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Nowhere-zero integral chains and flows in bidirected graphs

A Khelladi
1987 Journal of combinatorial theory. Series B (Print)  
ACKNOWLEDGMENTS The author would like to express his gratitute to the referees for their stimulating comments and suggestions.  ...  NOWHERE-ZERO INTEGRAL CHAINS Definitions and Basic Results Let N be an (integral) chain group on a finite set E.  ...  Every bidirected graph without m-isthmus can be provided with a nowhere-zero 6-flow.  ... 
doi:10.1016/0095-8956(87)90032-3 fatcat:ntdblcwah5f2vmhfphrmrcjpm4

Nowhere-zero integral flows on a bidirected graph

A Bouchet
1983 Journal of combinatorial theory. Series B (Print)  
We apply a similar method to bidirected graphs in the next section. NOWHERE-ZERO FLOW WITH A MINIMAL WIDTH Let G be a bidirected graph with no signed graphic isthmi.  ...  Finally Section 4 gives an upper bound for w, the minimal integer such that every bidirected graph with a nowhere-zero flow has a nowhere-zero flowfwith If(e)] < w on every edge e.  ... 
doi:10.1016/0095-8956(83)90041-2 fatcat:46zmnk6wqnhxbiesmozoesjciq

Page 3960 of Mathematical Reviews Vol. , Issue 88h [page]

1988 Mathematical Reviews  
(DZ-BOUM) Nowhere-zero integral chains and flows in bidirected graphs. J. Combin. Theory Ser. B 43 (1987), no. 1, 95-115.  ...  Let G be a bidirected graph which has a nowhere-zero flow.  ... 

The Number of Nowhere-Zero Flows on Graphs and Signed Graphs [article]

Matthias Beck, Thomas Zaslavsky
2006 arXiv   pre-print
We show that the existence of an integral flow polynomial that counts nowhere-zero k-flows on a graph, due to Kochol, is a consequence of a general theory of inside-out polytopes.  ...  The same holds for flows on signed graphs. We develop these theories, as well as the related counting theory of nowhere-zero flows on a signed graph with values in an abelian group of odd order.  ...  A nowhere-zero k-flow is an integral flow (i.e., A = Z) whose absolute values are in [k − 1] := {1, 2, . . . , k − 1}. Nowhere-zero flows are nicely surveyed in [10] and [19] .  ... 
arXiv:math/0309331v4 fatcat:yhkvr3wxvnb7jgbl7bu4ulve5e

The number of nowhere-zero flows on graphs and signed graphs

Matthias Beck, Thomas Zaslavsky
2006 Journal of combinatorial theory. Series B (Print)  
We show that the existence of an integral flow polynomial that counts nowhere-zero k-flows on a graph, due to Kochol, is a consequence of a general theory of inside-out polytopes.  ...  The same holds for flows on signed graphs. We develop these theories, as well as the related counting theory of nowhere-zero flows on a signed graph with values in an abelian group of odd order.  ...  Acknowledgments The authors are grateful for corrections and comments by Aaron Pixton and an anonymous referee.  ... 
doi:10.1016/j.jctb.2006.02.011 fatcat:kl32sgkx4vbj5hmjzaikv25k24

Page 1336 of Mathematical Reviews Vol. , Issue 85d [page]

1985 Mathematical Reviews  
He proposes the following analogue of Tutte’s 5-flow problem. Conjecture: Every bidirected graph which has a nowhere-zero flow has a nowhere-zero flow with all edge values in (—6, +6).  ...  Bouchet, A. 85d:05109 Nowhere-zero integral flows on a bidirected graph. J. Combin. Theory Ser. B 34 (1983), no. 3, 279-292. Let G be a finite undirected graph.  ... 

Dualities and reciprocities on graphs on surfaces [article]

Woo-Seok Jung, Jaeseong Oh
2021 arXiv   pre-print
In addition, we provide a reciprocity theorem connecting local tensions and boundary acyclic orientations.  ...  We extend the duality between acyclic orientations and totally cyclic orientations on planar graphs to dualities on graphs on orientable surfaces by introducing boundary acyclic orientations and totally  ...  Tutte [21, 22] proved that nowhere-zero Z k -flow exists if and only if nowhere-zero integral k-flow exists.  ... 
arXiv:2005.01590v2 fatcat:ubsujef37jccbh7nj5bdgfhyz4

Dispersion of discontinuous periodic waves

G. Chen, P. J. Olver
2012 Proceedings of the Royal Society A  
(BBM) model's is asymptotically zero, while that of some standard bidirectional Boussinesq systems is asymptotically constant.  ...  which models small vibrations of a thin elastic beam, and has bidirectional quadratic dispersion: ω(k) = ±k 2 .  ...  We also thank the anonymous referees for helpful and thought-provoking comments. The work of second author is supported in part by NSF grant no. DMS-1108894.  ... 
doi:10.1098/rspa.2012.0407 fatcat:lsiobb5fpjdajhbsftwcyftjm4

FSCRank: A Failure-Sensitive Structure-Based Component Ranking Approach for Cloud Applications

Na WU, Decheng ZUO, Zhan ZHANG, Peng ZHOU, Yan ZHAO
2019 IEICE transactions on information and systems  
In addition, factors that affect application availability optimization are analyzed and summarized.  ...  To address this problem, we propose a failure-sensitive structure-based component ranking approach (FSCRank), which integrates component failure impact and application structure information into component  ...  The invocation chain indicates the flow of business processing, including a sequential list of all components that are involved with processing the event.  ... 
doi:10.1587/transinf.2018edp7197 fatcat:em26753elna6lcsszxkvejiitu

Trading accuracy for speed in approximate consensus

Jacob Beal
2016 Knowledge engineering review (Print)  
O(diameter 2) for Laplacian-based), unidirectional PLD-consensus is faster and more resilient than bidirectional PLD-consensus, but exhibits higher variance in the converged value.  ...  Both a unidirectional and bidirectional algorithm based on this approach are studied. Although both have the same asymptotic O(diameter) convergence time (vs.  ...  The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of DARPA  ... 
doi:10.1017/s0269888916000175 fatcat:4ciyfkjjffd6rfsqc5vlnsy6xe

Differentiable Visual Computing [article]

Tzu-Mao Li
2019 arXiv   pre-print
Simulating light transport in the presence of multi-bounce glossy effects and motion in 3D rendering is challenging due to the hard-to-sample high-contribution areas.  ...  We present a Markov Chain Monte Carlo rendering algorithm that extends Metropolis Light Transport by automatically and explicitly adapting to the local integrand, thereby increasing sampling efficiency  ...  Control Flow and Recursion Handling control flow and recursion in forward-mode is trivial. We do not need to modify the flow at all.  ... 
arXiv:1904.12228v2 fatcat:mlhfrmp4rzhenbwk4yuljunctm

An Algorithmic Approach to Collective Behavior

Bernard Chazelle
2014 Journal of statistical physics  
This article examines the merits and challenges of an algorithmic approach to the emergence of collective order.  ...  While powerful tools from dynamics and statistical mechanics have been brought to bear, sometimes with great success, an algorithmic perspective has been lacking.  ...  Acknowledgments I wish to thank the anonymous referees for many useful comments and suggestions. This work was supported in part by NSF Grants CCF-0832797, CCF-0963825, and CCF-1016250.  ... 
doi:10.1007/s10955-014-1140-6 fatcat:gaysmo7xffaabnfbns4xatb4aa

Dynamical differential covariance recovers directional network structure in multiscale neural systems [article]

Yusi Chen, Burke Q Rosen, Terrence J Sejnowski
2021 bioRxiv   pre-print
DDC can be generalized to a wide range of dynamical models and recording techniques.  ...  The method is first validated on networks with false positive motifs and multiscale neural simulations where the ground truth connectivity is known.  ...  Can DDC track the information flow in a nonlinear Rössler system, which is deterministic but chaotic? The three equations for this system in Fig. 1D have a nonlinear bidirectional confounder motif.  ... 
doi:10.1101/2021.06.18.448901 fatcat:ptstvhwn7zatrkx7knfhcrdjt4

Characteristic flows on signed graphs and short circuit covers

Edita Máčajová, Martiň Skoviera
2016 unpublished
As an application of this result we show that a signed graph G admitting a nowhere-zero k-flow has a covering with signed circuits of total length at most 2(k − 1)|E(G)|.  ...  In our generalisation, the rôle of circuits is taken over by signed circuits of a signed graph which are known to occur in two types-either balanced circuits or pairs of disjoint unbalanced circuits connected  ...  In 1983, Bouchet [3] conjectured that every signed graph that admits a nowhere-zero integer flow has a nowhere-zero 6-flow.  ... 
fatcat:2eofuzifc5f2dd7f4dfxydp3si

Mapping Vertical Trade

Benno Ferrarini
2011 Social Science Research Network  
Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten  ...  economic analysis, and statistical data and measurement.  ...  Nowhere has the expansion of vertical trade networks and supply chains been more pronounced than in Asia, largely in relation to the People's Republic of China's (PRC) ascension as a regional hub of assembly  ... 
doi:10.2139/ssrn.1906493 fatcat:pmkoeatzpre7rmw266mx47mcbu
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