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On Order Types of Random Point Sets
[article]
2020
arXiv
pre-print
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A simple method to produce a random order type is to take the order type of a random point set. ...
Second, we study algorithms for determining the order type of a point set in terms of the number of coordinate bits they require to know. ...
It is easy to produce a random order type by first generating a random point set, then reading off its order type, but let us stress that it is not clear how the probability distribution on point sets ...
arXiv:1812.08525v3
fatcat:pkw2ob4xvrbznh6h6wimimv3ye
Convex Hulls of Random Order Types
2020
International Symposium on Computational Geometry
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The number of extreme points in an n-point order type, chosen uniformly at random from all such order types, is on average 4+o(1). ...
(b) The (labeled) order types read off a set of n points sampled independently from the uniform measure on a convex planar domain, smooth or polygonal, or from a Gaussian distribution are concentrated, ...
There are no results, however, on how well or badly distributed the order types of such random point sets are. ...
doi:10.4230/lipics.socg.2020.49
dblp:conf/compgeom/GoaocW20
fatcat:42ibtjbl5zhvrcl5zl7m5w355q
Convex Hulls of Random Order Types
[article]
2020
arXiv
pre-print
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The number of extreme points in an n-point order type, chosen uniformly at random from all such order types, is on average 4+o(1). ...
(b) The (labeled) order types read off a set of n points sampled independently from the uniform measure on a convex planar domain, smooth or polygonal, or from a Gaussian distribution are concentrated, ...
Acknowledgements The authors thank Boris Aronov for helpful discussions, Gernot Stroth for help on the group theoretic aspects of the paper, and Pierre Calka for help on probabilistic geometry. ...
arXiv:2003.08456v2
fatcat:auqxaga4cffp7d72lqmbmvlbla
Computer production of punched paper tapes for controlling experiments
1971
Behavior Research Methods
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After all set-order commands have been entered, the user types an exclamation point to move on to the next section of the program. Producing Tapes At this point, the program produces two tapes. ...
As this first tape is produced, the set names are typed on the Teletype as a record of the random orders that have been generated. ...
The binary tapes required for running this program and an operating manual are available from the first author at the Department of PSYchology, Princeton University. Princeton. New Jersey 08540. ...
doi:10.3758/bf03209958
fatcat:ow7wq4h2yna6fbe3t2y4vojnfe
Chirotopes of Random Points in Space are Realizable on a Small Integer Grid
[article]
2020
arXiv
pre-print
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This result is a high-dimensional generalization of previous results on order types of random planar point sets due to Fabila-Monroy and Huemer (2017) and Devillers, Duchon, Glisse, and Goaoc (2018). ...
Therefore, chirotopes of random point sets can be encoded with O(nlog n) bits. This is in stark contrast to the worst case, where the grid may be forced to have step size 1/2^2^Ω(n) even for d=2. ...
The question of random order types has first been tackled by Bokowski, Richter-Gebert, and Schindler [5] . ...
arXiv:2001.08062v1
fatcat:re2gibzj4rfiletbs75ncmne7e
Page 319 of Behavior Research Methods Vol. 3, Issue 6
[page]
1971
Behavior Research Methods
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As this first tape is produced, the set names are typed on the Teletype as a record of the random orders that have been generated. ...
After all set-order commands have been entered, the user types an exclamation point to move on to the next section of the program.
Producing Tapes
At this point, the program produces two tapes. ...
Efficient Exhaustive Generation of Functional Programs Using Monte-Carlo Search with Iterative Deepening
[chapter]
2008
Lecture Notes in Computer Science
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In this paper we propose an algorithm applying random testing of program equivalences (or Monte-Carlo search for functional differences) to the search results of iterative deepening, by which we can totally ...
Our experimental results show that applying our algorithm to subexpressions during program generation remarkably reduces the computational costs when applied to rich primitive sets. [] :: ∀a. ...
We implemented a function that takes such a prioritized bag as an argument and returns its complete set of representatives as a prioritized infinite set of functions. ...
doi:10.1007/978-3-540-89197-0_21
fatcat:z3g7wirqfbdh3fh3br4w7nb7m4
Cuttrees in the topological analysis of branching patterns
1984
Bulletin of Mathematical Biology
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In this paper the effects of the occurrence of cut trees in the topological analysis of branching patterns have been studied. It is assumed that branches are removed at random from the trees. ...
We prove that, for both the segmental and terminal growth models, the probability distributions of the cut trees are identical to those of complete trees. ...
points, segment between a bifurcation point and a terminal point,
Subtree Subtree pair Degree of a tree Order of a segment Order of subtree Terminal growth Segmental growth part of a tree that proceeds ...
doi:10.1007/bf02460075
fatcat:x3gjwczjxre43eo6j2sc2btbia
Cut trees in the topological analysis of branching patterns
1984
Bulletin of Mathematical Biology
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In this paper the effects of the occurrence of cut trees in the topological analysis of branching patterns have been studied. It is assumed that branches are removed at random from the trees. ...
We prove that, for both the segmental and terminal growth models, the probability distributions of the cut trees are identical to those of complete trees. ...
points, segment between a bifurcation point and a terminal point,
Subtree Subtree pair Degree of a tree Order of a segment Order of subtree Terminal growth Segmental growth part of a tree that proceeds ...
doi:10.1016/s0092-8240(84)80025-7
fatcat:zqetgu7qtjfjxioz7qyr7cnapi
Limits of Order Types
[article]
2018
arXiv
pre-print
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We apply ideas from the theory of limits of dense combinatorial structures to study order types, which are combinatorial encodings of finite point sets. ...
Next we establish results on the analytic representation of limits of order types by planar measures. ...
We define the density p(ω, ω ) of an order type ω in another order type ω as the probability that |ω| random points chosen uniformly from a point set realizing ω have order type ω. ...
arXiv:1811.02236v1
fatcat:mdlyff4ffjctbgs6grv72yfyva
On Obstacle Numbers
[article]
2013
arXiv
pre-print
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Our proof makes use of an upper bound of Mukkamala etal on the number of graphs having obstacle number at most h in such a way that any subsequent improvements to their upper bound will improve our lower ...
Acknowledgement This work was initiated at the Workshop on Geometry and Graphs, held at the Bellairs Research Institute, March 10-15, 2013. ...
Fix some simple super-order type on n points. By Lemma 2, all point sets with this super-order type support an obstacle representation of G with o(n/(log log n) 2 ) obstacles or none of them do. ...
arXiv:1308.4321v1
fatcat:sdqvprfnrjdrdkcquz3herymoy
A Simple Sampling Lemma: Analysis and Applications in Geometric Optimization
2001
Discrete & Computational Geometry
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In the more restricted but still general setting of LP-type problems, we prove tail estimates for the sampling lemma, giving Cherno -type bounds for the number of constraints violated by the solution of ...
As an application, we provide the rst theoretical analysis of multiple pricing, a heuristic used in the simplex method for linear programming in order to reduce a large problem to few small ones. ...
In particular, we are grateful for the question concerning the sharpness of our main Cherno -type bound. ...
doi:10.1007/s00454-001-0006-2
fatcat:xqoycarznzcqfetcvagc7rbbnq
Strongly Asymmetric Tricriticality of Quenched Random-Field Systems
1999
Physical Review Letters
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1998 accepted arXiv:cond-mat/9811235v2 fatcat:d2bvt62befazdnxlctc5c4yf6eOther Versions
In view of the recently seen dramatic effect of quenched random bonds on tricritical systems, we have conducted a renormalization-group study on the effect of quenched random fields on the tricritical ...
We find that random fields convert first-order phase transitions into second-order, in fact more effectively than random bonds. ...
[5, 8] No such information has existed on the effect of quenched field randomness on tricritical points. ...
doi:10.1103/physrevlett.82.2572
fatcat:kufcvpfxi5azhljin34vudb7yq
A Proposal to Speed up the Computation of the Centroid of an Interval Type-2 Fuzzy Set
2013
Advances in Fuzzy Systems
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This paper presents two new algorithms that speed up the centroid computation of an interval type-2 fuzzy set. ...
The algorithms include precomputation of the main operations and initialization based on the concept of uncertainty bounds. ...
Conflict of Interests The authors hereby declare that they do not have any direct financial relation with the commercial identities mentioned in this paper. ...
doi:10.1155/2013/158969
fatcat:vxkfy2o2p5fbhpwzjbx3gb7riu
Constructing Order Type Graphs using an Axiomatic Approach
[article]
2020
arXiv
pre-print
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A given order type in the plane can be represented by a point set. However, it might be difficult to recognize the orientations of some point triples. ...
We provide experimental results on all order types of up to nine points in the plane including a comparative analysis of exit graphs and OT-graphs. ...
In many cases there are different OT-graphs of minimum size for the same order type. One can use other criteria to optimize OT-graphs, for example, crossings. ...
arXiv:2011.14282v1
fatcat:r4owo5toijegvadefj7euk3oxi
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