Some Penrose transforms in complex differential geometry

In this article, we review a construction in the complex geometry often known as the Penrose transform. We then present two new applications of this transform. One concerns the construction of symmetries of the massless field equations from mathematical physics. The other concerns obstructions to the embedding of CR structures on the three-sphere. Dedicated to Professor Sheng GONG on the occasion of his 75th birthday     

Quantum Bayesian computation

Quantum Bayesian computation is an emerging field that levers the computational gains available from quantum computers. They promise to provide an exponential speed-up in Bayesian computation. Our article adds to the literature in three ways. First, we describe how quantum von Neumann measurement provides quantum versions of popular machine learning algorithms such as Markov chain Monte Carlo and deep learning that are fundamental to Bayesian learning. Second, we describe quantum data encoding methods needed to implement quantum machine learning including the counterparts to traditional feature extraction and kernel embeddings methods. Third, we show how quantum algorithms naturally calculate Bayesian quantities of interest such as posterior distributions and marginal likelihoods. Our goal then is to show how quantum algorithms solve statistical machine learning problems. On the theoretical side, we provide quantum versions of high dimensional regression, Gaussian processes and stochastic gradient descent. On the empirical side, we apply a quantum FFT algorithm to Chicago house price data. Finally, we conclude with directions for future research.     

非线性问题严格互补极点－鞍点定理

本文给出两个具有新的非线性型式问题的严格互补极点－鞍点定理，同时论述了建议的二次变分－凸分析方法的一般性和有效性。其一是旋转叶轮问题，通过引进周期性自由面变量，揭示了隐含的一类对偶变分原理，从而给出了可能存在的全部互补原理。其二是带转动变量的非Ｋ－Ｌ壳体，具有超出常规的几何非线性性质，目前只知道使用这里的方法可以建立互补原理。     

有限变形弹性动力学的非传统Gurtin型变分原理

根据古典阴阳互补和现代对偶互补的基本思想，通过作者早已提出的一条简单而统一的途径，系统地建立了有限变形弹性动力学的各类非传统Gurtin型变分原理，给出一个以卷积表示的重要关系式，可以认为，该式是有限变形动力学的广义虚功原理的表式。从该式出发，不仅能得到有限变形动力学的虚功原理，而且通过给出的一系列广义Legendre变换，还能系统地成对导出5类变量，3类变量，2类变量和1类变量非传统Gurtin型变分原理的互补泛函。通过这条途径还能清楚地阐明这些原理之间的内在联系。     

Deciphering composition and connectivity of a natural product with the assistance of MS and 2D NMR

A complementary application of three analytical techniques, viz. multidimensional nuclear magnetic resonance spectroscopy (NMR), mass spectrometry (MS), and single‐crystal X‐ray diffractometry was required to identify and refine two natural products isolated from Millettia versicolor and solvent of crystallization. The two compounds, namely 3‐(2H‐1,3‐benzodioxol‐5‐yl)‐6‐methoxy‐8,8‐dimethyl‐4H ,8H‐pyrano[2,3‐h ]chromen‐4‐one, or durmillone, (I), and (2E )‐1‐(4‐{[(2E )‐3,7‐dimethylocta‐2,6‐dien‐1‐yl]oxy}‐2‐hydroxyphenyl)‐3‐(4‐hydroxyphenyl)prop‐2‐en‐1‐one, (II), could not be separated by routine column chromatography and cocrystallized in a 2:1 ratio with 0.13 molecules of ethanol solvent. Compound (II) and ethanol could not be initially identified by single‐crystal X‐ray analysis due to complex disorder in the aliphatic chain region of (II). Mass spectrometry ensured that (II) represented only one species disordered over several positions in the solid state, rather than several species cohabitating on the same crystallographic site. The atomic identification and connectivity in (II) were established by several 2D (two‐dimensional) NMR techniques, which in turn relied on a knowledge of its exact mass. The derived connectivity was then used in the single‐crystal analysis to model the disorder of the aliphatic chain in (II) over three positions and allowed identification of a partially occupied ethanol solvent molecule that was disordered over an inversion center. The disordered moieties were refined with restraints and constraints.     

Corrigendum to “New algebraic properties of an amalgamated algebra along an ideal”

At some point, after publication, we realized that Proposition 4.1(2) and Theorem 4.4 in [2 D’Anna, M., Finocchiaro, C. A., Fontana, M. (2016). New algebraic properties of an amalgamated algebra along an ideal. Commun. Algebra 44(5):1836–1851.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]] hold under the assumption (not explicitly declared) that B = f(A)+J. Furthermore, we provide here the exact value for the embedding dimension of A?^fJ, also when B≠f(A)+J, under the hypothesis that J is finitely generated as an ideal of the ring f(A)+J.     

稀疏特征空间嵌入正则化：鲁棒的半监督学习框架

在机器学习领域,半监督学习作为一种有力工具吸引了越来越多的关注,其利用少量带标签数据和大量无标签数据进行有效学习,其中基于图的半监督学习方法因其优雅的数学形式和良好的学习性能而引起更广泛的研究。针对现有基于图的半监督学习方法所存在的模型参数敏感和数据判别信息不充分等问题,提出一种稀疏特征空间嵌入正则化（Sparse Feature Space embedding Regularization ,SFSR ）半监督学习框架,其主要思想为：首先分别将原始数据嵌入到线性特征空间,然后利用特征空间嵌入投影点集来稀疏重构原始数据,随后在由原始数据线性张成的标签空间通过保留这种稀疏表示关系来构建一个Laplacian正则化项,或称SFSR ,最后提出一个鲁棒的基于SFSR的半监督学习框架,在几个实际基准数据库上的综合实验结果证实了所提框架的鲁棒有效性。     

Design and analysis of noise margin,write ability and read stability of organic and hybrid 6-T SRAM cell

This paper analyzes SRAM cell designs based on organic and inorganic thin film transistors (TFTs). The performance in terms of static noise margin (SNM), read stability and write ability for all-p organic (Pentacene–Pentacene), organic complementary (Pentacene–C₆₀) and hybrid complementary (Pentacene–ZnO) configurations of SRAM cell is evaluated using benchmarked industry standard Atlas 2-D numerical device simulator. Moreover, the cell behaviour is analyzed at different cell and pull-up ratios. The electrical characteristics and performance parameters of individual TFT used in SRAM cell is verified with reported experimental results. Furthermore, the analytical result for SNM of all-p organic SRAM cell is validated with respect to the simulated result. Besides this, the cell and pull-up ratios of the hybrid and organic SRAM cells are optimized for achieving best performance of read and write operations and thereafter, the results are verified analytically also. The SNM of hybrid cell is almost two times higher than the all-p SRAM, whereas this improvement is just 18% in comparison to the organic memory cell. On the other hand, the organic complementary SRAM cell shows an improvement of 26% and 22% for the read stability in comparison to the all-p organic and hybrid SRAM cells, respectively. Contrastingly, this organic cell demonstrates a reduction of 16% in the SNM and an increment of 76% in write access time in comparison to the hybrid cell. To achieve an overall improved performance, the organic complementary SRAM cell is designed such that the access transistors are pentacene based p-type instead of often used n-type transistor. Favorably, this organic SRAM design shows reasonably lower write access time in comparison to the cell with n-type access OTFTs. Moreover, this cell shows adequate SNM and read stability that too at substantially lower width of p-type access OTFTs.     

Reducing PAPR of SC‐FDMA Signals through Simple Amplitude Predistortion

A novel peak‐to‐average power ratio (PAPR) reduction method is proposed for single‐carrier frequency‐division multiple access (SC‐FDMA) signals. The proposed method deliberately distorts the amplitude values of a few of the complex modulated symbols that cause peaks beyond a predetermined threshold in the samples of the output signal. The method then marks the location indices of the distorted symbols by using a pilot block at the transmitter without transmitting side information. At the receiver, the method is then able to recover the distorted amplitude values through the marked location indices. Computer simulation results show that when compared to conventional SC‐FDMA signals, the proposed scheme can effectively reduce the PAPR of SC‐FDMA signals with asymptotically consistent bit error rate (BER) performance.