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Equivalences between hamiltonicity and flow conjectures, and the sublinear defect property
2002
Discrete Mathematics
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We show that many conjectures and theorems about graphs could be proved if one could show that they are true apart from some "errors", provided that the number of these errors grows asymptotically slower ...
than the order of these graphs. ...
Acknowledgements This paper was written during the Alexander von Humboldt Fellowship in Germany. The author thanks AvH, Freie University and Professor Aigner for the hospitality. ...
doi:10.1016/s0012-365x(01)00372-7
fatcat:ku4scjy3jzawnfqoybuyf3frqa
Page 1602 of Mathematical Reviews Vol. , Issue 2003C
[page]
2003
Mathematical Reviews
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Brian Alspach (3-RGN; Regina, SK)
2003¢:05140 05C45 05C38 Kochol, Martin (SK-AOS; Bratislava) Equivalences between Hamiltonicity and flow conjectures, and the sublinear defect property. ...
Summary: “Barnette’s conjecture (BC) states that every 3- connected cubic bipartite planar graph admits a Hamilton cycle. It is shown that BC is equivalent to a conjecture stated in this pa- per. ...
How Many Conjectures Can You Stand? A Survey
2011
Graphs and Combinatorics
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These conjectures have lead to a wealth of interesting concepts, techniques, results and equivalent conjectures. ...
We survey results and open problems in hamiltonian graph theory centered around two conjectures of the 1980s that are still open: every 4-connected claw-free graph (line graph) is hamiltonian. ...
Kochol [40] proved equivalence with seemingly weaker versions, using a concept called sublinear defect. As an example, he proved that Conjecture 2 is equivalent to the following conjecture. ...
doi:10.1007/s00373-011-1090-6
fatcat:jj7oxvyx5vhrzdjtv2qyj7nysy
Algorithm for Overcoming the Curse of Dimensionality for State-dependent Hamilton-Jacobi equations
[article]
2018
arXiv
pre-print
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In this paper, we develop algorithms to overcome the curse of dimensionality in possibly non-convex state-dependent Hamilton-Jacobi equations (HJ PDEs) arising from optimal control and differential game ...
We extend [5, 6, 8], and conjecture a (Lax-type) minimization principle when the Hamiltonian is convex, as well as a (Hopf-type) maximization principle when the Hamiltonian is non-convex. ...
Wilfrid Gangbo for exploring if the conjectures made in this paper are sound. We also thank Alex Tong Lin for many discussions of insights in our paper. ...
arXiv:1704.02524v3
fatcat:4kcoklehknelfccu37ixsywwpm
Page 172 of Mathematical Reviews Vol. , Issue Index
[page]
Mathematical Reviews
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(English summary) 2003f:05078
Kochol, Martin Equivalences between Hamiltonicity and flow conjectures, and the sublinear defect property. (English summary) 2003c:05140
Kostochka, A. ...
(English summary)
— (with Ong, Siew-Hui) On Barnette’s conjecture and CBP graphs with given number of Hamilton cycles. ...
Linear growth of the entanglement entropy and the Kolmogorov-Sinai rate
2018
Journal of High Energy Physics
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Finally, we conjecture that the same rate Λ_A appears in the entanglement growth of chaotic quantum systems prepared in a semiclassical state. ...
We show that the entanglement entropy S_A of a Gaussian state grows linearly for large times in unstable systems, with a rate Λ_A ≤ h_KS determined by the Lyapunov exponents and the choice of the subsystem ...
The second term measures energy flow between the subsystem A and its complement, as measured by the effective Hamilto-nianH A of the subsystem defined in eq. (7.5). ...
doi:10.1007/jhep03(2018)025
fatcat:vyolxhc3m5ejznqtvseeogchqq
Subject Index Volumes 1–200
2001
Discrete Mathematics
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Erdös and Sós, 4925 Erdös and Szekeres, 4879 Erdös et al., 5529, 5888 Erdös Rubin Taylor, 3815 Erdös Sós Turán, 506 Everett, 2901 Faigle and Sands, 2122 Faudree et al., 4399 Faudree Gould Jacobson ...
Slater, 5299 Hertz and de Werra, 3748 Hibi, 4839 Hoàng, 3748, 4811 Holton, 1660 Holyer and Cockayne, 1118 Howorka, 2636 ...
, see also Hamiltonian and Hamiltonicity Hamiltonian, 51, 146, 205, 250, 442, 447, 477, 527, 603, 708, 805, 1106 , 1132 , 1133 , 1141 , 1207 , 1302 , 1398 , 1417 , 1524 , 1525 , 1639 , 1752 , 1971 , 2067 ...
doi:10.1016/s0012-365x(00)00471-4
fatcat:znxg54q6ifgutnhzj3urcw455y
Twentieth Annual Meeting February 24–27, 1976 Olympic Hotel, Seattle, Washington
1976
Biophysical Journal
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In contrast, rabbit troponin increases the Ca2+-sensitivity of the scallop fibers ten-fold such that the relationship between % Ca2+-activated tension and % Ca2+ binding to troponin is the same for identical ...
The frictional coefficient measured by these techniques was compared to the calculated value for an equivalent hydrated sphere of the same molecular weight. The data of I. D. ...
.), and both of the above
conjectures were confirmed. ...
doi:10.1016/s0006-3495(76)85676-7
fatcat:q2qfvlueibahpdvcbyuwef3ygm
Mathematical and Algorithmic Analysis of Network and Biological Data
[article]
2014
arXiv
pre-print
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This dissertation contributes to mathematical and algorithmic problems that arise in the analysis of network and biological data. ...
Equivalently, the effective resistance is the potential difference that appears across terminals i and j when we apply a unit current source between them. ...
Main Program Flow: The main flow comprises iterative execution of SQL statements with appropriate user defined functions. ...
arXiv:1407.0375v1
fatcat:6s2qka5fazbl7bzxz4k3u75hzm
A framework for three-dimensional navigation research
2013
Behavioral and Brain Sciences
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Three broad categories organize the experimental and theoretical issues raised by the commentators: (1) frames of reference, (2) comparative cognition, and (3) the role of experience. ...
AbstractWe have argued that the neurocognitive representation of large-scale, navigable three-dimensional space is anisotropic, having different properties in vertical versus horizontal dimensions. ...
(G1100669), and the Biotechnology and Biological Sciences Research Council (BB/J009792/1), and by a grant to Axona Ltd from the European Commission's Seventh Framework Programme (SPACEBRAIN). ...
doi:10.1017/s0140525x13001556
fatcat:2fw4lfhzirfxxhz2nppwaqstum
Making a stronger case for comparative research to investigate the behavioral and neurological bases of three-dimensional navigation
2013
Behavioral and Brain Sciences
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This comparative approach may offer unique insights into some of the important questions raised by Jeffery et al. ...
We propose some hypotheses relating differences in natural history to potential behavioral and neurological adaptations possessed by contrasting bird species. ...
(G1100669), and the Biotechnology and Biological Sciences Research Council (BB/J009792/1), and by a grant to Axona Ltd from the European Commission's Seventh Framework Programme (SPACEBRAIN). ...
doi:10.1017/s0140525x13000472
pmid:24103612
fatcat:y72x5vnckbcihl3ks35sy7wj3u
Map fragmentation in two- and three-dimensional environments
2013
Behavioral and Brain Sciences
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How map fragments are linked, which brain circuits are involved, and whether metric is preserved across fragments are questions that remain to be determined. ...
AbstractThe suggestion that three-dimensional space is represented by a mosaic of neural map fragments, each covering a small area of space in the plane of locomotion, receives support from studies in ...
(G1100669), and the Biotechnology and Biological Sciences Research Council (BB/J009792/1), and by a grant to Axona Ltd from the European Commission's Seventh Framework Programme (SPACEBRAIN). ...
doi:10.1017/s0140525x13000605
pmid:24103625
fatcat:yizukbxq7zezhnidhlaobldn6q
Navigating in a Three-Dimensional World
[chapter]
2011
Animal Thinking
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The present article reviews the emerging behavioral and neurobiological literature on spatial cognition in non-horizontal environments. ...
However, the real world is three-dimensional, having a complex topography including both horizontal and vertical features, which presents additional challenges for representation and navigation. ...
(G1100669), and the Biotechnology and Biological Sciences Research Council (BB/J009792/1), and by a grant to Axona Ltd from the European Commission's Seventh Framework Programme (SPACEBRAIN). ...
doi:10.7551/mitpress/9780262016636.003.0003
fatcat:6dlac5a63nhhth776y5scyluwa
Think local, act global: How do fragmented representations of space allow seamless navigation?
2013
Behavioral and Brain Sciences
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AbstractIn this commentary, we highlight a difficulty for metric navigation arising from recent data with grid and place cells: the integration of piecemeal representations of space in environments with ...
One implication of this is that the capacity for spatial inferences may be limited. ...
(G1100669), and the Biotechnology and Biological Sciences Research Council (BB/J009792/1), and by a grant to Axona Ltd from the European Commission's Seventh Framework Programme (SPACEBRAIN). ...
doi:10.1017/s0140525x13000368
pmid:24103601
fatcat:sbioi44ngbavbk26znoqx7kvjy
Navigating in a three-dimensional world
2013
Behavioral and Brain Sciences
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The present article reviews the emerging behavioral and neurobiological literature on spatial cognition in non-horizontal environments. ...
However, the real world is three-dimensional, having a complex topography including both horizontal and vertical features, which presents additional challenges for representation and navigation. ...
(G1100669), and the Biotechnology and Biological Sciences Research Council (BB/J009792/1), and by a grant to Axona Ltd from the European Commission's Seventh Framework Programme (SPACEBRAIN). ...
doi:10.1017/s0140525x12002476
pmid:24103594
fatcat:z6wa67wr3jar3m2p2b6qf6g3zm
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