10,539 research outputs found
Classification of Symmetry-Protected Phases for Interacting Fermions in Two Dimensions
Recently, it has been shown that two-dimensional bosonic symmetry-protected
topological(SPT) phases with on-site unitary symmetry can be completely
classified by the group cohomology class . Later, group
super-cohomology class was proposed as a partial classification for SPT phases
of interacting fermions. In this work, we revisit this problem based on the
mathematical framework of -extension of unitary braided tensor
category(UBTC) theory. We first reproduce the partial classifications given by
group super-cohomology, then we show that with an additional structure, a complete classification of SPT phases for
two-dimensional interacting fermion systems for a total symmetry group
can be achieved. We also discuss the classification of
interacting fermionic SPT phases protected by time-reversal symmetry.Comment: references added; published versio
Unbiased Learning to Rank with Unbiased Propensity Estimation
Learning to rank with biased click data is a well-known challenge. A variety
of methods has been explored to debias click data for learning to rank such as
click models, result interleaving and, more recently, the unbiased
learning-to-rank framework based on inverse propensity weighting. Despite their
differences, most existing studies separate the estimation of click bias
(namely the \textit{propensity model}) from the learning of ranking algorithms.
To estimate click propensities, they either conduct online result
randomization, which can negatively affect the user experience, or offline
parameter estimation, which has special requirements for click data and is
optimized for objectives (e.g. click likelihood) that are not directly related
to the ranking performance of the system. In this work, we address those
problems by unifying the learning of propensity models and ranking models. We
find that the problem of estimating a propensity model from click data is a
dual problem of unbiased learning to rank. Based on this observation, we
propose a Dual Learning Algorithm (DLA) that jointly learns an unbiased ranker
and an \textit{unbiased propensity model}. DLA is an automatic unbiased
learning-to-rank framework as it directly learns unbiased ranking models from
biased click data without any preprocessing. It can adapt to the change of bias
distributions and is applicable to online learning. Our empirical experiments
with synthetic and real-world data show that the models trained with DLA
significantly outperformed the unbiased learning-to-rank algorithms based on
result randomization and the models trained with relevance signals extracted by
click models
A Study on the Cohesion of English Teaching Materials Between Primary and Junior High School
English teaching materials, as the main teaching media, play an important role in teaching. Many scholars have attached great importance to teaching materials, but they took little heed to the cohesion of teaching materials between different stages of basic education. This study intended to investigate the cohesion of primary-secondary teaching materials by exploring the problems in terms of language knowledge and language skills in the selected English teaching materials for primary and secondary schools, which was finally succeeded by some practical suggestions for the English teachers and the students alike to effectively facilitate the cohesion problems in the primary-secondary stages
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