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Universal approximation of symmetric and anti-symmetric functions [article]

Jiequn Han, Yingzhou Li, Lin Lin, Jianfeng Lu, Jiefu Zhang, Linfeng Zhang
2022 arXiv   pre-print
We consider universal approximations of symmetric and anti-symmetric functions, which are important for applications in quantum physics, as well as other scientific and engineering computations.  ...  We give constructive approximations with explicit bounds on the number of parameters with respect to the dimension and the target accuracy ϵ.  ...  In this paper we aim to study the universal approximation of general symmetric and anti-symmetric functions for any d ≥ 1.  ... 
arXiv:1912.01765v2 fatcat:flz4dlznwbhl3frstsxre7jwye

On Representing (Anti)Symmetric Functions [article]

Marcus Hutter
2020 arXiv   pre-print
We provide a complete and explicit universality proof of the Equivariant MultiLayer Perceptron, which implies universality of symmetric MLPs and the FermiNet.  ...  Applications often require most or all of the following properties: (a) a large class of such functions can be approximated, e.g. all continuous function, (b) only the (anti)symmetric functions can be  ...  We reviewed a variety of representations for (anti)symmetric function (ψ)φ : (R d ) n → R. The most direct and natural way is as a sum over n! permutations of some other function χ.  ... 
arXiv:2007.15298v1 fatcat:auffhfe23vhtnpxhhm5cczudkq

Spectral Analysis of Symmetric and Anti-Symmetric Pairwise Kernels [article]

Tapio Pahikkala, Markus Viljanen, Antti Airola, Willem Waegeman
2015 arXiv   pre-print
Such prior knowledge is commonly enforced by symmetrizing or anti-symmetrizing pairwise kernel functions.  ...  We consider the problem of learning regression functions from pairwise data when there exists prior knowledge that the relation to be learned is symmetric or anti-symmetric.  ...  , the resulting kernel allows approximating arbitrarily well any symmetric or anti-symmetric continuous function.  ... 
arXiv:1506.05950v1 fatcat:hiej3htbbvbsrhbkd5avewikqe

Beyond the Lambertian assumption: A generative model for Apparent BRDF fields of faces using anti-symmetric tensor splines

Angelos Barmpoutis, Ritwik Kumar, Baba C. Vemuri, Arunava Banerjee
2008 2008 IEEE Conference on Computer Vision and Pattern Recognition  
In this paper, we present a novel anti-symmetric tensor spline (a spline for tensorvalued functions) based method for the estimation of the Apparent BRDF (ABRDF) field for human faces that seamlessly accounts  ...  In order to validate the accuracy of our antisymmetric tensor spline model, we present a novel approximation of the ABRDF using a continuous mixture of singlelobed spherical functions.  ...  smoothing/weighting function of our anti-symmetric tensor-fields.  ... 
doi:10.1109/cvpr.2008.4587770 dblp:conf/cvpr/BarmpoutisKVB08 fatcat:zsgh77ew5rbf3fv3nim2r2t52u

On the Free Oscillation of Water in a Lake of Elliptic Boundary

Yoshio SHIBAOKA, Fusako IIDA
1965 Journal of Engineering Physics and Thermophysics  
The fundamental normal mode of the free oscillation of water in a lake of elliptic boundary and of uniform depth is investigated exactly by the use of Mathieu functions and modified Mathieu functions in  ...  Also, an approximate formula for said relationship is derived, which may be adequately used to find the approximate value of the frequency.  ...  is symmetrical about the major axis but anti-symmetrical about the minor axis.  ... 
doi:10.5928/kaiyou1942.21.103 fatcat:rdzmkrybzfhelha2lwynefmhqe

Page 696 of The Journal of Chemical Physics Vol. 5, Issue 9 [page]

1937 The Journal of Chemical Physics  
a and c, and since the Hamiltonian in this case was symmetric in these nuclei, the four symmetrical and the four anti- symmetrical combinations were mutually non- combining.  ...  * a +e w= (<5"), é sé “é ‘ sé é a apa For the symmetrical case previously considered, it was possible to take linear combinations of these states which were either symmetric or anti- symmetric in the nuclei  ... 

Solving Many-Electron Schrödinger Equation Using Deep Neural Networks [article]

Jiequn Han, Linfeng Zhang, Weinan E
2018 arXiv   pre-print
The optimal trial wave-function is obtained through variational Monte Carlo and the computational cost scales quadratically with the number of electrons.  ...  Yet it is able to represent accurately the ground-states of the tested systems, including He, H2, Be, B, LiH, and a chain of 10 hydrogen atoms.  ...  We are grateful for the computing time provided by the High-performance Computing Platform of Peking University and the TIGRESS High Performance Computing Center at Princeton University.  ... 
arXiv:1807.07014v3 fatcat:iqpsgoiezfhaxmtzqix26ayfny

Free Vibration of AFG Circular Arch with Symmetric and Anti‐symmetric Boundary Conditions at Mid‐Arc

Joon Kyu Lee, Byoung Koo Lee
2020 Symmetry  
The governing differential equations of the motion are derived, andthe symmetric and antisymmetric boundary conditions of the arches are developed for applyinginitial and boundary value problems in the  ...  This paper studies the in‐plane free vibration of axially functionally graded (AFG) circulararches with non‐uniform cross‐section.  ...  Appendix A The first and second derivatives of a function of a real variable at a point can be approximated using a 5-point stencil as follows [22] . 2ℎ 8 ℎ 8 ℎ 2ℎ 12ℎ (A1) 2ℎ 16 ℎ 30 16 ℎ 2ℎ 12ℎ (A2)  ... 
doi:10.3390/sym12030417 fatcat:c7txbqqvtfbrxd2kcdyg6wabc4

Constructing Symmetric-Antisymmetric Multi-wavelets and Transforming Digital Image by Multi-wavelets

Xiaorong Tan, Peng Li
2018 IOP Conference Series: Materials Science and Engineering  
Theoretically, this algorithm can construct arbitrary multiple symmetric-antisymmetric multi-wavelets and obtain quantitative coefficients of multiwavelet filters.  ...  The results show that the low-frequency components of the decomposed images account for 99.52% of the total, and the MSNR of the restored images can reach 88.4096 dB, 18.2928 dB higher than the classical  ...  1 2 / ,..., 1 , 0   N r is defined as multi scaling function of symmetric anti-symmetric.  ... 
doi:10.1088/1757-899x/466/1/012062 fatcat:dvkmqmzdt5c2fclykxwou7igja

Molecular dynamics of a proguanil derivative

A Muhammad, L.S. Taura, C.E. Ndikilar
2017 Bayero Journal of Pure and Applied Sciences  
Also, Density Functional Theory (DFT) calculations at B3LYP with 6 31G(d,p) and 6-31++G basis sets were carried out for incl moments, thermal energies, quadrupole moment, polarizibility and optimized bond  ...  The molecular geometries of chemical calculations at the Restricted Hatree 31G(d,p) and 6-31++G.  ...  Acknowledment We wish to acknowledge Sule Lamido University Research Committee for providing the funds for this research.  ... 
doi:10.4314/bajopas.v10i1.26 fatcat:qpwt6fl6ezchxloziykv2l7fz4

Stable Characteristics Optimization of Anti-Symmetric Cylindrical Shell with Laminated Carbon Fiber Composite

Min Sun, Huping Zhou, Chongjie Liao, Zheng Zhang, Guang Zhang, Shaofei Jiang, Feng Zhang
2022 Materials  
application prospects in the application of deformable structures and bionic structures that require composite functions such as having light weight, high strength, and large clamping force.  ...  the design space of the anti-symmetric cylindrical shell; the design points of the anti-symmetric cylindrical shell are verified by experimental methods.  ...  Experimental Verification Figure 13 shows the load-displacement curves of three types of anti-symmetric cylindrical shells measured by a universal tensile testing machine and prepared specimen in the  ... 
doi:10.3390/ma15030933 pmid:35160878 pmcid:PMC8838192 fatcat:4disid7rtncldnobriv76rneim

Eigenvalue Distribution In The Self-Dual Non-Hermitian Ensemble [article]

M. B. Hastings
1999 arXiv   pre-print
This ensemble is closely related to a previously defined ensemble of anti-symmetric matrices with arbitrary complex entries. We study the two-level correlation functions numerically.  ...  This argument is based on combining the method of hermitization of Feinberg and Zee with Zirnbauer's classification of ensembles in terms of symmetric spaces.  ...  This family includes parameters measuring the strength of the real and imaginary, symmetric and anti-symmetric parts of the matrix. By adjusting the parameters, one can obtain various ensembles.  ... 
arXiv:cond-mat/9909234v2 fatcat:26itgppjgngatkumwatckgmaxm

Vowel constrictions are recoverable from formants

Khalil Iskarous
2010 Journal of Phonetics  
University of Wisconsin, Madison, WI].  ...  The area function of the vocal tract in all of its spatial detail is not directly computable from the speech signal.  ...  Whalen, Christine Shadle, Louis Goldstein, Tine Mooshammer, and Carol Fowler for many helpful discussions and thoughtful comments.  ... 
doi:10.1016/j.wocn.2010.03.002 pmid:20871808 pmcid:PMC2944035 fatcat:sp7vgv3jaje2jfh2w77atibspi

Identifying eigenmodes of averaged small-amplitude perturbations to turbulent channel flow

A. S. Iyer, F. D. Witherden, S. I. Chernyshenko, P. E. Vincent
2019 Journal of Fluid Mechanics  
Moreover, while the eigenvalue associated with the slowest-decaying anti-symmetric eigenmode mode is found to be real, the eigenvalue associated with the slowest-decaying symmetric eigenmode mode is found  ...  In addition to elucidating aspects of the flow physics, the findings provide guidance for development of new unsteady Reynolds-averaged Navier–Stokes turbulence models, and constitute a new and accessible  ...  Supercomputing Centre for access to Piz Daint and Cambridge University for access to Wilkes.  ... 
doi:10.1017/jfm.2019.520 fatcat:3djclz2u45f5vcaxdy6ybmfpke

Quadruple symmetric real signals spectral even and odd decomposition

Venelin Jivkov, Philip Philipoff
2016 Gradjevinski materijali i konstrukcije  
ACKNOWLEDGEMENT The authors express their acknowledgment to "GPS Control" SA, "Aquapartner" Ltd and "Tokuda broker" Ltd for the financial support of this study.  ...  The row 4 of Table 1 shows symmetric component of the initial function and the row 6 of Table 1 shows anti symmetric component of the initial function.  ...  The complex Fourier F(jω) spectra of the anti symmetric real functions in the first and third quadrant are anti conjugated as well as.  ... 
doi:10.5937/grmk1603063j fatcat:l7c3fqukxrgkbh7puuxvr2xv2u
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