Accelerated parallel and distributed algorithm using limited internal memory for nonnegative matrix factorization

Nonnegative matrix factorization (NMF) is a powerful technique for dimension reduction, extracting latent factors and learning part-based representation. For large datasets, NMF performance depends on some major issues such as fast algorithms, fully parallel distributed feasibility and limited internal memory. This research designs a fast fully parallel and distributed algorithm using limited internal memory to reach high NMF performance for large datasets. Specially, we propose a flexible accelerated algorithm for NMF with all its \(L_1\) \(L_2\) regularized variants based on full decomposition, which is a combination of exact line search, greedy coordinate descent, and accelerated search. The proposed algorithm takes advantages of these algorithms to converges linearly at an over-bounded rate \((1-\frac{\mu }{L})(1 - \frac{\mu }{rL})^{2r}\) in optimizing each factor matrix when fixing the other factor one in the sub-space of passive variables, where r is the number of latent components, and \(\mu \) and L are bounded as \(\frac{1}{2} \le \mu \le L \le r\). In addition, the algorithm can exploit the data sparseness to run on large datasets with limited internal memory of machines, which is is advanced compared to fast block coordinate descent methods and accelerated methods. Our experimental results are highly competitive with seven state-of-the-art methods about three significant aspects of convergence, optimality and average of the iteration numbers.     

Synthesis of polysubstituted 5-hydroxyhydantoins via ring-opening of isatins

A simple and efficient tandem reaction approach was developed for the synthesis of 5-hydroxyhydantoins from one-pot reaction of isatins, phthalic anhydride or succinic anhydride, and 1,3-dimethylurea (1,3-diethylurea). The products were gained through the ring-opening of isatins process. The advantages of this report are simple operation, mild reaction conditions, good yields and easily available raw materials. It was very important for us to obtain the intermediate product and that provided a solid basis for the correct interpretation of the reaction mechanism.     

Error estimates for space–time discontinuous Galerkin formulation based on proper orthogonal decomposition

In this study, proper orthogonal decomposition (POD) method is applied to diffusion–convection–reaction equation, which is discretized using space–time discontinuous Galerkin (dG) method. We provide estimates for POD truncation error in dG-energy norm, dG-elliptic projection, and space–time projection. Using these new estimates, we analyze the error between the dG and the POD solution, and the error between the exact and the POD solution. Numerical results, which are consistent with theoretical convergence rates, are presented.     

Embeddings between weighted Copson and Cesàro function spaces

In this paper, characterizations of the embeddings between weighted Copson function spaces \(Co{p_{{p_1},{q_1}}}\left( {{u_1},{v_1}} \right)\) and weighted Cesàro function spaces \(Ce{s_{{p_2},{q_2}}}\left( {{u_2},{v_2}} \right)\) are given. In particular, two-sided estimates of the optimal constant c in the inequality

$${\left( {\int_0^\infty {{{\left( {\int_0^t {f{{\left( \tau \right)}^{{p_2}}}{v_2}\left( \tau \right)d\tau } } \right)}^{{q_2}/{p_2}}}{u_2}\left( t \right)dt} } \right)^{1/{q_2}}} \leqslant c{\left( {\int_0^\infty {{{\left( {\int_t^\infty {f{{\left( \tau \right)}^{{p_1}}}{v_1}\left( \tau \right)d\tau } } \right)}^{{q_1}/{p_1}}}{u_1}\left( t \right)dt} } \right)^{1/{q_1}}},$$

where p₁, p₂, q₁, q₂ ∈ (0,∞), p₂ ≤ q₂ and u₁, u₂, v₁, v₂ are weights on (0,∞), are obtained. The most innovative part consists of the fact that possibly different parameters p₁ and p₂ and possibly different inner weights v₁ and v₂ are allowed. The proof is based on the combination of duality techniques with estimates of optimal constants of the embeddings between weighted Cesàro and Copson spaces and weighted Lebesgue spaces, which reduce the problem to the solutions of iterated Hardy-type inequalities.

     

CHEMICAL STRUCTURE AND FUNCTIONAL PROPERTIES OF AMORPHOUS BORON CARBONITRIDE FILMS

Journal of Structural Chemistry - We report a comprehensive study of the effect of the chemical structure of boron carbonitride films on the variability of their functional characteristics. The...     

Dynamic Optical Vortex Trajectory Guided by the Symmetric Pearcey Gaussian Vortex Beam in the Uniformly Moving Parabolic Potential

This paper analytically and numerically proposes the propagation dynamics of the symmetric Pearcey Gaussian vortex beam (SPGVB) in the uniformly moving parabolic potential. The optical vortex located in the initial plane produces a vortex channel in the presence of the uniformly moving parabolic potential, called the vortex trajectory. The vortex trajectory can be manipulated dynamically by configuring different combinations of the parameters, and the optical intensity and the focal position can also be affected. Moreover, the spatial dynamic vortex trajectory is derived analytically, and the 2D on-axis and off-axis vortex scenarios are also presented. Our work expands the methods of the vortex trajectory manipulation and may broaden more practical potential applications in the particle manipulation.     

Controlling the Trajectory of Swallowtail Gaussian Beams in Dynamic Parabolic Potentials

The propagation dynamics of finite-energy Swallowtail beams in a dynamic parabolic potential, including uniformly moving, accelerating, and oscillating potentials, are investigated. The strong influence of dynamic potentials on the propagation trajectory of Swallowtail beams is demonstrated and various effective manipulations of the beams, including trajectory control, are validated. The intensity and the focal position can also be affected. In addition, the extension to 2D scenarios is also presented. The results theoretically provide more diverse manipulation possibilities for Swallowtail beams, and thus may broaden their potential applications in trajectory and particle manipulation.     

The Shackling Effect in Cyclic Azobenzene Liquid Crystal

We demonstrate here a novel method for the design of liquid crystals (LCs) via the cyclization of mesogens by flexible chains. For two azobenzene-4,4′-dicarboxylate derivatives, the cyclic dimer, cyclic bis(tetraethylene glycol azobenzene-4,4′-dicarboxylate) (CBTAD), shows LC properties with smectic A phase, while its linear counterpart, bis(2-(2′-hydroxyethyloxy)ethyl azobenzene-4,4′-dicarboxylate (BHAD), has no LC phase. The difference is ascribed to the shackling effect from the cyclic topology, which leads to the much smaller entropy change during phase transitions and increases the isotropic temperature greatly for cyclics. In addition, the trans-to-cis isomerization of azobenzene groups under UV-light is also limited in CBTAD. With the reversible isomerization of azobenzene groups, CBTAD showed interesting isothermal phase transition behaviors, where the LC phase disappeared upon photoirradiation of 365 nm UV-light, and recovered when the UV-light was off. Combined with the smectic LC nature, a novel UV-light tuned visible light regulator was designed, by simply placing CBTAD in two glass plates. The scattered phase of smectic LC was utilized as the “OFF” state for light passage, while the UV-light induced isotropic phase was utilized as the “ON” state. The shackling effect outlined here should be applicable for the design of cyclic LC oligomers/polymers with special properties.

     

Mn-Ce-M复合改性无硅残渣炭催化剂的NH3选择性还原NO性能研究

生物质作为极具潜力的可再生能源,其热解制油技术备受关注,副产物残渣炭的高值化利用是当下重要的研究内容之一。脱硅处理不仅可实现硅的资源化利用,同时可以实现炭材料的结构改性。本文开展了残渣炭煮溶脱硅研究,并基于最佳脱硅方式,探究不同金属M（M：Ho、Sb、La、Nd）对无硅残渣炭（FRB）催化剂的脱硝性能的影响规律。结果表明：煅烧预处理结合煮溶脱硅可以脱除99%以上的SiO2,脱硅的同时理化性质显著改善,表现出较大的比表面积（1923 m2/g）、丰富的介/微孔结构以及表面含氧官能团,并促进了催化剂的SCR反应活性（250℃时NOx脱除率可达100%）。此外,Ho改性无硅残渣炭脱硝催化剂具有最好的低温脱硝活性,在200~300℃范围内保持80%以上的脱硝效率。表征结果显示,MnCeHo/FRB催化剂具有较强的表面酸性和氧化还原性,活性组分在载体上均匀分散,且表面化学吸附氧较为丰富。此外,In-situ DRIFTs实验表明MnCe/FRB催化剂表面同时存在E-R和L-H机理,但E-R机理占主要地位。     

复杂载荷作用下圆柱壳的弹塑性动力屈曲研究

对复杂载荷作用下圆柱壳的弹塑性动力屈曲问题进行了研究。基于Hamilton变分原理导出圆柱壳的运动方程 ,本构关系采用增量理论 ,借助增量数值算法求解动力方程组。结果表明 ,均匀径向外压对圆柱壳的轴向冲击的过程或冲击性态有较大的影响 ,并讨论了径向压力与轴向冲击载荷的幅值对结构临界动力屈曲载荷和临界动力失效载荷的影响。