scholarly journals Enumeration of Alternating Sign Matrices of Even Size (Quasi-)Invariant under a Quarter-Turn Rotation

10.37236/323 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Jean-Christophe Aval ◽  
Philippe Duchon
Keyword(s):  
Alternating Sign Matrices ◽  
Enumeration Formula ◽  
Half Turn

The aim of this work is to enumerate alternating sign matrices (ASM) that are quasi-invariant under a quarter-turn. The enumeration formula (conjectured by Duchon) involves, as a product of three terms, the number of unrestricted ASM's and the number of half-turn symmetric ASM's.

scholarly journals Enumeration of alternating sign matrices of even size (quasi)-invariant under a quarter-turn rotation

2009 ◽  
Vol DMTCS Proceedings vol. AK,... (Proceedings) ◽  
Author(s):  
Jean-Christophe Aval ◽  
Philippe Duchon
Keyword(s):  
Alternating Sign Matrices ◽  
International Audience ◽  
Enumeration Formula ◽  
Half Turn

International audience The aim of this work is to enumerate alternating sign matrices (ASM) that are quasi-invariant under a quarter-turn. The enumeration formula (conjectured by Duchon) involves, as a product of three terms, the number of unrestrited ASm's and the number of half-turn symmetric ASM's. L'objet de ce travail est d'énumérer les matrices à signes alternants (ASM) quasi-invariantes par rotation d'un quart-de-tour. La formule d'énumération, conjecturée par Duchon, fait apparaître trois facteurs, comprenant le nombre d'ASM quelconques et le nombre d'ASM invariantes par demi-tour.

scholarly journals Enumerations of half-turn-symmetric alternating-sign matrices of odd order

2006 ◽  
Vol 148 (3) ◽  
pp. 1174-1198 ◽  
Author(s):  
A. V. Razumov ◽  
Yu. G. Stroganov
Keyword(s):  
Alternating Sign Matrices ◽  
Odd Order ◽  
Half Turn

Gender and the Gift

2018 ◽  
Author(s):  
Pauline Stafford
Keyword(s):  
General Framework ◽  
Comparative History ◽  
Anglo Saxon ◽  
The Past ◽  
The Gift ◽  
Half Turn ◽  
Heuristic Devices ◽  
Constant Interest

This chapter responds to Chris’s interest in gifts and giving—and to his recent half-turn linguistically. It aims to fill—or to begin to fill—one of the acknowledged gaps in a recent volume with which he was associated, The Languages of Gift, by looking at marriage and the giving and receiving of women. It underlines some of the things which that volume stressed—notably that gifts are multivocal—and can and do change in meaning contextually, but also that the contextual and changing meaning of the gift is rooted in and constrained by structures—which set that general framework of meaning. This chapter is also concerned with those structures and thus, I hope, responds to Chris’s lifelong concern with the bigger models and heuristic devices which are necessary to our understanding of the past. It will be especially concerned with England—in particular late Anglo-Saxon England. But it will draw on wider material in an attempt to understand that—inspired, once again, by Chris’s constant interest in comparative history.

Non-cellulosic structural polysaccharides in algal cell walls I. Xylan in siphoneous green algae

1964 ◽  
Vol 160 (980) ◽  
pp. 293-313 ◽  
Keyword(s):  
Relative Humidity ◽  
Cell Walls ◽  
Marine Algae ◽  
Transverse Section ◽  
Algal Cell ◽  
Repeat Distance ◽  
X Ray ◽  
Face View ◽  
Half Turn ◽  
Parallel Arrays

The cell walls of a number of marine algae, namely species of Bryopsis, Caulerpa, Udotea, Halimeda and Penicillus and of one freshwater alga, Dichotomosiphon , are examined using both chemical and physical techniques. It is shown that, with the possible exception of Bryopsis , cellulose is completely absent and that the walls contain instead β -l,3-linked xylan as the structural polysaccharide. Bryopsis contains, in addition, a glucan which is most abundant in the outer layers of the wall and which stains like cellulose. The xylan is microfibrillar but the microfibrils are more strongly adherent than they are in cellulose, and in some species appear in the electron microscope to be joined by short crossed rod-like bodies. The orientation of the microfibrils is found to vary, ranging from a net tendency to transverse orientation through complete randomness to almost perfect longitudinal alinement. The microfibrils are negatively birefringent, so that all walls seen in optical section, and all parallel arrays of microfibrils whether in face view or in section (except strictly transverse section) are negatively birefringent. With Bryopsis , the negative birefringence in face view is overcompensated by the positive birefringence of the incrusting glucan so that the true birefringence of the crystalline polysaccharide is observed only after the glucan is removed. The X-ray diagram of parallel arrays of microfibrils as found, for instance, in Penicillus dumetosus shows that the xylan chains are helically coiled, in harmony with the negative birefringence. It is deduced that the microfibrils consist of hexagonally packed, double-stranded helices. The diameter of the helices increases with increasing relative humidity, as water is taken into the lattice, from 13.7 Å in material dried over phosphorus pentoxide to a maximum of 1.54 Å at 65 % relative humidity when the xylan contains 30 % of its weight as water. The repeat distance along the helix axis ranges from 5.85 Å (dry) to 6.06 Å (wet), the length of a half turn of each helix containing three xylose residues. The incrusting substances in these walls often include a glucan which is said also to be 1,3-linked. The significance of the extensive differences between this xylan and cellulose are examined both as regards some of the physical properties of the respective cell walls and in relation to the taxonomic position of these plants.

scholarly journals Inverses and eigenvalues of diamond alternating sign matrices

2014 ◽  
Vol 2 (1) ◽  
Author(s):  
Minerva Catral ◽  
Minghua Lin ◽  
D. D. Olesky ◽  
P. van den Driessche
Keyword(s):  
Alternating Sign Matrices

AbstractAn

scholarly journals Half-turn symmetric FPLs with rare couplings and tilings of hexagons

2013 ◽  
Vol 502 ◽  
pp. 143-152
Author(s):  
Jean-Christophe Aval ◽  
Philippe Duchon
Keyword(s):  
Half Turn

scholarly journals Opposite asymmetries of face and trunk and of kissing and hugging, as predicted by the axial twist hypothesis

2019 ◽  
Author(s):  
Marc HE de Lussanet
Keyword(s):  
Bilateral Symmetry ◽  
Optic Chiasm ◽  
Early Embryo ◽  
The Body ◽  
Head Region ◽  
Evolutionary Selection ◽  
Left Handed ◽  
Secondary Feature ◽  
Half Turn ◽  
Axial Twist

The contralateral organization of the forebrain and the crossing of the optic nerves in the optic chiasm represent a long-standing conundrum. According to the Axial Twist Hypothesis (ATH) the rostral head and the rest of the body are twisted with respect to each other to form a left-handed half turn. This twist is the result, mainly, of asymmetric, twisted growth in the early embryo. Evolutionary selection tends to restore bilateral symmetry. Since selective pressure will decrease as the organism approaches symmetry, we expected a small control error in the form of a small, residual right-handed twist. We found that the mouth-eyes-nose (rostral head) region shows a left-offset with respect to the ears (posterior head) by up to 0.8° (P<0.01, Bonferroni-corrected). Moreover, this systematic aurofacial asymmetry was larger in young children (on average up to 3°) and reduced with age. Finally, we predicted and found a right-sided bias for hugging (78%) and a left-sided bias for kissing (69%). Thus, all predictions were confirmed by the data. These results are all in support of the ATH, whereas the pattern of results is not explained by existing alternative theories. As of the present results, the ATH is the first theory for the contralateral forebrain and the optic chiasm whose predictions have been tested empirically. We conclude that humans (and all other vertebrates) are fundamentally asymmetric, both in their anatomy and their behavior. This supports the thesis that the approximate bilateral symmetry of vertebrates is a secondary feature, despite their being bilaterians.

scholarly journals A bijection for nonorientable general maps

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Jérémie Bettinelli
Keyword(s):  
Simple Form ◽  
Asymptotic Enumeration ◽  
International Audience ◽  
Enumeration Formula

International audience We give a different presentation of a recent bijection due to Chapuy and Dołe ̨ga for nonorientable bipartite quadrangulations and we extend it to the case of nonorientable general maps. This can be seen as a Bouttier–Di Francesco–Guitter-like generalization of the Cori–Vauquelin–Schaeffer bijection in the context of general nonori- entable surfaces. In the particular case of triangulations, the encoding objects take a particularly simple form and we recover a famous asymptotic enumeration formula found by Gao.

Calibrate the Turning of Micromouse

2014 ◽  
Vol 971-973 ◽  
pp. 1088-1091
Author(s):  
Hao Ming Zhang ◽  
Lian Soon Peh ◽  
Ying Hai Wang
Keyword(s):  
High Speed ◽  
Complex Maze ◽  
Half Turn

Perfect turn can help micromouse get a right maze information and high turning speed in complex maze, lead to a win in the competition, but high speed makes control the micromouse very difficult. How to calibrate a turning of a micromouse has become very important. Through analysis of a turn different motion results, get perfect turning reference, then set start and end to record position ratio, get the converted data, sum the data until the mouse complete half turn. After checking, the mouse know whether it is on the under path or over path, then it will automatically ask motors make some action to put itself back to the perfect path, a perfect turn is realized.

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