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.     

Certain properties related to well posedness of switching diffusions

This work is devoted to switching diffusions that have two components (a continuous component and a discrete component). Different from the so-called Markovian switching diffusions, in the setup, the discrete component (the switching) depends on the continuous component (the diffusion process). The objective of this paper is to provide a number of properties related to the well posedness. First, the differentiability with respect to initial data of the continuous component is established. Then, further properties including uniform continuity with respect to initial data, and smoothness of certain functionals are obtained. Moreover, Feller property is obtained under only local Lipschitz continuity. Finally, an example of Lotka–Volterra model under regime switching is provided as an illustration.     

Discreteness of interior transmission eigenvalues revisited

This paper is devoted to the discreteness of the transmission eigenvalue problems. It is known that this problem is not self-adjoint and a priori estimates are non-standard and do not hold in general. Two approaches are used. The first one is based on the multiplier technique and the second one is based on the Fourier analysis. The key point of the analysis is to establish the compactness and the uniqueness for Cauchy problems under various conditions. Using these approaches, we are able to rediscover quite a few known discreteness results in the literature and obtain various new results for which only the information near the boundary are required and there might be no contrast of the coefficients on the boundary.     

Highly sensitive fluorescent sensor targeting CuCl2 based on thiophene attached anthracene compound (TA)

A novel thiophene attached anthracene (TA) based fluorescent compound was designed and synthesized. The TA showed a high quantum yield (Qy = 0.34) in regard to fluorescence. We applied this TA compound to detect specific metal compound and found that it could identify CuCl₂ from other metals through dramatic fluorescence change at λ_max = 460 nm. It showed strong quenching fluorescence property with CuCl₂ while with other metal compounds it exhibited strong blue fluorescence emission. UV/Vis absorption spectroscopy clearly demonstrated that the quenching property of TA at λ_max = 460 nm was due to overlapping of the fluorescence peak of TA at λ_max = 460 nm and the absorption band of CuCl₂ (from 190 nm to 525 nm). Binding constant (K′), which was 0.0895 mM^?2, indicated a complexation ratio between TA and CuCl₂ as 1:2 and this interaction induced quenching property.     

Two acridones and two coumarins from the roots of Paramignya trimera

Two acridones, paratrimerins C (1) and D (2), and two coumarins, paratrimerins E (3) and F (4), were isolated from the CHCl₃ and EtOAc extracts of Paramignya trimera (Rutaceae), together with twelve known compounds (5–16). Their structures were elucidated on the basis of spectroscopic data. All isolated compounds possessed significant α-glucosidase inhibitory activity in a concentration-dependent manner, and showed more potent inhibitory activity, with IC₅₀ values ranging from 14.6 to 112.2 μM, than the positive control acarbose (IC₅₀, 214.5 μM). The biosynthesis of the isolated coumarins and acridones was proposed.     

Straightforward access to new vinca-alkaloids via selective reduction of a nitrile containing anhydrovinblastine derivative

A procedure to exclusively obtain 3′S-cyanoanhydrovinblastine 12 from two naturally occurring vinca-alkaloids (catharanthine and vindoline) in one step with good yield is described. Stereoselective reductions of 12, providing straightforward access to three new vinca-alkaloids, including two diastereomers 3′S-cyano-(4′R,5′-dihydro)-anhydrovinblastine and 3′S-cyano-(4′S,5′-dihydro)-anhydrovinblastine as well as (3′S-aminomethyl)-(4′S,5′-dihydro)-anhydrovinblastine in good yields is also reported.     

Copper ferrite superparamagnetic nanoparticles as a heterogeneous catalyst for directed phenol/formamide coupling

The copper ferrite-catalyzed, directed coupling of ortho-arylated phenols and dialkylformamides in the presence of a peroxide oxidant is described. Acyclic and cyclic amides were compatible with the reaction conditions. The copper ferrite catalyst is heterogeneous since substantial leaching was not detected and re-use of the catalyst for 9 consecutive reactions proceeded without a significant decrease in yield. To the best of our knowledge, this transformation has not been previously performed under heterogeneous catalysis conditions.     

Electrochemical Characterization of the Interaction of Multiwalled Carbon Nanotubes with Doxorubicin

It has been suggested that multiwalled carbon nanotubes (MWCNTs) interacting with pharmaceutics may be introduced into the body as nanocarriers. To deliver the anticancer drugs, covalent or noncovalent functionalization of MWCNTs is required. In this study, the influence of oxidation on MWCNTs in the interaction with chemotherapeutic drug, doxorubicin, was characterized. The binding of doxorubicin with MWCNTs decreased rapidly with the increasing oxidation period with sulfuric acid. However, with nitric acid, the interaction increased initially and slowly decreased with time. The best results were obtained for sulfuric and nitric acid following 1 and 3?h of oxidation, respectively. The results show that sulfuric acid provided more favorable interaction for MWCNTs with doxorubicin than nitric acid.     

Ruthenium hydride catalyzed silylvinylation of terminal alkynes under ethylene atmosphere at 80 psi

The development of methods for the stereoselective synthesis of polysubstituted 1,3-dienes is a challenge to synthetic chemistry. Herein is reported a selective approach for the synthesis of polysubstituted 1,3-dienes using the ruthenium hydride catalyzed intramolecular silylvinylation of alkynes under 80 psi of ethylene gas. This strategy affords a single diene isomer, is applicable to substrates with aryl and alkyl substitution at the propargyl and homopropargyl positions, and has been utilized in the synthesis of 5- and 6-membered oxasilacycles.     

Asymptotic Solution of a Singularly Perturbed Linear-Quadratic Problem in Critical Case with Cheap Control

Using the direct scheme method, we construct an asymptotic expansion for the solution of a singularly perturbed optimal problem in critical case with cheap control and two fixed end-points. The asymptotic solution contains the outer series and two boundary-layer series in the vicinities of the two end-points. The error estimates for state and control variables and the functional are obtained. It is shown that the value of minimized functional does not increase when a higher-order approximation to the optimal control is used. An illustrative example is given.