Nearest neighbor spacing distribution

Figure 1. Nearest-neighbor spacing distributions of eigenvalues for a circle (left) and the Bunimovich stadium (right). Taken from Ref. (McDonald and Kaufman, 1979).

Figure 4 Nearest-neighbor spacing distribution P(s) for the free Dirac operator on a 53 x 47 x 43 x 41 lattice compared with a Poisson distribution, e-s.

Figure 5. Nearest-neighbor spacing distribution P(s) for U(l) gauge theory on an 83 x 6 lattice in the confined phase (left) and in the Coulomb phase (right). The theoretical curves are the chUE result, Eq. (14), and the Poisson distribution, -Pp(s) = exp(-s).

Figure 8. Histograms of the nearest-neighbor spacing distribution for the nucleon (left plots) and the delta (right plots). The data is for Goldstone-boson exchange and for one-gluon exchange compared to a pure linear confinement potential of the same strength. Curves represent the Poisson and the GOE-Wigner distributions.

The effect can be applied, for example, to estimate a bond length or atomic spacing, to observe valence electron spin distribution around a specific atom and to derive information of the nearest neighbor atom distribution in a disordered system such as amorphous, under an expansion of the theory. 

One of the main characteristics of the statistical properies of the spectra is the level spacing distribution (Eckhardt, 1988 Gutzwiller, 1990) function. In this work we calculate the nearest-neighbor levelspacing distribution (Eckhardt, 1988 Gutzwiller, 1990). 

A similarity-related approach is k-nearest neighbor (KNN) analysis, based on the premise that similar compounds have similar properties. Compounds are distributed in multidimensional space according to their values of a number of selected properties the toxicity of a compound of interest is then taken as the mean of the toxicides of a number (k) of nearest neighbors. Cronin et al. [65] used KNN to model the toxicity of 91 heterogeneous organic chemicals to the alga Chlorella vulgaris, but found it no better than MLR. 

In random bond percolation, which is most widely used to describe gelation, monomers, occupy sites of a periodic lattice. The network formation is simulated by the formation of bonds (with a certain probability, p) between nearest neighbors of lattice sites, Fig. 7b. Since these bonds are randomly placed between the lattice nodes, intramolecular reactions are allowed. Other types of percolation are, for example, random site percolation (sites on a regular lattice are randomly occupied with a probability p) or random random percolation (also known as continuum percolation the sites do not form a periodic lattice but are distributed randomly throughout the percolation space). While the... 

Figure 1. The nearest neighbor level spacing distribution for various parameter of temperature a) zero temperature case b) (3 = 0.1 c) (3 = 0.01 ...

Figure 6. Histograms of the nearest-neighbor mass spacing distribution for hadron states with same quantum numbers. Curves represent the Poisson (dashed) and Wigner (solid) distributions. Taken from Ref. (Pascalutsa, 2003).

Abstract. Quantum chaos at finite-temperature is studied using a simple paradigm, two-dimensional coupled nonlinear oscillator. As an approach for the treatment of the finite-temperature a real-time finite-temperature field theory, thermofield dynamics, is used. It is found that increasing the temperature leads to a smooth transition from Poissonian to Gaussian distribution in nearest neighbor level spacing distribution. 

One disadvantage of the KNN method is that it does not provide an assessment of confidence in the class assignment result, hi addition, it does not sufficiently handle cases where an unknown sample belongs to none of the classes in the calibration data, or to more than one class. A practical disadvantage is that the user must input the number of nearest neighbors (K) to use in the classifier. In practice, the optimal value of K is influenced by the total number of calibration samples (N), the distribution of calibration samples between classes, and the degree of natural separation of the classes in the sample space. 

Figure 12. The error threshold of replication and mutation in phenotype space. The genotypic error threshold approaches zero in the case of selective neutrality. Despite changing genotypes a phenotype may be conserved in evolution whenever it has higher fitness than the other phenotypes in the population. The concept of error threshold can easily be extended to competition between phenotypes. The distribution of phenotypes is stationary provided the error rate does not exceed the maximum value pmax which is a function of the mean fraction of nearest neighbors, X, and the superiority of the master phenotype, a. The illustration shows the position of the phenotypic error threshold in the X, p plane. Selective neutrality allows more errors to be tolerated and pmax increases accordingly with increasing X. If X approaches the inverse superiority, X — a-1, the tolerated error may grow to pmax = 1, and this means the phenotype will never be lost, no matter how many errors are made in replication.

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