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Conflict-free Incidence Coloring of Outer-1-planar Graphs

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Acta Mathematicae Applicatae Sinica 2024年

作者： Meng-ke QI Xin ZHANG School of Mathematics and statistics Xidian University

An incidence of a graph G is a vertex-edge pair (v, e) such that v is incidence with e. A conflict-free incidence coloring of a graph is a coloring of the incidences in such a way that two incidences (u, e) and (v, f)get distinct colors if and only if they conflict each other, i.e.,(i) u=v,(ii) uv is e or f, or (iii) there is a vertex w such that uw=e and vw=f. The minimum number of colors used among all conflict-free incidence colorings of a graph is the conflict-free incidence chromatic number. A graph is outer-1-planar if it can be drawn in the plane so that vertices are on the outer-boundary and each edge is crossed at most once. In this paper, we show that the conflict-free incidence chromatic number of an outer-1-planar graph with maximum degree△is either 2△or 2△+1 unless the graph is a cycle on three vertices, and moreover, all outer-1-planar graphs with conflict-free incidence chromatic number 2△or 2△+1 are completely characterized. An efficient algorithm for constructing an optimal conflict-free incidence coloring of a connected outer-1-planar graph is given.

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Traveling Fronts for a Time-periodic Population Model with Dispersal

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Acta Mathematicae Applicatae Sinica 2024年

作者： Hai-qin ZHAO School of Mathematics and statistics Xidian University

In this paper, we study a class of time-periodic population model with dispersal. It is well known that the existence of the periodic traveling fronts has been established. However, the uniqueness and stability of such fronts remain unsolved. In this paper, we first prove the uniqueness of non-critical periodic traveling fronts. Then, we show that all non-critical periodic traveling fronts are exponentially asymptotically stable.

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Pricing Guaranteed Minimum Death Benefits with Dollar Cost Averaging Under Time-changed Le′vy Models

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Acta Mathematicae Applicatae Sinica 2024年

作者： Jia-ming WANG Mei-qiao AI Zhi-min ZHANG College of Mathematics and statistics Chongqing University

In this paper, we propose an efficient and accurate method for pricing Guaranteed Minimum Death Benefit (GMDB) under time-changed Le′vy processes. Suppose that the GMDB payoff depends on a dollar cost averaging (DCA) style periodic investment, and the activity rate process in stochastic time change is modeled by a square-root process. We develop a recursive method to derive the closed form valuation formula by using the frame duality projection method. Numerical examples are reported for demonstrating the effectiveness of our approach and illustrating the interplay between contract parameters and the valuation.

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Berry-Esseen bounds and Cramér-type moderate deviations for the sample mean and the MLE of the growth rate for a jump-type CIR process

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Acta Mathematica Sinica,English Series 2024年

作者： Fuqing GAO Zhi QU School of Mathematics and statistics Wuhan University

We study Berry-Esseen bounds and Cramér-type moderate deviations of a jump-type CoxIngersoll-Ross(CIR) process driven by a standard Wiener process and a subordinator. In the subcritical case, we obtain the best Berry-Esseen bound of the sample mean and the MLE of the growth rate if the Lévy measure of the subordinator has finite third order moment. Under the Cramér condition,we establish the Cramér-type moderate deviations of the MLE of the growth rate. We first derive a Berry-Esseen bound, a deviation inequality and the Cramér-type moderate deviations for the sample mean of the CIR process by analyzing the asymptotic behaviors of the characteristic function and the moment generating function of the sample mean. Then we analyze a type of additive functional of the jump-type CIR process and use a transformation to study the Berry-Esseen bound and the Cramér-type moderate deviations for the MLE of the growth rate.

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Random change point model with an application to the China Household Finance Survey

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Science China Mathematics 2024年

作者： Meng Li Lingxi Gao Guangming Lv Xingwei Tong School of statistics Beijing Normal University

We consider a linear model with a change point according to the unknown random threshold of a covariate. We give the expectation-maximization(EM) estimation of the regression and change point parameters. The existence of the random change point is detected by the supremum(SUP) test of score statistics. Theoretically, we establish the convergence and asymptotic distribution of the estimation and show that the EM estimates converge in distribution to a normal distribution. In addition, the numerical performance of the proposed approach is demonstrated through simulation studies. Finally, applying our methodology to household financial decisions, we see that the average debt tolerance of Chinese households is estimated to be 1.1364 times the sum of total household income and financial assets. The effect of assets and income on consumption shows a rapid decline if the household exceeds the average debt tolerance.

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A Potential Degree Sequence Problem of the Loebl-Komlós-Sós Conjecture

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Acta Mathematicae Applicatae Sinica 2024年

作者： Guang-ming LI Jian-hua YIN School of Mathematics and statistics Hainan University

A non-increasing sequenceπ=(d1,..., dn) of nonnegative integers is said to be a graphic sequence if it is realizable by a simple graph G on n vertices. In this case, G is referred to as a realization ofπ. In terms of graphic sequences, the Loebl-Komlós-Sós conjecture states that for any integers k and n, if π=(d1,..., dn)is a graphic sequence with d「n/2」≥k, then every realization ofπcontains all trees with k edges as *** problem can be viewed as a forcible degree sequence problem. In this paper, we consider a potential degree sequence problem of the Loebl-Komlós-Sós conjecture, that is, we prove that for any integers k and n, ifπ=(d1,..., dn) is a graphic sequence with d「n/2」≥k, then there is a realization ofπcontaining all trees with k edges as subgraphs.

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On monomial algebras with representation-finite enveloping algebras

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Acta Mathematica Sinica,English Series 2024年

作者： Jianguo ZHOU Yuzhe LIU Chao ZHANG School of Mathematics and statistics Guizhou University

The present paper mainly considers the representation type of the enveloping algebra of monomial *** A be a monomial algebra and Ae=A?kAopbe its enveloping *** is shown that Aeis representation-finite if and only if A～=An/rad2An,where Anis the path algebra k Q with Q=1-→2-→···-→***,we show that the number of all isoclasses of indecomposable (An/rad2An)e-modules is43n3+n2-73n+1,and classify all indecomposable modules over (An/rad2An)***,the Clebsch-Gordon problem over (A2n/radAn)eis studied.

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Data-Driven Earthquake Multi-impact Modeling: A Comparison of Models

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International Journal of Disaster Risk Science 2024年第3期15卷 421-433页

作者： Hamish Patten Max Anderson Loake David Steinsaltz Information Management International Federation of Red Cross and Red Crescent Societies (IFRC) Department of statistics University of Oxford

In this study, a broad range of supervised machine learning and parametric statistical, geospatial, and non-geospatial models were applied to model both aggregated observed impact estimate data and satellite image-derived geolocated building damage data for earthquakes, via regression-and classification-based models, respectively. For the aggregated observational data, models were ranked via predictive performance of mortality, population displacement, building damage, and building destruction for 375 observations across 161 earthquakes in 61 countries. For the satellite image-derived data, models were ranked via classification performance(damaged/unaff ected) of 369,813 geolocated buildings for 26 earthquakes in 15 countries. Grouped k-fold, 3-repeat cross validation was used to ensure out-of-sample predictive performance. Feature importance of several variables used as proxies for vulnerability to disasters indicates covariate utility. The 2023 Türkiye–Syria earthquake event was used to explore model limitations for extreme events. However, applying the AdaBoost model on the 27,032 held-out buildings of the 2023 Türkiye–Syria earthquake event, predictions had an AUC of 0.93. Therefore, without any geospatial, building-specific, or direct satellite image information, this model accurately classified building damage,with significantly improved performance over satellite image trained models found in the literature.

关键词： Disaster risk modeling Earthquake impact models Machine learning Disaster statistics Satellite image-derived building damage

■-dressing Method for the Coupled Two-component Kundu-Eckhaus Equations

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Acta Mathematicae Applicatae Sinica 2024年

作者： Zhen-jie NIU Biao LI School of Mathematics and statistics Ningbo University

In this paper,■-dressing method based on a local 3×3 matrix ■-problem with non-normalization boundary conditions is used to investigate coupled two-component Kundu-Eckhaus ***,we propose a new compatible system with singular dispersion relation,that is time spectral problem and spatial spectral problem of coupled two-component Kundu-Eckhaus equations via constraint ***,we derive a hierarchy of nonlinear evolution equations by introducing a recursive *** last,by solving constraint matrixes,a spectral transform matrix is given which is sufficiently important for finding soliton solutions of potential function,and we obtain N-soliton solutions of coupled two-component Kundu-Eckhaus equations.

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