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Columns of uniform color in a rectangular array with rows having cyclically repeated color patterns

S.R. Nagpaul, S.K. Jain
2002 Discrete Mathematics  
Given positive integers p1; : : : ; pn, consider a rectangular array of balls of m di erent colors, with the ith row containing, in repeated succession, pi balls of each color.  ...  This paper initiates the problem of ÿnding the number of columns having balls of the same color, and obtains the solution in various cases.  ...  These are arranged in a rectangular array with n rows, each row having P balls of each color in the following manner.  ... 
doi:10.1016/s0012-365x(01)00359-4 fatcat:aeoupd2xezcrrpfpyq2yjfm6pe

Page 817 of Mathematical Reviews Vol. , Issue 2003B [page]

2003 Mathematical Reviews  
[Jain, Surender Kumar] (1-OH; Athens, OH) Columns of uniform color in a rectangular array with rows having cyclically repeated color patterns.  ...  Consider the rectangular n-by-P array of balls of m different colours, where the ith row contains p; balls of each colour in repeated succession.  ... 

Minimum Forcing Sets for Miura Folding Patterns [article]

Brad Ballinger and Mirela Damian and David Eppstein and Robin Flatland and Jessica Ginepro and Thomas Hull
2014 arXiv   pre-print
At the heart of our results is a novel correspondence between flat-foldable Miura-ori maps and 3-colorings of grid graphs.  ...  Additionally, given a partial mountain/valley assignment to a subset of creases of a Miura-ori map, we determine whether the assignment domain can be extended to a locally flat-foldable pattern on all  ...  This repeats until all row pairs have been colored, so the algorithm completes in time linear in the size of G, which is O(mn).  ... 
arXiv:1410.2231v1 fatcat:iky32zrukngcze3knbltwqvl2u

Stochastic nonlinear dynamics pattern formation and growth models

Leonid P Yaroslavsky
2007 Nonlinear Biomedical Physics  
Stochastic evolutionary growth and pattern formation models are treated in a unified way in terms of algorithmic models of nonlinear dynamic systems with feedback built of a standard set of signal processing  ...  A number of concrete models is described and illustrated by numerous examples of artificially generated patterns that closely imitate wide variety of patterns found in the nature.  ...  formations that grow until their fragments form stable formations or die out; -Cyclic, in course of iterations, formation that repeat themselves with a certain period; -"Moving", in course of iterations  ... 
doi:10.1186/1753-4631-1-4 pmid:17908341 pmcid:PMC1997127 fatcat:rydfgqxi7zgqxbjkge3wzc34si

Symmetrology of art: coloured and generalized symmetries

Emil Makovicky
1986 Computers and Mathematics with Applications  
The paper describes general features and analyses a number of examples of various categories of colored and generalized symmetries used in visual arts.  ...  After a thorough discussion of the problems of symmetry analysis and construction of dichroic and colored patterns, examples of South American, Mexican, Egyptian, Celtic, New Guinean, Australian Aboriginal  ...  Many more examples have only one color in the plain-colored rows, whereas they have two-colored sequences for the cross-hatched lozenges, i.e. pb,mm; the uniform plain color rows then represent special  ... 
doi:10.1016/0898-1221(86)90435-9 fatcat:z5nx4gldhfcenp6rga23rl6lje

SYMMETROLOGY OF ART: COLOURED AND GENERALIZED SYMMETRIES [chapter]

EMIL MAKOVICKY
1986 Symmetry  
The paper describes general features and analyses a number of examples of various categories of colored and generalized symmetries used in visual arts.  ...  After a thorough discussion of the problems of symmetry analysis and construction of dichroic and colored patterns, examples of South American, Mexican, Egyptian, Celtic, New Guinean, Australian Aboriginal  ...  Many more examples have only one color in the plain-colored rows, whereas they have two-colored sequences for the cross-hatched lozenges, i.e. pb,mm; the uniform plain color rows then represent special  ... 
doi:10.1016/b978-0-08-033986-3.50066-5 fatcat:hrvuq56zkfdzxjtjw7rierpzcq

Sparse and Optimal Acquisition Design for Diffusion MRI and Beyond [article]

Cheng Guan Koay, Evren Özarslan, Kevin M Johnson, M. Elizabeth Meyerand
2012 arXiv   pre-print
Even though the number of distinct configurations for a given set of diffusion gradient directions is very large in general---e.g., in the order of 10^232 for a set of 144 diffusion gradient directions  ...  It was found that the square design is the most robust (i.e., with stable condition numbers and A-optimal measures under varying experimental conditions) among many other possible designs of the same sample  ...  Second, bit-reverse the array of numbers in each row then, for each k-th row, cyclically shift the elements by k positions from right to left.  ... 
arXiv:1212.0575v1 fatcat:gqtnnei7vzbwzi7dk47bphlesy

Deformable 96-well cell culture plate compatible with high-throughput screening platforms

Tsubasa S. Matsui, Hugejile Wu, Shinji Deguchi, Gernot Zissel
2018 PLoS ONE  
, but a stretch level of 10%-that has been employed in conventional studies on cellular response to stretch-was almost achieved with our setup.  ...  Conventionally, multi-well cell culture plates of standard configurations are used for comprehensive analyses in cell biology study to identify key molecules in a high-throughput manner.  ...  Acknowledgments The authors thank Yoshiyuki Sakaguchi for technical assistance in fabrication of the devices.  ... 
doi:10.1371/journal.pone.0203448 pmid:30188938 pmcid:PMC6126838 fatcat:tcxyzy4ecnhmxl54vxd2cqdmge

FROM PSEUDO-RANDOM NUMBERS TO STOCHASTIC GROWTH MODELS AND TEXTURE IMAGES [chapter]

LEONID P. YAROSLAVSKY
2000 Pattern Formation in Biology, Vision and Dynamics  
Pseudo-random number generators, stochastic evolutionary growth models and texture images are treated in a unified way in terms of dynamic systems with nonlinear feedback and their evolutionary behavior  ...  If the signal samples in this scheme are arranged in a form of a rectangular array they can be displayed as an image. Fig. 2b illustrates an example of evolution of an image taken as a "seed" .  ...  their fragments form stable formations or die out; cyclic formation that repeat themselves with a certain period; moving formations also featuring iteration-wise cycles ("gliders").  ... 
doi:10.1142/9789812817723_0003 fatcat:5ziv73reunbkzjhpvc5cm3gdwq

What Color Is Your Jacobian? Graph Coloring for Computing Derivatives

Assefaw Hadish Gebremedhin, Fredrik Manne, Alex Pothen
2005 SIAM Review  
Most of the methods for these problems treat a column or a row of a matrix as an atomic entity, and partition the columns or rows (or both).  ...  Several coloring problems occur in this context, depending on whether the matrix is a Jacobian or a Hessian, and on the specifics of the computational techniques employed.  ...  Paul Hovland and Lois McInnes have been enthusiastic about using this work in their software for AD and optimization.  ... 
doi:10.1137/s0036144504444711 fatcat:mlgqx4qmwbglvnbg7oqnyeeiym

Sub-band coding of hexagonal images

Md Mamunur Rashid, Usman R. Alim
2021 Signal processing. Image communication  
According to the circle-packing theorem, the packing efficiency of a hexagonal lattice is higher than an equivalent square tessellation.  ...  Both of these coding schemes respect the geometry of the hexagonal lattice and yield better compression results.  ...  Acknowledgements We acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), [funding reference number RGPIN-2019-05303].  ... 
doi:10.1016/j.image.2021.116494 fatcat:slffzxvzhrf5bp6v3nwpbxwkpy

Crack Front Segmentation and Facet Coarsening in Mixed-Mode Fracture

Chih-Hung Chen, Tristan Cambonie, Veronique Lazarus, Matteo Nicoli, Antonio J. Pons, Alain Karma
2015 Physical Review Letters  
Those results have important implications for understanding the failure of a wide range of materials.  ...  They further show that facet coarsening is a self- similar process driven by a spatial period-doubling instability of facet arrays with a growth rate dependent on mode mixity.  ...  Buchholz, who has broken the largest samples, we have further exploited here. We also thank L. Auffray, D. Bonamy, V. Doquet, J.-C. Eytard, R. Pidoux, A. Tanguy for their help in the experiments.  ... 
doi:10.1103/physrevlett.115.265503 pmid:26765005 fatcat:ndhfiiz2rzcfvbiwajqxurqyi4

Supramolecular DNA nanotechnology

Faisal A. Aldaye, Hanadi F. Sleiman
2009 Pure and Applied Chemistry  
Today, DNA is being used as a "smart" material to help solve a number of long-standing issues facing researchers in materials science and nanotechnology.  ...  This review will discuss the fruition and fundamentals of supramolecular DNA nanotechnology, as well as its future as a viable science in a material world.  ...  streptavidin arrays of either continuous or alternating protein patterns (Fig. 6a ).  ... 
doi:10.1351/pac-con-09-08-13 fatcat:qztp6h46dvga3cdkl3w5nhyemq

An overview of parallel algorithms for the singular value and symmetric eigenvalue problems

Michael Berry, Ahmed Sameh
1989 Journal of Computational and Applied Mathematics  
For the singular value decomposition, we discuss an efficient method for rectangular matrices in which the number of rows is substantially larger or smaller than the number of columns .  ...  With the advent of multiprocessor computer systems, the design of efficient parallel algorithms to determine these solutions becomes of paramount importance .  ...  Chris Hsiung of CRAY Research, Inc . for providing computing time on a CRAY X-MP/416 at Mendota Heights, MN, Paul Harten of Kuck and Associates, Inc ., Savoy, IL, for his help with the experiments on the  ... 
doi:10.1016/0377-0427(89)90366-x fatcat:2ptgqk2sbnfjdoqzppogjtjksa

Colour constancy under simultaneous changes in surface position and illuminant

K. Amano, D. H. Foster
2004 Proceedings of the Royal Society of London. Biological Sciences  
test surfaces and a spatial average over the whole pattern.  ...  It is shown here, however, that the ability of observers to make surface-colour matches across simultaneous changes in test-surface position and illuminant in computer-generated 'Mondrian' patterns is  ...  Each pattern consisted of an array of 121 (11 Â 11) or 49 (7 Â 7) uniform, square, Lambertian coloured surfaces, of side 1 , drawn randomly from 1269 samples in the Munsell book of color (Munsell Color  ... 
doi:10.1098/rspb.2004.2884 pmid:15556884 pmcid:PMC1691874 fatcat:aovlg5vipbhctoeik4i5ycc5nm
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