact method to find time series motifs under DTW. Our method automatically performs the best trade-off of time-to-compute versus tightness-of-lower-bounds for a novel hierarchy of lower bounds that we introduce. As we shall show through extensive experiments, our algorithm prunes up to 99.99% of the DTW computations under realistic settings and is up to three to four orders of magnitude faster than the brute force search, and two orders of magnitude faster than the only other competitor algorithm. This allows us to discover DTW motifs in massive datasets for the first time. As we will show, in many domains, DTW-based motifs represent semantically meaningful conserved behavior that would escape our attention using all existing Euclidean distance-based methods.

Variational data assimilation of sea surface height into a regional storm surge model: Benefits and limitations

ABSTRACT Storm surges are coastal sea-level variations caused by meteorological conditions. It is vital that they are forecasted accurately to reduce the potential for financial damage and loss of life. In this study, we investigate how effectively the variational assimilation of sparse sea level observations from tide gauges can be used for operational forecasting in the North Sea. Novel data assimilation ideas are considered and evaluated: a new shortest-path method for generating improved distance-based correlations in the presence of coastal boundaries and an adaptive error covariance model. An assimilation setup is validated by removing selections of tide gauges from the assimilation procedure for a North Sea case study. These experiments show widespread improvements in RMSE and correlations, reaching up to 16 cm and 0.7 (respectively) at some locations. Simulated forecast experiments show RMSE improvements of up to 5 cm for the first 24 h of forecasting, which is useful operationally. Beyond 24 h, improvements quickly diminish however. Using the setup based on the shortest path algorithm shows little difference when compared to a simpler Euclidean method at most locations. Analysis of this event shows that improvements due to data assimilation are bounded and relatively short lived.

Vacuum polarization on topological black holes with Robin boundary conditions

We compute the renormalized vacuum polarization for a massless, conformally coupled scalar field on asymptotically anti-de Sitter black hole backgrounds. Mixed (Robin) boundary conditions are applied on the spacetime boundary. We consider black holes with nonspherical event horizon topology as well as spherical event horizons. The quantum scalar field is in the Hartle-Hawking state, and we employ Euclidean methods to calculate the renormalized expectation values. Far from the black hole, we find that the vacuum polarization approaches a finite limit, which is the same for all boundary conditions except Dirichlet boundary conditions.

Blockwise Euclidean likelihood for spatio-temporal covariance models

A spatio-temporal blockwise Euclidean likelihood method for the estimation of covariance models when dealing with large spatio-temporal Gaussian data is proposed. The method uses moment conditions coming from the score of the pairwise composite likelihood. The blockwise approach guarantees considerable computational improvements over the standard pairwise composite likelihood method. In order to further speed up computation, a general purpose graphics processing unit implementation using OpenCL is implemented. The asymptotic properties of the proposed estimator are derived and the finite sample properties of this methodology by means of a simulation study highlighting the computational gains of the OpenCL graphics processing unit implementation. Finally, there is an application of the estimation method to a wind component data set.

A Convenient and High-Accuracy Multicamera Calibration Method Based on Imperfect Spherical Objects

Multicamera systems have important applications in industrial online measurement, attracting wide interest due to their encouraging performance. However, how to develop a convenient and high-accuracy multicamera calibration model is a big challenge. Traditional calibration methods based on 2-D objects require the preparation of high-precision and large-scale calibration objects and have poor adaptability to the spatial distribution of cameras. To address these issues, a convenient and accurate multicamera calibration method is proposed based on an imperfect spherical object. Specifically, a special calibration object, i.e., an imperfect sphere with many coded targets is designed for calibrating the multicamera system, where the optical axes of the cameras are different in orientations and converge into the measurement field. Then, a Euclidean reconstruction method is employed to calculate the camera poses and the spatial coordinates of feature points in the local coordinate system after the adaptive grouping of cameras is completed. Moreover, a graph theory-based optimal path transformation algorithm is developed to obtain the camera poses and spatial point coordinates in the global coordinate system (GCS), and a spherical projection optimization algorithm is designed to spheroidize the spatial coordinates of feature points. In the end, the camera poses and the spatial coordinates of feature points in the GCS are optimized by a bundle adjustment algorithm. We build a multicamera system and conduct extensive experiments to demonstrate the superiority of the proposed method.

Genetic diversity and correlation studies in rice (Oryza sativa L.)

The present investigation consists of 26 germplasm used for the experiment was conducted during Kharif-2019 in Randomized Block Design with three replications at Field Experimentation Centre, Department of Genetics and Plant Breeding, Sam Higginbottom University of Agriculture Technology and Sciences, Prayagraj (Allahabad). The data were recorded on thirteen quantitative characters to study genetic variability, heritability, genetic advance, correlation coefficient, path coefficient and genetic divergence. On the basis of mean performance highest grain yield per plant was exhibited by SHIATS DHAN-2 (38.4 g), followed by SHIATS DHAN-1 (38.0 g), SHIATS DHAN- 3 (37.60 g). Analysis of variance among 26 germplasm showed highly significant differences for all the characters under study indicated the presence of a substantial amount of genetic variability. Higher estimates of GCV and PCV were for higher estimates of GCV and PCV were for Spikelets per panicle followed by tillers and number of panicles. High heritability was recorded for days to maturity followed by Days to flowering 50%. High heritability coupled with high genetic advance is recorded for spikelets per panicle. Correlation study revealed that grain yield per plant showed the high positive significant association for all the characters plant height, flag leaf width, number of tillers, number of panicles, panicle length, biological yield per plant and spikeslets per panicle at both phenotypic and genotypic levels. Path coefficient analysis revealed that plant height, flag leaf width, number of panicles, panicle length, days to maturity, biological yield per hill and harvest index had positive direct effect on yield at phenotypic level for improvement of grain yield in rice. Based on the relative magnitude of D2 values, the genotypes were grouped into seven clusters by Euclidean methods of divergence study. Cluster I consist of a maximum of eight genotypes, followed by cluster II with six genotypes, cluster III with three genotypes, cluster IV with three genotypes, cluster V with two genotypes, cluster VI with one genotype, cluster VII with three genotypes. The maximum inter-cluster distance was observed between cluster VII and V followed by cluster V and IV. Thus, the genotypes from the clusters having maximum inter-cluster distance can be selected and used as parents for hybridization programme to develop desirable lines. Maximum genetic divergence was exhibited by grain yield per hill and test weight contributed to 78.77% of total divergence which is needed to be focused while selecting parents for hybridization programme.

Genetic diversity studies in finger millet: Eleusine coracana L. Gaertn

The present investigation was conducted to examine the genetic diversity among 34 genotypes of finger millet, during Kharif-2019 in Randomized Block Design with three replications. The data were recorded on fifteen quantitative characters to study variability, heritability, genetic advance and genetic divergence. Analysis of Variance showed significant differences among 34 finger millet genotypes for all the characters under study at 1% level of significance. Thus, indicating that a good amount of variability thus revealed that these genotypes have been developed from different genetic background. On the basis of per se performance for different quantitative traits, genotype IE3473 was found to be the best genotype in Prayagraj agro-climatic conditions. High estimates of GCV and PCV were observed for harvest index. High heritability coupled with high genetic advance was recorded for harvest index, followed by biological yield per plant, test weight, days to 50% flowering, indicating the predominance of additive gene effects and the possibilities of effective selection for the improvement of these characters. Based on the relative magnitude of D2 value, the genotypes were grouped into seven clusters by Euclidean method of divergence study. Cluster I constituted maximum number genotypes with 18 genotypes. Maximum inter- cluster distance (D2) was observed between cluster VII and VI, suggesting that the genotypes from these clusters can be selected to yield superior segregants and further genetic improvement. Grain yield appeared to be the most important trait contributing maximum towards genetic divergence. This indicated that this attributes should form the criteria for selection of parents for hybridization programme.

Multi-Target Tracking on Riemannian Manifolds via Probabilistic Data Association

Riemannian manifolds are attracting much interest in various technical disciplines, since generated data can often be naturally represented as points on a Riemannian manifold. Due to the non-Euclidean geometry of such manifolds, usual Euclidean methods yield inferior results, thus motivating development of tools adapted or specially tailored to the true underlying geometry. In this letter we propose a method for tracking multiple targets residing on smooth manifolds via probabilistic data association. By using tools of differential geometry, such as exponential and logarithmic mapping along with the parallel transport, we extend the Euclidean multi-target tracking techniques based on probabilistic data association to systems constrained to a Riemannian manifold. The performance of the proposed method was extensively tested in experiments simulating multi-target tracking on unit hyperspheres, where we compared our approach to the von Mises-Fisher and the Kalman filters in the embedding space that projects the estimated state back to the manifold. Obtained results show that the proposed method outperforms the competitive trackers in the optimal sub-pattern assignment metric for all the tested hypersphere dimensions. Although our use case geometry is that of a unit hypersphere, our approach is by no means limited to it and can be applied to any Riemannian manifold with closed-form expressions for exponential/logarithmic maps and parallel transport along the geodesic curve. The paper code is publicly available <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> .

Urban Flood Vulnerability Assessment Using the Entropy Weight Method

Locally concentrated heavy rainfall has led to an increase in the occurrence of flood damage. This is especially so in the urban areas, which are relatively more vulnerable to flood damage due to the high population and property density. In Seoul, which has 25 administrative districts, heavy rainfall triggered flood-related damage in 2010, 2011, and 2018. However, the flood characteristics of each district were different due to difference in flood impact factors such as topography, weather, and disaster prevention measures. The flood vulnerability of each district should be assessed based on local characteristics to reduce flood damage. This study collected and calculated 15 characteristic data points that can explain the climate exposure, sensitivity, and adaptive capacity of each district using the entropy weight method. Thereafter, the flood vulnerability of each district was calculated based on climate exposure, sensitivity, and adaptive capacity, using the Euclidean method. The results showed that the northern and western areas in Seoul are highly vulnerable due to high climate exposure, sensitivity, and low adaptive capacity. In contrast, the other parts of Seoul had low vulnerability due to high sensitivity, low climate exposure, and high adaptive capacity. These results will contribute to the establishment of a flood damage reduction plan that reflects local characteristics.

Learning Common Harmonic Waves on Stiefel Manifold - A New Mathematical Approach for Brain Network Analyses.

Converging evidence shows that disease-relevant brain alterations do not appear in random brain locations, instead, their spatial patterns follow large-scale brain networks. In this context, a powerful network analysis approach with a mathematical foundation is indispensable to understand the mechanisms of neuropathological events as they spread through the brain. Indeed, the topology of each brain network is governed by its native harmonic waves, which are a set of orthogonal bases derived from the Eigen-system of the underlying Laplacian matrix. To that end, we propose a novel connectome harmonic analysis framework that provides enhanced mathematical insights by detecting frequency-based alterations relevant to brain disorders. The backbone of our framework is a novel manifold algebra appropriate for inference across harmonic waves. This algebra overcomes the limitations of using classic Euclidean operations on irregular data structures. The individual harmonic differences are measured by a set of common harmonic waves learned from a population of individual Eigen-systems, where each native Eigen-system is regarded as a sample drawn from the Stiefel manifold. Specifically, a manifold optimization scheme is tailored to find the common harmonic waves, which reside at the center of the Stiefel manifold. To that end, the common harmonic waves constitute a new set of neurobiological bases to understand disease progression. Each harmonic wave exhibits a unique propagation pattern of neuropathological burden spreading across brain networks. The statistical power of our novel connectome harmonic analysis approach is evaluated by identifying frequency-based alterations relevant to Alzheimer's disease, where our learning-based manifold approach discovers more significant and reproducible network dysfunction patterns than Euclidean methods.

Experimental and numerical research on the bond‐slip behavior of square‐rebar reinforced concrete during the republic of China (1912–1949)

AbstractSquare‐rebar reinforced concrete structures during the republic of China (ROC) (1912–1949) have special material properties and structural characteristics. To perform nonlinear finite element simulations of this special type of structure more accurately, a specialized bond‐slip constitutive model is built. Eighteen central pullout specimens were designed based on the ROC concrete mix proportions and the square‐rebar. Then, the test data were fitted with the universal global optimization method and the minimum Euclidean distance point method was chosen to calculate the inflection point matrix of the bond‐slip constitutive model. Finally, the main factors influencing the bond‐slip behavior of the ROC square‐rebar reinforced concrete were analyzed. The research results show that the corrosion of the square‐rebar produces a negative effect on the whole structure and a modified bond‐slip regression curve considering the size effect is obtained. The research results can provide a scientific basis for the nonlinear calculation of ROC square‐rebar reinforced concrete structures considering the bond‐slip behaviors.

Procesamiento a imágenes de video para verificación de distanciamiento social durante la pandemia de la COVID-19

El aumento exponencial del número de contagios por COVID-19 alrededor del mundo ha originado que los gobiernos, en acompañamiento de comunidades médicas y científicas, recomienden el distanciamiento social de al menos dos metros entre personas, para evitar el crecimiento en el número de contagios. Con el propósito de determinar el cumplimiento de la medida de distanciamiento social, se realiza una prueba piloto mediante el procesamiento a imágenes de video para la detección de personas en espacios abiertos de la zona céntrica de la ciudad de Cúcuta, Colombia. El método propuesto consiste en el análisis de información de videos de personas con fondo estático, tomados desde una altura de 4.5 metros, además de ubicación de centroides por el método de momentos y estimación de distancia por el método euclidiano, esto, mediante lenguaje de programación Python. Como resultado se obtiene un acierto en la detección de personas del 92.43 % y que el 84.21 % de quienes circularon por el cuadro de video y transitan en la zona céntrica de la ciudad de Cúcuta, Colombia, incumplen con el distanciamiento social de dos metros recomendado por la comunidad científica y expuesta en la circular municipal 023 de 2020.

Sensitivity of High Fill Slope Stability Factors under Seismic Conditions

An evaluation method based on vector similarity is introduced to determine the sensitivity of stability factors of high fill slope under seismic action in this paper. The Euclidean similarity and cosine similarity of slope stability factors are calculated. In addition, grey relational analysis method is used to calculate the case, and the three calculation results are compared. The results show that the sensitivity ranking results of high fill slope stability factors obtained by cosine similarity and grey correlation analysis are consistent, and slightly different from those obtained by Euclidean similarity. This indicates that cosine similarity method is more suitable for sensitivity evaluation of high fill slope stability factors than Euclidean similarity method.

Application of Fractal and Euclidean Methods to Differentiate Normal and Neoplastic Thyroid Cells

Abstract Context: The differentiated papillary and follicular thyroid neoplasms can be characterized from the notions of fractal and Euclidean geometry to overcome the challenges faced by the pathologist. This method was previously used in differentiating preinvasive lesions of cervical cancer. Aims: to characterize the irregularity of histologic samples of normal thyroid cells as well as benign and malignant thyroid papillary and follicular carcinomas, through the box-counting method using the principles of fractal and Euclidian geometry. Settings and Design: This is a retrospective study involving the measurement of thyroid cells through pixels in photographs, applying geometric methods. Subjects and Methods: Photographs of histological samples from normal and neoplastic biopsy samples were taken and processed by a software in order to delimit the borders of the nucleus and cytoplasm. Then, the box-counting method was applied by superimposing grids of 5 and 10 pixels to measure the fractal dimension and the occupied spaces of the cellular surface. Results: The set of papillary and follicular cells evaluated from the occupied spaces from the borders and surfaces of the nucleus and cytoplasm in the 5-pixel grid showed that normal cells are included within a range of values, while the neoplastic variations are differentiable from this range. Conclusions: Fractal and Euclidean geometries can differentiate normality from some benign and malignant thyroid lesions, which opens a path to develop methodologies that characterize more precisely distinctive features between normal and neoplastic cells independent of qualitative criteria from traditional pathology and histology.

Electromagnetic quasitopological gravities

We identify a set of higher-derivative extensions of Einstein-Maxwell theory that allow for spherically symmetric charged solutions characterized by a single metric function f (r) = −gtt = 1/grr. These theories are a non-minimally coupled version of the recently constructed Generalized Quasitopological gravities and they satisfy a number of properties that we establish. We study magnetically-charged black hole solutions in these new theories and we find that for some of them the equations of motion can be fully integrated, enabling us to obtain analytic solutions. In those cases we show that, quite generally, the singularity at the core of the black hole is removed by the higher-derivative corrections and that the solution describes a globally regular geometry. In other cases, the equations are reduced to a second order equation for f (r). Nevertheless, for all the theories it is possible to study the thermodynamic properties of charged black holes analytically. We show that the first law of thermodynamics holds exactly and that the Euclidean and Noether-charge methods provide equivalent results. We then study extremal black holes, focusing on the corrections to the extremal charge-to-mass ratio at a non-perturbative level. We observe that in some theories there are no extremal black holes below certain mass. We also show the existence of theories for which extremal black holes do not represent the minimal mass state for a given charge. The implications of these findings for the evaporation process of black holes are discussed.

Morris method with improved sampling strategy and Sobol’ variance-based method, as validation tool on numerical model of Richard’s equation

Richard’s equation was approximated by finite-difference numerical scheme to model water infiltration profile in variably unsaturated soil. The published data of Philip’s semi-analytical solution was used to validate the simulated results from the numerical scheme. A discrepancy was found between the simulated and the published semi-analytical results. Morris method as a global sensitivity tool was used as an alternative to local sensitivity analysis to assess the results discrepancy. Morris method with different sampling strategies were tested, of which Manhattan distance method have resulted a better sensitivity measures and also a better scan of input space than Euclidean method. Moreover, Morris method at and Manhattan distance sampling strategy, with only 2 extra simulation runs than local sensitivity analysis, was able to produce reliable sensitivity measures ( , ). The sensitivity analysis results were cross-validated by Sobol’ variance-based method with 150,000 simulation runs. The global sensitivity tool has identified three important parameters, of which spatial discretization size was the sole reason of the discrepancy observed. In addition, a high proportion of total output variance contributed by parameters and is suggesting a greater significant digits is required to reduce its input uncertainty range.

Meronic AdS black holes in Gauss-Bonnet theory

We examine analytical, intrinsically non-Abelian, black holes with SU(2) Yang-Mills matter content. Working in the extended thermodynamics scenario of Lovelock black holes we study the phase structure of a four and a five-dimensional spherically symmetric configuration. We work in Gauss-Bonnet-Einstein-Yang-Mills gravity with negative cosmological constant and use Euclidean methods to explore the thermodynamics of the systems. We observe that the solutions belong to the expected universality class of van der Waals and find a reentrant phase transition.

Voice Classification Based on Fast Independent Component Analysis to Support Nuclear Power Plant Security

National vital objects have important role in national development,so they require special protection. Nuclear power plant (NPP) is one of them. Access restriction is required to prevent the NPP from potential hazards. The restriction can be improved by using face, fingerprints, retina, iris, and voice password. The improvement will enhance the security of the NPP. This research has implemented pattern recognition and classification of voice passwords. The passwords were a, i, u, e, and o. The features vector was searched by using Fast ICA method while the pattern classification was performed by minimum Euclidean method. The purpose of this research is to recognize and classify those letter password, so people who have access to the nuclear area can be distinguished. The methodology of this research consists of input data, pre-processing data, feature extraction, and classification. Pre-processing was done by normalization, denoising, centering, and whitening. Feature extraction was performed by Fast ICA method, and classification was done by minimum Euclidean distance. The results show that Fast ICA and minimum Euclidean methods can 100 % distinguish between the employees who have access permit and those who have no access permit. When an employee with access permit says aiueo”, it will be recognized as password, whereas when an employee with no access permit says the password, it will be recognized not as the password.

Identifikasi Tulisan Tangan Huruf Katakana Jepang Dengan Metode Euclidean

Katakana is one of the traditional Japanese letters used to absorption words from other languanges. In the inttroduction of an object a learning process is needed, which is obtained through the characteristics and experience of observing similar objects after being acquired. But manually it is quite difficult to distinguish between 5 hiragana vowels starting from the image data acquisition process, image processing, feature extraction using Gray Level Co-occurance Matrix (GLCM) while classifiers use the euclidean distance method. The results of the tests carried out showed an accuracy rate of around 78% using the euclidean method.