Information-Theoretic Characterization of the Generalization Error for Iterative Semi-Supervised Learning

Using information-theoretic principles, we consider the generalization error (gen-error) of iterative semi-supervised learning (SSL) algorithms that iteratively generate pseudo-labels for a large amount of unlabelled data to progressively refine the model parameters. In contrast to most previous works that {\em bound} the gen-error, we provide an {\em exact} expression for the gen-error and particularize it to the binary Gaussian mixture model. Our theoretical results suggest that when the class conditional variances are not too large, the gen-error decreases with the number of iterations, but quickly saturates. On the flip side, if the class conditional variances (and so amount of overlap between the classes) are large, the gen-error increases with the number of iterations. To mitigate this undesirable effect, we show that regularization can reduce the gen-error. The theoretical results are corroborated by extensive experiments on the MNIST and CIFAR datasets in which we notice that for easy-to-distinguish classes, the gen-error improves after several pseudo-labelling iterations, but saturates afterwards, and for more difficult-to-distinguish classes, regularization improves the generalization performance.Comment: 52 pages, 17 figure

Extraction of Electron Self-Energy and Gap Function in the Superconducting State of Bi_2Sr_2CaCu_2O_8 Superconductor via Laser-Based Angle-Resolved Photoemission

Super-high resolution laser-based angle-resolved photoemission measurements have been performed on a high temperature superconductor Bi_2Sr_2CaCu_2O_8. The band back-bending characteristic of the Bogoliubov-like quasiparticle dispersion is clearly revealed at low temperature in the superconducting state. This makes it possible for the first time to experimentally extract the complex electron self-energy and the complex gap function in the superconducting state. The resultant electron self-energy and gap function exhibit features at ~54 meV and ~40 meV, in addition to the superconducting gap-induced structure at lower binding energy and a broad featureless structure at higher binding energy. These information will provide key insight and constraints on the origin of electron pairing in high temperature superconductors.Comment: 4 pages, 4 figure

Construction of Vascular Tissues with Macro-Porous Nano-Fibrous Scaffolds and Smooth Muscle Cells Enriched from Differentiated Embryonic Stem Cells

Vascular smooth muscle cells (SMCs) have been broadly used for constructing tissue-engineered blood vessels. However, the availability of mature SMCs from donors or patients is very limited. Derivation of SMCs by differentiating embryonic stem cells (ESCs) has been reported, but not widely utilized in vascular tissue engineering due to low induction efficiency and, hence, low SMC purity. To address these problems, SMCs were enriched from retinoic acid induced mouse ESCs with LacZ genetic labeling under the control of SM22α promoter as the positive sorting marker in the present study. The sorted SMCs were characterized and then cultured on three-dimensional macro-porous nano-fibrous scaffolds in vitro or implanted subcutaneously into nude mice after being seeded on the scaffolds. Our data showed that the LacZ staining, which reflected the corresponding SMC marker SM22α expression level, was efficient as a positive selection marker to dramatically enrich SMCs and eliminate other cell types. After the sorted cells were seeded into the three-dimensional nano-fibrous scaffolds, continuous retinoic acid treatment further enhanced the SMC marker gene expression level while inhibited pluripotent maker gene expression level during the in vitro culture. Meanwhile, after being implanted subcutaneously into nude mice, the implanted cells maintained the positive LacZ staining within the constructs and no teratoma formation was observed. In conclusion, our results demonstrated the potential of SMCs derived from ESCs as a promising cell source for therapeutic vascular tissue engineering and disease model applications