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Strong law of large numbers for the interface in ballistic deposition
2000
Annales de l'I.H.P. Probabilites et statistiques
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In this growth model particles rain down at random and stick to the growing cluster at the first point of contact. ...
We prove a hydrodynamic limit for ballistic deposition on a multidimensional lattice. ...
ACKNOWLEDGEMENTS I thank David Griffeath for an invitation to visit University of Wisconsin-Madison where this work was begun, and Janko Gravner, Harry Kesten, and Joachim Krug for valuable comments. ...
doi:10.1016/s0246-0203(00)00137-0
fatcat:ffyir5paqjbu7ftgi7xdfh6ika
Closed-Form Maximum Likelihood Estimates of Nearest Neighbor Spatial Dependence
2010
Geographical Analysis
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THE NEAREST NEIGHBOR GRAPH
Given n points or nodes, we consider their nearest neighbor graph. ...
Suppose the nearest neighbor directed graph has K subgraphs and construct the associated nearest neighbor adjacency matrix D for the n nodes according to the directed graph. ...
doi:10.1111/j.1538-4632.2000.tb00422.x
fatcat:dsxawq655rgyrcw3hjtrsljzlq
Cylinders' percolation: decoupling and applications
[article]
2021
arXiv
pre-print
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More precisely, we prove that for a small enough density of cylinders, a random walk on a connected component of the vacant set is transient for all dimensions d ≥ 3. ...
Our work introduces a new notion of fast decoupling, proves that it holds for the model in question and finishes with an application. ...
structure inherited from the nearest-
neighbors graph of Zd .
r:discrete Remark 5. ...
arXiv:2112.10055v1
fatcat:5o4v2mdupbdgzetxuxmr2h6lhq
Graph Clustering Using Early-Stopped Random Walks
[chapter]
2016
Lecture Notes in Computer Science
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Very fast growth of empirical graphs demands clustering algorithms with nearly-linear time complexity. We propose a novel approach to clustering, based on random walks. ...
Experimental results show that the use of the early stop procedure does not influence the quality of the clustering on the tested real world data sets. ...
The adjacency matrix was obtained with the help of a mutual k-nearest neighbor graph. The graph was constructed by connecting i to j if i is among the k-nearest neighbors of j and vice versa. ...
doi:10.1007/978-3-319-45378-1_37
fatcat:wpuptlwgtnegpnmes46q7s7g5a
The Infinite Volume Limit of Dissipative Abelian Sandpiles
2004
Communications in Mathematical Physics
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The finite volume rule now starts as follows: choose a site x at random from the volume V and add one grain to it. Suppose that x has N x nearest neighbors and that the new height at x is {+ 1. ...
Then, it topples by giving to each of its nearest neighbors one grain and dissipating {-N x grains to a sink associated to the volume. ...
doi:10.1007/s00220-003-1000-8
fatcat:o76fhj4xv5bvnjvcj2sv4g4uw4
A continuum limit for the PageRank algorithm
[article]
2021
arXiv
pre-print
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Semi-supervised and unsupervised machine learning methods often rely on graphs to model data, prompting research on how theoretical properties of operators on graphs are leveraged in learning problems. ...
We use the new framework to study the PageRank algorithm, and show how it can be interpreted as a numerical scheme on a directed graph involving a type of normalized graph Laplacian. ...
Yuan and J. Calder were partially supported by NSF-DMS grants 1713691 and 1944925, and a University of Minnesota Grant in Aid award. J. Calder was also partially supported by the Alfred P. ...
arXiv:2001.08973v3
fatcat:g5rlh2pxkfgohoaeie7nz77e7e
Neural Autoassociative Memories for Binary Vectors: A Survey
2017
Kibernetika i vyčislitelʹnaâ tehnika
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An interesting and still not completely resolved question is whether neural autoassociative memories can search for approximate nearest neighbors faster than other index structures for similarity search ...
This opens the possibility of a sublinear time search (in the number of stored items) for approximate nearest neighbors among vectors of high dimension. ...
Analysis and experiments for bases of random vectors with small random distortions of query vectors showed that up to a certain number of vectors in each network the nearest neighbor is found with a high ...
doi:10.15407/kvt188.02.005
fatcat:4fytuz4svnahrgsaqierg3eeim
Fast spectral clustering with self-weighted features
2022
Journal of Nonlinear and Variational Analysis
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Extensive experiments on synthetic and practical data sets illustrate the effectiveness and efficiency of the FSCSWF with respect to state-of-the-art methods. ...
As one of the mainstream clustering methods, the spectral clustering has aroused more and more attention recently because of its good performance, especially in nonlinear data sets. ...
Suppose that t, n, m, d, k are the number of optimization iterations, data points, anchor points, data features, and nearest neighbors. ...
doi:10.23952/jnva.6.2022.1.02
fatcat:m7i36giko5clrnscuxz32hsgp4
Percolation techniques in disordered spin flip dynamics: Relation to the unique invariant measure
1996
Communications in Mathematical Physics
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We consider lattice spin systems with short range but random and unbounded interactions. ...
The methods are based on relating the problem to an oriented percolation problem (contact process) and (for the general case) using a slightly modified version of the multiscale analysis of e.g. ...
Grimmett and E. Speer for interesting discussions in an early stage of this work while CM. was visiting the Newton Institute (Cambridge). We also thank A. van Enter and A. ...
doi:10.1007/bf02102431
fatcat:zbzr5ijn5vfm5hqm3tvu6ponwq
Equality of critical parameters for percolation of Gaussian free field level-sets
[article]
2020
arXiv
pre-print
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We consider level-sets of the Gaussian free field on Z^d, for d≥ 3, above a given real-valued height parameter h. ...
, and the onset of a local uniqueness regime in the supercritical phase, actually coincide, i.e. h_**(d)=h_*(d)= h̅(d) for any d ≥ 3. ...
Here y ∼ z means y
3
and z are nearest-neighbors in Zd . ...
arXiv:2002.07735v1
fatcat:7o6efzutczhd5picr4x6wxusd4
An Analysis of Poplar Growth and Quality Traits to Facilitate Identification of Climate-Adapted Plant Material for Sweden
2020
Bioenergy Research
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The results will facilitate decisions on the use of studied material in breeding, further testing and commercial deployment of poplar plantations in Sweden. ...
The significance of phenology and quality characteristics for growth performance and ranking of poplar clones was evaluated through genotypic correlations, and multivariate hierarchical cluster analysis ...
We also thank Marijke Steenackers from the Research Institute for Nature and Forest, Brussels (INBO) for providing the valuable information on the origin and pedigree of clones bred in Belgium. ...
doi:10.1007/s12155-020-10210-y
fatcat:hpamtax3vzbrbe6qasceuo3vku
Developments in the theory of randomized shortest paths with a comparison of graph node distances
2014
Physica A: Statistical Mechanics and its Applications
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There have lately been several suggestions for parametrized distances on a graph that generalize the shortest path distance and the commute time or resistance distance. ...
In this article, we develop the theory of one family of graph node distances, known as the randomized shortest path dissimilarity, which has its foundation in statistical physics. ...
We also performed semisupervised graph node classification based on a simple nearest neighbor learning algorithm. ...
doi:10.1016/j.physa.2013.09.016
fatcat:akxdokyi4bcv5nkmenplwkfyxm
Searching Remote Homology with Spectral Clustering with Symmetry in Neighborhood Cluster Kernels
2013
PLoS ONE
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The existing cluster kernel methods based on neighborhoods and profiles and the Markov clustering algorithms are currently the most popular methods for protein family recognition. ...
The deviation from random walks with inflation or dependency on hard threshold in similarity measure in those methods requires an enhancement for homology detection among multi-domain proteins. ...
walk on the graph. ...
doi:10.1371/journal.pone.0046468
pmid:23457439
pmcid:PMC3574063
fatcat:gz3mokeurnd65ffaxtw2wbxuam
A Single-Cell Network-Based Drug Repositioning Strategy for Post-COVID-19 Pulmonary Fibrosis
2022
Pharmaceutics
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The signature is functionally associated with the viral infection and lung fibrosis. Further, the signature has good performance in diagnosing and assessing pulmonary fibrosis. ...
By quantifying the proximity between the drug targets and the signature in the interactome, we identified several potential candidates and provided a drug list ranked by their proximity. ...
Acknowledgments: We would like to appreciate Chen-Hao Huang for his help and suggestion to this study.
Conflicts of Interest: The authors declare no conflict of interest. ...
doi:10.3390/pharmaceutics14050971
fatcat:saaj2t2rxfcm7gtbywckadp3fi
Going the Distance for Protein Function Prediction: A New Distance Metric for Protein Interaction Networks
2013
PLoS ONE
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We introduce diffusion state distance (DSD), a new metric based on a graph diffusion property, designed to capture finer-grained distinctions in proximity for transfer of functional annotation in PPI networks ...
typically measure proximity as the shortest-path distance in the network, but this has only a limited ability to capture fine-grained neighborhood distinctions, because most proteins are close to each other, and ...
Acknowledgments Crovella and Cowen thank the Institute for Mathematics and its Applications for inviting them to their ''Network Links: Connecting Social, Communication, and Biological Network Analysis ...
doi:10.1371/journal.pone.0076339
pmid:24194834
pmcid:PMC3806810
fatcat:zjetkv2iyjfb5ev2tvvusmxrta
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