The two electron molecular bond revisited: from Bohr orbits to two-center orbitals

In this review we first discuss extension of Bohr's 1913 molecular model and show that it corresponds to the large-D limit of a dimensional scaling (D-scaling) analysis, as developed by Herschbach and coworkers. In a separate but synergetic approach to the two-electron problem, we summarize recent advances in constructing analytical models for describing the two-electron bond. The emphasis here is not maximally attainable numerical accuracy, but beyond textbook accuracy as informed by physical insights. We demonstrate how the interplay of the cusp condition, the asymptotic condition, the electron-correlation, configuration interaction, and the exact one electron two-center orbitals, can produce energy results approaching chemical accuracy. Reviews of more traditional calculational approaches, such as Hartree-Fock, are also given. The inclusion of electron correlation via Hylleraas type functions is well known to be important, but difficult to implement for more than two electrons. The use of the D-scaled Bohr model offers the tantalizing possibility of obtaining electron correlation energy in a non-traditional way.Comment: 99 pages, 29 figures, review article, to appear in Advances in Atomic, Molecular and Optical Physic

Section Extension from Hyperbolic Geometry of Punctured Disk and Holomorphic Family of Flat Bundles

The construction of sections of bundles with prescribed jet values plays a fundamental role in problems of algebraic and complex geometry. When the jet values are prescribed on a positive dimensional subvariety, it is handled by theorems of Ohsawa-Takegoshi type which give extension of line bundle valued square-integrable top-degree holomorphic forms from the fiber at the origin of a family of complex manifolds over the open unit 1-disk when the curvature of the metric of line bundle is semipositive. We prove here an extension result when the curvature of the line bundle is only semipositive on each fiber with negativity on the total space assumed bounded from below and the connection of the metric locally bounded, if a square-integrable extension is known to be possible over a double point at the origin. It is a Hensel-lemma-type result analogous to Artin's application of the generalized implicit function theorem to the theory of obstruction in deformation theory. The motivation is the need in the abundance conjecture to construct pluricanonical sections from flatly twisted pluricanonical sections. We also give here a new approach to the original theorem of Ohsawa-Takegoshi by using the hyperbolic geometry of the punctured open unit 1-disk to reduce the original theorem of Ohsawa-Takegoshi to a simple application of the standard method of constructing holomorphic functions by solving the d-bar equation with cut-off functions and additional blowup weight functions

Functional DNA methylation signatures for autism spectrum disorder genomic risk loci: 16p11.2 deletions and CHD8 variants

Background: Autism spectrum disorder (ASD) is a common and etiologically heterogeneous neurodevelopmental disorder. Although many genetic causes have been identified (\u3e 200 ASD-risk genes), no single gene variant accounts for \u3e 1% of all ASD cases. A role for epigenetic mechanisms in ASD etiology is supported by the fact that many ASD-risk genes function as epigenetic regulators and evidence that epigenetic dysregulation can interrupt normal brain development. Gene-specific DNAm profiles have been shown to assist in the interpretation of variants of unknown significance. Therefore, we investigated the epigenome in patients with ASD or two of the most common genomic variants conferring increased risk for ASD. Genome-wide DNA methylation (DNAm) was assessed using the Illumina Infinium HumanMethylation450 and MethylationEPIC arrays in blood from individuals with ASD of heterogeneous, undefined etiology (n = 52), and individuals with 16p11.2 deletions (16p11.2del, n = 9) or pathogenic variants in the chromatin modifier CHD8 (CHD8 +/-, n = 7). Results: DNAm patterns did not clearly distinguish heterogeneous ASD cases from controls. However, the homogeneous genetically-defined 16p11.2del and CHD8 +/- subgroups each exhibited unique DNAm signatures that distinguished 16p11.2del or CHD8 +/- individuals from each other and from heterogeneous ASD and control groups with high sensitivity and specificity. These signatures also classified additional 16p11.2del (n = 9) and CHD8 (n = 13) variants as pathogenic or benign. Our findings that DNAm alterations in each signature target unique genes in relevant biological pathways including neural development support their functional relevance. Furthermore, genes identified in our CHD8 +/- DNAm signature in blood overlapped differentially expressed genes in CHD8 +/- human-induced pluripotent cell-derived neurons and cerebral organoids from independent studies. Conclusions: DNAm signatures can provide clinical utility complementary to next-generation sequencing in the interpretation of variants of unknown significance. Our study constitutes a novel approach for ASD risk-associated molecular classification that elucidates the vital cross-talk between genetics and epigenetics in the etiology of ASD

Positivity of relative canonical bundles and applications

Given a family $f:\mathcal X \to S$ of canonically polarized manifolds, the unique K\"ahler-Einstein metrics on the fibers induce a hermitian metric on the relative canonical bundle $\mathcal K_{\mathcal X/S}$. We use a global elliptic equation to show that this metric is strictly positive on $\mathcal X$, unless the family is infinitesimally trivial. For degenerating families we show that the curvature form on the total space can be extended as a (semi-)positive closed current. By fiber integration it follows that the generalized Weil-Petersson form on the base possesses an extension as a positive current. We prove an extension theorem for hermitian line bundles, whose curvature forms have this property. This theorem can be applied to a determinant line bundle associated to the relative canonical bundle on the total space. As an application the quasi-projectivity of the moduli space $\mathcal M_{\text{can}}$ of canonically polarized varieties follows. The direct images $R^{n-p}f_*\Omega^p_{\mathcal X/S}(\mathcal K_{\mathcal X/S}^{\otimes m})$, $m > 0$, carry natural hermitian metrics. We prove an explicit formula for the curvature tensor of these direct images. We apply it to the morphisms $S^p \mathcal T_S \to R^pf_*\Lambda^p\mathcal T_{\mathcal X/S}$ that are induced by the Kodaira-Spencer map and obtain a differential geometric proof for hyperbolicity properties of $\mathcal M_{\text{can}}$.Comment: Supercedes arXiv:0808.3259v4 and arXiv:1002.4858v2. To appear in Invent. mat

Attosecond electron spectroscopy using a novel interferometric pump-probe technique

We present an interferometric pump-probe technique for the characterization of attosecond electron wave packets (WPs) that uses a free WP as a reference to measure a bound WP. We demonstrate our method by exciting helium atoms using an attosecond pulse with a bandwidth centered near the ionization threshold, thus creating both a bound and a free WP simultaneously. After a variable delay, the bound WP is ionized by a few-cycle infrared laser precisely synchronized to the original attosecond pulse. By measuring the delay-dependent photoelectron spectrum we obtain an interferogram that contains both quantum beats as well as multi-path interference. Analysis of the interferogram allows us to determine the bound WP components with a spectral resolution much better than the inverse of the attosecond pulse duration.Comment: 5 pages, 4 figure

Extension of holomorphic functions and cohomology classes from non reduced analytic subvarieties

The goal of this survey is to describe some recent results concerning the L 2 extension of holomorphic sections or cohomology classes with values in vector bundles satisfying weak semi-positivity properties. The results presented here are generalized versions of the Ohsawa-Takegoshi extension theorem, and borrow many techniques from the long series of papers by T. Ohsawa. The recent achievement that we want to point out is that the surjectivity property holds true for restriction morphisms to non necessarily reduced subvarieties, provided these are defined as zero varieties of multiplier ideal sheaves. The new idea involved to approach the existence problem is to make use of L 2 approximation in the Bochner-Kodaira technique. The extension results hold under curvature conditions that look pretty optimal. However, a major unsolved problem is to obtain natural (and hopefully best possible) L 2 estimates for the extension in the case of non reduced subvarieties -- the case when Y has singularities or several irreducible components is also a substantial issue.Comment: arXiv admin note: text overlap with arXiv:1703.00292, arXiv:1510.0523

Cohomological characterizations of projective spaces and hyperquadrics

We confirm Beauville's conjecture that claims that if the p-th exterior power of the tangent bundle of a smooth projective variety contains the p-th power of an ample line bundle, then the variety is either the projective space or the p-dimensional quadric hypersurface.Comment: Added Lemma 2.8 and slightly changed proof of Lemma 6.2 to make them apply for torsion-free sheaves and not only to vector bundle

NSD1 mutations generate a genome-wide DNA methylation signature

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Geriatric hip fracture clinical pathway: the Hong Kong experience

Geriatric hip fracture is one of the commonest fractures in orthopaedic trauma. There is a trend of further increase in its incidence in the coming decades. Besides the development of techniques and implants to overcome the difficulties in fixation of osteoporosis bone, the general management of the hip fracture is also very challenging in terms of the preparation of the generally poorer pre-morbid state and complicate social problems associated with this group of patients. In order to cope with the increasing demand, our hospital started a geriatric hip fracture clinical pathway in 2007. The aim of this pathway is to provide better care for this group of patients through multidisciplinary approach. From year 2007 to 2009, we had managed 964 hip fracture patients. After the implementation of the pathway, the pre-operative and the total length of stay in acute hospital were shortened by over 5 days. Other clinical outcomes including surgical site infection, 30 days mortality and also incidence of pressure sore improved when compared to the data before the pathway. The rate of surgical site infection was 0.98%, and the 30 days mortality was 1.67% in 2009. The active participation of physiotherapists, occupational therapists as well as medical social workers also helped to formulate the discharge plan as early as the patient is admitted. In conclusion, a well-planned and executed clinical pathway for hip fracture can improve the clinical outcomes of the geriatric hip fractures

Neurogenesis Drives Stimulus Decorrelation in a Model of the Olfactory Bulb

The reshaping and decorrelation of similar activity patterns by neuronal networks can enhance their discriminability, storage, and retrieval. How can such networks learn to decorrelate new complex patterns, as they arise in the olfactory system? Using a computational network model for the dominant neural populations of the olfactory bulb we show that fundamental aspects of the adult neurogenesis observed in the olfactory bulb -- the persistent addition of new inhibitory granule cells to the network, their activity-dependent survival, and the reciprocal character of their synapses with the principal mitral cells -- are sufficient to restructure the network and to alter its encoding of odor stimuli adaptively so as to reduce the correlations between the bulbar representations of similar stimuli. The decorrelation is quite robust with respect to various types of perturbations of the reciprocity. The model parsimoniously captures the experimentally observed role of neurogenesis in perceptual learning and the enhanced response of young granule cells to novel stimuli. Moreover, it makes specific predictions for the type of odor enrichment that should be effective in enhancing the ability of animals to discriminate similar odor mixtures