512,759 research outputs found
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 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 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 80, 10 GeV 65 GeV, 260 GeV
620 GeV and 180 GeV 620 GeV after imposing the joint
constraints from the theory, the precision electroweak data, the 125 GeV Higgs
data, the leptonic/semi-hadronic decays, the leptonic decays and
Br. The direct searches from the channels can
impose stringent upper limits on Br and the multi-lepton event
searches can sizably reduce the allowed region of and (10 GeV
44 GeV and 32 60). Finally, we find that the model can
produce a strong first-order phase transition in the region of 14 GeV
25 GeV, 310 GeV 355 GeV and 250 GeV 295 GeV, allowed by
the explanation of the muon 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
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