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Dynamics of Advantageous Mutant Spread in Spatial Death-Birth and Birth-Death Moran Models

Communications on Applied mathematics and Computation 2024年第1期6卷 576-604页

作者： Jasmine Foo Einar Bjarki Gunnarsson Kevin Leder David Sivakoff School of mathematics University of MinnesotaTwin CitiesMN55455USA Department of Industrial and Systems Engineering University of MinnesotaTwin CitiesMN55455USA departments of Statistics and mathematics The Ohio State UniversityColumbusOH43210USA

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.

关键词： Spatial death-birth models Spatial birth-death models Spatial evolutionary models Spatial cancer models Evolutionary graph theory Stochastic processes Biased voter model Dual process Fixation probability Shape theorem

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Global Stability to Steady Supersonic Rayleigh Flows in One-Dimensional Duct

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Chinese Annals of mathematics,Series B 2024年第2期45卷 279-296页

作者： Fenglun WEI Jianli LIU Department of mathematics Shanghai University Newtouch Center for mathematics of Shanghai University

Heat exchange plays an important role in hydrodynamical systems,which is an interesting topic in theory and application.In this paper,the authors consider the global stability of steady supersonic Rayleigh flows for the one-dimensional compressible Euler equations with heat exchange,under the small perturbations of initial and boundary conditions in a finite rectilinear duct.

关键词： Compressible Euler equations Heat exchange Supersonic Rayleigh fow Steady solution Classical solution

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The Complete Classification of Graphs Whose Second Largest Eigenvalue of the Eccentricity Matrix is Less than 1

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Acta Mathematica Sinica,English Series 2024年第7期40卷 1741-1766页

作者： Jian Feng WANG Xing Yu LEI Shu Chao LI Zoran STANI? School of mathematics and Statistics Shandong University of Technology Faculty of mathematics and Statistics Central China Normal University Faculty of mathematics University of Belgrade

The eccentricity matrix of a graph is obtained from the distance matrix by keeping the entries that are largest in their row or column, and replacing the remaining entries by zero. This matrix can be interpreted as an opposite to the adjacency matrix, which is on the contrary obtained from the distance matrix by keeping only the entries equal to 1. In the paper, we determine graphs having the second largest eigenvalue of eccentricity matrix less than 1.

关键词： Eccentricity matrix eigenvalue diameter principal submatrix forbidden subgraph 05C50

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Semi-derived Ringel-Hall algebras and Hall algebras of odd-periodic relative derived categories

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Science China mathematics 2024年第8期67卷 1735-1760页

作者： Ji Lin Liangang Peng Department of mathematics and Statistics Fuyang Normal University School of mathematics Sichuan University

Let t be a positive integer and A be a hereditary abelian category satisfying some finiteness conditions. We define the semi-derived Ringel-Hall algebra of A from the category CZ/t（A） of Z/t-graded complexes and obtain a natural basis of the semi-derived Ringel-Hall algebra. Moreover, we describe the semiderived Ringel-Hall algebra by the generators and defining relations. In particular, if t is an odd integer, we show an embedding of the derived Hall algebra of the odd-periodic relative derived category in the extended semi-derived Ringel-Hall algebra.

关键词： hereditary abelian categories the categories of $\mathbb{Z}/t$-graded complexes semi-derived Ringel-Hall algebras derived Hall algebras

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Generic Existence of Infinitely Many Non-contractible Closed Geodesics on Compact Space Forms

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Acta Mathematica Sinica,English Series 2024年第7期40卷 1674-1684页

作者： Hui LIU Yu Chen WANG School of mathematics and Statistics Wuhan University School of mathematics Tianjin Normal University

Let M = S~n/Γ and h be a nontrivial element of finite order p in π1（M）, where the integers n, p ≥ 2, Γ is a finite abelian group which acts freely and isometrically on the n-sphere and therefore M is diffeomorphic to a compact space form. In this paper, we prove that there are infinitely many noncontractible closed geodesics of class [h] on the compact space form with Cr-generic Finsler metrics,where 4 ≤ r ≤ ∞. The conclusion also holds for Cr-generic Riemannian metrics for 2 ≤ r ≤ ∞. The proof is based on the resonance identity of non-contractible closed geodesics on compact space forms.

关键词： Compact space forms non-contractible closed geodesics generic Finsler metrics resonance identity 53C22 58E05 58E10

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Finite Groups with Some Bounded Codegrees

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Acta Mathematica Sinica,English Series 2024年第7期40卷 1778-1784页

作者： Dong Fang YANG Yu ZENG Heng LV School of mathematics and Statistics Southwest University Department of mathematics Changshu Institute of Technology

For a character χ of a finite group G, the number cod（χ） := |G : ker（χ）|/χ（1） is called the codegree of χ. In this paper, we give a solvability criterion for a finite group G depending on the minimum of the... 详细信息

关键词： Finite group codegree degree simple group 20C15 20D10

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Building the toolbox for in vivo glia-to-neuron reprogramming

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Neural Regeneration Research 2024年第6期19卷 1171-1172页

作者： Ye Xie Bo Chen departments of Ophthalmology and Neuroscience Icahn School of Medicine at Mount Sinai

Unlike regenerative-competent species that possess a remarkable intrinsic capacity to replenish lost neurons and restore neurocircuits spontaneously, the central nervous system in adult mammals lacks the ability to compensate for the neuronal loss caused by neurodegenerative diseases or traumatic injuries resulting in permanent loss of functionality. Inspired by earlier discoveries that radial glia or astrocytes isolated from the postnatal cortex can generate neurons,

关键词： CONVERSION DISEASE

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Non-symmetric differentially subordinate martingales and sharp weak-type bounds for Fourier multipliers

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Science China mathematics 2024年第8期67卷 1807-1826页

作者： Meryem Akboudj Yong Jiao Adam Os?kowski School of mathematics and Statistics Hunan Key Laboratory of Analytical Mathematics and ApplicationsCentral South University Faculty of mathematics Informatics and MechanicsUniversity of Warsaw

Let p>2 be a given exponent. In this paper, we prove, with the best constant, the weak-type(p, p)inequality ■ for a large class of non-symmetric Fourier multipliers Tm obtained via modulation of jumps of certain Lévy processes. In particular, the estimate holds for appropriate linear combinations of second-order Riesz transforms and skew versions of the Beurling-Ahlfors operator on the complex plane. The proof rests on a novel probabilistic bound for Hilbert-space-valued martingales satisfying a certain non-symmetric subordination principle. Further applications to harmonic functions and Riesz systems on Euclidean domains are indicated.

关键词： weak-type bound Fourier multiplier martingale differential subordination laminate

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Parametric “non-nested” discriminants for multiplicities of univariate polynomials

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Science China mathematics 2024年第8期67卷 1911-1932页

作者： Hoon Hong Jing Yang Department of mathematics North Carolina State University SMS–HCIC–School of mathematics and Physics Center for Applied Mathematics of GuangxiGuangxi Minzu University

We consider the problem of complex root classification, i.e., finding the conditions on the coefficients of a univariate polynomial for all possible multiplicity structures on its complex roots. It is well known that such conditions can be written as conjunctions of several polynomial equalities and one inequality in the coefficients. Those polynomials in the coefficients are called discriminants for multiplicities. It is also known that discriminants can be obtained using repeated parametric greatest common divisors. The resulting discriminants are usually nested determinants, i.e., determinants of matrices whose entries are determinants, and so on. In this paper, we give a new type of discriminant that is not based on repeated greatest common divisors. The new discriminants are simpler in the sense that they are non-nested determinants and have smaller maximum degrees.

关键词： parametric polynomial complex roots discriminant multiplicity resultant

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Normalized and self-normalized Cramér-type moderate deviations for the Euler-Maruyama scheme for the SDE

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Science China mathematics 2024年第8期67卷 1865-1880页

作者： Xiequan Fan Haijuan Hu Lihu Xu Center for Applied mathematics Tianjin University School of mathematics and Statistics Northeastern University at Qinhuangdao Department of mathematics Faculty of Science and TechnologyUniversity of Macau

In this paper, we establish normalized and self-normalized Cramér-type moderate deviations for the Euler-Maruyama scheme for SDE. Due to our results, Berry-Esseen's bounds and moderate deviation principles are also o... 详细信息

关键词： Euler-Maruyama scheme Cramér-type moderate deviations self-normalized sequences Berry-Esseen's bounds

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