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Strong law of large numbers for the interface in ballistic deposition

T Seppäläinen
2000 Annales de l'I.H.P. Probabilites et statistiques  
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

R. Kelley Pace, Dongya Zou
2010 Geographical Analysis  
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]

Alves, Caio and Teixeira, Augusto
2021 arXiv   pre-print
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]

Małgorzata Lucińska, Sławomir T. Wierzchoń
2016 Lecture Notes in Computer Science  
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

F. Redig, E. Saada, C. Maes
2004 Communications in Mathematical Physics  
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]

Amber Yuan, Jeff Calder, Braxton Osting
2021 arXiv   pre-print
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

Volodymyr GRITSENKO, A. RACHKOVSKIJ, A. FROLOV, R. GAYLER, D. KLEYKO, E. OSIPOV
2017 Kibernetika i vyčislitelʹnaâ tehnika  
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  
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

G. Gielis, C. Maes
1996 Communications in Mathematical Physics  
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]

Hugo Duminil-Copin, Subhajit Goswami, Pierre-François Rodriguez, Franco Severo
2020 arXiv   pre-print
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

Almir Karacic, Anneli Adler, Martin Weih, Lars Christersson
2020 Bioenergy Research  
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

Ilkka Kivimäki, Masashi Shimbo, Marco Saerens
2014 Physica A: Statistical Mechanics and its Applications  
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

Ujjwal Maulik, Anasua Sarkar, Ahmed Moustafa
2013 PLoS ONE  
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

Albert Li, Jhih-Yu Chen, Chia-Lang Hsu, Yen-Jen Oyang, Hsuan-Cheng Huang, Hsueh-Fen Juan
2022 Pharmaceutics  
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

Mengfei Cao, Hao Zhang, Jisoo Park, Noah M. Daniels, Mark E. Crovella, Lenore J. Cowen, Benjamin Hescott, Stefano Boccaletti
2013 PLoS ONE  
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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