Theoretical issues in deep networks by Poggio, Tomaso, Banburski, Andrzej, Liao, Qianli

“…We review our recent results toward this goal. In approximation theory both shallow and deep networks are known to approximate any continuous functions at an exponential cost. …”
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Using neural networks for approximating functions and equations by Li, Yongming

“…In Chapter 2, we begin with the recent results on neural network approximation theory, and operations used to construct neural networks. …”
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Computing with functions in two dimensions by Townsend, A

“…Explicit convergence rates are shown for the singular values of differentiable and separately analytic functions, and examples are given to demonstrate some paradoxical features of low rank approximation theory.</p> <p>Analogues of QR, LU, and Cholesky factorizations are introduced for matrices that are continuous in one or both directions, deriving a continuous linear algebra. …”

Asymmetries in nucleon transfer reactions induced by polarized protons by Nelson, J

“…</p> <p>An analysis of the data in terms of the distorted wave Born Approximation theory will be given in Chapter 5. The theory, in its two most frequently used forms, is outlined in Chapter 1. …”

Deterministic simulation of multi-beaded models of dilute polymer solutions by Figueroa, L, Leonardo E. Figueroa

“…Approx. 30: 621--651, 2009) in the case of Poisson's equation on a rectangular domain in $\mathbb{R}^2$, subject to a homogeneous Dirichlet boundary condition, where they exploited the connection of the approximation method with the greedy algorithms from nonlinear approximation theory explored, for example, by DeVore and Temlyakov (Adv. …”

RG-GCN: Improved Graph Convolution Neural Network Algorithm Based on Rough Graph by Weiping Ding, Bairu Pan, Hengrong Ju, Jiashuang Huang, Chun Cheng, Xinjie Shen, Yu Geng, Tao Hou

“…Specifically, the algorithm first constructs a rough graph using a combination of the upper and lower approximation theory of the rough set and the edge theory of the topological graph, the paired maximum-minimum relationship values are used to characterize the uncertain relationship between nodes. …”
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A Novel Feature Extraction Method Based on Legendre Multi-Wavelet Transform and Auto-Encoder for Steel Surface Defect Classification by Xiaoyang Zheng, Weishuo Liu, Yan Huang

“…More precisely, the finite element approximation theory is implemented to address the strong capacity of LW bases with various regularities and vanish moments for thoroughly matching the complex geometry characteristics of the steel surface defects, which provides strict theory foundation for the feature extraction in LWT frequency domain without losing any defect information due to its orthogonality. …”
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Bishop-Phelps Theorem for Normed Cones by Ildar Sadeghi, Ali Hassanzadeh

“…Introduction In the last few years there is a growing interest in the theory of quasi-metric spaces and other related structures such as quasi-normed cones and asymmetric normed linear spaces, because such a theory provides an important tool in the study of several problems in theoretical computer science, approximation theory, applied physics, convex analysis and optimization. …”
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Electroosmosis oriented flow of Jeffrey viscoelastic model through scraped surface heat exchanger by Ali Imran, Muhammad Shoaib, Kottakkaran Sooppy Nisar, Muhammad Asif Zahoor Raja, Ayman Zahra, Zulqurnain Sabir

“…The mathematical model is established with the aid of lubrication approximation theory and extracted analytical solution. Exact analytical expressions are gathered for velocities, volume fluxes, pressure gradients, pressure at the edges of the blades and stream functions in the various stations of SSHE. …”
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Three-Dimensional Simulation of Particle-Induced Mode Splitting in Large Toroidal Microresonators by Lei Chen, Cheng Li, Yumin Liu, Judith Su, Euan McLeod

“…In addition, applications of mode-splitting often involve bacteria or viruses, which are too large to be accurately described by the existing analytical dipole approximation theory. A numerical simulation approach could accurately explain mode splitting induced by these larger particles. …”
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Theoretical Issues in Deep Networks by Poggio, Tomaso, Banburski, Andrzej, Liao, Qianli

“…We review our recent results towards this goal. In {\it approximation theory} both shallow and deep networks are known to approximate any continuous functions on a bounded domain at a cost which is exponential (the number of parameters is exponential in the dimensionality of the function). …”
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Accelerating Asymptotically Exact MCMC for Computationally Intensive Models via Local Approximations by Conrad, Patrick R., Marzouk, Youssef M., Pillai, Natesh S., Smith, Aaron

“…Our approach introduces local approximations of these models into the Metropolis-Hastings kernel, borrowing ideas from deterministic approximation theory, optimization, and experimental design. …”
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Wide deep neural networks by Hayou, S

“…Classical results from approximation theory ensure that neural networks, even with a single hidden layer, are universal approximators, provided the model is big enough. …”

Printed Antennas : Design and Challenges / by Malik, Praveen Kumar, editor 650898, Naim, Arshi, 1976-, editor 650899, Singh, Ramendra, editor 650900

Vibration analysis of size dependent micro FML cylindrical shell reinforced by CNTs based on modified couple stress theory by Gang Zhao, Mostafa Hooman, Mahdireza Yarigarravesh, Mohammed Algarni, Maria Jade Catalan Opulencia, Fahad Alsaikhan, Abduladheem Turki Jalil, Abdullah Mohamed, Kareem M.AboRas, Md. Lutfor Rahman, Mohd Sani Sarjadi

“…Hamilton’s principle has been carried out for deriving the non-classical equations of motion of size-dependent thin micro cylindrical shell on the basis of Love’s first approximation theory. Mori-Tanaka and extended rule of mixture are utilized to estimate the mechanical attributes of carbon nanotubes (CNTs) and equivalent fiber, respectively. …”
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Darcy–Boussinesq Model of Cilia-Assisted Transport of a Non-Newtonian Magneto-Biofluid with Chemical Reactions by Ali Ahmad Farooq, Zahir Shah, Poom Kumam, Ebraheem O. Alzahrani, Meshal Shutaywi, Talha Anwar

“…These are highly nonlinear equations, which were simplified due to a physiologically valid approach known as LAT (lubrication approximation theory). Analytical solutions for temperature, concentration, and velocity profiles were evaluated. …”
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Hybrid Threshold Denoising Framework Using Singular Value Decomposition for Side-Channel Analysis Preprocessing by Yuanzhen Wang, Hongxin Zhang, Xing Fang, Xiaotong Cui, Wenxu Ning, Danzhi Wang, Fan Fan, Lei Shu

“…This framework is based on singular value decomposition and introduces low-rank matrix approximation theory to improve the rank selection methods of singular value decomposition. …”
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Trajectory Definition with High Relative Accuracy (HRA) by Parametric Representation of Curves in Nano-Positioning Systems by Lucía Díaz Pérez, Beatriz Rubio Serrano, José A. Albajez García, José A. Yagüe Fabra, Esmeralda Mainar Maza, Marta Torralba Gracia

“…This novel method has an interest in computer-aided geometric design and approximation theory, and allows high relative accuracy (HRA) in the computation of the representations of parametric curves while minimizing the numerical errors. …”
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Insight into the Significance of Viscous Dissipation and Heat Generation/Absorption in Magneto-Hydrodynamic Radiative Casson Fluid Flow With First-Order Chemical Reaction by Ali Hassan, Azad Hussain, Mubashar Arshad, Soumaya Gouadria, Jan Awrejcewicz, Ahmed M. Galal, Ahmed M. Galal, Fahad M. Alharbi, S. Eswaramoorthi

“…The constitutive relations for Casson fluid incorporated with suitable boundary layer approximation theory have been utilized to achieve the flow model equations. …”
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DISCRETE ATOMIC COMPRESSION OF DIGITAL IMAGES: ALMOST LOSSLESS COMPRESSION by Iryna Victorivna Brysina, Victor Olexandrovych Makarichev

“…We use the methods of digital image processing, atomic function theory, and approximation theory. The computer program "Discrete Atomic Compression: User Kit" with the mode "Almost Lossless Compression" is used to obtain results of the DAC processing of test images. …”
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