Number Of Spurious States Research Articles

Solution to the Dirac equation using the finite difference method

In this study, single-particle energy was examined using the finite difference method by taking $$^{208}$$Pb as an example. If the first derivative term in the spherical Dirac equation is discretized using a three-point formula, a one-to-one correspondence occurs between the physical and spurious states. Although these energies are exactly the same, the wave functions of the spurious states exhibit a much faster staggering than those of the physical states. Such spurious states can be eliminated when applying the finite difference method by introducing an extra Wilson term into the Hamiltonian. Furthermore, it was also found that the number of spurious states can be reduced if we improve the accuracy of the numerical differential formula. The Dirac equation is then solved in a momentum space in which there is no differential operator, and we found that the spurious states can be completely avoided in the momentum space, even without an extra Wilson term.

Reducing Spurious States by Rotor Associative Memory

Hopfield Associative Memory (HAM) is a typical model of associative memories. Complex-valued Associative Memory is a complex-valued version of HAM. They store not only learning patterns but other undesired patterns, which are called spurious states. The reversed patterns in HAM and the rotated patterns in CAM are typical spurious states. We propose to reduce spurious states by using Rotor Associative Memory (RAM). The RAM does not store the rotated patterns except the reversed patterns. So the RAM removes most of spurious states from the CAM. By adding a dummy state, the RAM also can remove them from the HAM. To find spurious states, we construct a searching system similar to the chaotic CAM. By using the searching system, we investigate whether the RAM can reduce the number of spurious states.

On the unlearning procedure yielding a high-performance associative memory neural network

We consider a fully connected Hopfield-like neural network as a set of N independent perceptrons. We trained these perceptrons using the so-called inverse perceptron rule, obtaining a matrix of synaptic couplings, that make a number of spurious states unstable. We numerically determine the optimum number of spurious states, obtained by random shooting, that must be destabilized in order to obtain an improvement in performance. The unlearning procedure generated, is shown to be able to give a high-performance associative memory characterized by: (1) an enhancement in storaging capacity; (2) an enlargement in the size of attraction basins; (3) a reduction in the number of spurious attractors and (4) a reliable and fast retrieval.

Unlearning algorithm in associative memory

We incorporate into a synthesis procedure for a class of discrete-time neural networks an unlearning capability. The proposed technique increases storage capacity while maximizing the domain of attraction of each desired pattern to be stored. Making use of learning and forgetting capabilities, neural networks generated by the method advanced herein are capable of learning new patterns as well as forgetting learned patterns without the necessity of recomputing the entire interconnection weights and external inputs. The unlearning algorithm developed is then utilized off-line to equalize the basins of attraction for each desired pattern to be stored, and to minimize the number of spurious states. Specific examples are given to illustrate the strengths and weaknesses of the methodology advocated herein.

Eigenstructure bidirectional associative memory: an effective synthesis procedure

We propose a computationally efficient synthesis procedure for a class of bidirectional associative memories. Networks are described by a system of first-order ordinary difference equations which are defined on a closed hypercube of the state-space with solutions extended to the corner of the hypercube. The proposed algorithm possesses several advantages since it is possible: 1) to exert control over the number of spurious states; 2) to estimate the basins of attraction of the stable memories; and 3) under certain constraints, to effectively store a number of desired stable memories which by far exceed the order of the network. The applicability of the present results is demonstrated by means of a specific application in reconfigurable control of flexible structures.

CONVERGENCE TIME ON THE RS MODEL FOR NEURAL NETWORKS

Convergence times and the corresponding dispersions have been studied numerically as parameters to measure the efficiency of neural network models. These quantities are also supposed to be related to the number of spurious states for each configuration of stored patterns. In this work we measure these quantities for a recent multineuron interaction model presenting an enhanced performance compared to other traditional schemes.

Inelastic-resonance quasiprojection operators

An explicit form of quasiprojection operator Q is given for theAn explicit form of quasiprojection operator Q is given for the calculation of resonances in the domain of inelastic scattering of electrons from atoms and atomic ions. This operator allows the calculation of the resonant spectrum through the diagonalization of QHQ with as many inelastic states projected out as desired. The technique gives rise to a limited number of spurious states, but they can be unambiguously identified and thus eliminated. The elimination procedure is illustrated in the case of three-electron (i.e., heliumlike target) ions whereby we explicitly determine the number of spurious states that arise in inelastic scattering below the 3 /sup 3/S state of the target.

The number of spurious states in n-dimensional harmonic oscillator systems

The fraction of the spurious states has been estimated using the harmonic shell model: a) for low energies by combinatorial, and b) for high energies by thermodynamic methods. The levels of 40Ca, classified by J, have been treated as a special example.