Predikcija položajne greške tačaka trigonometrijske mreže prvog reda

During the establishment of first order trigonometric network in Serbia, the influence of Earth’s gravitational field on measurements was not considered. As a consequence, all points have position errors. With additional measurements and calculations, these errors were later determined for X and Y coordinates of each point. This paper uses geostatistical methods (regression kriging) to estimate error prediction model for any location in Serbia.Zbornik radova Građevinskog fakultet

Beyond Diophantine Wannier diagrams: Gap labelling for Bloch-Landau Hamiltonians

It is well known that, given a $2d$ purely magnetic Landau Hamiltonian with a constant magnetic field $b$ which generates a magnetic flux $\varphi$ per unit area, then any spectral island $\sigma_b$ consisting of $M$ infinitely degenerate Landau levels carries an integrated density of states $\mathcal{I}_b=M \varphi$. Wannier later discovered a similar Diophantine relation expressing the integrated density of states of a gapped group of bands of the Hofstadter Hamiltonian as a linear function of the magnetic field flux with integer slope. We extend this result to a gap labelling theorem for any $2d$ Bloch-Landau operator $H_b$ which also has a bounded $\mathbb{Z}^2$-periodic electric potential. Assume that $H_b$ has a spectral island $\sigma_b$ which remains isolated from the rest of the spectrum as long as $\varphi$ lies in a compact interval $[\varphi_1,\varphi_2]$. Then $\mathcal{I}_b=c_0+c_1\varphi$ on such intervals, where the constant $c_0\in \mathbb{Q}$ while $c_1\in \mathbb{Z}$. The integer $c_1$ is the Chern character of the spectral projection onto the spectral island $\sigma_b$. This result also implies that the Fermi projection on $\sigma_b$, albeit continuous in $b$ in the strong topology, is nowhere continuous in the norm topology if either $c_1\ne0$ or $c_1=0$ and $\varphi$ is rational. Our proofs, otherwise elementary, do not use non-commutative geometry but are based on gauge covariant magnetic perturbation theory which we briefly review for the sake of the reader. Moreover, our method allows us to extend the analysis to certain non-covariant systems having slowly varying magnetic fields.Comment: 17 pages, no figure

A spatiotemporal ensemble machine learning framework for generating land use/land cover time-series maps for Europe (2000–2019) based on LUCAS, CORINE and GLAD Landsat

A spatiotemporal machine learning framework for automated prediction and analysis of long-term Land Use/Land Cover dynamics is presented. The framework includes: (1) harmonization and preprocessing of spatial and spatiotemporal input datasets (GLAD Landsat, NPP/VIIRS) including five million harmonized LUCAS and CORINE Land Cover-derived training samples, (2) model building based on spatial k-fold cross-validation and hyper-parameter optimization, (3) prediction of the most probable class, class probabilities and model variance of predicted probabilities per pixel, (4) LULC change analysis on time-series of produced maps. The spatiotemporal ensemble model consists of a random forest, gradient boosted tree classifier, and an artificial neural network, with a logistic regressor as meta-learner. The results show that the most important variables for mapping LULC in Europe are: seasonal aggregates of Landsat green and near-infrared bands, multiple Landsat-derived spectral indices, long-term surface water probability, and elevation. Spatial cross-validation of the model indicates consistent performance across multiple years with overall accuracy (a weighted F1-score) of 0.49, 0.63, and 0.83 when predicting 43 (level-3), 14 (level-2), and five classes (level-1). Additional experiments show that spatiotemporal models generalize better to unknown years, outperforming single-year models on known-year classification by 2.7% and unknown-year classification by 3.5%. Results of the accuracy assessment using 48,365 independent test samples shows 87% match with the validation points. Results of time-series analysis (time-series of LULC probabilities and NDVI images) suggest forest loss in large parts of Sweden, the Alps, and Scotland. Positive and negative trends in NDVI in general match the land degradation and land restoration classes, with “urbanization” showing the most negative NDVI trend. An advantage of using spatiotemporal ML is that the fitted model can be used to predict LULC in years that were not included in its training dataset, allowing generalization to past and future periods, e.g. to predict LULC for years prior to 2000 and beyond 2020. The generated LULC time-series data stack (ODSE-LULC), including the training points, is publicly available via the ODSE Viewer. Functions used to prepare data and run modeling are available via the eumap library for Python

Transfer learning approach based on satellite image time series for the crop classification problem

This paper presents a transfer learning approach to the crop classification problem based on time series of images from the Sentinel-2 dataset labeled for two regions: Brittany (France) and Vojvodina (Serbia). During preprocessing, cloudy images are removed from the input data, the time series are interpolated over the time dimension, and additional remote sensing indices are calculated. We chose TransformerEncoder as the base model for knowledge transfer from source to target domain with French and Serbian data, respectively. Even more, the accuracy of the base model with the preprocessing step is improved by 2% when trained and evaluated on the French dataset. The transfer learning approach with fine-tuning of the pre-trained weights on the French dataset outperformed all other methods in terms of overall accuracy 0.94 and mean class recall 0.907 on the Serbian dataset. Our partially fine-tuned model improved recall of crop types that were poorly classified by the base model. In the case of sugar beet, class recall is improved by 85.71%