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The universal homogeneous binary tree [article]

Manuel Bodirsky, David Bradley-Williams, Michael Pinsker, András Pongrácz
2016 arXiv   pre-print
We study the reducts of S2, that is, the relational structures with the same domain as S2 all of whose relations are first-order definable in S2.  ...  Our main result is a classification of the model-complete cores of the reducts of S2.  ...  Using Fraïssé's theorem [Hod93] one can show that in the case of (S 2 ; ≤), there exists a convex linear extension ≺ of ≤ such that (S 2 ; ≤, C, ≺) is homogeneous and such that (S 2 ; ≤, ≺) is universal  ... 
arXiv:1409.2170v4 fatcat:3oqd4iugmneajjzjlixs3v3ygy

The universal homogeneous binary tree

Manuel Bodirsky, David Bradley-Williams, Michael Pinsker, András Pongrácz
2018 Journal of Logic and Computation  
Our main result is a classification of the model-complete cores of the reducts of S2.  ...  We study the reducts of (S2; ≤), that is, the relational structures with domain S2, all of whose relations are first-order definable in (S2; ≤).  ...  Sokić and Jan Hubička for helpful pointers to relevant literature on structural Ramsey properties, and the anonymous referee for comments that helped us to improve the presentation.  ... 
doi:10.1093/logcom/exx043 fatcat:d6df7bofg5aqvlrztby7yrqzwi

Toric ideals of homogeneous phylogenetic models

Nicholas Eriksson
2004 Proceedings of the 2004 international symposium on Symbolic and algebraic computation - ISSAC '04  
Finally, we give a explicit description of the polytope associated to this toric ideal for an infinite family of binary trees and conjecture that there is a universal bound on the number of vertices of  ...  We consider the phylogenetic tree model in which every node of the tree is observed and binary and the transitions are given by the same matrix on each edge of the tree.  ...  First, we derive six inequalities that are satisfied by any binary tree, deriving a "universal" polytope for binary trees.  ... 
doi:10.1145/1005285.1005308 dblp:conf/issac/Eriksson04 fatcat:oppjydss5bed5ov6z4cl5ww6xm

Data structures for big data

Ranjit Biswas
2014 International Journal of Computing and Optimization  
The existing network topologies like tree topology or bus/ring/star/mesh/hybrid topologies seem to be weak topologies for big data processing.  ...  Needless to mention that the next important issue is how to integrate all these 'new' to make ultimately a single and simple scalable system to the laymen users.  ...  binary trees 'atrain binary tree' and 'rA-coach binary tree', homogeneous trees 'train tree' and 'rT-coach tree', heterogeneous trees 'atrain tree' and 'rA-coach tree', to enrich the new subject 'Data  ... 
doi:10.12988/ijco.2014.4813 fatcat:dz7k6zxzaja67d7jfxnqw7q73e

On the depth of decision trees over infinite 1-homogeneous binary information systems

Mikhail Moshkov
2021 Array  
We consider a number of examples of infinite 1-homogeneous binary information systems, including one closely related to the decision trees constructed by the CART algorithm.  ...  In this paper, we study decision trees, which solve problems defined over a specific subclass of infinite information systems, namely: 1-homogeneous binary information systems.  ...  Acknowledgments Research reported in this publication was supported by King Abdullah University of Science and Technology (KAUST). The author is thankful to Dr.  ... 
doi:10.1016/j.array.2021.100060 fatcat:5ewwn4ymcvhxnkejgedkx22xhe

Heterogeneous binary random-access lists

WOUTER SWIERSTRA
2020 Journal of functional programming  
Acknowledgments The Software Technology Reading Club, James McKinna and anonymous reviewers gave insightful and detailed feedback, for which I am most grateful.  ...  Types aside, the only real difference is the call to the heterogeneous lookup function on binary trees, rather than the homogeneous version we saw previously: Finally, the definition of cons and consTree  ...  The function Val : U → Set, defined in Figure 1 , maps the codes from the universe U to the corresponding types. While not strictly necessary, we will prefix 6 W.  ... 
doi:10.1017/s0956796820000064 fatcat:iumkieps4nectmszqubtn3uii4

Generic downwards accumulations

Jeremy Gibbons
2000 Science of Computer Programming  
The concept was originally introduced in an ad hoc way for just a couple of kinds of tree. We generalize the concept to an arbitrary regular datatype; the resulting deÿnition is co-inductive.  ...  A downwards accumulation is a higher-order operation that distributes information downwards through a data structure, from the root towards the leaves.  ...  Acknowledgements The members of the Problem Solving Club at Oxford University Computing Laboratory, especially Richard Bird, Jesà us Ravelo and Pedro Borges, have made many helpful suggestions and comments  ... 
doi:10.1016/s0167-6423(99)00022-2 fatcat:pqzfbgy33vbwrgycdisaevhbra

Canonical Partitions Of Universal Structures

C. Laflamme*, N. W. Sauer†, V. Vuksanovic
2006 Combinatorica  
Let U = (U, L) be a universal binary countable homogeneous structure and n ∈ ω.  ...  For the case of infinitely many colors we determine the canonical set of equivalence relations, extending the result of Erdős and Rado for the integers to countable universal binary homogeneous structures  ...  Let T be the regular ω-tree of degree k and U F = (U ; L) the universal binary homogeneous structure with constraints F.  ... 
doi:10.1007/s00493-006-0013-2 fatcat:atb6tklp2bfwrdco5v2r3ykx6u

Ramsey Theory on Trees and Applications [chapter]

Natasha Dobrinen
2016 Lecture Notes in Computer Science  
In this talk, we concentrate on Ramsey theory on trees and applications to homogeneous structures.  ...  The following is the Strong Tree Version of the Halpern-Läuchli Theorem, proved in another form in [8] . Theorem 2. Let d ≥ 1 and let T i , i < d, be finitely branching trees of height ω.  ...  The author gratefully acknowledges the support of NSF Grants DMS-142470 and DMS-1600781.  ... 
doi:10.1007/978-3-662-54069-5_2 fatcat:rwy5fsm2ovcvxjrischtx5nhlu

Multidimensional Binary Search Trees in Database Applications

J.L. Bentley
1979 IEEE Transactions on Software Engineering  
The multidimensional binary search tree (abbreviated k-d tree) is a data structure for storing multikey records.  ...  Index Terms-Best match query, binary trees, data structures, k-d 92 trees, multikey searching, partial match query, range query.  ...  The k-d trees that we have described above correspond to the homogeneous binary search trees; it is also possible to define nonhomogeneous k-d trees.  ... 
doi:10.1109/tse.1979.234200 fatcat:5wgpuumz45ahrk233naztbbmvi

Extreme-K categorical samples problem [article]

Elizabeth Chou, Catie McVey, Yin-Chen Hsieh, Sabrina Enriquez, Fushing Hsieh
2020 arXiv   pre-print
The criterion of choice rests on degrees of uniformness in column-blocks framed by this binary clustering tree.  ...  Upon the data matrix's row-axis, we discuss the pros and cons of Euclidean distance against its weighted version for building a binary clustering tree geometry.  ...  Two pieces of information are counted from one common code sequential segment: the length of a binary code segment and the size of tree-leaves sharing the same binary code sequential segment.  ... 
arXiv:2007.15039v1 fatcat:k55ezvck25fqhjkfaes6v76asi

Relationless Completeness and Separations

Pavel Hrubeš, Avi Wigderson, Amir Yehudayoff
2010 2010 IEEE 25th Annual Conference on Computational Complexity  
In the absence of associativity, the completeness proof gives rise to the following combinatorial problem: what is the smallest binary tree which contains as minors all binary trees with n leaves.  ...  We give an explicit construction of such a universal tree of polynomial size, a result of possibly independent interest.  ...  Binary trees and universal trees In this paper, binary trees are rooted, uniform and ordered.  ... 
doi:10.1109/ccc.2010.34 dblp:conf/coco/HrubesWY10 fatcat:2pn3stylc5gqpp7tm4o5mhbjpu

Analytic colorings

Wiesław Kubiś, Saharon Shelah
2003 Annals of Pure and Applied Logic  
We construct universal -compact colorings of any prescribed rank ¡ !1. These colorings consistently contain homogeneous sets of cardinality ℵ but they do not contain perfect homogeneous sets.  ...  We deÿne an absolute rank function on trees representing analytic colorings, which gives an upper bound for possible cardinalities of homogeneous sets and which decides whether there exists a perfect homogeneous  ...  We can assume without loss of generality that suppt(S) is a binary tree: embed suppt(S) into a binary tree B and then, using this embedding, deÿne a new -ranked coloring tree whose support is B.  ... 
doi:10.1016/s0168-0072(02)00110-0 fatcat:slfxympz7nhhtipoooeotevo6e

Binary trees, coproducts and integrable systems

B Erbe, H J Schmidt
2010 Journal of Physics A: Mathematical and Theoretical  
The coupling scheme of the iterated tensor product is encoded in a binary tree. The theory is exemplified by the case of a spin octahedron.  ...  We provide a unified framework for the treatment of special integrable systems which we propose to call "generalized mean field systems".  ...  We conclude that, in the case of classical mechanics and up to minor differences in the formulations, the loop coproduct theory [10, 11] contains the binary tree approach as a special case.  ... 
doi:10.1088/1751-8113/43/8/085215 fatcat:msnwpykpczfd5c7ws7yrj4oaku

TUTUPAN LAHAN GAMBUT MEMPENGARUHI KONDISI IKLIM MIKRO DI SEKITAR KAMPUS UNIVERSITAS PALANGKA RAYA (Preliminary Data Integrasi Wireless Sensor Network) The Peatland Cover Impact Micro Climate Conditions Near Campus of the University of Palangka Raya (Preli

Admin Journal
2019 Jurnal Agripeat  
The comprehension of composition transformation, structure, the environmentecosystems dynamic, and how is the transformation of all can be affecting the human life, indeedthis challenge are need detail  ...  The results of this study showed that the land use cover isinfluence on the environment conditions.Keywords: Wireless sensor networks (WSN), ecosystems, and environment  ...  Hasil pengolahan photo kanopi (Canopy Image) pohon/tanaman dengan menggunakan program Algoritma Canopy Binary dari Software Matlab© 1994 -2015.The MathWorks, Inc pada lokasi homogen forest/smalldiameter  ... 
doi:10.36873/agp.v19i02.164 fatcat:nfvbp4cvgvfovdpbfzqbnjhzpu
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