Fisher-like atomic divergences: Mathematical grounds and physical applications

Two different local divergence measures, the Fisher (FD) and the Jensen–Fisher (JFD) ones, are compared in this work by applying them to atomic one-particle densities in position and momentum spaces. They are defined in terms of the absolute and the relative Fisher information functionals. The analysis here afforded includes not only neutral atoms, but also singly-charged cations. The results are interpreted and justified according to (i) shell-filling patterns, (ii) short- and long-range behaviors of the atomic densities, and (iii) the value of the atomic ionization potential. The strengths of the FD measure, as compared to the JFD one, are emphasized.     

Natural gradient algorithm for stochastic distribution systems with output feedback

In this paper, we use natural gradient algorithm to control the shape of the conditional output probability density function for the stochastic distribution systems from the viewpoint of information geometry. The considered system here is of multi-input and single output with an output feedback and a stochastic noise. Based on the assumption that the probability density function of the stochastic noise is known, we obtain the conditional output probability density function whose shape is only determined by the control input vector under the condition that the output feedback is known at any sample time. The set of all the conditional output probability density functions forms a statistical manifold (M), and the control input vector and the output feedback are considered as the coordinate system. The Kullback divergence acts as the distance between the conditional output probability density function and the target probability density function. Thus, an iterative formula for the control input vector is proposed in the sense of information geometry. Meanwhile, we consider the convergence of the presented algorithm. At last, an illustrative example is utilized to demonstrate the effectiveness of the algorithm.     

An Objective Prior from a Scoring Rule

In this paper, we introduce a novel objective prior distribution levering on the connections between information, divergence and scoring rules. In particular, we do so from the starting point of convex functions representing information in density functions. This provides a natural route to proper local scoring rules using Bregman divergence. Specifically, we determine the prior which solves setting the score function to be a constant. Although in itself this provides motivation for an objective prior, the prior also minimizes a corresponding information criterion.     

Identification of functional divergence sites in dopamine receptors of vertebrates

Dopamine is one of the major neurotransmitters in the brain and body, and regulates a wide variety of functions via its binding with dopamine receptors. Abnormalities in dopamine receptors have also been found to be related to various neurological disorders. For such reason, dopamine receptors are among the key components to understanding the molecular mechanisms of many diseases, they are also the potential drug targets for the treatment of many diseases. Till now, five different dopamine receptors (D1-D5) have been identified in mammals, which are assumed to be evolved from a common ancestor after multiple gene duplication events and functional divergence. Thus, identifying the specific features of each dopamine receptor, will not only provide clues for understanding the functional differences between the receptors, but also help us to design drugs specific for a certain subtype of receptor. In this study, we investigated the functional divergence in dopamine receptors in representative vertebrate species by analyzing their molecular evolution features. Our results showed that the coefficients for type I functional divergence (θ_I) were significantly greater than 0 for all the pairwise comparisons between the five dopamine receptors, suggesting that type I functional divergence, i.e., altered functional constraints or different evolutionary rates, may have taken place at some amino acids in the receptors. We further identified 84 potential type I functional divergence peptide sites for the pairwise comparisons between the D1-like and D2-like are identified in total. When these sites were mapped to the 3D structure of dopamine receptors, most of them were included in ICL3, M6 and M7 domains. Especially, sixteen of these sites may be the major sites associated with the changes of properties between D1-like and D2-like receptors. These sites provide molecular basis for further studies such as dopamine receptor function exploration and subtype specific drug design and screening.     

Performance of a 80 W copper vapor laser with “alignment free” unstable CAT-EYE resonator and other configurations using intra-cavity apertures

Performance of a kinetically enhanced copper vapor laser (KE-CVL) with various stable/unstable “alignment free” CAT-EYE resonator configurations are presented here in this paper. The laser used in the experiment was a 45 mm bore (∼2 l discharge volume) kinetically enhanced copper vapor laser developed in our laboratory and capable of generating maximum power of ∼80 W (at ∼9.8 kHz). The efficiency of the laser was ∼1.4% and beam divergence of ∼3.5 mrad in a plane-plane standard multimode cavity. For the first time performance of unstable CAT-EYE resonator is demonstrated with a CVL/KE-CVL. On using unstable CAT-EYE resonator the divergence of the laser beam reduced to ∼0.22 mrad (∼20-fold reduction as compared to conventional plane-plane cavity), ∼40 W output power and with excellent misalignment tolerance. The laser output power was found to be within ∼5% drift/decline with misalignment angle of about 4 mrad between the mirrors. This is a significant improvement in comparison to standard conventional unstable resonator (M ∼ 50) CVL where ∼0.5 mrad divergence is achieved with power drift/decline of about 45% at ∼4 mrad misalignment angle.Off-axis unstable CAT-EYE unstable resonator was also demonstrated for the first time with further reduction in beam divergence to ∼0.13 mrad and with output power of ∼28 W. The misalignment tolerance was found to be highest in case of off-axis unstable CAT-EYE resonator with decline/drift in laser power of only ∼10% for misalignment angle as high as ∼8 mrad. Performance with intra-cavity apertures in plane-plane type CAT-EYE resonator for transverse mode control is also presented for the first time in CVLs. It is observed that the laser beam divergence reduces significantly to 1.25 mrad (a factor of 2) on using an aperture of ∼3.5 mm at the CAT-EYE reflector as compared to its normal (R = F = d) configuration without aperture. In case of stable CAT-EYE resonator the average beam divergence reduces from 8 mrad to 4 mrad (factor of 2) on using intra-cavity aperture of about 3 mm. It was also observed that high misalignment tolerance was retained on using intra-cavity apertures in almost all the CAT-EYE resonators. Use of intra-cavity mesh was also demonstrated for the first time with stable CAT-EYE resonator for improving the beam focus-ability. Average beam divergence was reduced by a factor of 2.5 (from 8 mrad to 3 mrad) on using intra-cavity mesh. These new configurations in CAT-EYE resonators in KE-CVLs are found to be effective in improving and controlling the laser beam divergence significantly with additional characteristic of high misalignment tolerance.     

基于均值距离测度的医学图像配准

针对互信息测度在配准医学图像时易陷入局部极值、速度慢的缺点,提出了基于均值不等式的均值距离测度.首先根据均值不等式推导出5种均值距离测度：方根-算术均值距离(SAM)、方根-几何均值距离(SGM)、方根-调和均值距离(SHM)、算术-几何均值距离(AGM)、算术-调和均值距离(AHM).然后通过人体脑部CT/MR和MR-T1/PD图像的刚体配准实验,从函数曲线、配准精度、计算时间和收敛性能方面,对互信息与5种均值距离信息测度进行了比较与分析.实验结果表明,在不损失配准精度的前提下,AHM和SAM测度可以获得更快的配准速度,对噪声有很强的鲁棒性.     

Gold-Catalyzed Divergent Ring-Opening Rearrangement of Cyclopropenes Enabled by Dichotomous Gold−Carbenes

The gold-catalyzed ring-opening rearrangement of cyclopropenes affords an efficient route to either polysubstituted naphthols or aryl-substituted furans. Owing to the unique dichotomy of gold−carbenes, this protocol provides a switchable reaction selectivity between naphthols and furans enabled by the use of TFP−Au(MeCN)SbF₆ (tri(2-furyl) phosphine) or PNP(AuNTf₂)₂ (bis(diphenylphosphino)(isopropyl) amine) as catalysts respectively. It is proposed that the gold−carbene intermediate might be involved in the cyclopropene→naphthol rearrangement while the gold-carbocation is more likely to be involved in the cyclopropene→furan rearrangement.     

Development of an improved divergence‐free‐condition compensated coupled framework to solve flow problems with time‐varying geometries

In this article a coupled version of the improved divergence‐free‐condition compensated method will be proposed to simulate time‐varying geometries by direct forcing immersed boundary method. The proposed method can be seen as a quasi‐multi‐moment framework due to the fact that the momentum equations are discretized by both cell‐centered and cell‐face velocity. For simulating time‐varying geometries, a semi‐implicit iterative method is proposed for calculating the direct forcing terms. Treatments for suppressing spurious force oscillations, calculating drag/lift forces, and evaluating velocity and pressure for freshly cells will also be addressed. In order to show the applicability and accuracy, analytical as well as benchmark problems will be investigated by the present framework and compared with other numerical and experimental results.     

Analysis of a micro–macro acceleration method with minimum relative entropy moment matching

We analyse convergence of a micro–macro acceleration method for the simulation of stochastic differential equations with time-scale separation. The method alternates short bursts of path simulations with the extrapolation of macroscopic state variables forward in time. After extrapolation, a new microscopic state is constructed, consistent with the extrapolated macroscopic state, that minimises the perturbation caused by the extrapolation in a relative entropy sense. We study local errors and numerical stability of the method to prove its convergence to the full microscopic dynamics when the extrapolation time step tends to zero and the number of macroscopic state variables tends to infinity.     

A note on transverse divergence and taut Riemannian foliations

In this note we give a characterization of taut Riemannian foliations using the transverse divergence. This result turns out to be a convenient tool in the case of some standard examples. Furthermore, we show that a classical tautness result of Haefliger can be obtained in our particular setting as a straightforward consequence. In the final part of the paper we obtain a tautness characterization for transversally oriented foliations with dense leaves.