A Simple Algorithm for Semi-supervised Learning with Improved Generalization Error Bound

In this work, we develop a simple algorithm for semi-supervised regression. The key idea is to use the top eigenfunctions of integral operator derived from both labeled and unlabeled examples as the basis functions and learn the prediction function by a simple linear regression. We show that under appropriate assumptions about the integral operator, this approach is able to achieve an improved regression error bound better than existing bounds of supervised learning. We also verify the effectiveness of the proposed algorithm by an empirical study.Comment: Appears in Proceedings of the 29th International Conference on Machine Learning (ICML 2012

On the multiplicity of Laplacian eigenvalues of graphs

summary:In this paper we investigate the effect on the multiplicity of Laplacian eigenvalues of two disjoint connected graphs when adding an edge between them. As an application of the result, the multiplicity of 1 as a Laplacian eigenvalue of trees is also considered

Quantum Borcherds-Bozec algebras via semi-derived Ringel-Hall algebras II: braid group actions

Based on the realization of quantum Borcherds-Bozec algebra $\widetilde{\mathbf{U}}$ and quantum generalized Kac-Moody algebra ${}^B\widetilde{\mathbf{U}}$ via semi-derived Ringel-Hall algebra of a quiver with loops, we deduce the braid group actions of $\widetilde{\mathbf{U}}$ introduced by Fan and Tong recently and establish braid group actions for ${}^B\widetilde{\mathbf{U}}$ by applying the BGP reflection functors to semi-derived Ringel-Hall algebras.Comment: 18 pages, minor changes, accepted by Bulletin of the London Mathematical Society. arXiv admin note: substantial text overlap with arXiv:2107.0316

Periodic Radio Variability in NRAO 530: Phase Dispersion Minimization Analysis

In this paper, a periodicity analysis of the radio light curves of the blazar NRAO 530 at 14.5, 8.0, and 4.8 GHz is presented employing an improved Phase Dispersion Minimization (PDM) technique. The result, which shows two persistent periodic components of $\sim 6$ and $\sim 10$ years at all three frequencies, is consistent with the results obtained with the Lomb-Scargle periodogram and weighted wavelet Z-transform algorithms. The reliability of the derived periodicities is confirmed by the Monte Carlo numerical simulations which show a high statistical confidence. (Quasi-)Periodic fluctuations of the radio luminosity of NRAO 530 might be associated with the oscillations of the accretion disk triggered by hydrodynamic instabilities of the accreted flow. \keywords{methods: statistical -- galaxies: active -- galaxies: quasar: individual: NRAO 530}Comment: 8 pages, 5 figures, accepted by RA

Controlling the Intrinsic Josephson Junction Number in a Bi2Sr2CaCu2O8+δ\mathbf{Bi_2Sr_2CaCu_2O_{8+\delta}} Mesa

In fabricating $\mathrm{Bi_2Sr_2CaCu_2O_{8+\delta}}$ intrinsic Josephson junctions in 4-terminal mesa structures, we modify the conventional fabrication process by markedly reducing the etching rates of argon ion milling. As a result, the junction number in a stack can be controlled quite satisfactorily as long as we carefully adjust those factors such as the etching time and the thickness of the evaporated layers. The error in the junction number is within $\pm 1$. By additional ion etching if necessary, we can controllably decrease the junction number to a rather small value, and even a single intrinsic Josephson junction can be produced.Comment: to bu published in Jpn. J. Appl. Phys., 43(7A) 200

Combining radiofrequency ablation and ethanol injection may achieve comparable long-term outcomes in larger hepatocellular carcinoma (3.1–4 cm) and in high-risk locations

AbstractRadiofrequency ablation (RFA) is more effective for hepatocellular carcinoma (HCC) < 3 cm. Combining percutaneous ethanol injection and RFA for HCC can increase ablation; however, the long-term outcome remains unknown. The aim of this study was to compare long-term outcomes between patients with HCC of 2–3 cm versus 3.1–4 cm and in high-risk versus non-high-risk locations after combination therapy. The primary endpoint was overall survival and the secondary endpoint was local tumor progression (LTP). Fifty-four consecutive patients with 72 tumors were enrolled. Twenty-two (30.6%) tumors and 60 (83.3%) tumors were of 3.1–4 cm and in high-risk locations, respectively. Primary technique effectiveness was comparable between HCC of 2–3 cm versus 3.1–4 cm (98% vs. 95.5%, p = 0.521), and HCC in non-high risk and high-risk locations (100% vs. 96.7%, p = 1.000). The cumulative survival rates at 1 year, 3 years, and 5 years were 90.3%, 78.9%, and 60.3%, respectively, in patients with HCC of 2–3 cm; 95.0%, 84.4%, and 69.3% in HCC of 3.1–4.0 cm (p = 0.397); 90.0%, 71.1%, and 71.1% in patients with HCC in non-high-risk locations; and 92.7%, 81.6%, and 65.4% in high-risk locations (p = 0.979). The cumulative LTP rates at 1 year, 3 years, and 5 years were 10.2%, 32.6%, and 32.6%, respectively, in all HCCs; 12.6%, 33.9%, and 33.9% in HCC of 2–3 cm; 4.8%, 29.5%, and 29.5% in HCC of 3.1–4 cm (p = 0.616); 16.7%, 50.0%, and 50.0% in patients with HCC in non-high-risk locations; and 8.8%, 29.9%, and 29.9% in patients with HCC in high-risk locations (p = 0.283). The cumulative survival and LTP rates were not significantly different among the various subgroups. Combining RFA and percutaneous ethanol injection achieved comparable long-term outcomes in HCCs of 2–3 cm versus 3.1–4.0 cm and in high-risk versus non-high-risk locations. A randomized controlled or cohort studies with larger sample size are warranted

Confirming the 115.5-day periodicity in the X-ray light curve of ULX NGC 5408 X-1

The Swift/XRT light curve of the ultraluminous X-ray (ULX) source NGC 5408 X-1 was re-analyzed with two new numerical approaches, Weighted Wavelet $Z$-transform (WWZ) and CLEANest, that are different from previous studies. Both techniques detected a prominent periodicity with a time scale of $115.5\pm1.5$ days, in excellent agreement with the detection of the same periodicity first reported by Strohmayer (2009). Monte Carlo simulation was employed to test the statisiticak confidence of the 115.5-day periodicity, yielding a statistical significance of $> 99.98$ (or $>3.8\sigma$). The robust detection of the 115.5-day quasi-periodic oscillations (QPOs), if it is due to the orbital motion of the binary, would infer a mass of a few thousand $M_\odot$ for the central black hole, implying an intermediate-mass black hole in NGC 5408 X-1.Comment: 6 pages, 2 figures, submitted to Research in Astronomy and Astrophysics (RAA

Few-Shot Non-Parametric Learning with Deep Latent Variable Model

Most real-world problems that machine learning algorithms are expected to solve face the situation with 1) unknown data distribution; 2) little domain-specific knowledge; and 3) datasets with limited annotation. We propose Non-Parametric learning by Compression with Latent Variables (NPC-LV), a learning framework for any dataset with abundant unlabeled data but very few labeled ones. By only training a generative model in an unsupervised way, the framework utilizes the data distribution to build a compressor. Using a compressor-based distance metric derived from Kolmogorov complexity, together with few labeled data, NPC-LV classifies without further training. We show that NPC-LV outperforms supervised methods on all three datasets on image classification in low data regime and even outperform semi-supervised learning methods on CIFAR-10. We demonstrate how and when negative evidence lowerbound (nELBO) can be used as an approximate compressed length for classification. By revealing the correlation between compression rate and classification accuracy, we illustrate that under NPC-LV, the improvement of generative models can enhance downstream classification accuracy.Comment: Accepted to NeurIPS202