Graph-Based Representations of Discrete Functions

1996 ◽  
pp. 1-28 ◽  
Author(s):  
Shin-ichi Minato
Keyword(s):  
Discrete Functions

scholarly journals Genome-wide Analysis Reveals Novel and Discrete Functions for Tubulin Carboxy-Terminal Tails

2014 ◽  
Vol 24 (12) ◽  
pp. 1295-1303 ◽  
Author(s):  
Jayne Aiken ◽  
David Sept ◽  
Michael Costanzo ◽  
Charles Boone ◽  
John A. Cooper ◽  
...  
Keyword(s):  
Genome Wide Analysis ◽  
Genome Wide ◽  
Carboxy Terminal ◽  
Discrete Functions

scholarly journals Deep Learning to Ternary Hash Codes by Continuation

2021 ◽  
Author(s):  
Mingrui Chen ◽  
Weiyu Li ◽  
weizhi lu
Keyword(s):  
Deep Learning ◽  
Image Retrieval ◽  
Continuation Method ◽  
Binary Codes ◽  
Hard Thresholding ◽  
Joint Learning ◽  
Ternary Codes ◽  
First Time ◽  
Hash Codes ◽  
Discrete Functions

Recently, it has been observed that $\{0,\pm1\}$-ternary codes which are simply generated from deep features by hard thresholding, tend to outperform $\{-1, 1\}$-binary codes in image retrieval. To obtain better ternary codes, we for the first time propose to jointly learn the features with the codes by appending a smoothed function to the networks. During training, the function could evolve into a non-smoothed ternary function by a continuation method, and then generate ternary codes. The method circumvents the difficulty of directly training discrete functions and reduces the quantization errors of ternary codes. Experiments show that the proposed joint learning indeed could produce better ternary codes.

scholarly journals Deep Learning to Ternary Hash Codes by Continuation

2021 ◽  
Author(s):  
Mingrui Chen ◽  
Weiyu Li ◽  
weizhi lu
Keyword(s):  
Deep Learning ◽  
Image Retrieval ◽  
Continuation Method ◽  
Binary Codes ◽  
Hard Thresholding ◽  
Joint Learning ◽  
Ternary Codes ◽  
First Time ◽  
Hash Codes ◽  
Discrete Functions

Recently, it has been observed that $\{0,\pm1\}$-ternary codes which are simply generated from deep features by hard thresholding, tend to outperform $\{-1, 1\}$-binary codes in image retrieval. To obtain better ternary codes, we for the first time propose to jointly learn the features with the codes by appending a smoothed function to the networks. During training, the function could evolve into a non-smoothed ternary function by a continuation method, and then generate ternary codes. The method circumvents the difficulty of directly training discrete functions and reduces the quantization errors of ternary codes. Experiments show that the proposed joint learning indeed could produce better ternary codes.

scholarly journals TWO-SCALE ESTIMATES FOR SPECIAL FINITE DISCRETE OPERATORS

2017 ◽  
Vol 22 (3) ◽  
pp. 300-310 ◽  
Author(s):  
Alexander V. Vasilyev ◽  
Vladimir B. Vasilyev
Keyword(s):  
Integral Operator ◽  
Discrete Approximation ◽  
Discrete Operators ◽  
Discrete Functions

We consider a certain finite discrete approximation for multidimensional Calderon–Zygmund integral operator and give a comparison between solutions of corresponding equations in some spaces of discrete functions.

scholarly journals The Centre of the Spaces of Banach Lattice-Valued Continuous Functions on the Generalized Alexandroff Duplicate

2011 ◽  
Vol 2011 ◽  
pp. 1-5 ◽  
Author(s):  
Faruk Polat
Keyword(s):  
Banach Lattice ◽  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Continuous Functions ◽  
Isolated Points ◽  
Discrete Functions

We characterize the centre of the Banach lattice of Banach lattice -valued continuous functions on the Alexandroff duplicate of a compact Hausdorff space in terms of the centre of , the space of -valued continuous functions on . We also identify the centre of whose elements are the sums of -valued continuous and discrete functions defined on a compact Hausdorff space without isolated points, which was given by Alpay and Ercan (2000).

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