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Phase Transitions in Random Dyadic Tilings and Rectangular Dissections

Sarah Cannon, Sarah Miracle, Dana Randall
2018 SIAM Journal on Discrete Mathematics  
We show there is a phase transition in the dyadic setting: when λ < 1, the edge-flipping chain mixes in time O(n 2 log n), and when λ > 1, the mixing time is exp(Ω(n 2 )).  ...  As in the dyadic case, we show that the edge-flipping Markov chain for rectangular dissections requires exponential time when λ > 1.  ...  There has also been interest in the special case of dyadic tilings, or equitable rectangular dissections into dyadic rectangles.  ... 
doi:10.1137/17m1157118 fatcat:trdh4oa6vren3j4c6xzgcxlicq

Phase Transitions in Random Dyadic Tilings and Rectangular Dissections [chapter]

Sarah Cannon, Sarah Miracle, Dana Randall
2014 Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms  
We show there is a phase transition in the dyadic setting: when λ < 1, the edge-flipping chain mixes in time O(n 2 log n), and when λ > 1, the mixing time is exp(Ω(n 2 )).  ...  As in the dyadic case, we show that the edge-flipping Markov chain for rectangular dissections requires exponential time when λ > 1.  ...  There has also been interest in the special case of dyadic tilings, or equitable rectangular dissections into dyadic rectangles.  ... 
doi:10.1137/1.9781611973730.104 dblp:conf/soda/CannonMR15 fatcat:f2v4kgjh4vhgjnmtrhjqv3neba

Sampling weighted perfect matchings on the square-octagon lattice

Prateek Bhakta, Dana Randall
2017 Theoretical Computer Science  
However, unlike Markov chains for sampling perfect matchings on the square and hexagonal lattices, corresponding to domino and lozenge tilings,  ...  Acknowledgments The authors thank Jim Propp for introducing this problem and for several useful discussions.  ...  Such an approach was taken recently in the context of triangulations [4] and rectangular dissections and dyadic tilings [3] , revealing similar dichotomies.  ... 
doi:10.1016/j.tcs.2017.01.014 fatcat:dxliujjjvrfz3kc6hcevgdjtwe

Image Transforms [chapter]

2011 Still Image and Video Compression with MATLAB  
Tiles are rectangular subblocks of an image component and are numbered sequentially in a raster scanning order as shown in Figure 8 . 10 . Note that all tiles in a component are of the same size.  ...  Note that if the input components in equation ( Tile 0 Tile 1 Tile 2 Tile 3 Tile 4 Tile 5 Tile 6 Tile 7 Tile 8 Tile 9 Tile 10 Tile 11 Tile 12 Tile 13 Tile 14 Figure 8 .10 Division  ...  phase and % FIR filter with linear phase are considered. % IIR filter is 9th order and FIR filter has 9 taps  ... 
doi:10.1002/9780470886922.ch3 fatcat:gjjunlemu5alhbobqd27tec5zi

A Lyapunov function for Glauber dynamics on lattice triangulations

Alexandre Stauffer
2016 Probability theory and related fields  
We study random triangulations of the integer points [0, n] 2 ∩ Z 2 , where each triangulation σ has probability measure λ |σ | with λ > 0 being a real parameter and |σ | denoting the sum of the length  ...  In a very recent work with Caputo, Martinelli and Sinclair, we apply this Lyapunov function to establish tight bounds on the mixing time of Glauber dynamics in thin rectangles that hold for all λ < 1.  ...  reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.  ... 
doi:10.1007/s00440-016-0735-z fatcat:2i2dfbuymjd3rcqpw7r6veac7m

A Lyapunov function for Glauber dynamics on lattice triangulations [article]

Alexandre Stauffer
2015 arXiv   pre-print
We study random triangulations of the integer points [0,n]^2 ∩Z^2, where each triangulation σ has probability measure λ^|σ| with |σ| denoting the sum of the length of the edges in σ.  ...  In a very recent work with Caputo, Martinelli and Sinclair, we apply this Lyapunov function to establish tight bounds on the mixing time of Glauber dynamics in thin rectangles that hold for all λ<1.  ...  Acknowledgments I am grateful to Pietro Caputo, Fabio Martinelli and Alistair Sinclair for several useful discussions, and to Grégory Miermont for suggesting the problem of local limits of lattice triangulations  ... 
arXiv:1504.07980v1 fatcat:auail6wjsff2zdo56pwuquf7rm

New Developments in Science and Technology - 60th Anniversary Special Issue, Beihang University (BUAA)

2012 Science  
provides cutting-edge research and education in advanced structural and functional materials, nanomaterials, new materials for clean energy, polymers and composites, nonequilibrium fabrication, corrosion  ...  There are 75 full-time teachers in the school, which annually graduates 150 undergraduates, 180 postgraduates, 50 Ph.D.s, and 10 students from abroad.  ...  , and analyzed its phase transition property and complexity.  ... 
doi:10.1126/science.338.6104.274-c fatcat:iurk5neuwvh2jgbohwevb5dicy

Configraphics Graph Theoretical Methods for Design and Analysis of Spatial Configurations 14 2016 Configraphics Graph Theoretical Methods for Design and Analysis of Spatial Configurations

Pirouz Nourian, Pirouz Nourian
unpublished
This tool, independently from the rectangular drawing tool, can convert a rectangular dissection (rectangular cell division) into a topologically homoeomorphic (say equivalent) dissection whose cells have  ...  We, however, tried alternative paths, which could possibly result in solutions that are more generic (free form) than rectangular dissections. § 3.11.6 A Note on Rectangular Floor Plan Layout March &  ...  equations in this case will be applied to transition probability matrices , which actually mean the following: Probability of being at state at time is the entry of the transition probability matrix raised  ... 
fatcat:hv277qo4w5ctzmfg23n35v77he

CUA 2020 Annual Meeting Abstracts

Editor CUAJ
2020 Canadian Urological Association Journal  
There was no significant difference in the risk of an unplanned hospital admission between OUR and MIS.  ...  TDABC demonstrates significant cost variability in VUR treatment modalities and identified local cost drivers to target.  ...  , open-label, phase 3 randomized controlled trial.  ... 
doi:10.5489/cuaj.6732 fatcat:wbyvxypjhbgydfcb64yc6wrrb4

Carving Curriculum out of Chaos: Exploring Teacher Interventions and the Patterning of Small Groups in Mathematics Class

Nathaniel Banting
2017
Small group work is becoming an increasingly popular structure for promoting communication, sense-making, and reasoning in the mathematics class.  ...  with the mathematical environment while operating in certain curriculum spaces.  ...  central clusters, posed in three distinct phases.  ... 
doi:10.7939/r3028pr54 fatcat:4bcvu2mi7jfffn4pdmbm7slzcy

Abstracts

1991 American Zoologist  
Males overlapped with both adult males and females, and were not t e r r i t o r i a l in their larger home ranges (29.9±7.78 m ) .  ...  Profiles of sex steroid hormones in the breeding season were measured by RIA.  ...  The width of the lipid phase transition also depended on rearing temperature, with narrower phase transitions occurring in skins from 34°C individuals.  ... 
doi:10.1093/icb/31.5.1 fatcat:ym7sisaugjct5nswvg2kilnu3a

In vitro neuronal cultures on MEA: an engineering approach to study physiological and pathological brain networks [article]

ILARIA COLOMBI
2019
Spike Tiling Figure 6 . 3 . 63 Cortical cultures on MEA and data analysis.  ...  tiling timing coefficient) values and the higher IBR (inverse burst ratio) value.  ... 
doi:10.15167/colombi-ilaria_phd2019-02-21 fatcat:jttnydjk5bc2pg773n5tm3vpfq

JSE 29:4 Whole Issue PDF

Kathleen E. Erickson
2015 Journal of Scientific Exploration  
National Academy of Sciences, which he dissects for us in his Essay Review.  ...  Procedure Phase 1: Participant Recruitment and Screening Participation in the proposed study will involve claimant mediums and 'sitters-in-absentia' (each medium will read two pairs of sitters-in-absentia  ...  He lived in the home of a relative whose wife was interested in experimenting with table turning and séances.  ... 
doaj:b7025227a9584a90bdb85c1dc9ae555d fatcat:ftt6sgxjyzhhrfjlhlu4isw2wq

Abstracts of the 16th European Conference on Eye Movements 2011 [article]

Vitu, Françoise; CNRS, Université De Provence, Castet, Eric; CNRS, Université De La Méditerranée, Goffart, Laurent; CNRS, Université De La Méditerranée
2001
We are also indebted to Maria Ktori who conceived the program booklet and contributed in coordination with Françoise Kern, Andrew Meso, Rachel Ostrand and Kim Uittenhove to the edition and the proofreading  ...  We would like to warmly thank Stéphanie Desous for the enormous work she did in putting together all the selected abstracts and the scientific program of the conference.  ...  Robin and Richard Patton through the E. Bronson Ingram Chair in Neuroscience Acknowledgments: Ann Lablans, Donald Brien, Sean Hickman and Mike Lewis for technical assistance.  ... 
doi:10.16910/jemr.4.3.1 fatcat:5ttwswfz7beanlztoni3bpbz4q

Proceedings. 9th 3DGeoInfo Conference 2014, [11-13 November 2014, Dubai]

Martin [Hrsg.] Breunig, Mulhim [Hrsg.] Al-Doori, Edgar [Hrsg.] Butwilowski, Paul Vincent [Hrsg.] Kuper, Joachim [Hrsg.] Benner, Karl-Heinz [Hrsg.] Haefele
2014
It is known that, scientific disciplines such as geology, geophysics, and reservoir exploration intrinsically use 3D geo-information in their models and simulations.  ...  The conference in Dubai offers an interdisciplinary forum of sub- and above-surface 3D geo-information researchers and practitioners dealing with data acquisition, modeling, management, maintenance, visualization  ...  and interoperable data for use within archaeological research and in other fields, such as land administration and other policy decisions.  ... 
doi:10.5445/ir/1000043804 fatcat:56zwdnlvyrcpld3qzjiwvql53i