The spread of an advantageous mutation through a population is of fundamental interest in population genetics. While the classical Moran model is formulated for a well-mixed population, it has long been recognized tha...The spread of an advantageous mutation through a population is of fundamental interest in population genetics. While the classical Moran model is formulated for a well-mixed population, it has long been recognized that in real-world applications, the population usually has an explicit spatial structure which can significantly influence the dynamics. In the context of cancer initiation in epithelial tissue, several recent works have analyzed the dynamics of advantageous mutant spread on integer lattices, using the biased voter model from particle systems theory. In this spatial version of the Moran model, individuals first reproduce according to their fitness and then replace a neighboring individual. From a biological standpoint, the opposite dynamics, where individuals first die and are then replaced by a neighboring individual according to its fitness, are equally relevant. Here, we investigate this death-birth analogue of the biased voter model. We construct the process mathematically, derive the associated dual process, establish bounds on the survival probability of a single mutant, and prove that the process has an asymptotic shape. We also briefly discuss alternative birth-death and death-birth dynamics, depending on how the mutant fitness advantage affects the dynamics. We show that birth-death and death-birth formulations of the biased voter model are equivalent when fitness affects the former event of each update of the model, whereas the birth-death model is fundamentally different from the death-birth model when fitness affects the latter event.展开更多
A graph G is said to be determined by its spectrum if any graph having the same spectrum as G is isomorphic to G. An H-shape is a tree with exactly two of its vertices having maximal degree 3. In this paper, a formula...A graph G is said to be determined by its spectrum if any graph having the same spectrum as G is isomorphic to G. An H-shape is a tree with exactly two of its vertices having maximal degree 3. In this paper, a formula of counting the number of closed 6-walks is given on a graph, and some necessary conditions of a graph Γ cospectral to an H-shape are given.展开更多
We present an effective spectral matching method based on a shape association graph for finding region correspondences between two cel animation keyframes.We formulate the correspondence problem as an adapted quadrati...We present an effective spectral matching method based on a shape association graph for finding region correspondences between two cel animation keyframes.We formulate the correspondence problem as an adapted quadratic assignment problem,which comprehensively considers both the intrinsic geometric and topology of regions to find the globally optimal correspondence.To simultaneously represent the geometric and topological similarities between regions,we propose a shape association graph(SAG),whose node attributes indicate the geometric distance between regions,and whose edge attributes indicate the topological distance between combined region pairs.We convert topological distance to geometric distance between geometric objects with topological features of the pairs,and introduce Kendall shape space to calculate the intrinsic geometric distance.By utilizing the spectral properties of the affinity matrix induced by the SAG,our approach can efficiently extract globally optimal region correspondences,even if shapes have inconsistent topology and severe deformation.It is also robust to shapes undergoing similarity transformations,and compatible with parallel computing techniques.展开更多
Drainage pattern recognition is crucial for geospatial understanding and hydrologic modelling.Currently,drainage pattern recognition methods employ geometric measures of overall and local features of river networks bu...Drainage pattern recognition is crucial for geospatial understanding and hydrologic modelling.Currently,drainage pattern recognition methods employ geometric measures of overall and local features of river networks but lack measures of river basin unit shape features,so that potential correlations between river segments are usually ignored,resulting in poor drainage pattern recognition results.In order to overcome this problem,this paper proposes a supervised graph neural network method that considers the local basin unit shape of river networks.First,based on the overall hierarchy of the river networks,the confluence angle of river segments and the shape of river basin units,multiple drainage pattern classification features are extracted.Then,typical drainage pattern samples from the multi-scale NSDI and USGS databases are used to complete the training,validation and testing steps.Experimental results show that the drainage pattern indexes proposed can describe the characteristics of different drainage patterns.The method can effectively sample the adjacent river segments,flexibly transfer the associated pattern features among river segment neighbours,and aggregate the deeper characteristics of the river networks,thus improving the drainage pattern recognition accuracy relative to other methods and reliably distinguishing different drainage patterns.展开更多
基金supported in part by the NIH grant R01CA241134supported in part by the NSF grant CMMI-1552764+3 种基金supported in part by the NSF grants DMS-1349724 and DMS-2052465supported in part by the NSF grant CCF-1740761supported in part by the U.S.-Norway Fulbright Foundation and the Research Council of Norway R&D Grant 309273supported in part by the Norwegian Centennial Chair grant and the Doctoral Dissertation Fellowship from the University of Minnesota.
文摘The spread of an advantageous mutation through a population is of fundamental interest in population genetics. While the classical Moran model is formulated for a well-mixed population, it has long been recognized that in real-world applications, the population usually has an explicit spatial structure which can significantly influence the dynamics. In the context of cancer initiation in epithelial tissue, several recent works have analyzed the dynamics of advantageous mutant spread on integer lattices, using the biased voter model from particle systems theory. In this spatial version of the Moran model, individuals first reproduce according to their fitness and then replace a neighboring individual. From a biological standpoint, the opposite dynamics, where individuals first die and are then replaced by a neighboring individual according to its fitness, are equally relevant. Here, we investigate this death-birth analogue of the biased voter model. We construct the process mathematically, derive the associated dual process, establish bounds on the survival probability of a single mutant, and prove that the process has an asymptotic shape. We also briefly discuss alternative birth-death and death-birth dynamics, depending on how the mutant fitness advantage affects the dynamics. We show that birth-death and death-birth formulations of the biased voter model are equivalent when fitness affects the former event of each update of the model, whereas the birth-death model is fundamentally different from the death-birth model when fitness affects the latter event.
文摘A graph G is said to be determined by its spectrum if any graph having the same spectrum as G is isomorphic to G. An H-shape is a tree with exactly two of its vertices having maximal degree 3. In this paper, a formula of counting the number of closed 6-walks is given on a graph, and some necessary conditions of a graph Γ cospectral to an H-shape are given.
基金supported by the National Key R&D Program of China(2020YFC1523302)the National Natural Science Foundation of China(61972041,62072045).
文摘We present an effective spectral matching method based on a shape association graph for finding region correspondences between two cel animation keyframes.We formulate the correspondence problem as an adapted quadratic assignment problem,which comprehensively considers both the intrinsic geometric and topology of regions to find the globally optimal correspondence.To simultaneously represent the geometric and topological similarities between regions,we propose a shape association graph(SAG),whose node attributes indicate the geometric distance between regions,and whose edge attributes indicate the topological distance between combined region pairs.We convert topological distance to geometric distance between geometric objects with topological features of the pairs,and introduce Kendall shape space to calculate the intrinsic geometric distance.By utilizing the spectral properties of the affinity matrix induced by the SAG,our approach can efficiently extract globally optimal region correspondences,even if shapes have inconsistent topology and severe deformation.It is also robust to shapes undergoing similarity transformations,and compatible with parallel computing techniques.
基金supported by the National Natural Science Foundation of China[grant number 41930101,42161066,42261076]State Key Laboratory of Geo-Information Engineering and Key Laboratory of Surveying and Mapping Science and Geospatial Information Technology of MNR,CASM[grant number 2022-03-03]+2 种基金Major Project for Science and Technology of Gansu Province[grant number 22ZD6GA010]Youth Science and Technology Foundation of Gansu Province[grant number 22JR11RA140]Young Scholars Science Foundation of Lanzhou Jiaotong University[grant number 2022007].
文摘Drainage pattern recognition is crucial for geospatial understanding and hydrologic modelling.Currently,drainage pattern recognition methods employ geometric measures of overall and local features of river networks but lack measures of river basin unit shape features,so that potential correlations between river segments are usually ignored,resulting in poor drainage pattern recognition results.In order to overcome this problem,this paper proposes a supervised graph neural network method that considers the local basin unit shape of river networks.First,based on the overall hierarchy of the river networks,the confluence angle of river segments and the shape of river basin units,multiple drainage pattern classification features are extracted.Then,typical drainage pattern samples from the multi-scale NSDI and USGS databases are used to complete the training,validation and testing steps.Experimental results show that the drainage pattern indexes proposed can describe the characteristics of different drainage patterns.The method can effectively sample the adjacent river segments,flexibly transfer the associated pattern features among river segment neighbours,and aggregate the deeper characteristics of the river networks,thus improving the drainage pattern recognition accuracy relative to other methods and reliably distinguishing different drainage patterns.
