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An octomino of high order

Karl A Dahlke, Solomon W Golomb, Herbert Taylor
1995 Journal of combinatorial theory. Series A  
When the minimum rectangles tiled by I I I I ] I and v--r-q I tl I J I of order 92 and 76, respectively, were found by one of us (Dahlke [1, 2]), the question of which polyominoes are able to tile F]GtYRE  ...  The octomino -~ has order 24 first observed D. Klarner (cf. [3] ), by as was [4] .  ...  However, one of us (Taylor) has found a tiling of the half-strip with this figure, shown in Fig. 2 . FIG. 2 . 2 An octomino that tiles a 32 x oe halt-strip. Can it tile any rectangle?  ... 
doi:10.1016/0097-3165(95)90085-3 fatcat:p2rmb74u7rb4lgrrbk2ucwhauu

Irregular Polyomino-Shaped Subarrays for Space-Based Active Arrays

R. J. Mailloux, S. G. Santarelli, T. M. Roberts, D. Luu
2009 International Journal of Antennas and Propagation  
This technology can reduce the number of phase controls in arrays used for limited sector coverage or the number of time delay devices for wideband radar or communications, and so can reduce the cost of  ...  This paper presents new results showing the application of polyomino-based subarrays to limited field of view and wideband, wide-angle scanning.  ...  It also shows four rotations of an L-tetromino and two kinds of octominos, an L-octomino and a "point-up" octomino, that we use to fill the array.  ... 
doi:10.1155/2009/956524 fatcat:niunks5pqneadnhjkty6spftim

Page 639 of Mathematical Reviews Vol. , Issue 96b [page]

1996 Mathematical Reviews  
octomino of high order.  ...  , Helly property, elimination orderings, recognition of  ... 

Application of evolutionary algorithms and neural network concepts to the design of low-cost, wideband antenna arrays

Scott G. Santarelli, Robert J. Mailloux, Tian-Li Yu, Thomas M. Roberts, Michelle H. Champion, David E. Goldberg, Misty Blowers, Alex F. Sisti
2007 Evolutionary and Bio-inspired Computation: Theory and Applications  
Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden to Department of Defense, Washington Headquarters Services  ...  the data needed, and completing and reviewing this collection of information.  ...  ACKNOWLEDGEMENTS This work was supported by the Air Force Office of Scientific Research, Mathematics and Space Sciences Directorate, under Dr. A. Nachman.  ... 
doi:10.1117/12.724968 fatcat:qmkaxo3flngjjgoybe7yutaziu

A SUBARRAY DESIGN METHOD FOR LOW SIDELOBE LEVELS

Kai Yang, Yuqiang Wang, Hai Tang
2020 Progress In Electromagnetics Research Letters  
In order to reduce the coupling among the elements, the minimum element distance measured in Euclidean space is restricted in the procedure of optimization.  ...  The periodical structure in a large array is broken down by changing the orientations of the subarrays.  ...  With the consideration of system cost, usually only one or two types of subarrays are used to partition an aperture, such as L-octomino shaped subarrays and polyhex-shaped subarrays.  ... 
doi:10.2528/pierl19110301 fatcat:dipuxn6tubdhnly3smc3mdotfe

Shape and Weighting Optimization of a Subarray for an mm-Wave Phased Array Antenna

Taeyong Jeong, Juho Yun, Kyunghyun Oh, Jihyung Kim, Dae Woong Woo, Keum Cheol Hwang
2021 Applied Sciences  
objective function is composed of the quadratic function form, with the actual number identical to the standard objective function of QP.  ...  Next, in order to analyze the SLL, a 24 × 24 phased array antenna was compared with 96 transmit–receive modules (TRMs) attached only to the subarray stage and a phased array antenna with 576 TRMs attached  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/app11156803 fatcat:phupipevtnggxnnu2p5tmafs7i

Electronically Scanned Arrays

Robert J. Mailloux
2007 Synthesis Lectures on Antennas  
In order to describe the needs for scanned array development, this book begins with a brief discussion of the history that led to present array antennas.  ...  They also present a multitude of new opportunities and new challenges that need to be addressed.  ...  polynomial of order N.  ... 
doi:10.2200/s00081ed1v01y200612ant006 fatcat:3mpmbbjppjdmloc3jvddcnwehm

Page 128 of Mathematical Reviews Vol. 28, Issue Index [page]

Mathematical Reviews  
(with Golomb, Solomon W.; Taylor, Herbert) An octomino of high order. 96b:05049 Dawson, Robert A forbidden-suborder characterization of binarily-composable diagrams in double categories.  ...  .; Taylor, Herbert) An octomino of high order. 96b:05049 Dei Lungo, Alberto see Barcucci, Elena; et al., 96j:05034 Fereti¢, Svjetlan The area generating function for the column-convex polyominoes on the  ... 

A Review of Emerging Research Directions in Abstract Visual Reasoning [article]

Mikołaj Małkiński, Jacek Mańdziuk
2022 arXiv   pre-print
Recently, the AVR problems have become popular as a proxy to study machine intelligence, which has led to emergence of new distinct types of problems and multiple benchmark sets.  ...  human intelligence, where multiple types of problems are combined within a single IQ test.  ...  Instead of advocating for a single approach or reviewing Fig. 3 . Octomino puzzle.  ... 
arXiv:2202.10284v2 fatcat:ahd2maf52fhihpt7lxeh7mw3im

A Parallelizable Integer Linear Programming Approach for Tiling Finite Regions of the Plane with Polyominoes

Marcus Garvie, John Burkardt
2022 Algorithms  
Problems that are amenable to this approach are embarrassingly parallel, and our work provides proof of concept of a parallelizable algorithm.  ...  The general problem of tiling finite regions of the plane with polyominoes is NP-complete, and so the associated computational geometry problem rapidly becomes intractable for large instances.  ...  , one copy of the cross-shaped pentomino, and one copy of an octomino.  ... 
doi:10.3390/a15050164 fatcat:d2lfpj3zcbb2bmbh6izy4o3g6y

Advanced Fruit Fly Optimization Algorithm and Its Application to Irregular Subarray Phased Array Antenna Synthesis

Wentao Li, Yudong Zhang, Xiaowei Shi
2019 IEEE Access  
In this paper, an advanced fruit fly algorithm (FOA) is proposed and applied in subarray phased array antenna synthesis.  ...  The proposed algorithm introduces orthogonal crossover, quantum selection and simulated annealing operations on the individuals, and then combines them by using an adaptive expansion-contraction factor  ...  A subarray with an L-octomino shape consisting eight connected elements is desired. Fig. 8 and 10 show the acceptable exact partition of the aperture by using the X algorithm.  ... 
doi:10.1109/access.2019.2953544 fatcat:6a5dvmxdd5c6nbli24pjfqb4wm

Evolutionary dynamics in a simple model of self-assembly

Iain G. Johnston, Sebastian E. Ahnert, Jonathan P. K. Doye, Ard A. Louis
2011 Physical Review E  
We investigate the evolutionary dynamics of an idealised model for the robust self-assembly of two-dimensional structures called polyominoes.  ...  The corresponding, complex fitness landscape generates rich evolutionary dynamics as a function of parameters such as the population size, search space size, mutation rate, and method of recombination.  ...  In this plot, we see first of all that even though the search space is many orders of magnitude larger, the optimal adaptation and discovery times are at most an order of magnitude larger.  ... 
doi:10.1103/physreve.83.066105 pmid:21797439 fatcat:6h4ny66c7zbf5pgbg5xumd6lfu

Page 1463 of Mathematical Reviews Vol. 28, Issue Index [page]

Mathematical Reviews  
An octomino of high order. J. Combin. Theory Ser. A'70 (1995), no. 1, 157-158. (A.C. Liu) 96b:05049 05B50 (05B45) Taylor, J.C. see Taylor, John Clayton Taylor, Jean E.  ...  Digital reduced-order modeling and feedback design for nonlinear systems.  ... 

Solving Generalized Polyomino Puzzles Using the Ising Model

Kazuki Takabatake, Keisuke Yanagisawa, Yutaka Akiyama
2022 Entropy  
We propose an improved Hamiltonian design that introduces new constraints and guiding terms to weakly encourage favorable spins and pairs in the early stages of computation.  ...  A solution to the puzzle is obtained by searching for a ground state of Hamiltonian by simulating the dynamics of the multiple-spin system.  ...  The computational experiments were performed using the TSUBAME3.0 supercomputer at Tokyo Institute of Technology. Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/e24030354 pmid:35327865 pmcid:PMC8947422 fatcat:hvryhklzpnem5ftxojq5wqyypq

A new mathematical model for tiling finite regions of the plane with polyominoes

Marcus Garvie, John Burkardt
2020
We present a new mathematical model for tiling finite subsets of $\mathbb{Z}^2$ using an arbitrary, but finite, collection of polyominoes.  ...  Unlike previous approaches that employ backtracking and other refinements of 'brute-force' techniques, our method is based on a systematic algebraic approach, leading in most cases to an underdetermined  ...  We are also very grateful to an anonymous referee for their careful corrections and valuable suggestions that improved this paper.  ... 
doi:10.11575/cdm.v15i2.62866 fatcat:a4ukktj2djam3abl5dxqhlf6je
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