Sulfate encapsulation in a metal-assisted capsule based on a mono-pyridylurea ligand

A sulfate-encapsulating complex, [Cu(1)L(6)]·3[Cu(2)L(2)(DMF)(4)](SO(4))(4) (1, L = N-(1-naphthyl)-N'-(3-pyridyl)urea) is synthesized in which two C(3)-clefts of the octahedral complexes interdigitate to form a cavity to encapsulate the sulfate ion by six urea groups.     

A feasible method for optimization with orthogonality constraints

Minimization with orthogonality constraints (e.g., $X^\top X = I$ ) and/or spherical constraints (e.g., $\Vert x\Vert _2 = 1$ ) has wide applications in polynomial optimization, combinatorial optimization, eigenvalue problems, sparse PCA, p-harmonic flows, 1-bit compressive sensing, matrix rank minimization, etc. These problems are difficult because the constraints are not only non-convex but numerically expensive to preserve during iterations. To deal with these difficulties, we apply the Cayley transform—a Crank-Nicolson-like update scheme—to preserve the constraints and based on it, develop curvilinear search algorithms with lower flops compared to those based on projections and geodesics. The efficiency of the proposed algorithms is demonstrated on a variety of test problems. In particular, for the maxcut problem, it exactly solves a decomposition formulation for the SDP relaxation. For polynomial optimization, nearest correlation matrix estimation and extreme eigenvalue problems, the proposed algorithms run very fast and return solutions no worse than those from their state-of-the-art algorithms. For the quadratic assignment problem, a gap 0.842 % to the best known solution on the largest problem “tai256c” in QAPLIB can be reached in 5 min on a typical laptop.     

吡嗪类碳酰肼化合物与CT-DNA相互作用及体外抑菌

以5-氯吡嗪-2-羧酸甲酯和水合肼为原料,经亲核取代和脱水缩合反应合成了3种新型吡嗪类碳酰肼化合物C13H14N6O(a)、C13H14N6O2(b)和C12H12N6O2(c)。采用元素分析与核磁共振氢谱对化合物a~c进行了表征,结果表明合成的产物即为目标化合物。通过溶剂挥发法培养得到了化合物a的单晶并利用X-射线单晶衍射测定化合物a的晶体结构为单斜晶系。根据紫外-可见光谱可知,化合物a~c均以插入模式与CT-DNA作用。利用微量热实验测定了化合物a~c与CT-DNA的相互作用,发现反应过程放热,热效应ΔH依次为-5.77×103、 -5.50×103和-5.96×103 kJ·moL-1,反应时间均小于40 min。通过分子对接模拟计算明确了化合物a和b与DNA的具体结合位点包括A链DC4和DG5以及B链DC4、 DG5和DA6,化合物c与DNA的具体结合位点包括A链DC4和DG5以及B链DC4和DG5。采用牛津杯法测定了化合物a~c对枯草芽孢杆菌、金黄色葡萄球菌、铜绿假单胞菌以及大肠杆菌四种细菌的抑菌活性,结果表明化合物a~c均对铜绿假单胞菌表现出优于阳性对照组四环素的抑菌活性。     

An alternating direction algorithm for matrix completion with nonnegative factors

This paper introduces an algorithm for the nonnegative matrix factorization-and-completion problem, which aims to find nonnegative low-rank matrices X and Y so that the product XY approximates a nonnegative data matrix M whose elements are partially known (to a certain accuracy). This problem aggregates two existing problems: (i) nonnegative matrix factorization where all entries of M are given, and (ii) low-rank matrix completion where nonnegativity is not required. By taking the advantages of both nonnegativity and low-rankness, one can generally obtain superior results than those of just using one of the two properties. We propose to solve the non-convex constrained least-squares problem using an algorithm based on the classical alternating direction augmented Lagrangian method. Preliminary convergence properties of the algorithm and numerical simulation results are presented. Compared to a recent algorithm for nonnegative matrix factorization, the proposed algorithm produces factorizations of similar quality using only about half of the matrix entries. On tasks of recovering incomplete grayscale and hyperspectral images, the proposed algorithm yields overall better qualities than those produced by two recent matrix-completion algorithms that do not exploit nonnegativity.     

A stochastic extra-step quasi-Newton method for nonsmooth nonconvex optimization

In this paper, a novel stochastic extra-step quasi-Newton method is developed to solve a class of nonsmooth nonconvex composite optimization problems. We assume that the gradient of the smooth part of the objective function can only be approximated by stochastic oracles. The proposed method combines general stochastic higher order steps derived from an underlying proximal type fixed-point equation with additional stochastic proximal gradient steps to guarantee convergence. Based on suitable bounds on the step sizes, we establish global convergence to stationary points in expectation and an extension of the approach using variance reduction techniques is discussed. Motivated by large-scale and big data applications, we investigate a stochastic coordinate-type quasi-Newton scheme that allows to generate cheap and tractable stochastic higher order directions. Finally, numerical results on large-scale logistic regression and deep learning problems show that our proposed algorithm compares favorably with other state-of-the-art methods.

     

Alternating direction augmented Lagrangian methods for semidefinite programming

We present an alternating direction dual augmented Lagrangian method for solving semidefinite programming (SDP) problems in standard form. At each iteration, our basic algorithm minimizes the augmented Lagrangian function for the dual SDP problem sequentially, first with respect to the dual variables corresponding to the linear constraints, and then with respect to the dual slack variables, while in each minimization keeping the other variables fixed, and then finally it updates the Lagrange multipliers (i.e., primal variables). Convergence is proved by using a fixed-point argument. For SDPs with inequality constraints and positivity constraints, our algorithm is extended to separately minimize the dual augmented Lagrangian function over four sets of variables. Numerical results for frequency assignment, maximum stable set and binary integer quadratic programming problems demonstrate that our algorithms are robust and very efficient due to their ability or exploit special structures, such as sparsity and constraint orthogonality in these problems.     

A new sulfonamide derivative as magnesium ion receptor: N-tosyl-2,6-diisopropyl-4-(2,3-dimethoxylbenzoylamide)aniline

N-Tosyl-2,6-diisopropyl-4-(2,3-dimethoxylbenzoylamide)aniline (1) has been synthesized and its metal ion (Na⁺, K⁺, Ca²⁺, Mg²⁺) coordinating properties investigated by FT-IR, ESI-MS, and ¹H NMR methods. Among the tested metal ions, the overall stability constant (log K) for Mg²⁺ (6.89) is the highest (Na⁺, 5.64; K⁺, 5.43; Ca²⁺, 5.51) in 10% water/THF at 25.0 ± 0.5 °C determined by UV-vis spectroscopy, indicating that 1 is a potent ionophore for Mg²⁺ ion.     

On the local convergence of a stochastic semismooth Newton method for nonsmooth nonconvex optimization

Science China Mathematics - In this work, we present probabilistic local convergence results for a stochastic semismooth Newton method for a class of stochastic composite optimization problems...     

2-吡咯类酰腙的合成、晶体结构及与小牛胸腺DNA的相互作用

以2-吡咯甲酰肼与2,4-二羟基苯甲醛和2-羟基-3-甲氧基苯甲醛经缩合反应合成2,4-二羟基苯甲醛-2-吡咯甲酰腙C₁₂H₁₁N₃O₃(Ⅰ)和2-羟基-3-甲氧基苯甲醛-2-吡咯甲酰腙C₁₃H₁₅N₃O₄(Ⅱ),并利用红外光谱、元素分析、¹H NMR、X射线单晶衍射和热重分析进行表征,结果表明晶体Ⅰ属单斜晶系,空间群为P2₁/c,Z=4,晶胞参数为a=1.2586(4) nm,b=0.8050(3) nm,c=1.1914(4) nm;晶体Ⅱ为正交晶系,空间群为P2₁2₁2₁,Z=4,晶胞参数为a=0.4756(2) nm,b=1.2491(6) nm,c=2.2145(11) nm。 热重结果显示,化合物Ⅰ和Ⅱ最大热分解峰分别出现在267.59和284.79 ℃,表观活化能分别为176.6和122.9 kJ/mol,表明化合物Ⅰ和Ⅱ具有较高的热稳定性。 利用粘度实验和微量热实验研究了化合物Ⅰ和Ⅱ与CT-DNA的相互作用,均显示两种化合物均与CT-DNA发生了插入作用,且相互作用过程放热,焓变值分别为ΔH(Ⅰ)=4.67 kJ/mol和ΔH(Ⅱ)=4.40 kJ/mol。