Metal Chalcogenide Clusters with Closed Electronic Shells and the Electronic Properties of Alkalis and Halogens

Clusters with filled electronic shells and a large gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are generally energetically and chemically stable. Enabling clusters to become electron donors with low ionization energies or electron acceptors with high electron affinities usually requires changing the valence electron count. Here we demonstrate that a metal cluster may be transformed from an electron donor to an acceptor by exchanging ligands while the neutral form of the clusters has closed electronic shells. Our studies on Co6Te8(PEt3),(CO) (m + n = 6) clusters show that Co6Te8(PEt3)(6) has a closed electronic shell and a low ionization energy of 4.74 eV, and the successive replacement of PEt3 by CO ligands ends with Co6Te8(CO)(6) exhibiting halogen-like behavior. Both the low ionization energy Co6Te8(PEt3)(6) and high electron affinity Co6Te8(CO)(6) have closed electronic shells marked by high HOMO-LUMO gaps of 1.24 and 1.39 eV, respectively. Further, the clusters with an even number of ligands favor a symmetrical placement of ligands around the metal core

The Incremental Multiresolution Matrix Factorization Algorithm

Multiresolution analysis and matrix factorization are foundational tools in computer vision. In this work, we study the interface between these two distinct topics and obtain techniques to uncover hierarchical block structure in symmetric matrices -- an important aspect in the success of many vision problems. Our new algorithm, the incremental multiresolution matrix factorization, uncovers such structure one feature at a time, and hence scales well to large matrices. We describe how this multiscale analysis goes much farther than what a direct global factorization of the data can identify. We evaluate the efficacy of the resulting factorizations for relative leveraging within regression tasks using medical imaging data. We also use the factorization on representations learned by popular deep networks, providing evidence of their ability to infer semantic relationships even when they are not explicitly trained to do so. We show that this algorithm can be used as an exploratory tool to improve the network architecture, and within numerous other settings in vision.Comment: Computer Vision and Pattern Recognition (CVPR) 2017, 10 page

Speeding up Permutation Testing in Neuroimaging

Multiple hypothesis testing is a significant problem in nearly all neuroimaging studies. In order to correct for this phenomena, we require a reliable estimate of the Family-Wise Error Rate (FWER). The well known Bonferroni correction method, while simple to implement, is quite conservative, and can substantially under-power a study because it ignores dependencies between test statistics. Permutation testing, on the other hand, is an exact, non-parametric method of estimating the FWER for a given $\alpha$-threshold, but for acceptably low thresholds the computational burden can be prohibitive. In this paper, we show that permutation testing in fact amounts to populating the columns of a very large matrix ${\bf P}$. By analyzing the spectrum of this matrix, under certain conditions, we see that ${\bf P}$ has a low-rank plus a low-variance residual decomposition which makes it suitable for highly sub--sampled --- on the order of $0.5\%$ --- matrix completion methods. Based on this observation, we propose a novel permutation testing methodology which offers a large speedup, without sacrificing the fidelity of the estimated FWER. Our evaluations on four different neuroimaging datasets show that a computational speedup factor of roughly $50\times$ can be achieved while recovering the FWER distribution up to very high accuracy. Further, we show that the estimated $\alpha$-threshold is also recovered faithfully, and is stable.Comment: NIPS 1