CUR Algorithm for Partially Observed Matrices

CUR matrix decomposition computes the low rank approximation of a given matrix by using the actual rows and columns of the matrix. It has been a very useful tool for handling large matrices. One limitation with the existing algorithms for CUR matrix decomposition is that they need an access to the {\it full} matrix, a requirement that can be difficult to fulfill in many real world applications. In this work, we alleviate this limitation by developing a CUR decomposition algorithm for partially observed matrices. In particular, the proposed algorithm computes the low rank approximation of the target matrix based on (i) the randomly sampled rows and columns, and (ii) a subset of observed entries that are randomly sampled from the matrix. Our analysis shows the relative error bound, measured by spectral norm, for the proposed algorithm when the target matrix is of full rank. We also show that only $O(n r\ln r)$ observed entries are needed by the proposed algorithm to perfectly recover a rank $r$ matrix of size $n\times n$, which improves the sample complexity of the existing algorithms for matrix completion. Empirical studies on both synthetic and real-world datasets verify our theoretical claims and demonstrate the effectiveness of the proposed algorithm

One-step synthesis of Lycopodium alkaloid (-)-huperzine W via Suzuki-Miyaura coupling

The first total synthesis of (−)-huperzine W (1) has been achieved. Key element of the synthesis is a highly convergent assemblage for the two rings system of target molecule utilizing an efficient Suzuki-Miyaura coupling reaction between chiral iodide 2 and 2-allylpyrrolidinone 4. Evaluation of the AchE inhibition of synthetic huperzine W was also carried out. [Image: see text] ELECTRONIC SUPPLEMENTARY MATERIAL: Supplementary material is available for this article at 10.1007/s13659-012-0084-2 and is accessible for authorized users

Argon laser treatment of central serous chorioretinopathy

AIM: To observe the efficacy of the argon laser photocoagulation treatment of central serous chorioretinopathy(CSC). METHODS: The treatment groups: 18 patients(18 eyes), argon laser photocoagulation and oral jolethin, vitamin B1, inosine and venoruton tablets. Control group: 18 patients(18 eyes), oral lecithin complex iodine, vitamin B1, inosine, venoruton tablets. Foveal thickness and neuroepithelial layer detachment range were measured by optical coherence tomography(OCT)before treatment, after 1 month and 3 months post-operation to compare the decline in value of foveal thickness and neuroepithelial layer detachment range of the two groups. RESULTS: After 1 month of treatment, the decline in value of the center foveal thickness: the value of treatment group was 256±72μm; the value of the control group was 82±57μm, and the difference of the two groups, P <0.05; the decline in value of neuroepithelial layer detachment range: the value of the treatment group was 3 548±168μm, the value of the control group was 1 520±143μm, And the difference of the two groups, P<0.05. After three months of treatment, the decline in value of the center foveal thickness: the value of treatment group was 383±75μm, the value of the control group was 312±67 μm, and the difference of the two groups, P<0.05; decline in value of neuroepithelial layer detachment range: the value of the treatment group was 4 908±172μm, the value of the control group was 4 211±153μm, and the difference of the two groups, P <0.05. The differences were statistically significant between the treatment and the control groups(two independent samples t-test). CONCLUSION:Argon laser photocoagulation treatment of CSC is an effective treatment method and can significantly shorten the course

Neuroprotective effects of bis(7)-tacrine against glutamate-induced retinal ganglion cells damage

<p>Abstract</p> <p>Background</p> <p>Glutamate-mediated excitotoxicity, primarily through N-methyl-D-aspartate (NMDA) receptors, may be an important cause of retinal ganglion cells (RGCs) death in glaucoma and several other retinal diseases. Bis(7)-tacrine is a noncompetitive NMDA receptors antagonist that can prevent glutamate-induced hippocampal neurons damage. We tested the effects of bis(7)-tacrine against glutamate-induced rat RGCs damage in vitro and in vivo.</p> <p>Results</p> <p>In cultured neonatal rats RGCs, the MTT assay showed that glutamate induced a concentration- and time-dependent toxicity. Bis(7)-tacrine and memantine prevented glutamate-induced cell death in a concentration-dependent manner with IC50 values of 0.028 μM and 0.834 μM, respectively. The anti-apoptosis effects of bis(7)-tacrine were confirmed by annexin V-FITC/PI staining. In vivo, TUNEL analysis and retrograde labeling analysis found that pretreatment with bis(7)-tacrine(0.2 mg/kg) induced a significant neuroprotective effect against glutamate-induced RGCs damage.</p> <p>Conclusions</p> <p>Our results showed that bis(7)-tacrine had neuroprotective effects against glutamate-induced RGCs damage in vitro and in vivo, possibly through the drug's anti-NMDA receptor effects. These findings make bis(7)-tacrine potentially useful for treating a variety of ischemic or traumatic retinopathies inclusive of glaucoma.</p

Shape coexistence and evolution in neutron-deficient krypton isotopes

Total Routhian Surface (TRS) calculations have been performed to investigate shape coexistence and evolution in neutron-deficient krypton isotopes 72,74,76Kr. The ground-state shape is found to change from oblate in 72Kr to prolate in 74,76Kr, in agreement with experimental data. Quadrupole deformations of the ground states and coexisting 0+2 states as well as excitation energies of the latter are also well reproduced. While the general agreement between calculated moments of inertia and those deduced from observed spectra confirms the prolate nature of the low-lying yrast states of all three isotopes (except the ground state of 72Kr), the deviation at low spins suggests significant shape mixing. The role of triaxiality in describing shape coexistence and evolution in these nuclei is finally discussed