Filters

2,225,832 Hits in 5.5 sec

### On Order Types of Random Point Sets [article]

Olivier Devillers
2020 arXiv   pre-print
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  ...

### Convex Hulls of Random Order Types

Xavier Goaoc, Emo Welzl, Danny Z. Chen, Sergio Cabello
2020 International Symposium on Computational Geometry
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.  ...

### Convex Hulls of Random Order Types [article]

Xavier Goaoc, Emo Welzl
2020 arXiv   pre-print
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.  ...

### Computer production of punched paper tapes for controlling experiments

Walter vom Saal, Robert vom Saal
1971 Behavior Research Methods
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.  ...

### Chirotopes of Random Points in Space are Realizable on a Small Integer Grid [article]

Jean Cardinal, Ruy Fabila-Monroy, Carlos Hidalgo-Toscano
2020 arXiv   pre-print
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] .  ...

### Page 319 of Behavior Research Methods Vol. 3, Issue 6 [page]

1971 Behavior Research Methods
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]

Susumu Katayama
2008 Lecture Notes in Computer Science
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.  ...

### Cuttrees in the topological analysis of branching patterns

J. Van Pelt, R. W. H. Verwer
1984 Bulletin of Mathematical Biology
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  ...

### Cut trees in the topological analysis of branching patterns

J VANPELT, R VERWER
1984 Bulletin of Mathematical Biology
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  ...

### Limits of Order Types [article]

Xavier Goaoc and Alfredo Hubard and Rémi de Joannis de Verclos and Jean-Sébastien Sereni and Jan Volec
2018 arXiv   pre-print
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.  ...

### On Obstacle Numbers [article]

Vida Dujmović, Pat Morin
2013 arXiv   pre-print
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.  ...

### A Simple Sampling Lemma: Analysis and Applications in Geometric Optimization

B. Gärtner, E. Welzl
2001 Discrete & Computational Geometry
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.  ...

### Strongly Asymmetric Tricriticality of Quenched Random-Field Systems

Alkan Kabakçıoğlu, A. Nihat Berker
1999 Physical Review Letters
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.  ...

### A Proposal to Speed up the Computation of the Centroid of an Interval Type-2 Fuzzy Set

Carlos E. Celemin, Miguel A. Melgarejo