A block coordinate gradient descent method for regularized convex separable optimization and covariance selection

We consider a class of unconstrained nonsmooth convex optimization problems, in which the objective function is the sum of a convex smooth function on an open subset of matrices and a separable convex function on a set of matrices. This problem includes the covariance selection problem that can be expressed as an ℓ ₁-penalized maximum likelihood estimation problem. In this paper, we propose a block coordinate gradient descent method (abbreviated as BCGD) for solving this class of nonsmooth separable problems with the coordinate block chosen by a Gauss-Seidel rule. The method is simple, highly parallelizable, and suited for large-scale problems. We establish global convergence and, under a local Lipschizian error bound assumption, linear rate of convergence for this method. For the covariance selection problem, the method can terminate in O(n³/e){O(n^3/\epsilon)} iterations with an e{\epsilon}-optimal solution. We compare the performance of the BCGD method with the first-order methods proposed by Lu (SIAM J Optim 19:1807–1827, 2009; SIAM J Matrix Anal Appl 31:2000–2016, 2010) for solving the covariance selection problem on randomly generated instances. Our numerical experience suggests that the BCGD method can be efficient for large-scale covariance selection problems with constraints.     

Gold-catalyzed cycloisomerizations of 1-(2-(tosylamino)phenyl)prop-2-yn-1-ols to 1H-indole-2-carbaldehydes and (E)-2-(iodomethylene)indolin-3-ols

A method to prepare 1H-indole-2-carbaldehydes and (E)-2-(iodomethylene)indolin-3-ols by gold(I)-catalyzed cycloisomerization of 1-(2-(tosylamino)phenyl)prop-2-yn-1-ols with N-iodosuccinimide (NIS) is reported. The reactions were shown to be operationally simplistic and proceed efficiently for a wide variety of substrates, affording the corresponding products in good to excellent yields (70-99%). The mechanism is suggested to involve activation of the alkyne moiety of the substrate by the gold(I) catalyst. This triggers intramolecular addition of the tethered aniline moiety to give a vinyl gold intermediate, which undergoes iododeauration with NIS to give the (E)-2-(iodomethylene)indolin-3-ol adduct. Subsequent 1,3-allylic alcohol isomerization (1,3-AAI) followed by formylation of this vinyl iodide intermediate then gives the 1H-indole-2-carbaldehyde.     

169Re的转动带结构研究

利用在束γ谱学方法,通过反应¹⁴⁴Sm(²⁸Si,1p3n)¹⁶⁹Re研究了¹⁶⁹Re的激发态能级结构.实验进行了X-γ符合、γ-γ符合、DCO系数和带内B(M1)/B(E2)比率测量.基于这些测量,建立了组态为π9/2^－[514]的强耦合带和组态为π1/2^－[541]的退耦合带.通过比较¹⁶⁹Re的转动带与邻近奇质子核已知转动带的结构和B(M1)/B(E2)比率,指定了¹⁶⁹Re转动带的组态.实验观测到π9/2^－[514]和π1/2^－[541]转动带的中子AB带交叉的转动频率分别为0.23和0.27MeV.着重讨论了¹⁶⁹Re转动带的中子AB带交叉频率、转动角动量顺排和旋称劈列等,并讨论了奇ARe核转动带结构的系统性     

Globally and Quadratically Convergent Algorithm for Minimizing the Sum of Euclidean Norms

For the problem of minimizing the sum of Euclidean norms (MSN), most existing quadratically convergent algorithms require a strict complementarity assumption. However, this assumption is not satisfied for a number of MSN problems. In this paper, we present a globally and quadratically convergent algorithm for the MSN problem. In particular, the quadratic convergence result is obtained without assuming strict complementarity. Examples without strictly complementary solutions are given to show that our algorithm can indeed achieve quadratic convergence. Preliminary numerical results are reported.     

双奇核172Re高自旋态转动带结构实验研究

利用重离子熔合蒸发反应¹⁴⁹Sm(²⁷Al,4nγ)¹⁷²Re布居了形变双奇核¹⁷²Re的高自旋态,用12套带有BGO反康普顿抑制的高纯锗探测器阵列进行了在束γ实验测量,首次建立了形变双奇核¹⁷²Re由3个转动带构成的高自旋态能级纲图.研究和讨论了3个转动带的结构特征,基于已有的高自旋态核结构知识并通过系统学比较和分析指出它们的准粒子组态分别为πh_11/2⊙νi_13/2,πh_9/2⊙νi_13/2和π1/2^－[541]⊙ν1/2^－[521].发现前两个转动带在自旋小于18.5h时其转动能级呈现反常的旋称劈裂.     

Superlinear Convergence of a Newton-Type Algorithm for Monotone Equations

We consider the problem of finding solutions of systems of monotone equations. The Newton-type algorithm proposed in Ref. 1 has a very nice global convergence property in that the whole sequence of iterates generated by this algorithm converges to a solution, if it exists. Superlinear convergence of this algorithm is obtained under a standard nonsingularity assumption. The nonsingularity condition implies that the problem has a unique solution; thus, for a problem with more than one solution, such a nonsingularity condition cannot hold. In this paper, we show that the superlinear convergence of this algorithm still holds under a local error-bound assumption that is weaker than the standard nonsingularity condition. The local error-bound condition may hold even for problems with nonunique solutions. As an application, we obtain a Newton algorithm with very nice global and superlinear convergence for the minimum norm solution of linear programs.This research was supported by the Singapore-MIT Alliance and the Australian Research Council.     

The measurement of slope using shearography

This paper presents an optical method which is based on speckle-shearing interferometry for the measurement of the slope at any point of an object. The object under study is illuminated by an expanded laser beam and its image is recorded on a photographic plate placed at the image plane of an image-shearing camera. A second exposure on the photographic film is made after the light source is moved slightly. The resulting photograph yields a fringe pattern which represents lines of constant displacement gradients. Theory of the method as well as some experimental results are presented.     

179Au的1/2[660](πi13/2)转动带

利用能量为164—180MeV的³⁵Cl束流,通过重离子核反应¹⁴⁹Sm(³⁵Cl,5n)研究了¹⁷⁹Au的高自旋态能级结构.实验进行了γ射线的激发函数、X-γ和γ-γ-t符合测量.基于对实验测量结果的分析,首次建立了¹⁷⁹Au的1/2[660](πi_13/2)转动带.结合已有的实验数据,着重讨论了奇AAu核中1/2[660](πi_13/2)转动带的带头激发能随中子数的变化     

Graphene field-effect transistors with ferroelectric gating

Recent experiments on ferroelectric gating have introduced a novel functionality, i.e., nonvolatility, in graphene field-effect transistors. A comprehensive understanding in the nonlinear, hysteretic ferroelectric gating and an effective way to control it are still absent. In this Letter, we quantitatively characterize the hysteretic ferroelectric gating using the reference of an independent background doping (n(BG)) provided by normal dielectric gating. More importantly, we prove that n(BG) can be used to control the ferroelectric gating by unidirectionally shifting the hysteretic ferroelectric doping in graphene. Utilizing this electrostatic effect, we demonstrate symmetrical bit writing in graphene-ferroelectric field-effect transistors with resistance change over 500% and reproducible no-volatile switching over 10? cycles.     

Equivalences and differences in conic relaxations of combinatorial quadratic optimization problems

Various conic relaxations of quadratic optimization problems in nonnegative variables for combinatorial optimization problems, such as the binary integer quadratic problem, quadratic assignment problem (QAP), and maximum stable set problem have been proposed over the years. The binary and complementarity conditions of the combinatorial optimization problems can be expressed in several ways, each of which results in different conic relaxations. For the completely positive, doubly nonnegative and semidefinite relaxations of the combinatorial optimization problems, we discuss the equivalences and differences among the relaxations by investigating the feasible regions obtained from different representations of the combinatorial condition which we propose as a generalization of the binary and complementarity condition. We also study theoretically the issue of the primal and dual nondegeneracy, the existence of an interior solution and the size of the relaxations, as a result of different representations of the combinatorial condition. These characteristics of the conic relaxations affect the numerical efficiency and stability of the solver used to solve them. We illustrate the theoretical results with numerical experiments on QAP instances solved by SDPT3, SDPNAL+ and the bisection and projection method.