Analysis of remote sensing images by methods of convolutional neural networks and marked random point fields

The methodology of remote sensing image analysis for detection of dependences in the process of development of biological species is proposed. Classification methods based on convolutional networks are applied to a set of fragments of the input image. In order to increase the accuracy of classification by increasing the training and test samples, an original method of data augmentation is proposed. For a series of images of one part of the landscape, the fragments of images are classified by their numbers, which coincide with the numbers of the previously classified image of the training and test samples which are created manually. This approach has improved the accuracy of classification compared to known methods of data augmentation. Numerous studies of various convolutional neural networks have shown the similarity of the classification results of the remote sensing images fragments with increasing learning time with the complication of the network structure. A set of image fragment centers of a particular class is considered as random point configuration, the class labels are used as a mark for every point. Marked point field is considered as consisting of several sub-point fields in each of which all points have the same qualitative marks. We perform the analysis of the bivariate point pattern to reveal relationships between points of different types, using the characteristics of marked random point fields. Such relationships can characterize dependences and relative degrees of dominance. A series of remote sensing images are studied to identify the relationships between point configurations that describe different classes to monitor their development.

Diameters of Cocircuit Graphs of Oriented Matroids: An Update

Oriented matroids are combinatorial structures that generalize point configurations, vector configurations, hyperplane arrangements, polyhedra, linear programs, and directed graphs. Oriented matroids have played a key role in combinatorics, computational geometry, and optimization. This paper surveys prior work and presents an update on the search for bounds on the diameter of the cocircuit graph of an oriented matroid. The motivation for our investigations is the complexity of the simplex method and the criss-cross method. We review the diameter problem and show the diameter bounds of general oriented matroids reduce to those of uniform oriented matroids. We give the latest exact bounds for oriented matroids of low rank and low corank, and for all oriented matroids with up to nine elements (this part required a large computer-based proof). For arbitrary oriented matroids, we present an improvement to a quadratic bound of Finschi. Our discussion highlights an old conjecture that states a linear bound for the diameter is possible. On the positive side, we show the conjecture is true for oriented matroids of low rank and low corank, and, verified with computers, for all oriented matroids with up to nine elements. On the negative side, our computer search showed two natural strengthenings of the main conjecture are false.

New Method for Calculation of Radiation Defect Dipole Tensor and Its Application to Di-Interstitials in Copper

The effect of external and internal elastic strain fields on the anisotropic diffusion of radiation defects (RDs) can be taken into account if one knows the dipole tensor of saddle-point configurations of the diffusing RDs. It is usually calculated by molecular statics, since the insufficient accuracy of the available experimental techniques makes determining it experimentally difficult. However, for an RD with multiple crystallographically non-equivalent metastable and saddle-point configurations (as in the case of di-interstitials), the problem becomes practically unsolvable due to its complexity. In this paper, we used a different approach to solving this problem. The molecular dynamics (MD) method was used to calculate the strain dependences of the RD diffusion tensor for various types of strain states. These dependences were used to determine the dipole tensor of the effective RD saddle-point configuration, which takes into account the contributions of all real saddle-point configurations. The proposed approach was used for studying the diffusion characteristics of RDs, such as di-interstitials in FCC copper (used in plasma-facing components of fusion reactors under development). The effect of the external elastic field on the MD-calculated normalized diffusion tensor (ratio of the diffusion tensor to a third of its trace) of di-interstitials was fully consistent with analytical predictions based on the kinetic theory, the parameters of which were the components of the dipole tensors, including the range of non-linear dependence of the diffusion tensor on strains. The results obtained allowed for one to simulate the anisotropic diffusion of di-interstitials in external and internal elastic fields, and to take into account the contribution of di-interstitials to the radiation deformation of crystals. This contribution can be significant, as MD data on the primary radiation damage in copper shows that ~20% of self-interstitial atoms produced by cascades of atomic collisions are combined into di-interstitials.

Asymptotic Properties of Discrete Minimal s,logt-Energy Constants and Configurations

We investigated the energy of N points on an infinite compact metric space (A,d) of a diameter less than 1 that interact through the potential (1/ds)(log1/d)t, where s,t≥0 and d is the metric distance. With Elogts(A,N) denoting the minimal energy for such N-point configurations, we studied certain continuity and differentiability properties of Elogts(A,N) in the variable s. Then, we showed that in the limits, as s→∞ and as s→s0>0,N-point configurations that minimize the s,logt-energy tends to an N-point best-packing configuration and an N-point configuration that minimizes the s0,logt-energy, respectively. Furthermore, we considered when A are circles in the Euclidean space R2. In particular, we proved the minimality of N distinct equally spaced points on circles in R2 for some certain s and t. The study on circles shows a possibility for the utilization of N points generated through such new potential to uniformly discretize on objects with very high symmetry.