scholarly journals Explaining Algorithmic Fairness Through Fairness-Aware Causal Path Decomposition

Author(s):  
Weishen Pan ◽  
Sen Cui ◽  
Jiang Bian ◽  
Changshui Zhang ◽  
Fei Wang
1974 ◽  
Vol 10 (3) ◽  
pp. 421-427 ◽  
Author(s):  
Brian R. Alspach ◽  
Norman J. Pullman

A path decomposition of a digraph G (having no loops or multiple arcs) is a family of simple paths such that every arc of G lies on precisely one of the paths of the family. The path number, pn(G) is the minimal number of paths necessary to form a path decomposition of G.We show that pn(G) ≥ max{0, od(v)-id(v)} the sum taken over all vertices v of G, with equality holding if G is acyclic. If G is a subgraph of a tournament on n vertices we show that pn(G) ≤ with equality holding if G is transitive.We conjecture that pn(G) ≤ for any digraph G on n vertices if n is sufficiently large, perhaps for all n ≥ 4.


2021 ◽  
Vol 322 ◽  
pp. 129006
Author(s):  
Junhua Zhang ◽  
Heming Wang ◽  
Lin Ma ◽  
Jian Wang ◽  
Jiashi Wang ◽  
...  

1980 ◽  
Vol 12 (02) ◽  
pp. 291-293 ◽  
Author(s):  
Priscilla Greenwood ◽  
Jim Pitman

1978 ◽  
Vol 6 (2) ◽  
pp. 345-348 ◽  
Author(s):  
P. W. Millar

Kybernetes ◽  
2018 ◽  
Vol 47 (6) ◽  
pp. 1242-1261 ◽  
Author(s):  
Can Zhong Yao ◽  
Peng Cheng Kuang ◽  
Ji Nan Lin

Purpose The purpose of this study is to reveal the lead–lag structure between international crude oil price and stock markets. Design/methodology/approach The methods used for this study are as follows: empirical mode decomposition; shift-window-based Pearson coefficient and thermal causal path method. Findings The fluctuation characteristic of Chinese stock market before 2010 is very similar to international crude oil prices. After 2010, their fluctuation patterns are significantly different from each other. The two stock markets significantly led international crude oil prices, revealing varying lead–lag orders among stock markets. During 2000 and 2004, the stock markets significantly led international crude oil prices but they are less distinct from the lead–lag orders. After 2004, the effects changed so that the leading effect of Shanghai composite index remains no longer significant, and after 2012, S&P index just significantly lagged behind the international crude oil prices. Originality/value China and the US stock markets develop different pattens to handle the crude oil prices fluctuation after finance crisis in 1998.


Author(s):  
Graham R. Law ◽  
Rosie Green ◽  
George T. H. Ellison
Keyword(s):  

2014 ◽  
Vol 256 ◽  
pp. 678-695 ◽  
Author(s):  
L.D. Angulo ◽  
J. Alvarez ◽  
F.L. Teixeira ◽  
M.F. Pantoja ◽  
S.G. Garcia

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