Analysis Of Two-dimensional Patterns Research Articles

A statistical analysis of two-dimensional patterns and its application to astrometry

Here we develop a general statistical procedure for the analysis of finite two-dimensional (2D) patterns inspired by the analysis of heavy-ion data. The method is used in the study of publicly available data obtained by the Gaia-ESA mission. We prove that the procedure can be sensitive to the limits of accuracy of measurement, and can also clearly identify the real physical effects on the large background of random distributions. As an example, the method confirms the presence of binary and ternary star systems in the studied data. At the same time, the possibility of the statistical detection of the gravitational microlensing effect is discussed.

Evaluation of methods for one-dimensional spatial analysis of two-dimensional patterns in mouse chimaeras.

The relative extent of cell mixing in tissues of mouse chimaeras or mosaics can be studied by comparing the distributions of the two cell populations in the tissues. However, the mean patch size is misleading because it is affected by both the extent of cell mixing and the relative contributions of the two cell populations. Previous work suggested that effects attributable to differences in tissue composition among chimaeras can be factored out either by correcting the mean patch size or by using the median patch size for the minority cell population and restricting the analysis to grossly unbalanced chimaeras. In the present study, computer simulations of two-dimensional mosaic arrays of black and white squares (representing cells) were used to simulate chimaeric tissues. Random arrays simulated tissues with extensive cell mixing, arrays of cell clumps (representing coherent clones) simulated less mixed tissues, and striped arrays simulated tissues with elongated but fragmented descendent clones. The computer simulations predicted that (i) the median patch length (minority cell population) and the corrected mean patch length would both distinguish between random and clumped patterns and (ii) differences in the variation of the composition of two perpendicular series of one-dimensional transects would distinguished between stripes and randomly orientated patches. Both predictions were confirmed by analysis of histological sections of the retinal pigment epithelium from fetal and adult mouse chimaeras. This study demonstrates that two types of non-random two-dimensional variegated patterns (clumps and stripes) can be identified in chimaeras without two-dimensional reconstruction of serial sections.

Two-dimensional pattern analysis on dominant species and community in subalpine meadow of Luya Mountain, Shanxi Province, China

The spatial pattern analysis of population and community is important to understand community structure and has become one key topic in modern plant ecology. There are many techniques for analyzing one-dimensional pattern in ecological literature. Two-dimensional pattern analysis is better than one-dimensional analysis in the study on community spatial characteristics and structure. However, it is hard to analyze these two-dimensional patterns due to poor effective methodology. The two-dimensional sampling using two transects that meet at right angles was applied to get quadrat data in this work. And then the data from the two transects were analyzed separately by one-dimensional pattern analysis method, two-term local quadrat variance. The length, width, and area of patches at different scales of pattern for populations were obtained from the analysis. For community pattern, detrended correspondence analysis (DCA) was employed to summarize the species information firstly, and then the first DCA axis scores were analyzed to check its pattern. The application of this method to the pattern analysis on dominant populations and community for subalpine meadow (Comm. Polygonum viviparum + Carex rigescens + Kobresia bellardii) in the Luya mountains showed that it could release the characteristics of spatial pattern clearly and was a very effective technique. The method is easy to use and saves time with obvious advantages, compared with the two-dimensional pattern analysis methods presented in the literatures. In the study meadow, the patterns of the main dominant species, Polygonum viviparum, Carex rigescens, and Kobresia bellardii, were apparent and comparatively regular in shape with large areas of patches at the same scale compared with other species such as Festuca sp. and Thalictrum petaloideum. There were two or three scales of patterns for each plant population studied. This was related to population features, the interaction with environmental factors, and their dominant position in the community. The two scales of patterns for the meadow community were clear. The pattern of community was closely correlated with that of the main dominant species. The patches of dominant species were inter-distributed and overlapped, and formed the community pattern together. This is beneficial for utilization of resources, and keeping the community stable.

Rotation- and scale-invariant texture features based on spectral moment invariants

Moment invariants previously developed for the analysis of two-dimensional patterns and objects regardless of orientation, scale, and position are extended to the Fourier transform domain to quantify signatures of textures in the power spectrum of images. The moment invariants of the power spectrum, which we call spectral moment invariants (SMIs), systematically extract rotation- and scale-invariant texture features by complex spectral moments instead of by performing ad hoc measurements of the shape of the two-dimensional power spectrum as do most of the existing Fourier transform domain methods. To our knowledge, the method of using SMIs to quantify texture features is the first to extract invariant texture information directly from the Fourier spectrum. The discriminative capability of SMIs in recognizing rotation- and scale-independent texture features is demonstrated by texture classification experiments. The results indicate that algorithms using SMIs can achieve performances comparable with, or better than, those algorithms using the spatial or wavelet transform domain texture features.

A methylated human 9-kb repetitive sequence on acrocentric chromosomes is homologous to a subtelomeric repeat in chimpanzees.

We have implemented an approach for the detection of DNA alterations in cancer by means of computerized analysis of end-labeled genomic fragments, separated in two dimensions. Analysis of two-dimensional patterns of neuroblastoma tumors, prepared by first digesting DNA with the methylation-sensitive restriction enzyme Not I, yielded a multicopy fragment which was detected in some tumor patterns but not in normal controls. Cloning and sequencing of the fragment, isolated from two-dimensional gels, yielded a sequence with a strong homology to a subtelomeric sequence in chimpanzees and which was previously reported to be undetectable in humans. Fluorescence in situ hybridization indicated the occurrence of this sequence in normal tissue, for the most part in the satellite regions of acrocentric chromosomes. A product containing this sequence was obtained by telomere-anchored PCR using as a primer an oligonucleotide sequence from the cloned fragment. Our data suggest demethylation of cytosines at the cloned Not I site and in neighboring DNA in some tumors, compared with normal tissue, and suggest a greater similarity between human and chimpanzee subtelomeric sequences than was previously reported.

Two-dimensional pattern analysis and classification using a complex orthogonal estimation algorithm

An orthogonal estimation algorithm is derived for the estimation of parameters associated with the complex autoregressive boundary model of two-dimensional shapes. It is shown that the coefficients of the orthogonal model and the original system parameters are invariant to rotation around the origin, to the choice of starting point in tracing the boundary and to scale and translation. The error reduction ratios derived from the estimation algorithm can be used to detect which terms should be included in the system model, and classification based on the orthogonal parameters is shown to be less susceptible to incorrect model order specification. Classification based on orthogonal data sets is also derived, and it is demonstrated that this approach can avoid some problems associated with classification based on the model parameters alone.

Two-dimensional nonlinear-interferometer pattern analysis and decay of spirals

Akhmanov et al. [ JETP Lett.47, 707 ( 1988)] observed fascinating spatial patterns in their nonlinear-interferometer experiments. We report some results of our two-dimensional pattern analysis that showthat the spatial Fourier eigenmodes naturally give rise to filaments and other patterns of fully two-dimensional complexities and that spirals are likely to decay into petals as a result of the radial diffusion.

Coordinate accumulation of troponin subunits in chicken breast muscle

The accumulation of troponin subunits in developing chicken breast muscle was determined by two-dimensional gel electrophoresis and an image analyzing system. Many troponin T isoforms, including those hidden behind creatine kinase, were detected on the two-dimensional pattern by the addition of 6 M urea in the second dimension. These troponin T isoforms were classified into four types by developmental order, isoelectric point, and molecular weight: leg-muscle type (L), neonatal breast-muscle type (B N), young chicken breast-muscle type (B C), and adult breast-muscle type (B A). The L-, B N-, and B C-type troponin Ts were transiently expressed at specific developmental stages. Quantitative analysis of two-dimensional patterns of troponin subunits including troponin I and troponin C showed moderate coordination in accumulation among the three subunits throughout postnatal development, when the total amount of all isoforms of troponin T was taken into account.