PMID- 28415372
OWN - NLM
STAT- PubMed-not-MEDLINE
DCOM- 20180709
LR  - 20180709
IS  - 2470-0053 (Electronic)
IS  - 2470-0045 (Linking)
VI  - 95
IP  - 3-1
DP  - 2017 Mar
TI  - Ultrametricity of optimal transport substates for multiple interacting paths over 
      a square lattice network.
PG  - 030108
LID - 10.1103/PhysRevE.95.030108 [doi]
AB  - We model a set of point-to-point transports on a network as a system of 
      polydisperse interacting self-avoiding walks (SAWs) over a finite square lattice. 
      The ends of each SAW may be located both at random, uniformly distributed, 
      positions or with one end fixed at a lattice corner. The total energy of the 
      system is computed as the sum over all SAWs, which may represent either the time 
      needed to complete the transport over the network, or the resources needed to 
      build the networking infrastructure. We focus especially on the second aspect by 
      assigning a concave cost function to each site to encourage path overlap. A 
      simulated annealing optimization, based on a modified Berg-Foerster-Aragao de 
      Carvalho-Caracciolo-Froehlich (BFACF) algorithm developed for polymers, is used 
      to probe the complex conformational substate structure at zero temperature. We 
      characterize the average cost gains (and path-length variations) for increasing 
      polymer density with respect to a Dijkstra routing and find a nonmonotonic 
      behavior as recently found for random networks. We observe the emergence of 
      ergodicity breaking and of nontrivial overlap distributions among replicas when 
      switching from a convex to a concave cost function (e.g., x;gamma, where x 
      represents the node overlap). Finally, we show that the space of ground states 
      for gamma<1 is compatible with an ultrametric structure, as seen in many complex 
      systems such as some spin glasses.
FAU - Cogoni, Marco
AU  - Cogoni M
AD  - CRS4: Center for Advanced Studies, Research and Development in Sardinia, 09010 
      Pula (CA), Italy.
FAU - Busonera, Giovanni
AU  - Busonera G
AD  - CRS4: Center for Advanced Studies, Research and Development in Sardinia, 09010 
      Pula (CA), Italy.
FAU - Zanetti, Gianluigi
AU  - Zanetti G
AD  - CRS4: Center for Advanced Studies, Research and Development in Sardinia, 09010 
      Pula (CA), Italy.
LA  - eng
PT  - Journal Article
DEP - 20170328
PL  - United States
TA  - Phys Rev E
JT  - Physical review. E
JID - 101676019
EDAT- 2017/04/19 06:00
MHDA- 2017/04/19 06:01
CRDT- 2017/04/19 06:00
PHST- 2016/11/25 00:00 [received]
PHST- 2017/04/19 06:00 [entrez]
PHST- 2017/04/19 06:00 [pubmed]
PHST- 2017/04/19 06:01 [medline]
AID - 10.1103/PhysRevE.95.030108 [doi]
PST - ppublish
SO  - Phys Rev E. 2017 Mar;95(3-1):030108. doi: 10.1103/PhysRevE.95.030108. Epub 2017 
      Mar 28.