The Legendre Transform of the Holst Action

I start with a short introduction on 3+1 ADM form and the tetrad form of General Relativity, then I review the Legendre transform of the Einstein-Hilbert action and the Palatini action. The Holst action is a generalization of the Palatini action by including a topological term. I derive Ashtekar\u27s connection form directly from this action by doing the Legendre transformation rather than by a canonical transformation in the usual phase space. This is done in both Remmanian signature with half-flat connection and Lorentz signature with general Barbero-Immirzi parameter

Cosmological And Astrophysical Tests Of Modified Gravity

Three alternative theories to general relativity will be studied. The aim is to test these theories by applying them to astronomical objects or the cosmological background. The first one is unimodular relativity. The cosmological perturbation theory of this model is studied and the predictions on temperature fluctuations of the cmb are found. The second one is drgt massive gravity. In this theory a charged black hole solution is found and compared to those in gr, folloby constraints on the parameter space. The third one is a general massive gravity theory which shares the same background equation with the massless case except the evolution equation for the tensor perturbations. The signature of the graviton mass on the cmb polarization spectrum will be studied. A moderate graviton mass (comparable to the hubble rate during recombination) leads to interesting modifications on the b mode polarization power spectrum. A large graviton mass is found to suppress the spectrum, therefore a tight constraint on the graviton mass can be found

The Mini-batch Stochastic Conjugate Algorithms with the unbiasedness and Minimized Variance Reduction

We firstly propose the new stochastic gradient estimate of unbiasedness and minimized variance in this paper. Secondly, we propose the two algorithms: Algorithml and Algorithm2 which apply the new stochastic gradient estimate to modern stochastic conjugate gradient algorithms SCGA 7and CGVR 8. Then we prove that the proposed algorithms can obtain linearconvergence rate under assumptions of strong convexity and smoothness. Finally, numerical experiments show that the new stochastic gradient estimatecan reduce variance of stochastic gradient effectively. And our algorithms compared SCGA and CGVR can convergent faster in numerical experimentson ridge regression model.Comment: 17 pages, 3 figure

Influencing Factors Study of the Variable Speed Scroll Compressor with EVI Technology

Heating capacity of general air-condition system at low ambient temperature has been heavily attenuated. To solve the problem stated, the variable speed Scroll compressor with enhanced vapor injection (EVI) becomes the focus of the study in recent years. Influencing factors of the capacity and energy efficiency of the scroll compressor with EVI technology have been introduced in paper, including the area of Supplementary channel, the parameters of orbiting and fixed scroll profile, the position and number of Supplementary inlet. The different scheme of prototype is tested and the effect of the scheme is compared and analyzed. With the vapor injected into compress chambers, the Gas forces of working chambers change, and the characteristics of gas force about the scroll compressor with EVI Technology have also been analyzed

Three-Dimensional Shape Measurements of Specular Objects Using Phase-Measuring Deflectometry

The fast development in the fields of integrated circuits, photovoltaics, the automobile industry, advanced manufacturing, and astronomy have led to the importance and necessity of quickly and accurately obtaining three-dimensional (3D) shape data of specular surfaces for quality control and function evaluation. Owing to the advantages of a large dynamic range, non-contact operation, full-field and fast acquisition, high accuracy, and automatic data processing, phase-measuring deflectometry (PMD, also called fringe reflection profilometry) has been widely studied and applied in many fields. Phase information coded in the reflected fringe patterns relates to the local slope and height of the measured specular objects. The 3D shape is obtained by integrating the local gradient data or directly calculating the depth data from the phase information. We present a review of the relevant techniques regarding classical PMD. The improved PMD technique is then used to measure specular objects having discontinuous and/or isolated surfaces. Some influential factors on the measured results are presented. The challenges and future research directions are discussed to further advance PMD techniques. Finally, the application fields of PMD are briefly introduce

A novel ZRS variant causes preaxial polydactyly type I by increased sonic hedgehog expression in the developing limb bud.

PurposePreaxial polydactyly (PPD) is a common congenital hand malformation classified into four subtypes (PPD I-IV). Variants in the zone of polarizing activity regulatory sequence (ZRS) within intron 5 of the LMBR1 gene are linked to most PPD types. However, the genes responsible for PPD I and the underlying mechanisms are unknown.MethodsA rare large four-generation family with isolated PPD I was subjected to genome-wide genotyping and sequence analysis. In vitro and in vivo functional studies were performed in Caco-2 cells, 293T cells, and a knockin transgenic mouse model.ResultsA novel g.101779T>A (reference sequence: NG_009240.2; position 446 of the ZRS) variant segregates with all PPD I-affected individuals. The knockin mouse with this ZRS variant exhibited PPD I phenotype accompanying ectopic and excess expression of Shh. We confirmed that HnRNP K can bind the ZRS and SHH promoters. The ZRS mutant enhanced the binding affinity for HnRNP K and upregulated SHH expression.ConclusionOur results identify the first PPD I disease-causing variant. The variant leading to PPD I may be associated with enhancing SHH expression mediated by HnRNP K. This study adds to the ZRS-associated syndromes classification system for PPD and clarifies the underlying molecular mechanisms

Icariside II Ameliorates Cognitive Impairments Induced by Chronic Cerebral Hypoperfusion by Inhibiting the Amyloidogenic Pathway: Involvement of BDNF/TrkB/CREB Signaling and Up-Regulation of PPARα and PPARγ in Rats

Chronic cerebral hypoperfusion (CCH) is regarded as a high-risk factor for cognitive decline of vascular dementia (VD) as it is conducive to induce beta-amyloid (Aβ) aggregation. Icariside II (ICS II), a plant-derived flavonoid compound, has showed neuroprotective effect on animal models of Alzheimer’s disease (AD) by decreasing Aβ levels. Here, we assessed the effect of ICS II on CCH-induced cognitive deficits and Aβ levels in rats, and the possible underlying mechanisms were also explored. It was disclosed that CCH induced by bilateral common carotid artery occlusion (BCCAO) caused cognitive deficits, neuronal injury and increase of Aβ1-40 and Aβ1-42 levels in the rat hippocampus, while oral administration of ICS II for 28 days abolished the above deficits in the hippocampus of BCCAO rats. Meanwhile, ICS II significantly decreased the expression of beta-amyloid precursor protein (APP) and β-site amyloid precursor protein cleavage enzyme 1 (BACE1), as well as increased the expression of a disintegrin and metalloproteinase domain 10 (ADAM10) and insulin-degrading enzyme (IDE). ICS II also activated peroxisome proliferator-activated receptor (PPAR)α and PPARγ, enhanced the expression of brain-derived neurotrophic factor (BDNF), tyrosine receptor kinase B (TrkB), levels of Akt and cAMP response element binding protein (CREB) phosphorylation. Together, these findings suggested that ICS II attenuates CCH-induced cognitive deficits by inhibiting the amyloidogenic pathway via involvement of BDNF/TrkB/CREB signaling and up-regulation of PPARα and PPARγ in rats