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Partition Regular Structures Contained in Large Sets Are Abundant
2001
Journal of combinatorial theory. Series A
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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
2019
IEEE Access
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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]
2018
arXiv
pre-print
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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
2017
2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
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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
2015
2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
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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]
2014
arXiv
pre-print
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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]
2020
arXiv
pre-print
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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
2013
2013 IEEE International Geoscience and Remote Sensing Symposium - IGARSS
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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
2011
Oikos
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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
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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]
2020
arXiv
pre-print
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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
2004
Ecology
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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]
2017
arXiv
pre-print
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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]
2022
arXiv
pre-print
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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
2010
Pattern Recognition Letters
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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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