Neglect of four- and approximation of one-, two-, and three-center two-electron integrals in a symmetrically orthogonalized basis

A new integral approximation for use in molecular electronic structure calculations is proposed as an alternative to the traditional neglect of diatomic differential overlap models. The similarity between the symmetrically orthogonalized and the original basis functions (assumed orthonormal within each atomic set but nonorthogonal between different centers) is used to construct a robust approximation for the two-electron integrals, with the error being quadratic in the deviation between the products of the functions. Invariance properties of this procedure are rigorously proved. Numerical studies on a representative set of molecules at valence-only minimal basis Hartree-Fock level show that the approximation introduces relatively small errors, encouraging its future application in the semiempirical field.     

Cellular separations: a review of new challenges in analytical chemistry

The ability to generate a sample of cells of a given phenotype is a prerequisite for many cellular assays. In response to this growing need, numerous methods for cell separation have been developed in recent years. This Review covers recent progress in the field of cell separations and cell chromatography. Cell separation principles—such as size and affinity capture—are discussed, as well as conventional methods such as fluorescence-activated cell sorting and magnetic sorting. Planar flow cell arrays, dielectrophoresis, field-flow methods, and column separation devices are reviewed, as well as applications of these methods to medicine and biotechnology. Cell attachment and adhesion strategies and a comparison of techniques are also presented.     

Investigation of photobleaching and saturation of single molecules by fluorophore recrossing events

A method for investigation of photobleaching and saturation of single molecules by fluorophore recrossing events in a laser beam is described. The diffraction-limited probe volumes encountered in single-molecule detection (SMD) produce high excitation irradiance, which can decrease available signal. The single molecules of several dyes were detected and the data was used to extract interpeak times above a defined threshold value. The interpeak times revealed the number of fluorophore recrossing events. The number of molecules detected that were within 2 ms of each other represented a molecular recrossing for this work. Calcein, fluorescein and R-phycoerythrin were analyzed and the saturation irradiance and photobleaching effects were determined as a function of irradiance. This approach is simple and it serves as a method of optimizing experimental conditions for single-molecule detection.     

A rank six geometry related to the McLaughlin sporadic simple group

In the literature, there are but a few incidence geometries on which the McLaughlin sporadic group acts as a flag-transitive automorphism group. Their highest rank is four. In the present paper, we construct a geometry of rank six on which acts flag-transitively and which has the following diagram.      

Multiscale theory of fluctuating interfaces: renormalization of atomistic models

We describe a framework for the multiscale analysis of atomistic surface processes which we apply to a model of homoepitaxial growth with deposition according to the Wolf-Villain model and concurrent surface diffusion. Coarse graining is accomplished by calculating renormalization-group (RG) trajectories from initial conditions determined by the regularized atomistic theory. All of the crossover and asymptotic scaling regimes known from computer simulations are obtained, but we also find that two-dimensional substrates show an intriguing transition from smooth to mounded morphologies along the RG trajectory.     

Hydrogen in N-methylacetamide: positions and dynamics of the hydrogen atoms using neutron scattering

This work reports neutron diffraction and incoherent neutron scattering experiments on N-methylacetamide (NMA), which can be considered the model building block for the peptide linkage of polypeptides and proteins. Using the neutron data, we have been able to associate the onset of a striking negative thermal expansion (NTE) along the a-axis with a dynamical transition around 230 K, consistent with our calorimetric experiments. Observation of the NTE raises the question of possible proton transfer in NMA, which, from our data alone, still cannot be settled. We can only speculate that intermolecular repulsive forces increase as the O...H distance decreases upon cooling, and that around 230 K the lattice relaxes without observation of an actual proton transfer. However, the existence of a nonharmonic potential, reflected by the behavior of the phonon vibrations together with the observation of NTE, could be justified by the "vibrational" polaron theory in which a dynamic localization of the vibrational energy is created by coupling an internal molecular mode to a lattice phonon. More generally, this work shows that neutron powder diffraction techniques can be very powerful for investigating structural deformations in small peptide systems.     

A free analogue of Shannon's problem on monotonicity of entropy

We prove a free probability analog of a result of [S. Artstein, K. Ball, F. Barthe, A. Naor, Solution of Shannon's problem on monotonicity of entropy, J. Amer. Math. Soc. 17 (2004) 975-982]. In particular, we prove that if X₁,X₂,… are freely independent identically distributed random variables, then the function

     

Polytopes of high rank for the symmetric groups

In the Atlas of abstract regular polytopes for small almost simple groups by Leemans and Vauthier, the polytopes whose automorphism group is a symmetric group Sn of degree 5?n?9 are available. Two observations arise when we look at the results: (1) for n?5, the (n−1)-simplex is, up to isomorphism, the unique regular (n−1)-polytope having Sn as automorphism group and, (2) for n?7, there exists, up to isomorphism and duality, a unique regular (n−2)-polytope whose automorphism group is Sn. We prove that (1) is true for n≠4 and (2) is true for n?7. Finally, we also prove that Sn acts regularly on at least one abstract polytope of rank r for every 3?r?n−1.     

Incremental proximal methods for large scale convex optimization

We consider the minimization of a sum \({\sum_{i=1}^mf_i(x)}\) consisting of a large number of convex component functions f _i . For this problem, incremental methods consisting of gradient or subgradient iterations applied to single components have proved very effective. We propose new incremental methods, consisting of proximal iterations applied to single components, as well as combinations of gradient, subgradient, and proximal iterations. We provide a convergence and rate of convergence analysis of a variety of such methods, including some that involve randomization in the selection of components. We also discuss applications in a few contexts, including signal processing and inference/machine learning.