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Observability of Lattice Graphs
[article]

2015
*
arXiv
*
pre-print

This shows an interesting dependence

arXiv:1505.02224v1
fatcat:uittvvigbneiviugnhz6hxx7uu
*of**graph**observability*on the ratio between the dimension*of*the*lattice*and that*of*the walk. ... All*of*our results extend easily to non-square*lattices*: given a*lattice**graph**of*size N = n_1 * n_2 * ... * n_d, the number*of*colors for t-*observability*is Theta (N^(1/t)). ... We prove the results for subgraphs*of*square*lattices*, but the bounds are easily extended to rectangular*lattices*: given a*lattice**graph**of*size N = n 1 × n 2 × · · · × n d , the number*of*colors for t-*observability*...##
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Diagonalisation of quantum observables on regular lattices and general graphs

2011
*
Computer Physics Communications
*

This code is capable

doi:10.1016/j.cpc.2010.12.051
fatcat:2xokqjdxcjbpzmrtw3h4dwxwn4
*of*constructing and diagonalising the*observables*for spin 1 2 and spinless fermionic particles with many body interactions on arbitrary*graphs*using massively parallel distributed ... In the study*of*quantum mechanical systems, exact diagonalisation (ED) methods play an extremely important role. We have developed an ED code named DoQO (Diagonalisation*of*Quantum*Observables*). ... project nmphy002a "Topological Phases in Quantum*Lattice*Systems". ...##
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Minimax and Adaptive Estimation of Covariance Operator for Random Variables Observed on a Lattice Graph

2015
*
Figshare
*

In a range

doi:10.6084/m9.figshare.1298112
fatcat:qhnrk5dodbh57na4wd35wuyw5q
*of*applications including imaging analysis and fMRI studies, random variables are*observed*on a*lattice**graph*. ... The results show that the dimension*of*the*lattice**graph*significantly affects the optimal rates convergence, often much more so than the dimension*of*the random variables. ... S.5 Proof*of*Lemma 6*Observe*that E ∑ B∈B d Σ B − Σ B 4 ≤ p 6 E ∑ B∈B d Σ B − Σ B 4 ≤ p 6 E ∑ B∈B d ( ∥S B − Σ B ∥ + λ 0 √ s d (B) + log p n ) 4 ≤ Cp 6 E ∑ B∈B d ∥S B − Σ B ...##
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Minimax and Adaptive Estimation of Covariance Operator for Random Variables Observed on a Lattice Graph

2016
*
Journal of the American Statistical Association
*

In a range

doi:10.1080/01621459.2014.1001067
fatcat:ednwsuqvnbe5bhlbdkn4ipmp4e
*of*applications including imaging analysis and fMRI studies, random variables are*observed*on a*lattice**graph*. ... The results show that the dimension*of*the*lattice**graph*significantly affects the optimal rates convergence, often much more so than the dimension*of*the random variables. ...*lattice**graph*. ...##
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A Graph Lattice Approach to Maintaining Dense Collections of Subgraphs as Image Features

2011
*
2011 International Conference on Document Analysis and Recognition
*

The

doi:10.1109/icdar.2011.216
dblp:conf/icdar/Saund11
fatcat:favkvvory5b5xphnqav5dvcrf4
*graph**lattice*enables methods for adaptively growing a feature space*of*subgraphs tailored to*observed*document genres. ... This paper shows how large families*of*complex features can be built out*of*simpler ones through construction*of*a*graph**lattice*-a hierarchy*of*related subgraphs linked in a*lattice*. ... Thank you to Fang Liu for discussions and for building a preliminary implementation*of*the*graph**lattice*machinery. ...##
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A Graph Lattice Approach to Maintaining and Learning Dense Collections of Subgraphs as Image Features

2013
*
IEEE Transactions on Pattern Analysis and Machine Intelligence
*

Additionally, the

doi:10.1109/tpami.2012.267
pmid:23267200
fatcat:2324ywfd5fgx7lmaylfcsoexji
*graph**lattice*enables methods for adaptively growing a feature space*of*subgraphs tailored to*observed*data. ... Efficiency in exact matching is gained by exploitation*of*the*graph**lattice*data structure. ... Appreciation is also due to Fang Liu for discussions and for building a preliminary implementation*of*the*graph**lattice*machinery. ...##
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The relation graphs of finite lattices

2020
*
Malaya Journal of Matematik
*

We investigate the properties

doi:10.26637/mjm0804/0147
fatcat:vbdlxhw5mzadxpvqc2kee2y3ka
*of*relation*graphs*and characterize those*lattices*whose relation*graphs*are complete. The association between the relation*graphs**of*isomorphic*lattices*is studied. ... The relation*graph**of*a finite*lattice*L is defined to be a simple*graph*with the elements*of*L as vertices and two distinct vertices are adjacent if and only if they are comparable in L. ... Fig. 1 : 1*Lattice*and its associated relation*graph*G(L)*Observation*3.2. {0, 1} is the only*lattice*whose diagraph coincides with its relation*graph*. ...##
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Geometric properties of the three-dimensional Ising andXYmodels

2008
*
Physical Review E
*

The fractal structure

doi:10.1103/physreve.77.061108
pmid:18643218
fatcat:di52byywiff4jn4byiu4nphhzu
*of*high-temperature*graphs**of*the three-dimensional Ising and XY models is investigated by simulating these*graphs*directly on a cubic*lattice*and analyzing them with the help*of*... percolation*observables*. ...*Observables*The HT*graphs*are analyzed with the help*of*standard percolation*observables*͓10͔. An important characteristic is whether a*graph*spans the*lattice*or not. ...##
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Protein Evolution within a Structural Space

2003
*
Biophysical Journal
*

We develop a divergent evolution model based on the

doi:10.1016/s0006-3495(03)74716-x
pmid:14581198
pmcid:PMC1303574
fatcat:vrvh5jjr7jfzbffqklyk323rfe
*lattice*space which produces*graphs*that, within certain parameter regimes, recapitulate the scale-free behavior*observed*in similar*graphs**of*real protein ... We use this measure*of*structural relatedness to create a*graph**of**lattice*structures and compare this*graph*(in which nodes are*lattice*structures and edges are defined using structural similarity) to ... Given that such distributions can also be*observed*in random*graphs*(Dokholyan et al., 2002) , we desired to identify corresponding ''families''*of**lattice*structures. ...##
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Distributive Lattice Polymorphism on Reflexive Graphs
[article]

2014
*
arXiv
*
pre-print

In this paper we give two characterisations

arXiv:1411.7879v1
fatcat:cztb2gkfife3rb5w5qgcxqtxki
*of*the class*of*reflexive*graphs*admitting distributive*lattice*polymorphisms and use these characterisations to address the problem*of*recognition: for a reflexive ...*graph*G in which no two vertices have the same neighbourhood, we find a polynomial time algorithm to decide if G admits a distributive*lattice*polymorphism. ... PI Characterisation*of*DL*Graphs*We start with some*observations*relating*lattice*homomorphisms and*graph*homomorphisms. The first is clear. ...##
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General Fifth M- Zagreb Polynomials of the TUC4C8(R)[p, q] 2D-Lattice and its Derived Graphs

2020
*
Letters in Applied NanoBioScience
*

A molecular

doi:10.33263/lianbs101.17381747
fatcat:lpjb2736o5a55lcn4jdqxnvwna
*graph*or a chemical*graph*is a*graph*related to the structure*of*a chemical compound. ... , its subdivision, and para-line*graphs*. ... The authors would also like to thank the referees for their thoughtful suggestions for the improvement*of*the article. Conflicts*of*Interest The authors declare no conflict*of*interest. ...##
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The Z_6-symmetric model partition function on triangular lattice

2020
*
Malaysian Journal of Fundamental and Applied Sciences
*

Q = 6 on a triangular

doi:10.11113/mjfas.v16n3.1722
fatcat:swh7hspusze6xjx2fbff2i2fvm
*lattice*. Mainly, the model is defined on the triangular*lattice**graph*with the nearest neighbour interaction. ... There is a study on a square*lattice*that can predict the existence*of*multiple phase transitions on a complex plane. ... From our result on the zeros distribution, this behaviour is already*observed*. To support our claim and*observation*, we present the*graph**of*the specific heat for our model. ...##
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Numerical evidence against a conjecture on the cover time of planar graphs

2011
*
Physical Review E
*

We investigate a conjecture on the cover times

doi:10.1103/physreve.84.022103
pmid:21929045
fatcat:vmqnm2n3mjhfzik4wu622d6doy
*of*planar*graphs*by means*of*large Monte Carlo simulations. ... The conjecture states that the cover time τ(G_N)*of*a planar*graph*G_N*of*N vertices and maximal degree d is lower bounded by τ(G_N) ≥ C_d N( N)^2 with C_d = (d/4π) tan (π/d), with equality holding for ... Other*lattices**observe*the bound, with the square*lattice*being "borderline." ...##
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ダイヤモンドはなぜ美しい?

Why do diamonds look so beautiful?

2006
*
Expositions of Current Mathematics
*

Why do diamonds look so beautiful?

The

doi:10.11429/emath1996.2006.spring-meeting_26
fatcat:3ltl7u7z7nertae3mc4hd73dhq
*lattice*R0 will be said to be the maximal*lattice**of*X. (2) Try to define the d-dimensional diamond*lattice*, and*observe*that the hexagonal*lattice*is the 2-dimensional diamond*lattice*. 4 Crystal ... We may also define the notion*of*"inner symmetry in terms*of*automorphisms*of*the diamond*lattice*as an abstract*graph*. ...##
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On centrally symmetric graphs

1996
*
Mathematica Bohemica
*

I am grateful to the CNRS

doi:10.21136/mb.1996.125944
fatcat:ttbb7m624ncnzk2mqv7jhitqui
*of*France for inviting me to the Laboratoire de Mathematiques Discretes in Marseille, Luminy, during February/March 1994. In particular I thank Professor G. ... If the covering*graph**of*a*lattice*is a CS-*graph*or an S-*graph*, then the*lattice*will be called a CS-*lattice*or S-*lattice*, respectively. ... Let us*observe*that a*lattice*L which is graded and whose dual*lattice*is strong need not be upper semimodular: just take for L the dual*of*a nonmodular geometric*lattice*. ...
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