scholarly journals A BRIEF INTRODUCTION TO SOFIC ENTROPY THEORY

2019 ◽  
Author(s):  
LEWIS P. BOWEN
Keyword(s):  
Entropy Theory ◽  
Sofic Entropy

scholarly journals ADDITIVITY PROPERTIES OF SOFIC ENTROPY AND MEASURES ON MODEL SPACES

2016 ◽  
Vol 4 ◽  
Author(s):  
TIM AUSTIN
Keyword(s):  
Lower Bound ◽  
Probability Distributions ◽  
Cartesian Product ◽  
Sufficient Conditions ◽  
Entropy Theory ◽  
Reverse Inequality ◽  
Cartesian Products ◽  
Model Spaces ◽  
Sofic Entropy ◽  
Sofic Groups

Sofic entropy is an invariant for probability-preserving actions of sofic groups. It was introduced a few years ago by Lewis Bowen, and shown to extend the classical Kolmogorov–Sinai entropy from the setting of amenable groups. Some parts of Kolmogorov–Sinai entropy theory generalize to sofic entropy, but in other respects this new invariant behaves less regularly. This paper explores conditions under which sofic entropy is additive for Cartesian products of systems. It is always subadditive, but the reverse inequality can fail. We define a new entropy notion in terms of probability distributions on the spaces of good models of an action. Using this, we prove a general lower bound for the sofic entropy of a Cartesian product in terms of separate quantities for the two factor systems involved. We also prove that this lower bound is optimal in a certain sense, and use it to derive some sufficient conditions for the strict additivity of sofic entropy itself. Various other properties of this new entropy notion are also developed.

scholarly journals Examples in the entropy theory of countable group actions

2019 ◽  
Vol 40 (10) ◽  
pp. 2593-2680 ◽  
Author(s):  
LEWIS BOWEN
Keyword(s):  
Classical Theory ◽  
Group Actions ◽  
Countable Group ◽  
Classification Theory ◽  
Entropy Theory ◽  
Survey Article ◽  
Sofic Entropy ◽  
Factor Maps ◽  
Measure Preserving Actions ◽  
Classical Entropy

Kolmogorov–Sinai entropy is an invariant of measure-preserving actions of the group of integers that is central to classification theory. There are two recently developed invariants, sofic entropy and Rokhlin entropy, that generalize classical entropy to actions of countable groups. These new theories have counterintuitive properties such as factor maps that increase entropy. This survey article focusses on examples, many of which have not appeared before, that highlight the differences and similarities with classical theory.

Review of Social Entropy Theory.

1991 ◽  
Vol 36 (4) ◽  
pp. 347-347
Author(s):  
No authorship indicated
Keyword(s):  
Entropy Theory

Frontiers in Complex Dynamics

2014 ◽  
Author(s):  
Araceli Bonifant ◽  
Misha Lyubich ◽  
Scott Sutherland
Keyword(s):  
Historical Perspective ◽  
Complex Dynamics ◽  
Short Paper ◽  
Combinatorial Group Theory ◽  
Entropy Theory ◽  
Holomorphic Dynamics ◽  
Eightieth Birthday ◽  
Several Variables ◽  
Fields Medal ◽  
Combinatorial Group

John Milnor, best known for his work in differential topology, K-theory, and dynamical systems, is one of only three mathematicians to have won the Fields medal, the Abel prize, and the Wolf prize, and is the only one to have received all three of the Leroy P. Steele prizes. In honor of his eightieth birthday, this book gathers together surveys and papers inspired by Milnor's work, from distinguished experts examining not only holomorphic dynamics in one and several variables, but also differential geometry, entropy theory, and combinatorial group theory. The book contains the last paper written by William Thurston, as well as a short paper by John Milnor himself. Introductory sections put the papers in mathematical and historical perspective, color figures are included, and an index facilitates browsing.

Approach for cleaning uncertain data based on information entropy theory

2013 ◽  
Vol 33 (9) ◽  
pp. 2490-2492
Author(s):  
Yuanxiang QIN ◽  
Liang DUAN ◽  
Kun YUE
Keyword(s):  
Information Entropy ◽  
Uncertain Data ◽  
Entropy Theory

scholarly journals Research on Pattern Recognition Method of Blockage Signal in Pipeline Based on LMD Information Entropy and ELM

2017 ◽  
Vol 2017 ◽  
pp. 1-16 ◽  
Author(s):  
Jingzong Yang ◽  
Xiaodong Wang ◽  
Zao Feng ◽  
Guoyong Huang
Keyword(s):  
Pattern Recognition ◽  
Impulse Response ◽  
Information Entropy ◽  
Operating Conditions ◽  
Support Vector ◽  
Entropy Theory ◽  
Pattern Recognition Method ◽  
Response Signal ◽  
Recognition Method ◽  
Learning Machine

Aiming at the nonstationary and nonlinear characteristics of acoustic impulse response signal in pipeline blockage and the difficulty in identifying the different degrees of blockage, this paper proposed a pattern recognition method based on local mean decomposition (LMD), information entropy theory, and extreme learning machine (ELM). Firstly, the impulse response signals of pipeline extracted in different operating conditions were decomposed with LMD method into a series of product functions (PFs). Secondly, based on the information entropy theory, the appropriate energy entropy, singular spectrum entropy, power spectrum entropy, and Hilbert spectrum entropy were extracted as the input feature vectors. Finally, ELM was introduced for classification of pipeline blockage. Through the analysis of acoustic impulse response signal collected under the condition of health and different degrees of blockages in pipeline, the results show that the proposed method can well characterize the state information. Also, it has a great advantage in terms of accuracy and it is time consuming when compared with the support vector machine (SVM) and BP (backpropagation) model.

Seasonal precipitation variability in mainland China based on entropy theory

2021 ◽  
Author(s):  
Guocan Wu ◽  
Shun Qin ◽  
Chengcheng Huang ◽  
Zhanshan Ma ◽  
Chunming Shi
Keyword(s):  
Mainland China ◽  
Precipitation Variability ◽  
Seasonal Precipitation ◽  
Entropy Theory

scholarly journals Fuzzy Covering-Based Three-Way Clustering

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Dandan Yang
Keyword(s):  
Nearest Neighbor ◽  
Structural Information ◽  
Boundary Region ◽  
Global Perspective ◽  
Semantic Interpretation ◽  
Entropy Theory ◽  
Fuzzy Similarity ◽  
Fuzzy Similarity Relation ◽  
The Universe ◽  
Better Than

This paper investigates the three-way clustering involving fuzzy covering, thresholds acquisition, and boundary region processing. First of all, a valid fuzzy covering of the universe is constructed on the basis of an appropriate fuzzy similarity relation, which helps capture the structural information and the internal connections of the dataset from the global perspective. Due to the advantages of valid fuzzy covering, we explore the valid fuzzy covering instead of the raw dataset for RFCM algorithm-based three-way clustering. Subsequently, from the perspective of semantic interpretation of balancing the uncertainty changes in fuzzy sets, a method of partition thresholds acquisition combining linear and nonlinear fuzzy entropy theory is proposed. Furthermore, boundary regions in three-way clustering correspond to the abstaining decisions and generate uncertain rules. In order to improve the classification accuracy, the k-nearest neighbor (kNN) algorithm is utilized to reduce the objects in the boundary regions. The experimental results show that the performance of the proposed three-way clustering based on fuzzy covering and kNN-FRFCM algorithm is better than the compared algorithms in most cases.

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