NEW NON-NATURALLY REDUCTIVE EINSTEIN METRICS ON Sp(n)

In this paper, we consider a class of left invariant Riemannian metrics on Sp(n),which is invariant under the adjoint action of the subgroup Sp(n-3) × Sp(1) × Sp(1) × Sp(1).Based on the related formulae in the literature, we show that the existence of Einstein metrics is equivalent to the existence of solutions of some homogeneous Einstein equations. Then we use a technique of the Gr?bner basis to get a sufficient condition for the existence, and show that this method will lead to new non-naturally reductive metrics.

Influence of Non-Natural Ageing Temperature on the Microstructural Characteristics and Mechanical Properties of Cast Aluminum 6063 Alloy

This research considered the effect of non-natural aging on the microstructural characteristics and mechanical properties of as-cast aluminum 6063 alloys. The samples were developed through a sand casting process and machined into tensile and impact test samples before carrying out solution heat treatment at 550?C (0.83 Tm) on two parts of the samples while retaining one part as the control. The two parts were further divided into sets denoted A and B and were aged at 180?C (0.27 Tm) and 160?C (0.24 Tm), respectively, for 12 hours. The results showed that sample A has the optimal yield strength and ultimate tensile strength of 192 and 206 MPa, respectively. Likewise, the sample gave the highest impact strength value of about 9.63 J/mm2. The observed results were supported by the optical micrograph, which revealed that the sample has evenly dispersed precipitates in its microstructure. This is deemed responsible for the observed increase in strength of the sample.

Non-naturally reductive Einstein metrics on Sp(n)

We prove that Sp(2k+l)admits at least two non-naturally reductive Einstein metrics which are Ad(Sp(k)×Sp(k)×Sp(l))-invariant ifk<1.It implies that every compact simple Lie group Sp(n)for n≥4 admits at least 2[(n-1)/3]non-naturally reductive left-invariant Einstein metrics.

Creation of cytochrome P450 catalysis depending on a non-natural cofactor for fatty acid hydroxylation

Cytochrome P450 enzymes catalyze diverse oxidative transformations at the expense of reduced nicotinamide adenine dinucleotide phosphate(NADPH),however,their applications remain limited largely because NADPH is cost-prohibitive for biocatalysis at scale yet tightly regulated in host cells.A highly challenging task for P450 catalysis has been to develop an alternative and biocompatible electrondonating system.Here we engineered P450 BM3 to favor reduced nicotinamide cytosine dinucleotide(NCDH)and created non-natural cofactor-dependent P450 catalysis.Two outstanding mutants were identified with over 640-fold NCDH preference improvement and good catalytic efficiencies of over15,000 M^(-1)s^(-1)for the oxidation of the fatty acid probe 12-(para-nitrophenoxy)-dodecanoate.Molecular docking analysis indicated that these mutants bear a compacted cofactor entrance.Upon fusing with an NCD-dependent formate dehydrogenase,fused proteins functioned as NCDH-specific P450catalysts by using formate as the electron donor.Importantly,these mutants and fusions catalyzed NCDH-dependent hydroxylation of fatty acids with similar chain length preference to those by natural P450 BM3 in the presence of NADPH and also similar regioselectivity for subterminal hydroxylation of lauric acid.As P450 BM3 and its variants are catalytically powerful to take diverse substrates and convey different reaction paths,our results offer an exciting opportunity to devise advanced cell factories that convey oxidative biocatalysis with an orthogonal reducing power supply system.

Path Integral Quantization of Non-Natural Lagrangian

Path integral technique is discussed using Hamilton Jacobi method. The Hamilton Jacobi function of non-natural Lagrangian is obtained using separation of variables method. This function makes an important role in path integral quantization. The path integral is obtained as integration over the canonical phase space coordinates, which contains the generalized coordinate q and the generalized momentum p. One illustrative example is considered to explain the application of our formalism.

Law of iterated logarithm and model selection consistency for generalized linear models with independent and dependent responses

We study the law of the iterated logarithm (LIL) for the maximum likelihood estimation of the parameters (as a convex optimization problem) in the generalized linear models with independent or weakly dependent (ρ-mixing) responses under mild conditions. The LIL is useful to derive the asymptotic bounds for the discrepancy between the empirical process of the log-likelihood function and the true log-likelihood. The strong consistency of some penalized likelihood-based model selection criteria can be shown as an application of the LIL. Under some regularity conditions, the model selection criterion will be helpful to select the simplest correct model almost surely when the penalty term increases with the model dimension, and the penalty term has an order higher than O(log log n) but lower than O(n). Simulation studies are implemented to verify the selection consistency of Bayesian information criterion.

Site-Specific Conjugation of Cell Wall Polyrhamnose to Protein SpyAD Envisioning a Safe Universal Group A Streptococcal Vaccine

Development of an effective vaccine against the leading human bacterial pathogen group A Streptococcus(GAS)is a public health priority.The species defining group A cell wall carbohydrate(GAC,Lancefield antigen)can be engineered to remove its immunodominant N-acetylglucosamine(GlcNAc)side chain,implicated in provoking autoimmune cross-reactivity in rheumatic heart disease,leaving its polyrhamnose core(GACPR).Here we generate a novel protein conjugate of the GACPR and test the utility of this conjugate antigen in active immunization.Instead of conjugation to a standard carrier protein,we selected SpyAD,a highly conserved GAS surface protein containing both B-cell and T-cell epitopes relevant to the bacterium that itself shows promise as a vaccine antigen.SpyAD was synthesized using the XpressTM cell-free protein expression system,incorporating a non-natural amino acid to which GACpr was conjugated by site-specific click chemistry to yield high molecular mass SpyAD-GACPR conjugates and avoid disruption of important T-cell and B-cell immunological epitopes.The conjugated SpyAD-GACPR elicited antibodies that bound the surface of multiple GAS strains of diverse M types and promoted opsonophagocytic killing by human neutrophils.Active immunization of mice with a multivalent vaccine consisting of SpyAD-GACPR,together with candidate vaccine antigens streptolysin O and C5a peptidase,protected against GAS challenge in a systemic infection model and localized skin infection model,without evidence of cross reactivity to human heart or brain tissue epitopes.This general approach may allow GAC to be safely and effectively included in future GAS subunit vaccine formulations with the goal of broad protection without autoreactivity.