Integrand-Level Reduction of Loop Amplitudes by Computational Algebraic Geometry Methods

We present an algorithm for the integrand-level reduction of multi-loop amplitudes of renormalizable field theories, based on computational algebraic geometry. This algorithm uses (1) the Gr\"obner basis method to determine the basis for integrand-level reduction, (2) the primary decomposition of an ideal to classify all inequivalent solutions of unitarity cuts. The resulting basis and cut solutions can be used to reconstruct the integrand from unitarity cuts, via polynomial fitting techniques. The basis determination part of the algorithm has been implemented in the Mathematica package, BasisDet. The primary decomposition part can be readily carried out by algebraic geometry softwares, with the output of the package BasisDet. The algorithm works in both D=4 and $D=4-2\epsilon$ dimensions, and we present some two and three-loop examples of applications of this algorithm.Comment: published version: typos corrected; more examples adde

Language in Our Time: An Empirical Analysis of Hashtags

Hashtags in online social networks have gained tremendous popularity during the past five years. The resulting large quantity of data has provided a new lens into modern society. Previously, researchers mainly rely on data collected from Twitter to study either a certain type of hashtags or a certain property of hashtags. In this paper, we perform the first large-scale empirical analysis of hashtags shared on Instagram, the major platform for hashtag-sharing. We study hashtags from three different dimensions including the temporal-spatial dimension, the semantic dimension, and the social dimension. Extensive experiments performed on three large-scale datasets with more than 7 million hashtags in total provide a series of interesting observations. First, we show that the temporal patterns of hashtags can be categorized into four different clusters, and people tend to share fewer hashtags at certain places and more hashtags at others. Second, we observe that a non-negligible proportion of hashtags exhibit large semantic displacement. We demonstrate hashtags that are more uniformly shared among users, as quantified by the proposed hashtag entropy, are less prone to semantic displacement. In the end, we propose a bipartite graph embedding model to summarize users' hashtag profiles, and rely on these profiles to perform friendship prediction. Evaluation results show that our approach achieves an effective prediction with AUC (area under the ROC curve) above 0.8 which demonstrates the strong social signals possessed in hashtags.Comment: WWW 201

Revisiting lepton-specific 2HDM in light of muon g-2 anomaly

We examine the lepton-specific 2HDM as a solution of muon $g-2$ anomaly under various theoretical and experimental constraints, especially the direct search limits from the LHC and the requirement of a strong first-order phase transition in the early universe. We find that the muon g-2 anomaly can be explained in the region of 32 $<\tan\beta<$ 80, 10 GeV $<m_A<$ 65 GeV, 260 GeV $<m_H<$ 620 GeV and 180 GeV $<m_{H^\pm}<$ 620 GeV after imposing the joint constraints from the theory, the precision electroweak data, the 125 GeV Higgs data, the leptonic/semi-hadronic $\tau$ decays, the leptonic $Z$ decays and Br$(B_s \to \mu^+ \mu^-)$. The direct searches from the $h\to AA$ channels can impose stringent upper limits on Br$(h\to AA)$ and the multi-lepton event searches can sizably reduce the allowed region of $m_A$ and $\tan\beta$ (10 GeV $<m_A<$ 44 GeV and 32 $<\tan\beta<$ 60). Finally, we find that the model can produce a strong first-order phase transition in the region of 14 GeV $<m_A<$ 25 GeV, 310 GeV $<m_H<$ 355 GeV and 250 GeV $<m_{H^\pm}<$ 295 GeV, allowed by the explanation of the muon $g-2$ anomaly.Comment: 24 pages, 8 figures, 3 Tables, matches published versio

Electron correlation and spin-orbit coupling effects in US3 and USe3

A systematic density functional theory (DFT)+U study is conducted to investigate the electron correlation and spin-orbit coupling (SOC) effects in US3 and USe3. Our calculations reveal that inclusion of the U term is essential to get energy band gaps for them, indicating the strong correlation effects for uranium 5f electrons. Taking consideration of the SOC effect results in small reduction on the electronic band gaps of US3 and USe3, but largely changes the energy band shapes around the Fermi energy. As a result, US3 has a direct band gap while USe3 has an indirect one. Our calculations predict that both US3 and USe3 are antiferromagnetic insulators, in agreement with corresponding experimental results. Based on our DFT+U calculations, we systematically present the ground-state electronic, mechanical, and Raman properties for US3 and USe3.Comment: 6 pages, 6 figure