Dualities between Entropy Functions and Network Codes

Dualities Between Entropy Functions and Network Codes

IEEE Transactions on Information Theory ◽

10.1109/tit.2008.928963 ◽

2008 ◽

Vol 54 (10) ◽

pp. 4470-4487 ◽

Cited By ~ 46

Author(s):

Terence Chan ◽

Alex Grant

Keyword(s):

Network Codes ◽

Entropy Functions

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The motion of the particles volume corresponding to invariant solution of rank 2 submodel of hydrodynamic type

Proceedings of the Mavlyutov Institute of Mechanics ◽

10.21662/uim2016.2.030 ◽

2016 ◽

Vol 11 (2) ◽

pp. 205-209

Author(s):

D.T. Siraeva

Keyword(s):

Equation Of State ◽

Invariant Solution ◽

Hydrodynamic Type ◽

Lagrangian Coordinates ◽

Hydrodynamic Equations ◽

Rank 2 ◽

Invariant Submodel ◽

Entropy Functions

Invariant submodel of rank 2 on the subalgebra consisting of the sum of transfers for hydrodynamic equations with the equation of state in the form of pressure as the sum of density and entropy functions, is presented. In terms of the Lagrangian coordinates from condition of nonhyperbolic submodel solutions depending on the four essential constants are obtained. For simplicity, we consider the solution depending on two constants. The trajectory of particles motion, the motion of parallelepiped of the same particles are studied using the Maple.

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Reduction of partially invariant submodels of rank 3 defect 1 to invariant submodels

Multiphase Systems ◽

10.21662/mfs2018.3.009 ◽

2018 ◽

Vol 13 (3) ◽

pp. 59-63 ◽

Cited By ~ 1

Author(s):

D.T. Siraeva

Keyword(s):

Equation Of State ◽

Lie Algebra ◽

Lie Algebras ◽

Gas Dynamics ◽

Hydrodynamic Type ◽

System Of Equations ◽

Two Dimensional ◽

Equations Of Gas Dynamics ◽

Entropy Functions

Equations of hydrodynamic type with the equation of state in the form of pressure separated into a sum of density and entropy functions are considered. Such a system of equations admits a twelve-dimensional Lie algebra. In the case of the equation of state of the general form, the equations of gas dynamics admit an eleven-dimensional Lie algebra. For both Lie algebras the optimal systems of non-similar subalgebras are constructed. In this paper two partially invariant submodels of rank 3 defect 1 are constructed for two-dimensional subalgebras of the twelve-dimensional Lie algebra. The reduction of the constructed submodels to invariant submodels of eleven-dimensional and twelve-dimensional Lie algebras is proved.

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ImbTreeEntropy and ImbTreeAUC: Novel R Packages for Decision Tree Learning on the Imbalanced Datasets

Electronics ◽

10.3390/electronics10060657 ◽

2021 ◽

Vol 10 (6) ◽

pp. 657

Author(s):

Krzysztof Gajowniczek ◽

Tomasz Ząbkowski

Keyword(s):

Imbalanced Data ◽

Misclassification Cost ◽

Learning Time ◽

Misclassification Costs ◽

Split Point ◽

Speed Up ◽

R Packages ◽

Class Labels ◽

Entropy Functions ◽

Support Cost

This paper presents two R packages ImbTreeEntropy and ImbTreeAUC to handle imbalanced data problems. ImbTreeEntropy functionality includes application of a generalized entropy functions, such as Rényi, Tsallis, Sharma–Mittal, Sharma–Taneja and Kapur, to measure impurity of a node. ImbTreeAUC provides non-standard measures to choose an optimal split point for an attribute (as well the optimal attribute for splitting) by employing local, semi-global and global AUC (Area Under the ROC curve) measures. Both packages are applicable for binary and multiclass problems and they support cost-sensitive learning, by defining a misclassification cost matrix, and weighted-sensitive learning. The packages accept all types of attributes, including continuous, ordered and nominal, where the latter type is simplified for multiclass problems to reduce the computational overheads. Both applications enable optimization of the thresholds where posterior probabilities determine final class labels in a way that misclassification costs are minimized. Model overfitting can be managed either during the growing phase or at the end using post-pruning. The packages are mainly implemented in R, however some computationally demanding functions are written in plain C++. In order to speed up learning time, parallel processing is supported as well.

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