10,895 research outputs found
Lowering topological entropy over subsets revisited
Let be a topological dynamical system. Denote by and the covering entropy and dimensional entropy of ,
respectively. is called D-{\it lowerable} (resp. {\it lowerable}) if
for each there is a subset (resp. closed subset)
with (resp. ); is called D-{\it hereditarily
lowerable} (resp. {\it hereditarily lowerable}) if each Souslin subset (resp.
closed subset) is D-lowerable (resp. lowerable).
In this paper it is proved that each topological dynamical system is not only
lowerable but also D-lowerable, and each asymptotically -expansive system is
D-hereditarily lowerable. A minimal system which is lowerable and not
hereditarily lowerable is demonstrated.Comment: All comments are welcome. Transactions of the American Mathematical
Society, to appea
Local entropy theory for a countable discrete amenable group action
In the paper we throw the first light on studying systematically the local
entropy theory for a countable discrete amenable group action. For such an
action, we introduce entropy tuples in both topological and measure-theoretic
settings and build the variational relation between these two kinds of entropy
tuples by establishing a local variational principle for a given finite open
cover. Moreover, based the idea of topological entropy pairs, we introduce and
study two special classes of such an action: uniformly positive entropy and
completely positive entropy. Note that in the building of the local variational
principle, following Romagnoli's ideas two kinds of measure-theoretic entropy
are introduced for finite Borel covers. These two kinds of entropy turn out to
be the same, where Danilenko's orbital approach becomes an inevitable tool
Deep Learning Based on Orthogonal Approximate Message Passing for CP-Free OFDM
Channel estimation and signal detection are very challenging for an
orthogonal frequency division multiplexing (OFDM) system without cyclic prefix
(CP). In this article, deep learning based on orthogonal approximate message
passing (DL-OAMP) is used to address these problems. The DL-OAMP receiver
includes a channel estimation neural network (CE-Net) and a signal detection
neural network based on OAMP, called OAMP-Net. The CE-Net is initialized by the
least square channel estimation algorithm and refined by minimum mean-squared
error (MMSE) neural network. The OAMP-Net is established by unfolding the
iterative OAMP algorithm and adding some trainable parameters to improve the
detection performance. The DL-OAMP receiver is with low complexity and can
estimate time-varying channels with only a single training. Simulation results
demonstrate that the bit-error rate (BER) of the proposed scheme is lower than
those of competitive algorithms for high-order modulation.Comment: 5 pages, 4 figures, updated manuscript, International Conference on
Acoustics, Speech and Signal Processing (ICASSP 2019). arXiv admin note:
substantial text overlap with arXiv:1903.0476
Exploration on Intelligent Teaching of Probability and Statistics in Universities
Starting from the concept of Intelligent Teaching, this paper briefly introduces the meaning of intelligent classroom, then gives the description about tools of Intelligent teaching. Taking Probability and Statistics as an example, this paper explores the mild Intelligent teaching with Mosotech as the tool of Intelligent teaching which can be used before, during and after class under the Intelligent teaching mode. Keywords: Intelligent teaching, Intelligent teaching tools, Probability and statistics DOI: 10.7176/JEP/12-27-03 Publication date:September 30th 202
A New Testing Method for Justification Bias Using High-Frequency Data of Health and Employment
Justification bias, wherein retirees may report poorer health to rationalize
their retirement, poses a major concern to the widely-used measure of
self-assessed health in retirement studies. This paper introduces a novel
method for testing the presence of this bias in the spirit of regression
discontinuity. The underlying idea is that any sudden shift in self-assessed
health immediately following retirement is more likely attributable to the
bias. Our strategy is facilitated by a unique high-frequency data that offers
monthly, in contrast to the typical biennial, information on employment,
self-assessed health, and objective health conditions. Across a wider
post-retirement time frame, we observe a decline in self-assessed health,
potentially stemming from both justification bias and changes in actual health.
However, this adverse effect diminishes with shorter intervals, indicating no
evidence of such bias. Our method also validates a widely-used indirect testing
approach
A Survey and Study on the Current Status of Mathematics Study Habits of Rural Junior High School Students in China
The research is supported by the research project of higher education reform in Jiangsu Province. Nos. 2019JSJG257, 2017JSJG212, Special research project on Rural Education in Yancheng City. No. XCZX21090, and Yancheng educational science planning project in 2021. No. 2021-L-136. (Sponsoring information) Abstract Based on the relevant theories, the article adopts literature research, questionnaire survey, and interview records to first analyze and summarize the research related to " mathematics study habits" and to define and classify the concepts related to "mathematics study habits." Take rural junior high school students in a school in China as the target group, and analyze the current situation of mathematics study habits of rural junior high school students in this school through a questionnaire survey based on the results. Furthermore, through personal interviews with rural junior high school students, teachers, and parents in the region, we completed the analysis of the factors that contribute to the formation of good mathematics study habits in rural junior high school students from the perspectives of students, teachers, and parents. Finally, combined with the current situation and influencing factors of mathematics learning habits of rural junior high school students in the region, corresponding countermeasures are proposed for the cultivation of good mathematical learning habits from the three perspectives of students, teachers and parents. Keywords: Rural junior high school students, Mathematics study habits, Influence factors, Habit development measures DOI: 10.7176/JEP/13-29-04 Publication date:October 31st 202
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