-
1
-
-
84942305442
-
-
R. Pastor-Satorras, C. Castellano, P. Van Mieghem, and A. Vespignani, Rev. Mod. Phys. 87, 925 (2015). RMPHAT 0034-6861 10.1103/RevModPhys.87.925
-
(2015)
Rev. Mod. Phys.
, vol.87
, pp. 925
-
-
Pastor-Satorras, R.1
Castellano, C.2
Van Mieghem, P.3
Vespignani, A.4
-
4
-
-
84255196314
-
-
M. E. J. Newman, Nat. Phys. 8, 25 (2012). 1745-2473 10.1038/nphys2162
-
(2012)
Nat. Phys.
, vol.8
, pp. 25
-
-
Newman, M.E.J.1
-
5
-
-
84866088345
-
-
Y. Dabaghian, F. Mémoli, L. Frank, and G. Carlsson, PLoS Comput. Biol. 8, e1002581 (2012). 1553-7358 10.1371/journal.pcbi.1002581
-
(2012)
PLoS Comput. Biol.
, vol.8
, pp. e1002581
-
-
Dabaghian, Y.1
Mémoli, F.2
Frank, L.3
Carlsson, G.4
-
8
-
-
84951155754
-
-
L. Hébert-Dufresne, E. Laurence, A. Allard, J.-G. Young, and L. J. Dubé, Phys. Rev. E 92, 062809 (2015). PLEEE8 1539-3755 10.1103/PhysRevE.92.062809
-
(2015)
Phys. Rev. e
, vol.92
, pp. 062809
-
-
Hébert-Dufresne, L.1
Laurence, E.2
Allard, A.3
Young, J.-G.4
Dubé, L.J.5
-
15
-
-
84879275745
-
-
G. Petri, M. Scolamiero, I. Donato, and F. Vaccarino, PloS One 8, e66506 (2013). 1932-6203 10.1371/journal.pone.0066506
-
(2013)
PloS One
, vol.8
, pp. e66506
-
-
Petri, G.1
Scolamiero, M.2
Donato, I.3
Vaccarino, F.4
-
18
-
-
84928923288
-
-
G. Petri, P. Expert, F. Turkheimer, R. Carhart-Harris, D. Nutt, P. Hellyer, and F. Vaccarino, J. R. Soc. Interface 11, 20140873 (2014). 1742-5689 10.1098/rsif.2014.0873
-
(2014)
J. R. Soc. Interface
, vol.11
, pp. 20140873
-
-
Petri, G.1
Expert, P.2
Turkheimer, F.3
Carhart-Harris, R.4
Nutt, D.5
Hellyer, P.6
Vaccarino, F.7
-
19
-
-
84976542864
-
-
Y. Hiraoka, T. Nakamura, A. Hirata, E. G. Escolar, K. Matsue, and Y. Nishiura, PNAS 113, 7035 (2016). PNASA6 0027-8424 10.1073/pnas.1520877113
-
(2016)
PNAS
, vol.113
, pp. 7035
-
-
Hiraoka, Y.1
Nakamura, T.2
Hirata, A.3
Escolar, E.G.4
Matsue, K.5
Nishiura, Y.6
-
20
-
-
84940869196
-
-
M. Kahle, AMS Contemp. Math. 620, 201 (2014). 9780-8218 10.1090/conm/620
-
(2014)
AMS Contemp. Math.
, vol.620
, pp. 201
-
-
Kahle, M.1
-
24
-
-
84929646139
-
-
Z. Wu, G. Menichetti, C. Rahmede, and G. Bianconi, Sci. Rep. 5, 10073 (2015). 2045-2322 10.1038/srep10073
-
(2015)
Sci. Rep.
, vol.5
, pp. 10073
-
-
Wu, Z.1
Menichetti, G.2
Rahmede, C.3
Bianconi, G.4
-
26
-
-
84944930378
-
-
C. Orsini, M. M. Dankulov, A. Jamakovic, P. Mahadevan, P. Colomer-de Simón, A. Vahdat, K. E. Bassler, Z. Toroczkai, M. Boguñá, G. Caldarelli, Nat. Commun. 6, 8627 (2015). 2041-1723 10.1038/ncomms9627
-
(2015)
Nat. Commun.
, vol.6
, pp. 8627
-
-
Orsini, C.1
Dankulov, M.M.2
Jamakovic, A.3
Mahadevan, P.4
Colomer-De Simón, P.5
Vahdat, A.6
Bassler, K.E.7
Toroczkai, Z.8
Boguñá, M.9
Caldarelli, G.10
-
29
-
-
0004193355
-
-
(Cambridge University Press, Cambridge, UK)
-
A. Hatcher, Algebraic Topology (Cambridge University Press, Cambridge, UK, 2000).
-
(2000)
Algebraic Topology
-
-
Hatcher, A.1
-
32
-
-
85029835825
-
-
We provide a reference c ++ implementation of the sampler as well as tutorials at
-
We provide a reference c ++ implementation of the sampler as well as tutorials at https://www.github.com/jg-you/scm.
-
-
-
-
33
-
-
0001144639
-
-
M. Kato, T. Kakutani, T. Inoue, and T. Itino, Contr. Biol. Lab. Kyoto Univ. 27, 309 (1990).
-
(1990)
, vol.27
, pp. 309
-
-
Kato, M.1
Kakutani, T.2
Inoue, T.3
Itino, T.4
-
34
-
-
34547140875
-
-
K.-I. Goh, M. E. Cusick, D. Valle, B. Childs, M. Vidal, and A.-L. Barabási, PNAS 104, 8685 (2007). PNASA6 0027-8424 10.1073/pnas.0701361104
-
(2007)
PNAS
, vol.104
, pp. 8685
-
-
Goh, K.-I.1
Cusick, M.E.2
Valle, D.3
Childs, B.4
Vidal, M.5
Barabási, A.-L.6
-
35
-
-
0346068039
-
-
(University of Missouri, St. Louis)
-
S. Decker, C. W. Kohfeld, R. Rosenfeld, and J. Sprague, St. Louis Homicide Project: Local Responses to a National Problem (University of Missouri, St. Louis, 1991).
-
(1991)
St. Louis Homicide Project: Local Responses to A National Problem
-
-
Decker, S.1
Kohfeld, C.W.2
Rosenfeld, R.3
Sprague, J.4
-
36
-
-
85029854607
-
-
We represent the support of the SCM as a graph (Equation presented). If (Equation presented) is an expander, then the sampler yields uncorrelated configuration with high probability after (Equation presented) steps; the suggested (Equation presented) follows from the loose upper bound (Equation presented). A proof that (Equation presented) is in fact an expander will depend on (Equation presented); however, we note that (Equation presented) shares two important properties with all expanders for sufficiently large (Equation presented): It is connected and not bipartite
-
We represent the support of the SCM as a graph (Equation presented). If (Equation presented) is an expander, then the sampler yields uncorrelated configuration with high probability after (Equation presented) steps; the suggested (Equation presented) follows from the loose upper bound (Equation presented). A proof that (Equation presented) is in fact an expander will depend on (Equation presented); however, we note that (Equation presented) shares two important properties with all expanders for sufficiently large (Equation presented): It is connected and not bipartite.
-
-
-
-
37
-
-
42749099621
-
-
M. E. J. Newman, Phys. Rev. E 68, 026121 (2003). 1063-651X 10.1103/PhysRevE.68.026121
-
(2003)
Phys. Rev. e
, vol.68
, pp. 026121
-
-
Newman, M.E.J.1
|