Selected Columns of the Density Matrix in an Atomic Orbital Basis I: An Intrinsic and Non-iterative Orbital Localization Scheme for the Occupied Space.

In this work, we extend the selected columns of the density matrix (SCDM) methodology [J. Chem. Theory Comput. 2015, 11, 1463-1469]─a non-iterative and real-space procedure for generating localized occupied orbitals for condensed-phase systems─to the construction of local molecular orbitals (LMOs) in systems described using non-orthogonal atomic orbital (AO) basis sets. In particular, we introduce three different theoretical and algorithmic variants of SCDM (referred to as SCDM-M, SCDM-L, and SCDM-G) that can be used in conjunction with the AO basis sets used in standard quantum chemistry codebases. The SCDM-M and SCDM-L variants are based on a pivoted QR factorization of the Mulliken and Löwdin representations of the density matrix and are tantamount to selecting a well-conditioned set of projected atomic orbitals (PAOs) and projected (symmetrically-) orthogonalized atomic orbitals, respectively, as proto-LMOs that can be orthogonalized to exactly span the occupied space. The SCDM-G variant is based on a real-space (grid) representation of the wavefunction, and therefore has the added flexibility of considering a large number of grid points (or δ functions) when selecting a set of well-conditioned proto-LMOs. A detailed comparative analysis across molecular systems of varying size, dimensionality, and saturation level reveals that the LMOs generated by these three non-iterative/direct SCDM variants are robust, comparable in orbital locality to those produced with the iterative Boys or Pipek-Mezey (PM) localization schemes, and completely agnostic toward any single orbital locality metric. Although all three SCDM variants are based on the density matrix, we find that the character of the generated LMOs can differ significantly between SCDM-M, SCDM-L, and SCDM-G. In this regard, only the grid-based SCDM-G procedure (like PM) generates LMOs that qualitatively preserve σ-π symmetry (in systems such as s-trans alkenes), and are well-aligned with chemical (i.e., Lewis structure) intuition. While the direct and standalone use of SCDM-generated LMOs should suffice for most chemical applications, our findings also suggest that the use of these orbitals as an unbiased and cost-effective (initial) guess also has the potential to improve the convergence of iterative orbital localization schemes, in particular for large-scale and/or pathological molecular systems.

A Geometric Approach to Archetypal Analysis and Nonnegative Matrix Factorization.

Archetypal analysis and non-negative matrix factorization (NMF) are staples in a statisticians toolbox for dimension reduction and exploratory data analysis. We describe a geometric approach to both NMF and archetypal analysis by interpreting both problems as finding extreme points of the data cloud. We also develop and analyze an efficient approach to finding extreme points in high dimensions. For modern massive datasets that are too large to fit on a single machine and must be stored in a distributed setting, our approach makes only a small number of passes over the data. In fact, it is possible to obtain the NMF or perform archetypal analysis with just two passes over the data.

Detecting moxifloxacin-induced QTc prolongation in thorough QT and early clinical phase studies using a highly automated ECG analysis approach.

BACKGROUND AND PURPOSE: Exposure-response (ER) modelling (concentration-QTc analysis) is gaining as much acceptance as the traditional by-time analysis of the placebo-adjusted change from baseline in the QTc interval (ΔΔQTcF). It has been postulated that intensive ECG analysis and ER modelling during early-phase drug development could be a cost-effective approach of estimating QT liability of a new drug, in a small number of subjects. EXPERIMENTAL APPROACH: We used a highly automated analysis of ECGs from 46 subjects from a crossover thorough QT/QTc study to detect ΔΔQTcF with moxifloxacin. Using these data, we also simulated (bootstrapped) 1000 datasets of a parallel study with eight subjects receiving moxifloxacin and eight others receiving placebo. KEY RESULTS: The slope from the concentration-QTc analysis for moxifloxacin in 46 subjects was 4.12 ms of ΔΔQTcF per µg(-1) mL(-1) ; at mean Cmax of 2.95 µg·mL(-1) , estimated ΔΔQTcF was 13.4 ms (90% confidence interval 11.3, 15.4 ms). In the 1000 simulated datasets, in 996 datasets, ER modelling showed that the upper bound of the 90% confidence interval for ΔΔQTcF at geometric mean Cmax exceeded 10 ms. In 895 of these 996 datasets, the slope of the ER relationship was statistically significantly positive. Thus, with a small sample size (eight subjects on active drug and eight on placebo), moxifloxacin-induced QTc prolongation was demonstrated using ER analysis with statistical power of >80%. CONCLUSIONS AND IMPLICATIONS: Our study adds to the growing body of data supporting intensive ECG collection and analysis in early-phase studies to estimate QT liability.

Compressed Representation of Kohn-Sham Orbitals via Selected Columns of the Density Matrix.

Given a set of Kohn-Sham orbitals from an insulating system, we present a simple, robust, efficient, and highly parallelizable method to construct a set of optionally orthogonal, localized basis functions for the associated subspace. Our method explicitly uses the fact that density matrices associated with insulating systems decay exponentially along the off-diagonal direction in the real space representation. We avoid the usage of an optimization procedure, and the localized basis functions are constructed directly from a set of selected columns of the density matrix (SCDM). Consequently, the core portion of our localization procedure is not dependent on any adjustable parameters. The only adjustable parameters present pertain to the use of the SCDM after their computation (for example, at what value should the SCDM be truncated). Our method can be used in any electronic structure software package with an arbitrary basis set. We demonstrate the numerical accuracy and parallel scalability of the SCDM procedure using orbitals generated by the Quantum ESPRESSO software package. We also demonstrate a procedure for combining the orthogonalized SCDM with Hockney's algorithm to efficiently perform Hartree-Fock exchange energy calculations with near-linear scaling.

Left ventricular hypertrophy in hypertensive patients in Indian primary care: prevalence and effect of treatment with sustained release indapamide.

OBJECTIVE: Epidemiologic studies indicate an ethnic determinant of left ventricular hypertrophy (LVH), but its prevalence in hypertensive Asian Indians at diagnosis is not known. The observation that LVH regression reduces cardiovascular risk independent of blood pressure, suggests that initial antihypertensive treatment, which also regresses LVH is a desirable goal. This study investigates the prevalence of LVH and its regression with indapamide sustained release (Natrilix SR) in untreated Indian hypertensive patients managed in the primary care setting. DESIGN AND METHODS: Randomly selected physicians serving a defined population recruited untreated hypertensive patients to determine prevalence of LVH. All patients then received indapamide SR treatment for 6 months. LVH was assessed by echocardiography. All measurements were centralized and interpreted by a single blinded observer. MAIN OUTCOME MEASURES: The primary treatment outcomes were the percentage of patients whose LVH regressed with treatment and the number of patients who achieved a blood pressure below 140/90 mmHg. RESULTS: Of the 86 patients recruited, 21 (24.4%, 95% confidence interval (CI) 15.3-33.8) had LVH. There were 11 cases (26.2%) in men, 10 (22.7%) in women, and 15 (32.6%) in those above 50 years. Treatment regressed LVH in 16 (76.2%, 95%CI, 58.0-94.4) by a mean of 25.4 g/m2 (95%CI, 2.8-47.7, p< 0.05). Blood pressure was controlled in 71 (82.6%, 95%CI, 74.5-90.6) patients. CONCLUSION: Prevalence of LVH in untreated Indian hypertensive patients is similar to that in white western populations. Initial indapamide SR treatment is effective in both controlling blood pressure and regressing LVH in the primary care setting.