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Metric multidimensional scaling is one of the classical methods for embedding data into low-dimensional Euclidean space. It creates the low-dimensional embedding by approximately preserving the pairwise distances between the input points. However, current state-of-the-art approaches only scale to a few thousand data points. For larger data sets such as those occurring in single-cell RNA sequencing experiments, the running time becomes prohibitively large and thus alternative methods such as PCA are widely used instead. Here, we propose a neural network based approach for solving the metric multidimensional scaling problem that is orders of magnitude faster than previous state-of-the-art approaches, and hence scales to data sets with up to a few million cells. At the same time, it provides a non-linear mapping between high- and low-dimensional space that can place previously unseen cells in the same embedding.

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%.

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We present a parallel implementation of the randomized (1+ε) approximation algorithm for packing and covering linear programs presented by Koufogiannakis and Young (2007). Their approach builds on ideas of the sublinear time algorithm of Grigoriadis and Khachiyan's (Oper Res Lett 18(2):53-58, 1995) and Garg and Köne-mann's (SIAM J Comput 37(2):630-652, 2007) non-uniform-increment amortization scheme. With high probability it computes a feasible primal and dual solution whose costs are within a factor of 1 + ε of the optimal cost. In order to make their algorithm more parallelizable we also implemented a deterministic version of the algorithm, i.e. instead of updating a single random entry at each iteration we updated deterministically many entries at once. This slowed down a single iteration of the algorithm but allowed for larger step-sizes which lead to fewer iterations. We use NVIDIA's parallel computing architecture CUDA for the parallel environment. We report a speedup between one and two orders of magnitude over the times reported by Koufogiannakis and Young (2007).

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Abstract. This paper considers a linear relaxation of the cut-based integer programming formulation for the group Steiner tree problem (FGST). We combine the approach of Koufogiannakis and Young (2013) with the nearly-linear time approximation scheme for the minimum cut problem of Christiano et. al (2011) in order to develop a fully polynomial time approximation scheme for FGST problem. Our algorithm returns the solution to FGST where the objective function value is a maximum of 1+6ε times the optimal, for ε ∈ ⟨0, 1/6], inÕ(mk(m + n 4/3 ε −16/3 )/ε 2 ) time, where n, m and k are the numbers of vertices, edges and groups in the group Steiner tree instance, respectively. This algorithm has a better worst-case running time than algorithm by Garg and Khandekar (2002) where the number of groups is sufficiently large.