scholarly journals Variational relations for metric mean dimension and rate distortion dimension

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Tao Wang
Keyword(s):  
Rate Distortion ◽  
Variational Relations ◽  
Mean Dimension

scholarly journals Symbolic dynamics in mean dimension theory

2020 ◽  
pp. 1-19
Author(s):  
MAO SHINODA ◽  
MASAKI TSUKAMOTO
Keyword(s):  
Hausdorff Dimension ◽  
Topological Entropy ◽  
Ergodic Theory ◽  
Diophantine Approximation ◽  
Symbolic Dynamics ◽  
Rate Distortion ◽  
Dimension Theory ◽  
Minimal Sets ◽  
Mean Dimension ◽  
The Mean

Furstenberg [Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation. Math. Syst. Theory1 (1967), 1–49] calculated the Hausdorff and Minkowski dimensions of one-sided subshifts in terms of topological entropy. We generalize this to $\mathbb{Z}^{2}$ -subshifts. Our generalization involves mean dimension theory. We calculate the metric mean dimension and the mean Hausdorff dimension of $\mathbb{Z}^{2}$ -subshifts with respect to a subaction of $\mathbb{Z}$ . The resulting formula is quite analogous to Furstenberg’s theorem. We also calculate the rate distortion dimension of $\mathbb{Z}^{2}$ -subshifts in terms of Kolmogorov–Sinai entropy.

scholarly journals Metric mean dimension and analog compression

2020 ◽  
Author(s):  
Yonatan Gutman ◽  
Adam Śpiewak
Keyword(s):  
Stationary Process ◽  
Rate Distortion ◽  
Upper Bounds ◽  
Regularity Conditions ◽  
Box Dimension ◽  
Lower And Upper Bounds ◽  
Distortion Functions ◽  
Stationary Stochastic Processes ◽  
Mean Dimension ◽  
Infinite Sequences

<div>Wu and Verdú developed a theory of almost lossless analog compression, where one imposes various regularity conditions on the compressor and the decompressor with the input signal being modelled by a (typically infinite-entropy) stationary stochastic process. In this work we consider all stationary stochastic processes with trajectories in a prescribed set of (bi-)infinite sequences and find uniform lower and upper bounds for certain compression rates in terms of metric mean dimension and mean box dimension. An essential tool is the recent Lindenstrauss-Tsukamoto variational principle expressing metric mean dimension in terms of rate-distortion functions. We obtain also lower bounds on compression rates for a fixed stationary process in terms of the rate-distortion dimension rates and study several examples.</div>

scholarly journals Metric mean dimension and analog compression

2020 ◽  
Author(s):  
Yonatan Gutman ◽  
Adam Śpiewak
Keyword(s):  
Stationary Process ◽  
Rate Distortion ◽  
Upper Bounds ◽  
Regularity Conditions ◽  
Box Dimension ◽  
Lower And Upper Bounds ◽  
Distortion Functions ◽  
Stationary Stochastic Processes ◽  
Mean Dimension ◽  
Infinite Sequences

<div>Wu and Verdú developed a theory of almost lossless analog compression, where one imposes various regularity conditions on the compressor and the decompressor with the input signal being modelled by a (typically infinite-entropy) stationary stochastic process. In this work we consider all stationary stochastic processes with trajectories in a prescribed set of (bi-)infinite sequences and find uniform lower and upper bounds for certain compression rates in terms of metric mean dimension and mean box dimension. An essential tool is the recent Lindenstrauss-Tsukamoto variational principle expressing metric mean dimension in terms of rate-distortion functions. We obtain also lower bounds on compression rates for a fixed stationary process in terms of the rate-distortion dimension rates and study several examples.</div>

An Improvement of Rate-Distortion Optimized Quantization Process and its Hardware Implementation

2015 ◽  
Vol 135 (11) ◽  
pp. 1299-1306
Author(s):  
Genki Moriguchi ◽  
Takashi Kambe ◽  
Gen Fujita ◽  
Hajime Sawano
Keyword(s):  
Hardware Implementation ◽  
Rate Distortion

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.

Non-Equilibrium Green’s Functions: Variational Relations and Approximations for Particle Interactions

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Random Phase ◽  
Integration Contour ◽  
Differential Formulation ◽  
Variational Relations ◽  
Potential Perturbation ◽  
Non Equilibrium

Chapter 09 Nonequilibrium Green’s functions (NEGF), including coupled-correlated (C) single- and multi-particle Green’s functions, are defined as averages weighted with the time-development operator U(t0+τ,t0). Linear conductivity is exhibited as a two-particle equilibrium Green’s function (Kubo-type formulation). Admitting particle sources (S:η,η+) and non-conservation of number, the non-equilibrium multi-particle Green’s functions are constructed with numbers of creation and annihilation operators that may differ, and they may be derived as variational derivatives with respect to sources η,η+ of a generating functional eW=TrU(t0+τ,t0)CS/TrU(t0+τ,t0)C. (In the non-interacting case this yields the n-particle Green’s function as a permanent/determinant of single-particle Green’s functions.) These variational relations yield a symmetric set of multi-particle Green’s function equations. Cumulants and the Linked Cluster Theorem are discussed and the Random Phase Approximation (RPA) is derived variationally. Schwinger’s variational differential formulation of perturbation theories for the Green’s function, self-energy, vertex operator, and also shielded potential perturbation theory, are reviewed. The Langreth Algebra arises from analytic continuation of integration of products of Green’s functions in imaginary time to the real-time axis with time-ordering along the integration contour in the complex time plane. An account of the Generalized Kadanoff-Baym Ansatz is presented.

A Whole Rate-Distortion Optimize Pronounce Based on Wireless Sensor Network

2013 ◽  
Vol 756-759 ◽  
pp. 890-894 ◽  
Author(s):  
Qing Sheng Yu ◽  
Jian Zhang ◽  
Jin Xiang Peng
Keyword(s):  
Wireless Sensor Network ◽  
Sensor Network ◽  
Estimation Method ◽  
Rate Distortion ◽  
Video Encoding ◽  
Mode Decision ◽  
Wireless Sensor ◽  
Block Basis ◽  
Decision Scheme ◽  
Macro Block

Based on the Joint Video Team (JVT) of the ITU-T Video Coding Experts Group VC EG and the IS O/IEC Moving Picture Experts Group MPEG, an RD optimal Macro Block mode decision scheme for Internet error channel streaming is introduced. The scheme employs the luminance Rate Distortion (RD) optimal mode decision scheme so as to take the effects of video encoding distortion and the channel error propagation to get higher error robustness for error transmission. Based on the Wireless Sensor Network, this paper analyzes the data distortion problem when transmitting H.264 coded video stream over error-prone channel. And the authors also have discussed a widely accepted technique that introduces more intra-coded information on macro block basis. Additionally, this paper introduces a simple loss and multiplication factor estimation method, the rate-distortion optimized assessing strategy over the whole situation.

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