scholarly journals Conditional mean dimension

2021 ◽  
pp. 1-15
Author(s):  
BINGBING LIANG
Keyword(s):  
Dynamical Systems ◽  
Conditional Mean ◽  
Extension System ◽  
Mean Dimension ◽  
Factor Map ◽  
The Mean ◽  
Topological Dynamical Systems ◽  
Dynamical Embedding

Abstract We introduce some notions of conditional mean dimension for a factor map between two topological dynamical systems and discuss their properties. With the help of these notions, we obtain an inequality to estimate the mean dimension of an extension system. The conditional mean dimension for G-extensions is computed. We also exhibit some applications in dynamical embedding problems.

Embedding ℤk-actions in cubical shifts and ℤk-symbolic extensions

2010 ◽  
Vol 31 (2) ◽  
pp. 383-403 ◽  
Author(s):  
YONATAN GUTMAN
Keyword(s):  
Dynamical Systems ◽  
Universal Constant ◽  
Boundary Property ◽  
Entropy Theory ◽  
Topological Version ◽  
Symbolic Extension ◽  
Mean Dimension ◽  
Topological Dynamical Systems ◽  
Entropy Structure

AbstractMean dimension is an invariant which makes it possible to distinguish between topological dynamical systems with infinite entropy. Extending in part the work of Lindenstrauss we show that if (X,ℤk) has a free zero-dimensional factor then it can be embedded in the ℤk-shift on ([0,1]d)ℤk, where d=[C(k) mdim(X,ℤk)]+1 for some universal constant C(k), and a topological version of the Rokhlin lemma holds. Furthermore, under the same assumptions, if mdim(X,ℤk)=0, then (X,ℤk) has the small boundary property. One of the applications of this theory is related to Downarowicz’s entropy structure, a master invariant for entropy theory, which captures the emergence of entropy on different scales. Indeed, we generalize this invariant and prove the Boyle–Downarowicz symbolic extension entropy theorem in the setting of ℤk-actions. This theorem describes what entropies are achievable in symbolic extensions.

scholarly journals Weak forms of topological and measure-theoretical equicontinuity: relationships with discrete spectrum and sequence entropy

2016 ◽  
Vol 37 (4) ◽  
pp. 1211-1237 ◽  
Author(s):  
FELIPE GARCÍA-RAMOS
Keyword(s):  
Dynamical Systems ◽  
Discrete Spectrum ◽  
Haar Measure ◽  
Topological Category ◽  
Sequence Entropy ◽  
Ergodic Measures ◽  
Factor Map ◽  
Topological Dynamical Systems ◽  
Theoretical Sensitivity ◽  
Topological Sequence Entropy

We define weaker forms of topological and measure-theoretical equicontinuity for topological dynamical systems, and we study their relationships with sequence entropy and systems with discrete spectrum. We show that for topological systems equipped with ergodic measures having discrete spectrum is equivalent to$\unicode[STIX]{x1D707}$-mean equicontinuity. In the purely topological category we show that minimal subshifts with zero topological sequence entropy are strictly contained in diam-mean equicontinuous systems; and that transitive almost automorphic subshifts are diam-mean equicontinuous if and only if they are regular (i.e. the maximal equicontinuous factor map is one–one on a set of full Haar measure). For both categories we find characterizations using stronger versions of the classical notion of sensitivity. As a consequence, we obtain a dichotomy between discrete spectrum and a strong form of measure-theoretical sensitivity.

GAMBARAN BEBAN KERJA MENTAL PADA DOSEN FAKULTAS X UNIVERSITAS X

2019 ◽  
Vol 2 (3) ◽  
Author(s):  
Kartiani Dewi ◽  
Suryani S ◽  
Ahmad Yamin
Keyword(s):  
Community Service ◽  
Mental Workload ◽  
Sampling Technique ◽  
Mean Value ◽  
Descriptive Statistics ◽  
Large Contribution ◽  
Mean Dimension ◽  
The Mean ◽  
Quantitative Descriptive ◽  
University Lecturers

Lecturers are responsible for implementing the three main responsibilities in university (Tridharma Perguruan Tinggi) with 12 credits to 16 credits each semester. However, many lecturers feel that the workload is very excessive. The purpose of this study was to describe the mental workload of lecturers at the Faculty of X Padjadjaran University. The method of this research was quantitative descriptive by using a total sampling technique involving 43 lecturers. Data collection used NASA-TLX instruments. Data were analysed using descriptive statistics. The results of the study showed that overall the mental workload of the Faculty of X Padjadjaran University lecturers was included in the high category both in education and teaching assignments (74.4%), research assignments (76.7%), and community service assignments (74.4%). ) Effort dimensions have the highest mean value that is equal to 51.8, while the dimensions that have the lowest mean are Perfomance dimension, namely 9.4, where the greater the mean dimension shows the large contribution in the mental workload felt by the lecturer. The conclusions, this study show that most lecturers have a high mental workload. It is suggested that the lecturers need to have balance numbers of tasks according to their abilities, balance the time working with recreation, and meet the needs of rest. The results of this study need to be followed up by examining methods or efforts that can reduce the lecturers' mental workload.

scholarly journals Moduli Space of Brody Curves, Energy and Mean Dimension

2008 ◽  
Vol 192 ◽  
pp. 27-58 ◽  
Author(s):  
Masaki Tsukamoto
Keyword(s):  
Complex Plane ◽  
Moduli Space ◽  
Hermitian Manifold ◽  
Value Distribution ◽  
Holomorphic Map ◽  
Infinite Dimensional ◽  
Mean Dimension ◽  
The Mean ◽  
Moduli Theory ◽  
Bounded Derivative

AbstractA Brody curve is a holomorphic map from the complex plane ℂ to a Hermitian manifold with bounded derivative. In this paper we study the value distribution of Brody curves from the viewpoint of moduli theory. The moduli space of Brody curves becomes infinite dimensional in general, and we study its “mean dimension”. We introduce the notion of “mean energy” and show that this can be used to estimate the mean dimension.

scholarly journals Sensitivity for topologically double ergodic dynamical systems

2021 ◽  
Vol 6 (10) ◽  
pp. 10495-10505
Author(s):  
Risong Li ◽  
◽  
Xiaofang Yang ◽  
Yongxi Jiang ◽  
Tianxiu Lu ◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Metric Space ◽  
Inverse Limit ◽  
Compact Metric Space ◽  
Limit Space ◽  
Factor Map ◽  
Continuous Surjection ◽  
Inverse Limit Space

<abstract><p>As a stronger form of multi-sensitivity, the notion of ergodic multi-sensitivity (resp. strongly ergodically multi-sensitivity) is introduced. In particularly, it is proved that every topologically double ergodic continuous selfmap (resp. topologically double strongly ergodic selfmap) on a compact metric space is ergodically multi-sensitive (resp. strongly ergodically multi-sensitive). And for any given integer $ m\geq 2 $, $ f $ is ergodically multi-sensitive (resp. strongly ergodically multi-sensitive) if and only if so is $ f^{m} $. Also, it is shown that if $ f $ is a continuous surjection, then $ f $ is ergodically multi-sensitive (resp. strongly ergodically multi-sensitive) if and only if so is $ \sigma_{f} $, where $ \sigma_{f} $ is the shift selfmap on the inverse limit space $ \lim\limits_{\leftarrow}(X, f) $. Moreover, it is proved that if $ f:X\rightarrow X $ (resp. $ g:Y\rightarrow Y $) is a map on a nontrivial metric space $ (X, d) $ (resp. $ (Y, d') $), and $ \pi $ is a semiopen factor map between $ (X, f) $ and $ (Y, g) $, then the ergodic multi-sensitivity (resp. the strongly ergodic multi-sensitivity) of $ g $ implies the same property of $ f $.</p></abstract>

scholarly journals Q-entropy for general topological dynamical systems

2019 ◽  
Vol 39 (4) ◽  
pp. 2059-2075 ◽  
Author(s):  
Yun Zhao ◽  
◽  
Wen-Chiao Cheng ◽  
Chih-Chang Ho ◽  
◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Topological Dynamical Systems

scholarly journals The Revolving Door Flap: Revisiting an Elegant but Forgotten Flap for Ear Defect Reconstruction

2020 ◽  
Vol 53 (01) ◽  
pp. 064-070
Author(s):  
Anupam Golash ◽  
Sudipta Bera ◽  
Aditya V. Kanoi ◽  
Abhijit Golash
Keyword(s):  
Learning Curve ◽  
Operative Time ◽  
Donor Site ◽  
Case Series ◽  
Senior Author ◽  
Revolving Door ◽  
Harvest Technique ◽  
Flap Design ◽  
Mean Dimension ◽  
The Mean

Abstract Background The revolving door flap, although well described in the literature, is not widely used in general plastic surgery practice. The flap has been used for anterior auricular and conchal defects and is considered elegant for its unique flap design and peculiarity of flap harvest. However, due to its use for a very specific purpose and unique flap harvest technique that may be difficult to grasp, the flap is not very popular in reconstructive practice. Objectives This study aims to evaluate the understanding and learning curve of the revolving door flap, assess surgical outcome, and reemphasize its utility and elegance in reconstruction of ear defects. Methodology This is a case series of nine surgeries performed between January 2014 and 2018. Three cases were performed by the senior author and six cases by two junior authors. Patients were observed for complications and aesthetic outcomes. Results The mean dimension of the flaps was 27.22 mm × 22.78 mm. The mean operative time was 56.56 minutes (standard deviation 22.50, standard error of the mean 7.5). Flap congestion was noted in three cases postoperatively which resolved completely by the second week. Major “pinning” of the ear was noted in four cases. Conclusion Though infrequently performed, the revolving door flap has an easy learning curve once the proper harvest technique and flap movement has been grasped. The flap harvest is convenient, safe, and yields predictable results. Not only is total or partial flap loss extremely rare, the flap is sensate, color match is good, auricular contour is maintained, and the donor site can be closed primarily and remains well hidden.

scholarly journals COUNT AND DURATION TIME SERIES WITH EQUAL CONDITIONAL STOCHASTIC AND MEAN ORDERS

2020 ◽  
pp. 1-33
Author(s):  
Abdelhakim Aknouche ◽  
Christian Francq
Keyword(s):  
Time Series ◽  
Conditional Distribution ◽  
Stochastic Orders ◽  
Conditional Mean ◽  
Contraction Condition ◽  
Mixing Coefficients ◽  
The Mean ◽  
Quasi Maximum Likelihood ◽  
Geometric Decay ◽  
Mean Function

We consider a positive-valued time series whose conditional distribution has a time-varying mean, which may depend on exogenous variables. The main applications concern count or duration data. Under a contraction condition on the mean function, it is shown that stationarity and ergodicity hold when the mean and stochastic orders of the conditional distribution are the same. The latter condition holds for the exponential family parametrized by the mean, but also for many other distributions. We also provide conditions for the existence of marginal moments and for the geometric decay of the beta-mixing coefficients. We give conditions for consistency and asymptotic normality of the Exponential Quasi-Maximum Likelihood Estimator of the conditional mean parameters. Simulation experiments and illustrations on series of stock market volumes and of greenhouse gas concentrations show that the multiplicative-error form of usual duration models deserves to be relaxed, as allowed in this paper.

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