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Partition Regular Structures Contained in Large Sets Are Abundant

Vitaly Bergelson, Neil Hindman
2001 Journal of combinatorial theory. Series A  
We extend this result to apply to infinitely many notions of largeness in arbitrary semigroups and to other partition regular structures besides arithmetic progressions.  ...  progressions lying entirely in B is large among the set of all length l aritmetic progressions.  ...  Introduction A typical result of Ramsey Theory states that for any finite partition of a certain kind of an infinite structure, one of the cells of the partition contains an arbitrarily large structure  ... 
doi:10.1006/jcta.2000.3061 fatcat:3vlcc6ntmrezdipwqgjdtslyve

Joint-Sparse-Blocks Regression for Total Variation Regularized Hyperspectral Unmixing

Jie Huang, Ting-Zhu Huang, Xi-Le Zhao, Liang-Jian Deng
2019 IEEE Access  
only endmembers but also fractional abundances, and thus having similar structural sparsity.  ...  Sparse unmixing has attracted much attention in recent years. It aims at estimating the fractional abundances of pure spectral signatures in mixed pixels in hyperspectral images.  ...  It says that X is partitioned as X = [X 1 , X 2 , . . . , X 1875 ] and all X j contain d = 3 pixels.  ... 
doi:10.1109/access.2019.2943110 fatcat:dewrwniyzzbopey2mqnepdlgbi

Understanding Regularized Spectral Clustering via Graph Conductance [article]

Yilin Zhang, Karl Rohe
2018 arXiv   pre-print
Sparse and stochastic graphs create a lot of small trees that are connected to the core of the graph by only one edge. Graph conductance is sensitive to these noisy 'dangling sets'.  ...  Together, these results show that unbalanced partitions from spectral clustering can be understood as overfitting to noise in the periphery of a sparse and stochastic graph.  ...  Due to the abundance of g-dangling sets (Theorem 3.4), there are many small eigenvalues and their corresponding eigenvalues are localized on a small set of nodes.  ... 
arXiv:1806.01468v4 fatcat:nebtihbo6vfsfkjm7angbfr5oa

Improved Local Spectral Unmixing of hyperspectral data using an algorithmic regularization path for collaborative sparse regression

L. Drumetz, G. Tochon, M.A. Veganzones, J. Chanussot, C. Jutten
2017 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
The endmembers and their abundances in each pixel are extracted region-wise, instead of globally to mitigate spectral variability effects, which are less severe locally.  ...  We compute an algorithmic regularization path for this problem, giving access to the sequence of successive active sets of endmembers when the regularization parameter is increased.  ...  Since exactly solving the optimization problem for a large number of regularization parameters would be too time consuming, we are more interested in finding the active set of endmembers when the weight  ... 
doi:10.1109/icassp.2017.7953346 dblp:conf/icassp/DrumetzTVCJ17 fatcat:twkrewsp2jav5epek62sh5qsu4

A graph Laplacian regularization for hyperspectral data unmixing

Rita Ammanouil, Andre Ferrari, Cedric Richard
2015 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
The proposed graph framework promotes smoothness in the estimated abundance maps and collaborative estimation between homogeneous areas of the image.  ...  A special attention is given to the computational complexity of the algorithm, and Graphcut methods are proposed in order to reduce the computational burden.  ...  The simulations performed with Data2 show that this data set is more difficult than the previous since it contains a large number of endmembers: 15 compared to 5 in Data1.  ... 
doi:10.1109/icassp.2015.7178248 dblp:conf/icassp/AmmanouilFR15 fatcat:37t2fjwzozatlciqvirntin7sa

A graph Laplacian regularization for hyperspectral data unmixing [article]

Rita Ammanouil, André Ferrari, Cédric Richard
2014 arXiv   pre-print
The proposed graph framework promotes smoothness in the estimated abundance maps and collaborative estimation between homogeneous areas of the image.  ...  This paper introduces a graph Laplacian regularization in the hyperspectral unmixing formulation.  ...  The simulations performed with Data2 show that this data set is more difficult than the previous since it contains a large number of endmembers: 15 compared to 5 in Data1.  ... 
arXiv:1410.3699v1 fatcat:gketmi4oprfefmi6duci6itlym

Abundance of Matrices In Gaussian Integers [article]

Aninda Chakraborty
2020 arXiv   pre-print
In [HLS], N. Hindman, I. Leader and D. Strauss proved the abundance for a matrix with rational entries. In this paper we proved it for the ring of Gaussian integers.  ...  The main obstacle is in the field of complex numbers, no linear order relation exists. We overcome that in a tactful way.  ...  In [BH] , authors extend this result to apply to infinitely many notions of largeness in arbitrary semigroups and to other partition regular structures besides arithmetic progressions.  ... 
arXiv:2010.10305v1 fatcat:guzuwakwkvgsdgzf2lxbndna5y

A comparison study between windowing and binary partition trees for hyperspectral image information mining

M.A. Veganzones, G. Tochon, M. Dalla Mura, A.J. Plaza, J. Chanussot
2013 2013 IEEE International Geoscience and Remote Sensing Symposium - IGARSS  
In this work we explore the benefits of using Binary Partition Trees (BPT) instead of windowing to store hyperspectral large scenes.  ...  Recently, tree representations have been used as an alternative to windowing in order to structure and store large amounts of remote sensing data.  ...  The result is that each node R α contains a set of induced endmembers, E α , and their corresponding fractional abundances.  ... 
doi:10.1109/igarss.2013.6723804 dblp:conf/igarss/VeganzonesTMPC13 fatcat:44owwpm7kjhxrkqvgg6up6o66a

Spatial autocorrelation analysis allows disentangling the balance between neutral and niche processes in metacommunities

José Alexandre F. Diniz-Filho, Tadeu Siqueira, André Andrian Padial, Thiago Fernando Rangel, Victor Lemes Landeiro, Luis Mauricio Bini
2011 Oikos  
However, because environmental variation is often spatially structured, the decay could also be attributed to environmental factors that are missing from the analysis.  ...  Therefore, the hypothesis that spatial patterns in abundances are primarily due to pure neutral dynamics (rather than to missing spatiallystructured environmental factors) can be confirmed after taking  ...  Our workgroup in macroecology and biodiversity has been continuously supported by CNPq and CAPES.  ... 
doi:10.1111/j.1600-0706.2011.19563.x fatcat:w62hixhabvblhcexcboywvnh4u

Page 6367 of Mathematical Reviews Vol. , Issue 2002I [page]

2002 Mathematical Reviews  
6367 O5E 2002i:05116 05D10 Bergelson, Vitaly (1-OHS; Columbus, OH); Hindman, Neil (1-HWRD; Washington, DC) Partition regular structures contained in large sets are abundant. (English summary) J.  ...  We extend this result to apply to infinitely many notions of largeness in arbitrary semigroups and to partition regular structures other than arithmetic progressions.  ... 

Regular partitions of gentle graphs [article]

Yiting Jiang, Jaroslav Nesetril, Patrice Ossona de Mendez, and Sebastian Siebertz
2020 arXiv   pre-print
In particular, we stress the link to the theory of (structural) sparsity, which leads to alternative proofs, refinements and solutions of open problems.  ...  Szemeredi's Regularity Lemma is a very useful tool of extremal combinatorics. Recently, several refinements of this seminal result were obtained for special, more structured classes of graphs.  ...  Acknowledgments The authors are indebted to O-joung Kwon, who pointed out an error in an earlier version of this paper.  ... 
arXiv:2003.11692v2 fatcat:vww2q5r6lzcdbljsmzjnsfss4y

DISSECTING THE SPATIAL STRUCTURE OF ECOLOGICAL DATA AT MULTIPLE SCALES

Daniel Borcard, Pierre Legendre, Carol Avois-Jacquet, Hanna Tuomisto
2004 Ecology  
The data sets include Amazonian ferns, tropical marine zooplankton, chlorophyll in a marine lagoon, and oribatid mites in a peat bog.  ...  Spatial structures may not only result from ecological interactions, they may also play an essential functional role in organizing the interactions.  ...  C2 in Appendix C) and 0.339 with 4 PCNM for the large zooplankton ( Fig. C3 in Appendix C). The significant PCNM variables for the two fractions are given in Table C1 of Appendix C.  ... 
doi:10.1890/03-3111 fatcat:gdlnezvf3zgqvlouirckbgdezm

Testing hereditary properties of ordered graphs and matrices [article]

Noga Alon, Omri Ben-Eliezer, Eldar Fischer
2017 arXiv   pre-print
Along the way we develop a Ramsey-type lemma for k-partite graphs with "undesirable" edges, stating that one can find a Ramsey-type structure in such a graph, in which the density of the undesirable edges  ...  ., graphs with a totally ordered vertex set and a finite set of possible edge colors.  ...  The proof now follows from the proof for graphs: We can ask the partition I into large intervals to "respect the middle", so all parts of I are either fully contained in U or in V .  ... 
arXiv:1704.02367v1 fatcat:55xuj3rzt5d6xbrvczlj4jwdni

Key interaction patterns in proteins revealed by cluster expansion of the partition function [article]

M. Tajana, A. Trovato, G. Tiana
2022 arXiv   pre-print
We compared the entropies associated with different interaction patterns to their abundances in the native structures of real proteins.  ...  We found that patterns that contribute most to the partition function are cycles with even numbers of nodes, while cliques are typically detrimental.  ...  Small paths displaying large entropy (Fig. 7c ) are quite abundant in real proteins. Moreover, squares and 3-edge stars are abundant and display rather large entropy.  ... 
arXiv:2204.04030v1 fatcat:if4tsldjjrarxc7jh44mpvczh4

Using Gene Ontology annotations in exploratory microarray clustering to understand cancer etiology

Geoff Macintyre, James Bailey, Daniel Gustafsson, Izhak Haviv, Adam Kowalczyk
2010 Pattern Recognition Letters  
In addition, we show the potential of such methods for the exploration of cancer etiology.  ...  We have developed a novel clustering algorithm, which incorporates functional gene information from the Gene Ontology into the clustering process, resulting in more biologically meaningful clusters.  ...  In (a) the number of significant terms describing a cluster (x-axis) is shown for the top 20 clusters ranked by partition p-value, where C = 60. In this graph, large values are best.  ... 
doi:10.1016/j.patrec.2010.01.006 fatcat:7r4gkjy6j5br5fap3cs2chazzi
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