Efficient construction of nonorthogonal localized molecular orbitals in large systems.

Localized molecular orbitals (LMOs) are much more compact representations of electronic degrees of freedom than canonical molecular orbitals (CMOs). The most compact representation is provided by nonorthogonal localized molecular orbitals (NOLMOs), which are linearly independent but are not orthogonal. Both LMOs and NOLMOs are thus useful for linear-scaling calculations of electronic structures for large systems. Recently, NOLMOs have been successfully applied to linear-scaling calculations with density functional theory (DFT) and to reformulating time-dependent density functional theory (TDDFT) for calculations of excited states and spectroscopy. However, a challenge remains as NOLMO construction from CMOs is still inefficient for large systems. In this work, we develop an efficient method to accelerate the NOLMO construction by using predefined centroids of the NOLMO and thereby removing the nonlinear equality constraints in the original method ( J. Chem. Phys. 2004 , 120 , 9458 and J. Chem. Phys. 2000 , 112 , 4 ). Thus, NOLMO construction becomes an unconstrained optimization. Its efficiency is demonstrated for the selected saturated and conjugated molecules. Our method for fast NOLMO construction should lead to efficient DFT and NOLMO-TDDFT applications to large systems.

Two versions of life: emotionally negative and positive life events have different roles in the organization of life story and identity.

Over 2,000 adults in their sixties completed the Centrality of Event Scale (CES) for the traumatic or negative event that now troubled them the most and for their most positive life event, as well as measures of current PTSD symptoms, depression, well-being, and personality. Consistent with the notion of a positivity bias in old age, the positive events were judged to be markedly more central to life story and identity than were the negative events. The centrality of positive events was unrelated to measures of PTSD symptoms and emotional distress, whereas the centrality of the negative event showed clear positive correlations with these measures. The centrality of the positive events increased with increasing time since the events, whereas the centrality of the negative events decreased. The life distribution of the positive events showed a marked peak in young adulthood whereas the life distribution for the negative events peaked at the participants' present age. The positive events were mostly events from the cultural life script-that is, culturally shared representations of the timing of major transitional events. Overall, our findings show that positive and negative autobiographical events relate markedly differently to life story and identity. Positive events become central to life story and identity primarily through their correspondence with cultural norms. Negative events become central through mechanisms associated with emotional distress.

Biogeographic analysis of the woody plants of the Southern Appalachians: Implications for the origins of a regional flora.

PREMISE OF THE STUDY: We investigated the origins of 252 Southern Appalachian woody species representing 158 clades to analyze larger patterns of biogeographic connectivity around the northern hemisphere. We tested biogeographic hypotheses regarding the timing of species disjunctions to eastern Asia and among areas of North America. METHODS: We delimited species into biogeographically informative clades, compiled sister-area data, and generated graphic representations of area connections across clades. We calculated taxon diversity within clades and plotted divergence times. KEY RESULTS: Of the total taxon diversity, 45% were distributed among 25 North American endemic clades. Sister taxa within eastern North America and eastern Asia were proportionally equal in frequency, accounting for over 50% of the sister-area connections. At increasing phylogenetic depth, connections to the Old World dominated. Divergence times for 65 clades with intercontinental disjunctions were continuous, whereas 11 intracontinental disjunctions to western North America and nine to eastern Mexico were temporally congruent. CONCLUSIONS: Over one third of the clades have likely undergone speciation within the region of eastern North America. The biogeographic pattern for the region is asymmetric, consisting of mostly mixed-aged, low-diversity clades connecting to the Old World, and a minority of New World clades. Divergence time data suggest that climate change in the Late Miocene to Early Pliocene generated disjunct patterns within North America. Continuous splitting times during the last 45 million years support the hypothesis that widespread distributions formed repeatedly during favorable periods, with serial cooling trends producing pseudocongruent area disjunctions between eastern North America and eastern Asia.

Automatic verification of linear controller software

© 2015 IEEE.We consider the problem of verification of software implementations of linear time-invariant controllers. Commonly, different implementations use different representations of the controller's state, for example due to optimizations in a third-party code generator. To accommodate this variation, we exploit input-output controller specification captured by the controller's transfer function and show how to automatically verify correctness of C code controller implementations using a Frama-C/Why3/Z3 toolchain. Scalability of the approach is evaluated using randomly generated controller specifications of realistic size.

Persistent Homology Analysis of Brain Artery Trees.

New representations of tree-structured data objects, using ideas from topological data analysis, enable improved statistical analyses of a population of brain artery trees. A number of representations of each data tree arise from persistence diagrams that quantify branching and looping of vessels at multiple scales. Novel approaches to the statistical analysis, through various summaries of the persistence diagrams, lead to heightened correlations with covariates such as age and sex, relative to earlier analyses of this data set. The correlation with age continues to be significant even after controlling for correlations from earlier significant summaries.