Solving Generalized Polyomino Puzzles Using the Ising Model [PDF]
Entropy, 2022 In the polyomino puzzle, the aim is to fill a finite space using several polyomino pieces with no overlaps or blanks. Because it is an NP-complete combinatorial optimization problem, various probabilistic and approximated approaches have been applied to ...
Kazuki Takabatake +2 more
exaly +5 more sources
Zagreb connection indices on polyomino chains and random polyomino chains [PDF]
Open MathematicsIn this manuscript, we delve into the exploration of the first and second Zagreb connection indices of both polyomino chains and random polyomino chains. Our methodology relies on the utilization of Markov chain theory. Within this framework, the article
Hugo Cruz-Suárez
exaly +3 more sources
Polyomino reconstructs spatial transcriptomic profiles with single-cell resolution via a region-allocation method. [PDF]
Genome ResIntegration of single-cell and spatial transcriptomes represents a fundamental strategy to enhance spatial data quality. However, existing methods for mapping single-cell data to spatial coordinates struggle with large-scale data sets comprising millions
Cai Q, Lin L, Liu X, Chen J.
europepmc +2 more sources
Gene duplication and subsequent diversification strongly affect phenotypic evolvability and robustness [PDF]
Royal Society Open Science, 2021 We study the effects of non-determinism and gene duplication on the structure of genotype–phenotype (GP) maps by introducing a non-deterministic version of the Polyomino self-assembly model. This model has previously been used in a variety of contexts to
V. Jouffrey, A. S. Leonard, S. E. Ahnert
doaj +2 more sources
Extremal Matching Energy of Random Polyomino Chains
Entropy, 2017 Polyomino graphs is one of the research objectives in statistical physics and in modeling problems of surface chemistry. A random polyomino chain is a subgraph of a polyomino graph.
Tingzeng Wu, Huazhong Lu
exaly +3 more sources
Computations of the M-Polynomials and Degree-Based Topological Indices for Dendrimers and Polyomino Chains [PDF]
International Journal of Analytical Chemistry, 2018 Topological indices correlate certain physicochemical properties like boiling point, stability, and strain energy of chemical compounds. In this report, we compute M-polynomials for PAMAM dendrimers and polyomino chains.
Young Chel Kwun +5 more
doaj +2 more sources
A New Algorithm Based on Colouring Arguments for Identifying Impossible Polyomino Tiling Problems
Algorithms, 2022 Checkerboard colouring arguments for proving that a given collection of polyominoes cannot tile a finite target region of the plane are well-known and typically applied on a case-by-case basis. In this article, we give a systematic mathematical treatment
Marcus R. Garvie, John Burkardt
doaj +2 more sources
Zagreb Polynomials and redefined Zagreb indices of Dendrimers and Polyomino Chains
Open Chemistry, 2019 Dendrimers have an incredibly strong potential because their structure allows multivalent frameworks, i.e. one dendrimer molecule has many possible destinations to couple to a functioning species.
Farooq Adeel +4 more
doaj +2 more sources
A molecular T-pentomino for separating BTEX hydrocarbons [PDF]
Nature CommunicationsMethods to separate molecules (e.g., petrochemicals) are exceedingly important industrially. A common approach for separations is to crystallize a host molecule that either provides an enforced covalent cavity (intrinsic cavity) or packs inefficiently ...
Christopher J. Hartwick +2 more
doaj +2 more sources
Genetic Correlations Greatly Increase Mutational Robustness and Can Both Reduce and Enhance Evolvability. [PDF]
PLoS Computational Biology, 2016 Mutational neighbourhoods in genotype-phenotype (GP) maps are widely believed to be more likely to share characteristics than expected from random chance. Such genetic correlations should strongly influence evolutionary dynamics.
Sam F Greenbury +3 more
doaj +2 more sources