Inducibility of directed paths

Given a digraph D, a coloring 𝒞 of D is a partition of V(D) into stable sets. The k-norm of 𝒞 is defined as ΣC∈𝒞 min{|C|, k}. A coloring of D with minimum k-norm has its k-norm noted by χk(D). A (path)-k-pack of a digraph D is a set of k vertex-disjoint (directed) paths of D. The weight of a k-pack is the number of vertices covered by the k-pack. We denote by λk(D) the weight of a maximum k-pack. Linial conjectured that χk(D) ≤ λk(D) for every digraph. Such conjecture remains open, but has been proved for some classes of digraphs. We prove the conjecture for path-spine digraphs, defined as follows. A digraph D is path-spine if there exists a partition {X, Y} of V(D) such that D[X] has a Hamilton path and every arc in D[Y] belongs to a single path Q.

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K-domination number of products of two directed cycles and two directed paths

International Journal of Computing Science and Mathematics ◽

10.1504/ijcsm.2018.091734 ◽

2018 ◽

Vol 9 (2) ◽

pp. 197

Author(s):

Ramy Shaheen

Keyword(s):

Domination Number ◽

Directed Paths ◽

Directed Cycles

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Contact chains of cattle farms in Great Britain

Royal Society Open Science ◽

10.1098/rsos.180719 ◽

2019 ◽

Vol 6 (2) ◽

pp. 180719 ◽

Cited By ~ 3

Author(s):

Helen R. Fielding ◽

Trevelyan J. McKinley ◽

Matthew J. Silk ◽

Richard J. Delahay ◽

Robbie A. McDonald

Keyword(s):

Great Britain ◽

Bovine Tuberculosis ◽

Bimodal Distribution ◽

Disease Spread ◽

Scale Free ◽

Network Analyses ◽

Directed Paths ◽

System Data ◽

Epidemiological Characteristics ◽

Cattle Farms

Network analyses can assist in predicting the course of epidemics. Time-directed paths or ‘contact chains' provide a measure of host-connectedness across specified timeframes, and so represent potential pathways for spread of infections with different epidemiological characteristics. We analysed networks and contact chains of cattle farms in Great Britain using Cattle Tracing System data from 2001 to 2015. We focused on the potential for between-farm transmission of bovine tuberculosis, a chronic infection with potential for hidden spread through the network. Networks were characterized by scale-free type properties, where individual farms were found to be influential ‘hubs' in the network. We found a markedly bimodal distribution of farms with either small or very large ingoing and outgoing contact chains (ICCs and OCCs). As a result of their cattle purchases within 12-month periods, 47% of British farms were connected by ICCs to more than 1000 other farms and 16% were connected to more than 10 000 other farms. As a result of their cattle sales within 12-month periods, 66% of farms had OCCs that reached more than 1000 other farms and 15% reached more than 10 000 other farms. Over 19 000 farms had both ICCs and OCCs reaching more than 10 000 farms for two or more years. While farms with more contacts in their ICCs or OCCs might play an important role in disease spread, farms with extensive ICCs and OCCs might be particularly important by being at higher risk of both acquiring and disseminating infections.

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Directed paths in random media, function approximation and nonlinear regression

Physics Letters A ◽

10.1016/s0375-9601(97)00266-1 ◽

1997 ◽

Vol 230 (5-6) ◽

pp. 396-402

Author(s):

Zhiyong Yang ◽

Lulin Yuan

Keyword(s):

Nonlinear Regression ◽

Function Approximation ◽

Random Media ◽

Directed Paths

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Sign phase transition and directed paths in random media

JETP Letters ◽

10.1134/1.567189 ◽

1996 ◽

Vol 64 (4) ◽

pp. 312-318 ◽

Cited By ~ 2

Author(s):

B. Spivak ◽

S. Feng ◽

F. Zeng

Keyword(s):

Phase Transition ◽

Random Media ◽

Directed Paths

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Effects of environmental factors and landscape features on movement patterns of Florida black bears

Journal of Mammalogy ◽

10.1093/jmammal/gyx066 ◽

2017 ◽

Vol 98 (5) ◽

pp. 1463-1478 ◽

Cited By ~ 16

Author(s):

Dana L Karelus ◽

J Walter McCown ◽

Brian K Scheick ◽

Madelon van de Kerk ◽

Benjamin M Bolker ◽

...

Keyword(s):

Environmental Factors ◽

Urban Areas ◽

Animal Movement ◽

Movement Patterns ◽

Black Bears ◽

Temporal Scales ◽

Commercial Development ◽

Directed Movement ◽

Landscape Features ◽

Directed Paths

Abstract A greater understanding of how environmental factors and anthropogenic landscape features influence animal movements can inform management and potentially aid in mitigating human–wildlife conflicts. We investigated the movement patterns of 16 Florida black bears (Ursus americanus floridanus; 6 females, 10 males) in north-central Florida at multiple temporal scales using GPS data collected from 2011 to 2014. We calculated bi-hourly step-lengths and directional persistence, as well as daily and weekly observed displacements and expected displacements. We used those movement metrics as response variables in linear mixed models and tested for effects of sex, season, and landscape features. We found that step-lengths of males were generally longer than step-lengths of females, and both sexes had the shortest step-lengths during the daytime. Bears moved more slowly (shorter step-lengths) and exhibited less directed movement when near creeks, in forested wetlands, and in marsh habitats, possibly indicating foraging behavior. In urban areas, bears moved more quickly (longer step-lengths) and along more directed paths. The results were similar across all temporal scales. Major roads tended to act as a semipermeable barrier to bear movement. Males crossed major roads more frequently than females but both sexes crossed major roads much less frequently than minor roads. Our findings regarding the influence of landscape and habitat features on movement patterns of Florida black bears could be useful for planning effective wildlife corridors and understanding how future residential or commercial development and road expansions may affect animal movement.

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