Smooth stochastic density field reconstruction

We introduce a method for generating a continuous, mass-conserving and high-order differentiable density field from a discrete point distribution such as particles or haloes from an N-body simulation or galaxies from a spectroscopic survey. The method consists on generating an ensemble of point realizations by perturbing the original point set following the geometric constraints imposed by the Delaunay tessellation in the vicinity of each point in the set. By computing the mean field of the ensemble we are able to significantly reduce artifacts arising from the Delaunay tessellation in poorly sampled regions while conserving the features in the point distribution. Our implementation is based on the Delaunay Tessellation Field Estimation (DTFE) method, however other tessellation techniques are possible. The method presented here shares the same advantages of the DTFE method such as self-adaptive scale, mass conservation and continuity, while being able to reconstruct even the faintest structures of the point distribution usually dominated by artifacts in Delaunay-based methods. Additionally, we also present preliminary results of an application of this method to image denoising and artefact removal, highlighting the broad applicability of the technique introduced here.

DTO-SMOTE: Delaunay Tessellation Oversampling for Imbalanced Data Sets

One of the significant challenges in machine learning is the classification of imbalanced data. In many situations, standard classifiers cannot learn how to distinguish minority class examples from the others. Since many real problems are unbalanced, this problem has become very relevant and deeply studied today. This paper presents a new preprocessing method based on Delaunay tessellation and the preprocessing algorithm SMOTE (Synthetic Minority Over-sampling Technique), which we call DTO-SMOTE (Delaunay Tessellation Oversampling SMOTE). DTO-SMOTE constructs a mesh of simplices (in this paper, we use tetrahedrons) for creating synthetic examples. We compare results with five preprocessing algorithms (GEOMETRIC-SMOTE, SVM-SMOTE, SMOTE-BORDERLINE-1, SMOTE-BORDERLINE-2, and SMOTE), eight classification algorithms, and 61 binary-class data sets. For some classifiers, DTO-SMOTE has higher performance than others in terms of Area Under the ROC curve (AUC), Geometric Mean (GEO), and Generalized Index of Balanced Accuracy (IBA).

Structure and Properties of High and Low Free Volume Polymers Studied by Molecular Dynamics Simulation

Using molecular dynamics, a comparative study was performed of two pairs of glassy polymers, low permeability polyetherimides (PEIs) and highly permeable Si-containing polytricyclononenes. All calculations were made with 32 independent models for each polymer. In both cases, the accessible free volume (AFV) increases with decreasing probe size. However, for a zero-size probe, the curves for both types of polymers cross the ordinate in the vicinity of 40%. The size distribution of free volume in PEI and highly permeable polymers differ significantly. In the former case, they are represented by relatively narrow peaks, with the maxima in the range of 0.5–1.0 Å for all the probes from H2 to Xe. In the case of highly permeable Si-containing polymers, much broader peaks are observed to extend up to 7–8 Å for all the gaseous probes. The obtained size distributions of free volume and accessible volume explain the differences in the selectivity of the studied polymers. The surface area of AFV is found for PEIs using Delaunay tessellation. Its analysis and the chemical nature of the groups that form the surface of free volume elements are presented and discussed.