scholarly journals Bounds on the kth multi-g base index of nearly reducible sign pattern matrices

2008 ◽  
Vol 308 (21) ◽  
pp. 4846-4860 ◽  
Author(s):  
Qian Li ◽  
Bolian Liu
Keyword(s):  
Sign Pattern

scholarly journals Bounds on the bases of irreducible generalized sign pattern matrices

2007 ◽  
Vol 427 (2-3) ◽  
pp. 285-300 ◽  
Author(s):  
Lihua You ◽  
Jiayu Shao ◽  
Haiying Shan
Keyword(s):  
Sign Pattern

scholarly journals Sign pattern matrices that admit P0-matrices

2011 ◽  
Vol 435 (8) ◽  
pp. 2046-2053
Author(s):  
C. Mendes Araújo ◽  
Juan R. Torregrosa
Keyword(s):  
Sign Pattern

scholarly journals Disentangling environmental effects in microbial association networks

Microbiome ◽  
2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Ina Maria Deutschmann ◽  
Gipsi Lima-Mendez ◽  
Anders K. Krabberød ◽  
Jeroen Raes ◽  
Sergio M. Vallina ◽  
...  
Keyword(s):  
Data Processing ◽  
Simulated Data ◽  
Potential Interaction ◽  
Microbial Interactions ◽  
Ecological Interactions ◽  
Sign Pattern ◽  
Interaction Information ◽  
Microbial Association ◽  
Environmental Selection ◽  
Data Processing Inequality

Abstract Background Ecological interactions among microorganisms are fundamental for ecosystem function, yet they are mostly unknown or poorly understood. High-throughput-omics can indicate microbial interactions through associations across time and space, which can be represented as association networks. Associations could result from either ecological interactions between microorganisms, or from environmental selection, where the association is environmentally driven. Therefore, before downstream analysis and interpretation, we need to distinguish the nature of the association, particularly if it is due to environmental selection or not. Results We present EnDED (environmentally driven edge detection), an implementation of four approaches as well as their combination to predict which links between microorganisms in an association network are environmentally driven. The four approaches are sign pattern, overlap, interaction information, and data processing inequality. We tested EnDED on networks from simulated data of 50 microorganisms. The networks contained on average 50 nodes and 1087 edges, of which 60 were true interactions but 1026 false associations (i.e., environmentally driven or due to chance). Applying each method individually, we detected a moderate to high number of environmentally driven edges—87% sign pattern and overlap, 67% interaction information, and 44% data processing inequality. Combining these methods in an intersection approach resulted in retaining more interactions, both true and false (32% of environmentally driven associations). After validation with the simulated datasets, we applied EnDED on a marine microbial network inferred from 10 years of monthly observations of microbial-plankton abundance. The intersection combination predicted that 8.3% of the associations were environmentally driven, while individual methods predicted 24.8% (data processing inequality), 25.7% (interaction information), and up to 84.6% (sign pattern as well as overlap). The fraction of environmentally driven edges among negative microbial associations in the real network increased rapidly with the number of environmental factors. Conclusions To reach accurate hypotheses about ecological interactions, it is important to determine, quantify, and remove environmentally driven associations in marine microbial association networks. For that, EnDED offers up to four individual methods as well as their combination. However, especially for the intersection combination, we suggest using EnDED with other strategies to reduce the number of false associations and consequently the number of potential interaction hypotheses.

scholarly journals Sign patterns that require eventual exponential nonnegativity

2015 ◽  
Vol 30 ◽  
Author(s):  
Craig Erickson
Keyword(s):  
Sign Pattern ◽  
Sign Patterns ◽  
Necessary And Sufficient

Sign patterns that require exponential nonnegativity are characterized. A set of conditions necessary for a sign pattern to require eventual exponential nonnegativity are established. It is shown that these conditions are also sufficient for an upper triangular sign pattern to require eventual exponential nonnegativity and it is conjectured that these conditions are both necessary and sufficient for any sign pattern to require eventual exponential nonnegativity. It is also shown that the maximum number of negative entries in a sign pattern that requires eventual exponential nonnegativity is (n−1)(n−2)/2 + 2

scholarly journals The Bipartite Zero Forcing Set for a Full Sign Pattern Matrix

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 354
Author(s):  
Gu-Fang Mou ◽  
Tian-Fei Wang ◽  
Zhong-Shan Li
Keyword(s):  
Sign Pattern ◽  
Zero Forcing ◽  
Minimum Rank ◽  
Zero Forcing Number ◽  
Maximum Nullity ◽  
New Variant ◽  
Forcing Number ◽  
Pattern Matrix ◽  
Forcing Set ◽  
Zero Forcing Set

For an m × n sign pattern P, we define a signed bipartite graph B ( U , V ) with one set of vertices U = { 1 , 2 , … , m } based on rows of P and the other set of vertices V = { 1 ′ , 2 ′ , … , n ′ } based on columns of P. The zero forcing number is an important graph parameter that has been used to study the minimum rank problem of a matrix. In this paper, we introduce a new variant of zero forcing set−bipartite zero forcing set and provide an algorithm for computing the bipartite zero forcing number. The bipartite zero forcing number provides an upper bound for the maximum nullity of a square full sign pattern P. One advantage of the bipartite zero forcing is that it can be applied to study the minimum rank problem for a non-square full sign pattern.

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