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On halving line arrangements

Alina Beygelzimer, Stanisław Radziszowski
2002 Discrete Mathematics  
Let h(n) denote the maximum number of halving lines that can be realized by a planar set of n points.  ...  Given a set of n points in general position in the plane, where n is even, a halving line is a line going through two of the points and cutting the remaining set of n − 2 points in half.  ...  McKay and developed on top of nauty [19] . 1  ... 
doi:10.1016/s0012-365x(02)00430-2 fatcat:lpdg4k7y2ve67kn2xit3gct7qm

Page 307 of Proceedings of the American Philosophical Society Vol. 88, Issue 1 [page]

1944 Proceedings of the American Philosophical Society  
VISUAL AFTER-EFFECTS tively just one-half of the arrangement with which Gibson demonstrates the ‘‘bent line” effect (Fig. 57).  ...  Rather its two halves will both recede from the corresponding halves of the bent J-line, and as a result the 7-line will be seen as bent in the opposite direction.  ... 

Page 612 of Primary Education Vol. 21, Issue 10 [page]

1913 Primary Education  
Arrange on desk, then paste them in similar arrangements on paper. Cut circles in halves and arrange one circle, one-half circle, or one circle, two halves, or arrange border of half circles.  ...  Lesson II Review lesson on lines, but this time play that the lines are stems, and that we are going to draw these stems the way we drew the sticks, but this time we will add a little berry. 0 o|o}o|oo  ... 

Extreme point and halving edge search in abstract order types

Oswin Aichholzer, Tillmann Miltzow, Alexander Pilz
2013 Computational geometry  
This includes the straightforward algorithms for finding a halving line for a given planar point set, as well as finding a point on the convex hull, both in linear time.  ...  More precisely, we can find a halving line through any given point, as well as the vertices of the convex hull edges that are intersected by the supporting line of any two given points of the set in linear  ...  Acknowledgements We thank Thomas Hackl, and Günter Rote, as well as anonymous referees, for helpful suggestions on improving the presentation of the results.  ... 
doi:10.1016/j.comgeo.2013.05.001 pmid:24092953 pmcid:PMC3688538 fatcat:hxlxmvwskrdm5ez7x6gy7xe2lm

Halving lines and measure concentration in the plane

Rom Pinchasi
2009 Proceedings of the 25th annual symposium on Computational geometry - SCG '09  
We show how this problem is related to the halving lines problem and provide several consequences about measure concentration in R 2 .  ...  Given a set of n points in the plane and a collection of k halving lines of P ℓ1, . . . , ℓ k indexed according to the increasing order of their slopes, we denote by d(ℓj, ℓj+1) the number of points in  ...  This follows immediately if one considers the arrangement of lines dual to the set of points in P . Then the set of all halving lines for P which are equivalent forms a face in that arrangement.  ... 
doi:10.1145/1542362.1542393 dblp:conf/compgeom/Pinchasi09 fatcat:hnzinbejzrdadcvio5ilyhfune

Improved collimation testing using Talbot interferometry

Mahendra P. Kothiyal, Rajpal S. Sirohi
1987 Applied Optics  
If the central line AB of the two superposed gratings is inclined, the grating lines do not intersect at the same angle in the two halves, giving moire fringes of different spacing in the two halves.  ...  When these gratings are placed in the collimation test arrangement shown in Fig. 2 , parallel equally spaced moire fringes are formed as above when the collimated beam is incident on G 1 .  ... 
doi:10.1364/ao.26.004056 pmid:20490193 fatcat:lal3xc3g4fbhxdqmtd5fpxz5de

Temporal dynamics of mirror-symmetry perception

Rebecca J. Sharman, Sebastian Gregersen, Elena Gheorghiu
2018 Journal of Vision  
We varied the duration of the two images under five temporal-arrangement conditions: (a) whole patterns in which a symmetric pattern alternated with a noise pattern; (b) delayed halves-the halves of the  ...  (c), but with matched-pairs presented with delay; and (e) static-both images presented simultaneously as one.  ...  Logistic psychometric functions for the whole patterns (red solid line), delayed halves (red dashed line), matched-pairs (blue solid line), delayed matched-pairs (blue dashed line), and static (green line  ... 
doi:10.1167/18.5.10 pmid:29904785 pmcid:PMC5954970 fatcat:n2xcjd6sobd2nnzcsy32qd4t24

Mutual arrangement of histone H1 molecules in extended chromatin

Lev G. Nikolaev, Boris O. Glotov, Viktor K. Dashkevich, Sergei F. Barbashov, Eugenii S. Severin
1983 FEBS Letters  
In the chromatins tested, the chymotryptic halves of Hl were cross-linked in all possible combinations; i.e., C-C, C-N and N-N.  ...  Mutual arrangement of histone Hl molecules in chromatin extended in low salt-EDTA buffer and additionally in the presence of urea was studied by means of reversible cross-linking combined with chymotryptic  ...  Following the same line of argument as in [7] , one can conclude that the N-and C-terminal halves of neighbouring Hl histone molecules can be crosslinked to each other in all possible combinations (N-N  ... 
doi:10.1016/0014-5793(83)81164-8 pmid:6628690 fatcat:yar7qjkkznfg5fj5ec5l53aa7i

Page 225 of The Electrical Review Vol. 7, Issue 155 [page]

1879 The Electrical Review  
The arrangement will be understood from fig. 4. In this arrangement the keys B and B' separate the batteries into two portions, one of which contains 2 cells, and the other x cells.  ...  the maintenance of a strict proportion between the electro-motive forces of the two halves of the battery and the resistance of the true and artificial lines, the balance in the method of double substitution  ... 

Spatiotemporal arrangement of objects in activities with people with dementia

Ali Reza Majlesi, Anna Ekström, Lars-Christer Hydén
2019 Logopedics, Phoniatrics, Vocology  
The study is based on ethnomethodological conversation analysis of eight and a half hours of video recordings in three different settings.  ...  One of the significant uses of objects is how they contribute to the perceptual field where attention is organized for building actions.  ...  His research focuses on embodiment and the ecology of meaning making practices in social activities.  ... 
doi:10.1080/14015439.2018.1556771 pmid:30810439 fatcat:okielaatenamhcmlrr64jcq7ha

Page 247 of Journal of Anatomy Vol. 49, Issue [page]

1915 Journal of Anatomy  
An Anomalous Vertebral Column 247 right halves, and also between the three left halves, but there is no clear line between either of the 3rd and 4th left halves and the upper half on the right side; and  ...  It will be seen later that the arrangement of the nerve roots upsets this suggestion, and, in fact, as the right nerve which corresponds to the 4th and 5th left emerged between the two right halves of  ... 

Page 213 of RIBA [Royal Institute of British Architects] Journal Vol. 20, Issue 7 [page]

1913 RIBA [Royal Institute of British Architects] Journal  
On the western half of the river front of this block these enrichments are not arranged on centre lines, and the same lack of care in centering may be noticed in the main cornice of the two wings on the  ...  This arrange- ment obtains on the three outer faces of the eastern half of the King Charles block, and on the whole of the- south front.  ... 

Page 329 of The American Journal of Psychology Vol. 34, Issue 3 [page]

1923 The American Journal of Psychology  
Both errors were based on the same length of line, in the one case on half the line to be halved, and in the other case on an equal standard line.  ...  Fischer found that the error in halving a line was only about one-half the error in attempting to make one line equal to another.  ... 

On Combinatorial Depth Measures

Stephane Durocher, Robert Fraser, Alexandre Leblanc, Jason Morrison, Matthew Skala
2018 International journal of computational geometry and applications  
For comparison, these results match or slightly improve on the corresponding best-known running times for simplicial depth, whose definition involves similar combinatorial complexity.  ...  and eutomic depths of q with respect to P correspond respectively to the number of subsets of P whose convex hull contains q, and the number of combinatorially distinct bisections of P determined by a line  ...  Eutomic Depth Given a set P of n points in R 2 , a line L is a halving line if it partitions P into two sets whose cardinalities differ by at most one.  ... 
doi:10.1142/s0218195918500127 fatcat:fqzekyargncvtajwuzqek5mvjm

Page 65 of Energy Engineering Vol. 56, Issue 5 [page]

1959 Energy Engineering  
Motor connections established on the first step are in solid lines, those established on the second step are in broken lines.  ...  On each starting step, a full wye of winding halves is connected in the circuit. A permanent connection is made in the motor conduit box to form the wye point of one of the winding halves.  ... 
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