Artificial Neural Network Pruning to Extract Knowledge

Artificial Neural Networks (NN) are widely used for solving complex problems from medical diagnostics to face recognition. Despite notable successes, the main disadvantages of NN are also well known: the risk of overfitting, lack of explainability (inability to extract algorithms from trained NN), and high consumption of computing resources. Determining the appropriate specific NN structure for each problem can help overcome these difficulties: Too poor NN cannot be successfully trained, but too rich NN gives unexplainable results and may have a high chance of overfitting. Reducing precision of NN parameters simplifies the implementation of these NN, saves computing resources, and makes the NN skills more transparent. This paper lists the basic NN simplification problems and controlled pruning procedures to solve these problems. All the described pruning procedures can be implemented in one framework. The developed procedures, in particular, find the optimal structure of NN for each task, measure the influence of each input signal and NN parameter, and provide a detailed verbal description of the algorithms and skills of NN. The described methods are illustrated by a simple example: the generation of explicit algorithms for predicting the results of the US presidential election.Comment: IJCNN 202

CSD: Discriminance with Conic Section for Improving Reverse k Nearest Neighbors Queries

The reverse $k$ nearest neighbor (R$k$NN) query finds all points that have the query point as one of their $k$ nearest neighbors ($k$NN), where the $k$NN query finds the $k$ closest points to its query point. Based on the characteristics of conic section, we propose a discriminance, named CSD (Conic Section Discriminance), to determine points whether belong to the R$k$NN set without issuing any queries with non-constant computational complexity. By using CSD, we also implement an efficient R$k$NN algorithm CSD-R$k$NN with a computational complexity at $O(k^{1.5}\cdot log\,k)$. The comparative experiments are conducted between CSD-R$k$NN and other two state-of-the-art RkNN algorithms, SLICE and VR-R$k$NN. The experimental results indicate that the efficiency of CSD-R$k$NN is significantly higher than its competitors

Leibniz algebras associated with representations of filiform Lie algebras

In this paper we investigate Leibniz algebras whose quotient Lie algebra is a naturally graded filiform Lie algebra nn,1. We introduce a Fock module for the algebra nn,1 and provide classification of Leibniz algebras L whose corresponding Lie algebra L/I is the algebra nn,1 with condition that the ideal I is a Fock nn,1-module, where I is the ideal generated by squares of elements from L. We also consider Leibniz algebras with corresponding Lie algebra nn,1 and such that the action I × nn,1 ! I gives rise to a minimal faithful representation of nn,1. The classification up to isomorphism of such Leibniz algebras is given for the case of n = 4.Ministerio de Economía y Competitividad MTM2013-43687-

Data Assimilation by Artificial Neural Networks for an Atmospheric General Circulation Model: Conventional Observation

This paper presents an approach for employing artificial neural networks (NN) to emulate an ensemble Kalman filter (EnKF) as a method of data assimilation. The assimilation methods are tested in the Simplified Parameterizations PrimitivE-Equation Dynamics (SPEEDY) model, an atmospheric general circulation model (AGCM), using synthetic observational data simulating localization of balloon soundings. For the data assimilation scheme, the supervised NN, the multilayer perceptrons (MLP-NN), is applied. The MLP-NN are able to emulate the analysis from the local ensemble transform Kalman filter (LETKF). After the training process, the method using the MLP-NN is seen as a function of data assimilation. The NN were trained with data from first three months of 1982, 1983, and 1984. A hind-casting experiment for the 1985 data assimilation cycle using MLP-NN were performed with synthetic observations for January 1985. The numerical results demonstrate the effectiveness of the NN technique for atmospheric data assimilation. The results of the NN analyses are very close to the results from the LETKF analyses, the differences of the monthly average of absolute temperature analyses is of order 0.02. The simulations show that the major advantage of using the MLP-NN is better computational performance, since the analyses have similar quality. The CPU-time cycle assimilation with MLP-NN is 90 times faster than cycle assimilation with LETKF for the numerical experiment.Comment: 17 pages, 16 figures, monthly weather revie

On the discrepancies in the low energy neutron-deuteron breakup

In view of recent neutron-deuteron (nd) breakup data for neutron-neutron (nn) and neutron-proton (np) quasi-free-scattering (QFS) arrangements and the large discrepancy found between theoretical predictions and measured nn QFS cross sections, we analyze the sensitivity of the QFS cross sections to different partial wave components of the nucleon-nucleon (NN) interaction. We found that the QFS cross section is strongly dominated by the 1S0 and 3S1-3D1 contributions. Because the standard three-nucleon force (3NF) only weakly influence the QFS region, we conjecture, that it must be the nn 1S0 force component which is responsible for the discrepancy in the nn QFS peak. A stronger 1S0 nn force is required to bring theory and data into agreement. Such an increased strength of the nn interaction will, however, not help to explain the nd breakup symmetric-space-star (SST) discrepancy. Further experimental cross-checkings are required.Comment: 17 pages, 10 figure

A microscopic NN to NN*(1440) potential

By means of a NN to NN*(1440) transition potential derived in a parameter-free way from a quark-model based NN potential, we determine simultaneously the $\pi NN^*(1440)$ and $\sigma NN^*(1440)$ coupling constants. We also present a study of the target Roper excitation diagram contributing to the $p(d,d')$ reaction.Comment: Talk presented at the Fourth International Conference on Perspectives in Hadronic Physics (ICTP, Trieste, Italy, May 2003). To appear in EPJA. 6 pages, 9 figures, needs svepj.clo and svjour.cl

The Ground Ring of N=2 Minimal String Theory

We study the \NN=2 string theory or the \NN=4 topological string on the deformed CHS background. That is, we consider the \NN=2 minimal model coupled to the \NN=2 Liouville theory. This model describes holographically the topological sector of Little String Theory. We use degenerate vectors of the respective \NN=2 Verma modules to find the set of BRST cohomologies at ghost number zero--the ground ring, and exhibit its structure. Physical operators at ghost number one constitute a module of the ground ring, so the latter can be used to constrain the S-matrix of the theory. We also comment on the inequivalence of BRST cohomologies of the \NN=2 string theory in different pictures.Comment: 25 pages, latex, small correction

Muon capture on deuteron and the neutron-neutron scattering length

We study the capture rate in the doublet hyperfine initial state for the muon capture reaction \mu^- + \,^2{\rm H} \rightarrow \nu_\mu + n + n ($\Gamma^D$) and the total capture rate for the reaction \mu^- + \,^3{\rm He} \rightarrow \nu_\mu + \,^3{\rm H} ($\Gamma_0$). We investigate whether $\Gamma^D$ and $\Gamma_0$ could be sensitive to the $nn$ $S$-wave scattering length ($a_{nn}$). To this aim, we consider nuclear potentials and weak currents derived within $\chi$EFT. We employ the N3LO chiral potential with cutoff $\Lambda$=500 MeV, but the low-energy constant (LEC) determining $a_{nn}$ is varied so as to obtain $a_{nn}$=-18.95 (the present empirical value), -16.0, -22.0, and +18.22 fm. The last value leads to a $nn$ bound state with a binding energy of 139 keV. The LECs $c_D$ and $c_E$, present in the three-nucleon potential and axial-vector current, are fitted to reproduce the $A=3$ binding energies and the triton Gamow-Teller matrix element. The capture rate $\Gamma^D$ is found to be 399(3) s$^{-1}$ for $a_{nn}$=-18.95 and -16.0 fm; and 400(3) s$^{-1}$ for $a_{nn}$=-22.0 fm. For $a_{nn}$=+18.22 fm, we obtain 275(3) s$^{-1}$ (135(3) s$^{-1}$), when the final $nn$ system is unbound (bound). The rate $\Gamma_0$ is found to be 1494(15), 1491(16), 1488(18), and 1475(16) s$^{-1}$ for $a_{nn}$=-18.95, -16.0, -22.0, and +18.22 fm, respectively. The theoretical uncertainties are due to the fitting procedure and radiative corrections. Our results seem to exclude the possibility of constraining a negative $a_{nn}$ with an uncertainty of less than $\sim \pm$ 3 fm through an accurate determination of the muon capture rates, but the uncertainty on the present empirical value will not complicate the interpretation of the (forth-coming) experimental results for $\Gamma^D$. Finally, a comparison with the already available experimental data discourages the possibility of a bound $nn$ state.Comment: 5 pages, 2 figures; revisited version accepted for publication on Phys. Rev.