Well-posedness of the fractional Ginzburg-Landau equation

In this paper, we investigate the well-posedness of the real fractional Ginzburg-Landau equation in several different function spaces, which have been used to deal with the Burgers' equation, the semilinear heat equation, the Navier-Stokes equations, etc. The long time asymptotic behavior of the nonnegative global solutions is also studied in details

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

Mergers and acquisitions matching for performance improvement: a DEA-based approach

This article proposes a new data envelopment analysis (DEA)-based approach to deal with mergers and acquisitions (M&As) matching. To derive reliable matching degrees between bidder and target firms, we consider both technical efficiency and scale efficiency. Specifically, an inverse DEA model is developed for measuring the technical efficiency, while a conventional DEA model is employed to identify the return of scale of the merged decision-making units (DMUs). Then, an optimization model is formulated to generate matching results to improve DMUs’ performance. An empirical study of M&As matching Turkish energy firms is examined to illustrate the proposed approach. This study shows that both technical efficiency and scale efficiency have impacts on M&As matching practices

Evolution of pairing from weak to strong coupling on a honeycomb lattice

We study the evolution of the pairing from weak to strong coupling on a honeycomb lattice by Quantum Monte Carlo. We show numerical evidence of the BCS-BEC crossover as the coupling strength increases on a honeycomb lattice with small fermi surface by measuring a wide range of observables: double occupancy, spin susceptibility, local pair correlation, and kinetic energy. Although at low energy, the model sustains Dirac fermions, we do not find significant qualitative difference in the BCS-BEC crossover as compared to those with an extended Fermi surface, except at weak coupling, BCS regime.Comment: 5 page

Segatron: Segment-Aware Transformer for Language Modeling and Understanding

Transformers are powerful for sequence modeling. Nearly all state-of-the-art language models and pre-trained language models are based on the Transformer architecture. However, it distinguishes sequential tokens only with the token position index. We hypothesize that better contextual representations can be generated from the Transformer with richer positional information. To verify this, we propose a segment-aware Transformer (Segatron), by replacing the original token position encoding with a combined position encoding of paragraph, sentence, and token. We first introduce the segment-aware mechanism to Transformer-XL, which is a popular Transformer-based language model with memory extension and relative position encoding. We find that our method can further improve the Transformer-XL base model and large model, achieving 17.1 perplexity on the WikiText-103 dataset. We further investigate the pre-training masked language modeling task with Segatron. Experimental results show that BERT pre-trained with Segatron (SegaBERT) can outperform BERT with vanilla Transformer on various NLP tasks, and outperforms RoBERTa on zero-shot sentence representation learning.Comment: Accepted by AAAI 202