The choice of the optimal order of the neighborhood for separation a spatial point pattern into a cluster and noise component (by the example of analysis of location of antique settlements in the Kerch Peninsula)

When allocating spatial clusters of point objects, the problem of noise in the data often arises. This noise prevents clear boundaries of the clusters. One of the popular methods for separating the cluster and noise components of a point image is NNCR (Nearest Neighbor Clutter Removal), proposed in 1998 by Bayers and A.E. Raftery. The method is based on using the distance to the nearest neighbor in the calculations. The result of applying NNCR is highly dependent on the user selected neighborhood order. This paper describes a method for selecting the optimal neighborhood order for NNCR. This method focuses on the implementation of NNCR using the optional spatstat package of the programming language R. It is proposed to use the probability of the presence of a cluster component in the data as the main criterion for the optimal order of the neighborhood. With an optimal order of neighborhood, its value reaches its maximum value. In addition to this, it is proposed to analyze the probability of belonging to a cluster for all points assigned to the cluster component. For this, graphs of the dependence of the median and interquartile range of the probability of belonging on the order of the neighborhood are built. With an increase in the order of neighborhood, the median of the probability of belonging to the cluster component increases, tending to a value of 1.0. The interquartile range of the probability of belonging, on the contrary, decreases with an increase in the order of neighborhood, tending to a value of 0.0. The inflection in these graphs indicates the optimal order of the neighborhood. A user function is written in the programming language R, which makes it possible to automate the comparison of the NNCR results obtained in various orders of the neighborhood. It returns a matrix whose columns are the median of the probability of belonging, the interquartile range of the probability of belonging, and the probability of the presence of a cluster component in the data. The proposed method for choosing the optimal neighborhood order has been tested to analyze the point layer of ancient settlements of the Kerch Peninsula. For this data, the third order of neighborhood was optimal.

ALPHA-DECAY VERSUS ALPHA-CLUSTERING

The strength and shape of α-clusters in medium and heavy nuclei are analyzed by using α-decay experimental data. It turns out that the emitters above magic nuclei contain an important α-cluster component, not described within the standard mean field plus pairing approach.

t+t clustering in He-isotopes

t+t clustering in He isotopes is investigated by using two theoretical approaches. A role of the t+t cluster component in the ground state is examined with AMD triple-S, allowing the wider configuration space containing simultaneously the "t+t+valence neutrons" structure and "4 He +valence neutrons" structure. We understand the importance of the t + t component even for the ground state. Further, t + t resonances are investigated with RGM type approach. We obtained many t + t states as resonances near to t + t threshold.

Faint Surface Photometry of the Halo of M31

We have obtained counts of stars near the tip of the red giant branch of M31, and have used these counts to estimate the surface brightness of the halo of M31 down to a level of μV ∼ 30 mag arcsec–2 (R ∼ 20 kpc). The surface brightness along the minor axis of the M31 halo is well-represented by a single de Vaucouleurs law (0.2 ≃ R[kpc] ≃ 20). Alternatively, the outer halo of M31 can also be modelled by a power-law density distribution of the form ρ(R) ∞ R–5. This result suggests that the globular cluster component of the halo of M31 (for which ρ ∞R–3) is more extended than the stellar halo of this galaxy. At μv à 28 mag arcsec–2 (R à 10 kpc), the axial ratio of the halo of M31 is found to be c/a = 0.55 ± 0.05.