26 papers · ranked by Valyu relevance
Ke Bao, Wei Fang, Yourong Ding
Although the integrated model has good convergence ability, it is difficult to solve the multimodal problem and noisy problem due to the lack of uncertainty evaluation. Radial basis function model performs best for different degrees of nonlinear problems with small-scale and noisy training datasets but is insensitive…
Corrado Groth, Andrea Chiappa, Stefano Porziani, Marco Evangelos Biancolini + 3 more
'Marco Evangelos Biancolini' 'Emanuele Marotta' 'Pietro Salvini' 'Dimitrios Tzetzis'] Digital image correlation methods allow the determination of the displacement (and thus the strain) field of a target by picture comparisons, without the application of strain gauges or other invasive devices. Homologous sites are…
Dixin Qu
Dance is constantly discovering truth, goodness, and beauty in human social life, spreading truth, goodness, and beauty, and fully expressing the artistic pursuit of dance beauty. It shapes different dance images, expresses the aesthetic consciousness and feelings of dance, and resonates with the audience to meet their…
Kun Wei, Guokai Xiong, Zhenghua Xu, Yong Liu
A new analysis method for the environmental stability of uranium tailing ponds is established in this paper, and the stability intervals and environmental stability rates of indicators are defined in precise mathematical language and analyzed with examples. The results show that the overall environmental stability of…
Liru Mu, Xinlong Feng, José F. F. Mendes
In this paper, the radial basis function finite difference method is used to solve two-dimensional steady incompressible Navier-Stokes equations. First, the radial basis function finite difference method with polynomial is used to discretize the spatial operator. Then, the Oseen iterative scheme is used to deal with…
Amirhossein Fashamiha, David Salac
Accurate interpolation of functions and derivatives is crucial in solving partial differential equations (PDEs). The Radial Basis Function (RBF) method has become an extremely popular and robust approach for interpolation on scattered data. Hermite Radial Basis Function (HRBF) methods are an extension of the RBF and…
Sonia Bhattacharya, Himadri Chakraborty Bhattacharyya
Severe Thunderstorms are the extreme weather convective features. It causes local calamities in various ways. Proper prediction with lead time is an important factor to prevent such calamities from saving people. Here, both probabilistic and machine learning techniques are applied to weather data to obtain proper…
Yuhang Wu, Ziyuan Liu, Wenjun Sun, Qian Xu
Elliptic Equations Authors: ['Yuhang Wu' 'Ziyuan Liu' 'Wenjun Sun' 'Qian Xu'] Abstract: Ordinary deep neural network-based methods frequently encounter difficulties when tackling multiscale and high-frequency partial differential equations. To overcome these obstacles and improve computational accuracy and efficiency…
Aysu Ismayilova, Muhammad Ismayilov
In this paper we consider a new class of RBF (Radial Basis Function) neural networks, in which smoothing factors are replaced with shifts. We prove under certain conditions on the activation function that these networks are capable of approximating any continuous multivariate function on any compact subset of the…
RuiYao Zhang
With the development of digital media technology, its application in teaching and learning is becoming more widespread. Digital media technology helps present information in transmitting knowledge or skills, reduces cognitive load, and promotes understanding of knowledge. Evaluation of the effectiveness of digital…
Yixuan Huang, Zongmin Wu, Shengxin Zhu
We prove that the native space of a Wu function is a dense subspace of a Sobolev space. An explicit characterization of the native spaces of Wu functions is given. Three definitions of Wu functions are introduced and proven to be equivalent. Based on these new equivalent definitions and the so called f-form tricks, we…
Sergio Díaz-Elbal, Andrei Martínez-Finkelshtein, Darío Ramos-López
Compactly Supported Radial Basis Functions (CS-RBFs) are a fundamental tool in multivariate approximation theory. However, their use in statistics and probability modeling remains underexplored, having been used mainly to express covariance functions in Gaussian processes or as kernel functions. This work explores…
Anoop Kumar Kushwaha
In recent years, the applications of first-principles density functional theory (DFT) is diversified and expanded in a wide range due to the development of robust algorithms and more powerful computer systems. In general, DFT is used in condensed matter physics, chemistry, material science and biology to predict and…
Authors not listed
STO-mG type basis functions for 1s to 4f Hydrogen-like orbitals by “energy fit” are reported as simple functions of running parameter atomic number Z and quantum numbers to utilize the basis set from these functions in molecular electronic structure and energy calculations. We mimic the accurate solution of Slater-type…
Oleg V. Favorov, Olcay Kursun
Neurons throughout the neocortex exhibit selective sensitivity to particular features of sensory input patterns. According to the prevailing views, cortical strategy is to choose features that exhibit predictable relationship to their spatial and/or temporal context. Such contextually predictable features likely make…
Authors not listed
Metastable states and the conformational transitions in between them are key to understanding dynamical behaviour and function of large-scale molecular systems. By combining basic dimensionality reduction techniques with a state-of-the art approximation of the Koopman operator associated to molecular dynamics…
Michaël Unser
A ridge is a function that is characterized by a one-dimensional profile (activation) and a multidimensional direction vector. Ridges appear in the theory of neural networks as functional descriptors of the effect of a neuron, with the direction vector being encoded in the linear weights. In this paper, we investigate…
Carlos Ramos-Carreño, José L. Torrecilla, Miguel Carbajo-Berrocal, Pablo Marcos + 1 more
'Pablo Marcos' 'Alberto Suárez'] The library scikit-fda is a Python package for Functional Data Analysis (FDA). It provides a comprehensive set of tools for representation, preprocessing, and exploratory analysis of functional data. The library is built upon and integrated in Python's scientific ecosystem. In…
Sucheta Ghosh, Shankar Prasad Bhattacharyya
The quantum states of hydrogen atom in one dimension can be obtained by a careful application of the well-known Frobenius method. The exercise is highly educative and brings to focus the subtle aspects of quantum mechanics. The allowed states turn out to be only of odd parity and non-degenerate, having energy given by…
Richard Mandle
The cylindrical distribution function (CDF) is a convenient anisotropic analogue of the radial distribution function, the difference being the use of cylindrical shells for binning. As such, CDF analysis can be a powerful tool for the analysis of positional correlations within anisotropic systems, such as liquid…
Authors not listed
The analysis of nonadiabatic molecular dynamics (NAMD) data presents significant challenges due to its high dimensionality and complexity. To address these issues, we introduce ULaMDyn, a Python-based, open-source package designed to automate the unsupervised analysis of large datasets generated by NAMD simulations.…
Zeyu Yao, Jake Y. Chen
Low-dimensional embeddings such as UMAP and t-SNE are routinely used to visually interpret high-dimensional omics data, yet claims based on embedding geometry are often qualitative, embedding-sensitive, and weakly calibrated. We present BioRSP (Biological Radar Scanning Plots), a geometry-first framework that…
Tomoya Wakayama, Hidetoshi Matsui
As the development of measuring instruments and computers has accelerated the collection of massive amounts of data, functional data analysis (FDA) has experienced a surge of attention. The FDA methodology treats longitudinal data as a set of functions on which inference, including regression, is performed.…
Jungin Choi, Abhirup Datta, Martin A. Lindquist
Task-based fMRI is commonly analyzed using voxel-wise general linear models, a non-spatial scalable approach that can yield fragmented activation maps. Spatial alternatives such as kernel smoothing and Bayesian models address this but either blur activation boundaries or are computationally prohibitive at modern…
Jake S. Rhodes, Adrien Aumon, Sacha Morin, Marc Girard + 15 more
Dimensionality reduction-based data visualization is pivotal in comprehending complex biological data. The most common methods, such as PHATE, t-SNE, and UMAP, are unsupervised and therefore reflect the dominant structure in the data, which may be independent of expert-provided labels. Here we introduce a supervised…
Hyung G. Park
Sensor-space EEG analyses typically rely on electrode layouts or data-driven components and rarely encode cortical geometry, making scalp patterns difficult to link to anatomy and to compare across participants. We introduce a sensor-space basis dictionary that explicitly integrates cortical geometry. Laplace–Beltrami…