A Comparison of Structure, Stability of Neutral and Cationic Vanadium-doped Germanium Clusters GenV0/+ (n = 2 - 8) by using Density Function Theorym clusters GenV0/+ (n = 2 - 8) by using density function theory

The geometries, stabilities and electronic properties of vanadium-doped germanium clusters GenV0/+ (n=2-8) were systematically investigated by using density functional theory (DFT) at the PBE level and the 6-311+G(d) basis set. The results show that the geometries of lowest-energy structures of the cationic clusters are only significant different from those of the neutral at n = 6 or 7. The ground state of neutral clusters is a doublet, except Ge2V which is a quartet while that of cationic clusters is a triplet, except Ge8V+, which is a singlet. The average binding energy values generally increase with increasing cluster size. The results from average binding energies showed that it is more stable for the cationic than neutral clusters at the same size. Furthermore, the calculated values of fragmentation energy, second-order energy difference, HOMO-LUMO gap and adiabatic ionization potential suggest that the neutral clusters possess higher stability when n = 2, 5, 8 and the cations are more stable when n = 2, 3, 5 and 6.

Probability Density Function Analysis Based on Logistic Regression Model

The data fitting level in probability density function analysis has great influence on the analysis results, so it is of great significance to improve the data fitting level. Therefore, a probability density function analysis method based on logistic regression model is proposed. The logistic regression model with kernel function is established, and the optimal window width and mean square integral error are selected to limit the solution accuracy of probability density function. Using the real probability density function, the probability density function with the smallest error is obtained. The estimated probability density function is analyzed from two aspects of consistency and convergence speed. The experimental results show that compared with the traditional probability density function analysis method, the probability density function analysis method based on logistics regression model has a higher fitting level, which is more suitable for practical research projects.

Manifold-adaptive dimension estimation revisited

Data dimensionality informs us about data complexity and sets limit on the structure of successful signal processing pipelines. In this work we revisit and improve the manifold adaptive Farahmand-Szepesvári-Audibert (FSA) dimension estimator, making it one of the best nearest neighbor-based dimension estimators available. We compute the probability density function of local FSA estimates, if the local manifold density is uniform. Based on the probability density function, we propose to use the median of local estimates as a basic global measure of intrinsic dimensionality, and we demonstrate the advantages of this asymptotically unbiased estimator over the previously proposed statistics: the mode and the mean. Additionally, from the probability density function, we derive the maximum likelihood formula for global intrinsic dimensionality, if i.i.d. holds. We tackle edge and finite-sample effects with an exponential correction formula, calibrated on hypercube datasets. We compare the performance of the corrected median-FSA estimator with kNN estimators: maximum likelihood (Levina-Bickel), the 2NN and two implementations of DANCo (R and MATLAB). We show that corrected median-FSA estimator beats the maximum likelihood estimator and it is on equal footing with DANCo for standard synthetic benchmarks according to mean percentage error and error rate metrics. With the median-FSA algorithm, we reveal diverse changes in the neural dynamics while resting state and during epileptic seizures. We identify brain areas with lower-dimensional dynamics that are possible causal sources and candidates for being seizure onset zones.

P-block tin single atom catalyst for improved electrochemistry in lithium-sulfur battery: a theoretical and experimental study

Main group metals are routinely considered as catalytically inactive hence never employed for optimizing the lithium-sulfur electrochemistry. Herein, density function theory calculations reveal that atomically dispersed tin on nitrogen doped...