Numerically stable,scalable formulas for parallel and online computation of higher-order multivariate central moments with arbitrary weights

Formulas for incremental or parallel computation of second order central moments have long been known, and recent extensions of these formulas to univariate and multivariate moments of arbitrary order have been developed. Such formulas are of key importance in scenarios where incremental results are required and in parallel and distributed systems where communication costs are high. We survey these recent results, and improve them with arbitrary-order, numerically stable one-pass formulas which we further extend with weighted and compound variants. We also develop a generalized correction factor for standard two-pass algorithms that enables the maintenance of accuracy over nearly the full representable range of the input, avoiding the need for extended-precision arithmetic. We then empirically examine algorithm correctness for pairwise update formulas up to order four as well as condition number and relative error bounds for eight different central moment formulas, each up to degree six, to address the trade-offs between numerical accuracy and speed of the various algorithms. Finally, we demonstrate the use of the most elaborate among the above mentioned formulas, with the utilization of the compound moments for a practical large-scale scientific application.     

EDTA-catalyzed synthesis of 3,4-dihydroquinoxalin-2-amine derivatives by a three-component coupling of one-pot condensation reactions in an aqueous medium

This paper describes a simple and efficient one-pot synthetic approach for the preparation of biologically interesting 3,4-dihydroquinoxalin-2-amine derivatives using EDTA-catalyzed three-component reactions of o-phenylenediamines, carbonyl compounds, and isocyanides in an aqueous medium. This method is of great value because of its environmentally benign character, high yields, and ease of handling.     

Benzopentalenonaphthalenones from the intramolecular capture of a merocyanine derived from a naphthopyran

Novel, highly coloured benzopentalenonaphthalenones result from a cascade process initiated by the thermally-induced ring-opening of diarylmethanol substituted 2H-naphtho[1,2-b]pyrans in the presence of acid.     

A weight-function approach for determining watershed initial conditions for combustion waves

In many generic combustion models, one finds that a combustionwave will develop with a specific wave speed. However, thereare possible initial temperature profiles which do not evolveinto such waves, but rather die out to the ambient temperature.There can exist, in some models, a clear distinction betweenthose initial conditions that do evolve into combustion wavesand those that do not; this is sometimes referred to as thewatershed initial condition. When fuel consumption is consideredto be negligible, analytical methods can be used to obtain theexact watershed. In this paper, we consider the problem of determiningpseudo-watersheds and ascertaining the relationship betweenthese pseudo-watersheds and the exact watersheds. In the processa novel weight-function approach for infinite spatial domainsis developed.     

An efficient synthesis of dexlansoprazole employing asymmetric oxidation strategy

An alternative and scalable synthesis of dexlansoprazole ((R)-(+)-1); the (R)-enantiomer of Lansoprazole with an enantiomeric excess of >99.8% is presented.     

Influence of cross diffusions on mixed convection chemical reaction flow in a vertical channel with Navier slip: Homotopy approach

This paper is to examine the incompressible, laminar mixed convective Navier slip flow between vertical plates with cross diffusion effects. This research includes the first order chemical reaction also. The resulting equations with boundary conditions are reduced into dimensionless form using appropriate transformations. The series solutions are developed through a modern technique known as the homotopy analysis method. The convergent expressions of velocity components and temperature are derived. The influence of emerging parameters on fluid flow quantities have been presented graphically. Also, the nature of physical quantities are shown in tabular form.     

Site-Specific Hyperphosphorylation Inhibits,Rather than Promotes,Tau Fibrillization,Seeding Capacity,and Its Microtubule Binding

The consistent observation of phosphorylated tau in the pathology of Alzheimer's disease has contributed to the emergence of a model where hyperphosphorylation triggers both tau disassociation from microtubules and its subsequent aggregation. Herein, we applied a total chemical synthetic approach to site-specifically phosphorylate the microtubule binding repeat domain of tau (K18) at single (pS356) or multiple (pS356/pS262 and pS356/pS262/pS258) residues. We show that hyperphosphorylation of K18 inhibits 1) its aggregation in vitro, 2) its seeding activity in cells, 3) its binding to microtubules, and 4) its ability to promote microtubule polymerization. The inhibition increased with increasing the number of phosphorylated sites, with phosphorylation at S262 having the strongest effect. Our results argue against the hyperphosphorylation hypothesis and underscore the importance of revisiting the role of site-specific hyperphosphorylation in regulating tau functions in health and disease.     

One-dimensional effects in low-temperature conductivity of ultrathin metallic filaments

The resistance of ultrathin filaments (UF) of Hg (with diameters 20–40 Å) increases as the temperature is lowered as $\text{ΔR/R ～ T}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}\text{(T < 60}\text{K}\text{)}$ and decreases with the applied electrical field as $\text{ΔR/R ～}\text{1}\text{E}$. The magnitude 1113 1104 of this effects increases as the diameter of UF is made smaller. Such temperature dependence is interpreted in terms of weak electron localization in one-dimension. The non-linearity of current-voltage characteristics of UF is due to electron-electron interactions in one-dimensional tunnel junctions.