A Proposed Algorithm Toward Uniform-distribution Monotone DNF Learning

In 1984 Valiant introduced the distribution-independent model of Probably Approximately Correct (PAC) learning from random examples and brought up the problem of whether polynomial-size DNF functions are PAC learnable in polynomial time. It has been about twenty years that the DNF learning problem has been widely regarded as one of the most important ---and challenging --- open questions in Computational Learning Theory. We consider a related but simpler question: are polynomial-size monotone DNF functions PAC learnable in polynomial time if examples of the function are uniformly generated? Our research develops an algorithm that we hope to learn a monotone DNF in polynomial time by using Threshold Function Hypotheses. We tested with some interesting cases and got some impressive and encouraging results. However, further testing revealed other cases for which the algorithm appears to fail. Some ideas for addressing these problem cases will be discussed

Enhancements of Sparse Clustering with Resampling and Considerations on Tuning Parameter

Clustering methods are widely used to explore subgroupings in data when the true group membership is unknown. These techniques are very useful when identifying potential subpopulations of interest in the medical and public health setting. Examples of these types of subpopulations include subjects who have certain gene expression profiles related to a cancer subtype, and subjects who are in the very early, asymptomatic phase, of a chronic illness. All of these examples are of great public health relevance. Many of the datasets of interest arise from the development of new technologies and are subject to the common problem where p, the number of variables, is significantly larger than the sample size, n. The relatively small sample size, n, may result from the difficulties of subject recruitment and/or the financial burden of the actual data collection in fields such as imaging and genetic analysis. The earlier approaches to clustering treat all of the variables equally, which may not work well when not all of them are relevant to the subgroupings. Clustering methods with variable selection, also called sparse clustering, have been recently developed to deal with this problem. We propose a method to add resampling onto sparse clustering to improve upon the current clustering methodology. The addition of resampling methods to sparse clustering results in variable selection that is more accurate. The method is also used to assign an “observed proportion of cluster membership” to each observation, providing a new metric by which to measure membership certainty. The performance of the method is studied via simulation and illustrated in the motivating data example. We also propose an alternative approach for the choice of tuning parameter based on an adjusted Bayesian Information Criterion (BIC). Variable selection in sparse clustering is realized by applying Lasso or related penalties and the tuning parameter for these penalties has to be determined beforehand. The gap statistic, a distance-based approach, is used to choose the tuning parameter through permutation and it may behave poorly at times. The proposed BIC approach is an alternative developed under the more sophisticated model-based likelihood framework. Its performance is evaluated with simulations

Post-mortem correlates of in vivo PiB-PET amyloid imaging in a typical case of Alzheimer's disease

The positron emission tomography (PET) radiotracer Pittsburgh Compound-B (PiB) binds with high affinity to β-pleated sheet aggregates of the amyloid-β (Aβ) peptide in vitro. The in vivo retention of PiB in brains of people with Alzheimer's disease shows a regional distribution that is very similar to distribution of Aβ deposits observed post-mortem. However, the basis for regional variations in PiB binding in vivo, and the extent to which it binds to different types of Aβ-containing plaques and tau-containing neurofibrillary tangles (NFT), has not been thoroughly investigated. The present study examined 28 clinically diagnosed and autopsy-confirmed Alzheimer's disease subjects, including one Alzheimer's disease subject who had undergone PiB-PET imaging 10 months prior to death, to evaluate region- and substrate-specific binding of the highly fluorescent PiB derivative 6-CN-PiB. These data were then correlated with region-matched Aβ plaque load and peptide levels, [3H]PiB binding in vitro, and in vivo PET retention levels. We found that in Alzheimer's disease brain tissue sections, the preponderance of 6-CN-PiB binding is in plaques immunoreactive to either Aβ42 or Aβ40, and to vascular Aβ deposits. 6-CN-PiB labelling was most robust in compact/cored plaques in the prefrontal and temporal cortices. While diffuse plaques, including those in caudate nucleus and presubiculum, were less prominently labelled, amorphous Aβ plaques in the cerebellum were not detectable with 6-CN-PiB. Only a small subset of NFT were 6-CN-PiB positive; these resembled extracellular ‘ghost’ NFT. In Alzheimer's disease brain tissue homogenates, there was a direct correlation between [3H]PiB binding and insoluble Aβ peptide levels. In the Alzheimer's disease subject who underwent PiB-PET prior to death, in vivo PiB retention levels correlated directly with region-matched post-mortem measures of [3H]PiB binding, insoluble Aβ peptide levels, 6-CN-PiB- and Aβ plaque load, but not with measures of NFT. These results demonstrate, in a typical Alzheimer's disease brain, that PiB binding is highly selective for insoluble (fibrillar) Aβ deposits, and not for neurofibrillary pathology. The strong direct correlation of in vivo PiB retention with region-matched quantitative analyses of Aβ plaques in the same subject supports the validity of PiB-PET imaging as a method for in vivo evaluation of Aβ plaque burden

Synthesis of novel phosphorylated chrysin derivatives by 1, 3-dipolar cycloaddition reaction

<p></p> <p>Through 1,3-dipolar cycloaddition reaction, 1,4,5-trisubstituted-1,2,3-triazole and phosphate-containing chrysin derivatives were synthesized with high yields. The target compounds were characterized by ¹H, ³¹P, ¹³C NMR spectroscopy and HRMS.</p

A Practical Method to Synthesize 1,2,3-Triazole-amino-bisphosphonates Derivatives

<div><p></p><p>A practical and efficient method for the synthesis of 1,2,3-triazole-amino-bisphosphonates derivatives was developed through two steps; a Michael addition reaction of propargyl amine with vinylidene bisphosphonate and a 1,3-dipolar click cycloaddition assisted by ultrasound irradiation. This approach has significant advantages in terms of experimental simplicity, mild reaction condition and can be easily scaled up. The target compounds were characterized by ¹H, ³¹P, ¹³C NMR spectroscopy and HR MS.</p><p></p></div