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Page 6977 of Mathematical Reviews Vol. , Issue 99j [page]

<span title="">1999</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Multidimensional binary trees arise in the construction of search trees for multidimensional keys.  ...  Mutafchiev (BG-AOS-A; Sofia) 99j:60013 60C05 05C05 Kemp, Rainer (D-FRNK-I; Frankfurt am Main) On the joint distribution of the nodes in uniform multidimensional binary trees.  ... 
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Indexing method for multidimensional vector data

Justin Terry, Bela Stantic
<span title="">2013</span> <i title="National Library of Serbia"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/rhtuh2ifczhapmhplqzald63za" style="color: black;">Computer Science and Information Systems</a> </i> &nbsp;
This problem stems from the fact that multidimensional data has no order that preserves proximity.  ...  Efficient management of multidimensional data is a challenge when building modern database applications that involve many fold data such as temporal, spatial, data warehousing, bio-informatics, etc.  ...  Each region can be uniquely identified by an address, which is, roughly speaking, a compact binary representation of the sequence of splits that have generated it.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2298/csis120702022t">doi:10.2298/csis120702022t</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kcw22u5fgbe75lvtot3azdzwim">fatcat:kcw22u5fgbe75lvtot3azdzwim</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170811071807/http://elib.mi.sanu.ac.rs/files/journals/csis/27/100306.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/c1/be/c1bef6368403b6b64d0d2bb4d52731f7634bd448.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2298/csis120702022t"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Page 791 of Mathematical Reviews Vol. , Issue 81B [page]

<span title="">1981</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Contentions resolving tree algo- rithms are introduced, and they are analyzed for a Poisson source model. In the tree algorithm, each source has its own binary number.  ...  b) >b,>b,> --- >0 and the a, are iid. zero-mean random variables with equally likely values +1.  ... 
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Variable Granularity Space Filling Curve for Indexing Multidimensional Data [chapter]

Justin Terry, Bela Stantic, Paolo Terenziani, Abdul Sattar
<span title="">2011</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
This problem stems from the fact that multidimensional data have no given order that preserves proximity.  ...  A detailed empirical study demonstrates that the proposed method outperforms the best available off-theshelf methods for accessing multidimensional data.  ...  In our approach, each region can be uniquely identified by an address, which is, roughly speaking, a compact binary representation of the sequence of splits that have generated it.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-23737-9_9">doi:10.1007/978-3-642-23737-9_9</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/iwvdoiyclje2fnpvd7pajog6ee">fatcat:iwvdoiyclje2fnpvd7pajog6ee</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170706135216/https://research-repository.griffith.edu.au/bitstream/handle/10072/43325/76152_1.pdf%3bjsessionid=9D43DCE6A8AB32D418CBFCFA8FD137B4?sequence%2525253D1" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a8/55/a8555f270e7ddacfc6c49b4c2f90f6e3760173ea.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-23737-9_9"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

A*-tree

Tingjian Ge, Stan Zdonik
<span title="2010-09-01">2010</span> <i title="VLDB Endowment"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p6rqwwpkkjbcldejepcehaalby" style="color: black;">Proceedings of the VLDB Endowment</a> </i> &nbsp;
We devise a novel data structure, called the A*-tree (multidimensional Array tree), demonstrating that by taking advantage of the predictable and structured correlations of multidimensional data, we can  ...  Multidimensional array database systems are suited for scientific and engineering applications.  ...  To think about it another way, as a random walk is performed from the root to a leaf, we are in fact doing a random walk on two binary trees with the same height, one for each dimension.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.14778/1920841.1920963">doi:10.14778/1920841.1920963</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5sbbhh6idzg7hdrcchmzzrcnu4">fatcat:5sbbhh6idzg7hdrcchmzzrcnu4</a> </span>
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A Compact Representation of Raster Time Series [article]

Nataly Cruces, Diego Seco, Gilberto Gutiérrez
<span title="2019-01-07">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Compact data structures have proven successful to provide space-efficient representations of rasters with query capabilities.  ...  Finally, to deal with the curse of dimensionality of the k 3 -tree a 3D version of the heavy path tree in [21] may improve the space usage.  ...  As future work, a more detailed experimental evaluation is necessary to compare with all the compact data structures for rasters existing in the literature [7] [8] [9] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1901.01944v1">arXiv:1901.01944v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xbfzi4fzf5csveiu7f2bi5bd34">fatcat:xbfzi4fzf5csveiu7f2bi5bd34</a> </span>
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On Universal Complexity Measures [article]

John Scoville
<span title="2011-09-16">2011</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Such a measure may be used to test the quasi-randomness of binary sequences with regard to first-order set membership. Next, strings over general alphabets are considered.  ...  This is the complexity of the representation recursively decoding a Godel number having the value of the string; the result is a tree of prime numbers which forms a universal representation of the string's  ...  quasi-randomness of finite binary strings.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1005.2254v9">arXiv:1005.2254v9</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/szmxsz4o7ber7a7ehmpfs4zr3m">fatcat:szmxsz4o7ber7a7ehmpfs4zr3m</a> </span>
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K 2-Treaps: Range Top-k Queries in Compact Space [chapter]

Nieves R. Brisaboa, Guillermo de Bernardo, Roberto Konow, Gonzalo Navarro
<span title="">2014</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We introduce a data structure, the K 2 -treap, that represents grids in compact form and supports efficient prioritized range queries.  ...  Efficient processing of top-k queries on multidimensional grids is a common requirement in information retrieval and data mining, for example in OLAP cubes.  ...  We introduce a new compact data structure that performs fast range top-k queries on multidimensional grids and is smaller than state-of-the-art compact data structures.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-11918-2_21">doi:10.1007/978-3-319-11918-2_21</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/itmt4ixtirfu5fwmrymuhc65gy">fatcat:itmt4ixtirfu5fwmrymuhc65gy</a> </span>
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Statistical analysis of cross-correlation sample of 3XMM-DR4 with SDSS-DR10 and UKIDSS-DR9

Yan-Xia Zhang, Yong-Heng Zhao, Xue-Bing Wu, Hai-Jun Tian
<span title="">2014</span> <i title="Cambridge University Press (CUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/djnl2eulfjdwxplyqzspykhc2m" style="color: black;">Proceedings of the International Astronomical Union</a> </i> &nbsp;
Comparing the classification accuracy of random forests with that of rotation forests, rotation forests show better performance.  ...  Based on this X-ray/optical/infrared catalog, we probe the distribution of various types of X-ray emitters in the multidimensional parameter space.  ...  X-ray satellites are helpful to explore some types of objects, notably active galaxies (AGN), clusters of galaxies, interacting compact binaries and active stellar coronae.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1017/s1743921315000022">doi:10.1017/s1743921315000022</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/x76v2dqxcrbmlcwqvy3xzkys2a">fatcat:x76v2dqxcrbmlcwqvy3xzkys2a</a> </span>
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BOOL-AN: A method for comparative sequence analysis and phylogenetic reconstruction

Éena Jakó, Eszter Ari, Péter Ittzés, Arnold Horváth, János Podani
<span title="">2009</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/zwkqsjbocjgcxpybdbxxdyl45e" style="color: black;">Molecular Phylogenetics and Evolution</a> </i> &nbsp;
The binary encoded sequence information is transformed into a compact analytical form, called the Iterative Canonical Form (or ICF) of Boolean functions, which can then be used as a generalized molecular  ...  The new method and the associated software for inferring phylogenetic trees are called the Boolean analysis or BOOL-AN.  ...  After randomization of the initial ordering of sequence sites, these trees did not change their topology (tree b = tree e; tree c = tree f).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ympev.2009.04.019">doi:10.1016/j.ympev.2009.04.019</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/19422923">pmid:19422923</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/iqf6itdkpzdnlhipvce7h4vf7i">fatcat:iqf6itdkpzdnlhipvce7h4vf7i</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170922045820/http://real.mtak.hu/2774/1/jako_mpl09_ms.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/57/ee/57eec2cb0274e7e54e148f1a8f0ad3981143c41a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ympev.2009.04.019"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Multidimensional trees

William A. Baldwin, George O. Strawn
<span title="">1991</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
Although this is a binary encoding of the multidimensional forest, it does not correspond to the usual binary encoding of trees.  ...  The multidimensional tree could be encoded by having a binary node encode each multidimensional tree where the two children of any node are the encodings of the multidimensional subtrees which make up  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0304-3975(91)90165-x">doi:10.1016/0304-3975(91)90165-x</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7kzsdunlwzbldolpvzm4rw3zqm">fatcat:7kzsdunlwzbldolpvzm4rw3zqm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170928100919/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/63e/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS8wMzA0Mzk3NTkxOTAxNjV4.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ac/47/ac47036f79df2a7def1a48db4d76a9725195d9c5.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0304-3975(91)90165-x"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Memory-Efficient Global Refinement of Decision-Tree Ensembles and its Application to Face Alignment [article]

Nenad Markuš, Ivan Gogić, Igor S. Pandžić, Jörgen Ahlberg
<span title="2018-09-03">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Ren et al. recently introduced a method for aggregating multiple decision trees into a strong predictor by interpreting a path taken by a sample down each tree as a binary vector and performing linear  ...  They provided experimental evidence that the method offers advantages over the usual approaches for combining decision trees (random forests and boosting).  ...  This means that the multidimensional output ∆(x) for the input sample x is computed as ∆(x) = ∑ i w i , where the ith vector is output by the ith tree: w i = Tree i (x). Ren et al.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1702.08481v2">arXiv:1702.08481v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2c5nc7nuprdwblnavpwfstn3ha">fatcat:2c5nc7nuprdwblnavpwfstn3ha</a> </span>
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FLSSS: A Novel Algorithmic Framework for Combinatorial Optimization Problems in the Subset Sum Family [article]

Charlie Wusuo Liu
<span title="2018-11-23">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The framework offers exact algorithms for the multidimensional knapsack problem and the generalized assignment problem.  ...  Multidimensional extension follows a novel decomposition of the problem and is friendly to multithreading. Data structures supporting the algorithms have trivial space complexity.  ...  Virtually, the current subspacing method constructs a binary tree while the previous ones construct a variable-branch tree.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1612.04484v3">arXiv:1612.04484v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ibwjhov6kvbovenbfrf4xof4vu">fatcat:ibwjhov6kvbovenbfrf4xof4vu</a> </span>
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Using Proximity Graph Cut for Fast and Robust Instance-Based Classification in Large Datasets

Stanislav Protasov, Adil Mehmood Khan
<span title="">2021</span> <i title="Hindawi-Wiley"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/y3fh56bfunh5fgneywwba6d4ke" style="color: black;">Complexity</a> </i> &nbsp;
However, large-scale datasets are a big problem for building fast and compact neighbourhood-based classifiers.  ...  This work presents the design and implementation of a classification algorithm with index data structures, which would allow us to build fast and scalable solutions for large multidimensional datasets.  ...  Quad-trees [21] and KD-trees [22] have been used for indexing multidimensional vector data.  ... 
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Page 406 of Mathematical Reviews Vol. , Issue 89A [page]

<span title="">1989</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
A random vector Z;, i= 1,2, has a multidimensional normal distribution with zero mean and covariance matrix o7{(1 — pil - p;E}, where a?  ...  It is called multi- ple multidimensional scaling, and puts the objects into clusters by ordinary multidimensional scaling of the variables.  ... 
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