Do algebraic operations on neural networks. We seek here to implement
  in R, operations on neural networks and their resulting approximations. Our operations derive
  their descriptions mainly from
  Rafi S., Padgett, J.L., and Nakarmi, U. (2024), "Towards an Algebraic Framework For Approximating Functions Using Neural Network Polynomials", <doi:10.48550/arXiv.2402.01058>, 
  Grohs P., Hornung, F., Jentzen, A. et al. (2023), "Space-time error estimates for deep neural network approximations for differential equations", <doi:10.1007/s10444-022-09970-2>,
  Jentzen A., Kuckuck B., von Wurstemberger, P. (2023), "Mathematical Introduction to Deep Learning Methods, Implementations, and Theory" <doi:10.48550/arXiv.2310.20360>.
  Our implementation is meant mainly as a pedagogical tool, and proof of concept. Faster implementations with 
  deeper vectorizations may be made in future versions.

Nonlinear nonparametric statistics using partial moments.  Partial moments are the elements of variance and asymptotically approximate the area of f(x).  These robust statistics provide the basis for nonlinear analysis while retaining linear equivalences.  NNS offers: Numerical integration, Numerical differentiation, Clustering, Correlation, Dependence, Causal analysis, ANOVA, Regression, Classification, Seasonality, Autoregressive modeling, Normalization, Stochastic dominance and Advanced Monte Carlo sampling.  All routines based on: Viole, F. and Nawrocki, D. (2013), Nonlinear Nonparametric Statistics: Using Partial Moments (ISBN: 1490523995).

Contains the functions for testing the spatial patterns (of segregation, spatial symmetry, 
      association, disease clustering, species correspondence, and reflexivity) based on nearest neighbor relations, 
      especially using contingency tables such as 
      nearest neighbor contingency tables (Ceyhan (2010) <doi:10.1007/s10651-008-0104-x> and 
      Ceyhan (2017) <doi:10.1016/j.jkss.2016.10.002> and references therein),
      nearest neighbor symmetry contingency tables (Ceyhan (2014) <doi:10.1155/2014/698296>),
      species correspondence contingency tables and reflexivity contingency tables (Ceyhan (2018) 
      <doi:10.2436/20.8080.02.72> for two (or higher) dimensional data. 
      The package also contains functions for generating patterns of segregation, association,
      uniformity in a multi-class setting (Ceyhan (2014) <doi:10.1007/s00477-013-0824-9>), 
      and various non-random labeling patterns for disease clustering 
      in two dimensional cases (Ceyhan (2014)
      <doi:10.1002/sim.6053>), and for visualization of all these patterns 
      for the two dimensional data.
      The tests are usually (asymptotic) normal z-tests or chi-square tests.