Learning on-top: regressing the on-top pair density for real-space visualization of electron correlation

The on-top pair density [$\Pi(\mathrm{\mathbf{r}})$] is a local quantum-chemical property that reflects the probability of two electrons of any spin to occupy the same position in space. Being the simplest quantity related to the two-particle density matrix, the on-top pair density is a powerful indicator of electron correlation effects, and as such, it has been extensively used to combine density functional theory and multireference wavefunction theory. The widespread application of $\Pi(\mathrm{\mathbf{r}})$ is currently hindered by the need for post-Hartree--Fock or multireference computations for its accurate evaluation. In this work, we propose the construction of a machine learning model capable of predicting the CASSCF-quality on-top pair density of a molecule only from its structure and composition. Our model, trained on the GDB11-AD-3165 database, is able to predict with minimal error the on-top pair density of organic molecules, bypassing completely the need for $\textit{ab initio}$ computations. The accuracy of the regression is demonstrated using the on-top ratio as a visual metric of electron correlation effects and bond-breaking in real-space. In addition, we report the construction of a specialized basis set, built to fit the on-top pair density in a single atom-centered expansion. This basis, cornerstone of the regression, could be potentially used also in the same spirit of the resolution-of-the-identity approximation for the electron density.Comment: Article and Supporting Informatio

Median eminence myelin continuously turns over in adult mice

OBJECTIVE: Oligodendrocyte progenitor cell differentiation is regulated by nutritional signals in the adult median eminence (ME), but the consequences on local myelination are unknown. The aim of this study was to characterize myelin plasticity in the ME of adult mice in health or in response to chronic nutritional challenge and determine its relevance to the regulation of energy balance. METHODS: We assessed new oligodendrocyte (OL) and myelin generation and stability in the ME of healthy adult male mice using bromodeoxyuridine labelling and genetic fate mapping tools. We evaluated the contribution of microglia to ME myelin plasticity in PLX5622-treated C57BL/6J mice and in Pdgfra-Cre/ERT2;R26R-eYFP;Myrffl/fl mice, where adult oligodendrogenesis is blunted. Next, we investigated how high-fat feeding or caloric restriction impact ME OL lineage progression and myelination. Finally, we characterized the functional relevance of adult oligodendrogenesis on energy balance regulation. RESULTS: We show that myelinating OLs are continuously and rapidly generated in the adult ME. Paradoxically, OL number and myelin amounts remain remarkably stable in the adult ME. In fact, the high rate of new OL and myelin generation in the ME is offset by continuous turnover of both. We show that microglia are required for continuous OL and myelin production, and that ME myelin plasticity regulates the recruitment of local immune cells. Finally, we provide evidence that ME myelination is regulated by the body's energetic status and demonstrate that ME OL and myelin plasticity are required for the regulation of energy balance and hypothalamic leptin sensitivity. CONCLUSIONS: This study identifies a new mechanism modulating leptin sensitivity and the central control of energy balance and uncovers a previously unappreciated form of structural plasticity in the ME

Low Momentum Scattering in the Dirac Equation

It is shown that the amplitude for reflection of a Dirac particle with arbitrarily low momentum incident on a potential of finite range is -1 and hence the transmission coefficient T=0 in general. If however the potential supports a half-bound state at k=0 this result does not hold. In the case of an asymmetric potential the transmission coefficient T will be non-zero whilst for a symmetric potential T=1.Comment: 12 pages; revised to include additional references; to be published in J Phys

Forming a biomathematical learning alliance across traditional academic departments

Across the United States, many generalized programs have focused on retention of minority students in the sciences with varying degrees of success. Paradoxically, this challenge exists despite expanding career opportunities in industry, academia, and government for those skilled at the intersection of biology and mathematics. Here we describe a cross-departmental learning alliance (iBLEND- an Integrative Biomathematics Learning and Empowerment Network for Diversity) which directly targets these recognized challenges. Our goal is for the iBLEND project to have significant spillover effects for our university by developing new interdisciplinary collaborations that benefit our students. The iBLEND is a proactive, intensive approach in order to bridge campus chasms for both faculty and undergraduate students by positively influencing academic programs through interdisciplinary training coupled with strong evaluation and assessments. By leveraging our recent surge of competitive research activity, innovative instruction, and collaboration, the iBLEND advances our transformation to the next level by establishing a broader bridge for our undergraduates at the interface of mathematics and biology. In working together, the math and biology students learned to bridge language barriers inhibiting interdisciplinary explorations. Students were closely involved with faculty mentors in core laboratories and developed cross-disciplinary research skills that enhanced their post-graduate career opportunities. Using systems biology tools combined with targeted mathematics classroom work, students merged data from their lab bench experiments with mathematical models to determine how various changes impacted an overall organism and its functions. The students had hands-on training with a myriad of computational, simulations, data mining and data analysis tools needed in approaching their projects

Toward in silico Catalyst Optimization

In this minireview, we overview a computational pipeline developed within the framework of NCCR Catalysis that can be used to successfully reproduce the enantiomeric ratios of homogeneous catalytic reactions. At the core of this pipeline is the SCINE Molassembler module, a graph-based software that provides algorithms for molecular construction of all periodic table elements. With this pipeline, we are able to simultaneously functionalizenand generate ensembles of transition state conformers, which permits facile exploration of the influencenof various substituents on the overall enantiomeric ratio. This allows preconceived back-of-the-envelope designnmodels to be tested and subsequently refined by providing quick and reliable access to energetically low-lyingntransition states, which represents a key step in undertaking in silico catalyst optimization

An Optimization Model for Modernizing the Army's Helicopter Fleet

Interfaces, 21, pp. 39-52.The helicopter has grown in military stature for more than 40 years: its ascendancy has reformed the US Army. Unfortunately, the current army helicopter fleet consists predominantly of Vietnam-era aircraft approaching the end of their useful lives. We have captured complex procurement and modernization tasks in optimization based decision support system, christened PHOENIX, which recognizes yearly operating, maintenance, retirement, service-life extention, and new procurement costs while enforcing constraints on fleet age, technology mix, composition, and budgets over a multi-year planning horizon. The army has applied PHOENIX to helicopters with such success that it has already been adapted to tactical wheeled vehicles and is under consideration for further applications

Lanthanide appended rotaxanes respond to changing chloride concentration

Lanthanide appended rotaxanes have been prepared by the CuAAC ‘click’ reaction between an azide appended rotaxane and lanthanide complexes of propargyl DO3A. The resulting complexes are luminescent, and exhibit chloride responsive luminescence behavior consistent with the existence of two independent halide binding pockets, one in the rotaxane cavity and one on the ninth (axial) coordination site of the lanthanide. Strong halide binding to europium gives rise to changes in the relative intensity of the hypersensitive ΔJ = 2 transition compared to the rest of the europium emission spectrum, combined with quenching of the overall intensity of emission as a consequence of non-radiative quenching by the bound halide. The weaker interaction with the rotaxane pocket mediates a subsequent recovery of intensity of the europium centered luminescence despite the considerable separation between the lanthanide and the rotaxane binding pocket