Journal of Theoretical Biology最新文献_第7页

Delayed loss of stability of periodic travelling waves: Insights from the analysis of essential spectra 周期性行波的延迟失稳：本质光谱分析的启示

IF 1.9 4区数学

Journal of Theoretical Biology Pub Date : 2024-09-16 DOI: 10.1016/j.jtbi.2024.111945

Lukas Eigentler , Mattia Sensi

{"title":"Delayed loss of stability of periodic travelling waves: Insights from the analysis of essential spectra","authors":"Lukas Eigentler , Mattia Sensi","doi":"10.1016/j.jtbi.2024.111945","DOIUrl":"10.1016/j.jtbi.2024.111945","url":null,"abstract":"<div><div>Periodic travelling waves (PTW) are a common solution type of partial differential equations. Such models exhibit multistability of PTWs, typically visualised through the Busse balloon, and parameter changes typically lead to a cascade of wavelength changes through the Busse balloon. In the past, the stability boundaries of the Busse balloon have been used to predict such wavelength changes. Here, motivated by anecdotal evidence from previous work, we provide compelling evidence that the Busse balloon provides insufficient information to predict wavelength changes due to a delayed loss of stability phenomenon. Using two different reaction–advection–diffusion systems, we relate the delay that occurs between the crossing of a stability boundary in the Busse balloon and the occurrence of a wavelength change to features of the essential spectrum of the destabilised PTW. This leads to a predictive framework that can estimate the order of magnitude of such a time delay, which provides a novel “early warning sign” for pattern destabilisation. We illustrate the implementation of the predictive framework to predict under what conditions a wavelength change of a PTW occurs.</div></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"595 ","pages":"Article 111945"},"PeriodicalIF":1.9,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022519324002303/pdfft?md5=3013d4efdcdbd16448a87c3fd0061653&pid=1-s2.0-S0022519324002303-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142301237","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Persistent biological invasions alter ecological network topology, impacting disease transmission during community assembly 持续性生物入侵改变生态网络拓扑结构，影响群落集结过程中的疾病传播

IF 1.9 4区数学

Journal of Theoretical Biology Pub Date : 2024-09-15 DOI: 10.1016/j.jtbi.2024.111950

Min Su , Xiaowei Chen , Cang Hui

{"title":"Persistent biological invasions alter ecological network topology, impacting disease transmission during community assembly","authors":"Min Su , Xiaowei Chen , Cang Hui","doi":"10.1016/j.jtbi.2024.111950","DOIUrl":"10.1016/j.jtbi.2024.111950","url":null,"abstract":"<div><p>Ecological networks experiencing persistent biological invasions may exhibit distinct topological properties, complicating the understanding of how network topology affects disease transmission during invasion-driven community assembly. We developed a trait-based network model to assess the impact of network topology on disease transmission, measured as community- and species-level disease prevalence. We found that trait-based feeding interactions between host species determine the frequency distribution of the niche of co-occurring species in steady-state communities, being either bimodal or multimodal. The width of the growth kernel influences the degree-biomass relationship of species, being either weakly positive or strongly negative. When this relationship is weakly positive, species-level disease prevalence is primarily correlated with biomass. However, when the degree-biomass relationship is strongly negative, species-level disease prevalence is determined by the difference between a host species’ in-degree and out-degree closeness centrality. At the community level, disease prevalence is generally amplified by increasing host richness, community biomass, and the standard deviation of interaction generality, while it is diluted by higher network connectance. Our framework verifies the amplification effects of host richness during invasion-driven community assembly and offers valuable insights for estimating disease prevalence based on host network topology.</p></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"595 ","pages":"Article 111950"},"PeriodicalIF":1.9,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142242601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Genomic compliance with Chargaff’s second parity rule may have originated non-adaptively, but stem-loops now function adaptively 基因组遵守查尔加夫的第二条奇偶性规则可能是非适应性的，但茎环现在的功能是适应性的

IF 1.9 4区数学

Journal of Theoretical Biology Pub Date : 2024-09-12 DOI: 10.1016/j.jtbi.2024.111943

Donald R. Forsdyke

{"title":"Genomic compliance with Chargaff’s second parity rule may have originated non-adaptively, but stem-loops now function adaptively","authors":"Donald R. Forsdyke","doi":"10.1016/j.jtbi.2024.111943","DOIUrl":"10.1016/j.jtbi.2024.111943","url":null,"abstract":"<div><p>Of Chargaff’s four rules on DNA base quantity, his second parity rule (PR-2) is the most contentious. Various biometricians (e.g., Sueoka, Lobry) regarded PR-2 compliance as a non-adaptive feature of modern genomes that could be modeled through interrelations among mutation rates. However, PR-2 compliance with stem-loop potential was considered adaptively relevant by biochemists familiar with analyses of nucleic acid structure (e.g., of Crick) and of meiotic recombination (e.g., of Kleckner). Meanwhile, other biometricians had shown that PR-2 complementarity extended beyond individual bases (1-mers) to oligonucleotides (k-mers), possibly reflecting “advantageous DNA structure” (Nussinov). An “introns early” hypothesis (Reanney, Forsdyke) had suggested a primordial nucleic acid world with recombination-mediated error-correction requiring genome-wide stem-loop potential to have evolved prior to localized intrusions of protein-encoding potential (exons). Thus, a primordial genome was equivalent to one long intron. Indeed, when assessed as the base order-dependent component (correcting for local influences of GC%), modern genes, especially when evolving rapidly under positive Darwinian selection, display high intronic stem-loop potential. This suggests forced migration from neighboring exons by competing protein-encoding potential. PR-2 compliance may have first arisen non-adaptively. Primary prototypic structures were later strengthened by their adaptive contribution to recombination. Thus, contentious views may actually be in harmony.</p></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"595 ","pages":"Article 111943"},"PeriodicalIF":1.9,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022519324002285/pdfft?md5=519c85205d674dc45843d7e184f3269f&pid=1-s2.0-S0022519324002285-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142233037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Solving the prisoner’s dilemma trap in Hamilton’s model of temporarily formed random groups 在汉密尔顿的临时随机群体模型中破解囚徒困境陷阱

IF 1.9 4区数学

Journal of Theoretical Biology Pub Date : 2024-09-11 DOI: 10.1016/j.jtbi.2024.111946

José F. Fontanari , Mauro Santos

{"title":"Solving the prisoner’s dilemma trap in Hamilton’s model of temporarily formed random groups","authors":"José F. Fontanari , Mauro Santos","doi":"10.1016/j.jtbi.2024.111946","DOIUrl":"10.1016/j.jtbi.2024.111946","url":null,"abstract":"<div><p>Explaining the evolution of cooperation in the strong altruism scenario, where a cooperator does not benefit from her contribution to the public goods, is a challenging problem that requires positive assortment among cooperators (i.e., cooperators must tend to associate with other cooperators) or punishment of defectors. The need for these drastic measures stems from the analysis of a group selection model of temporarily formed random groups introduced by Hamilton nearly fifty years ago to describe the fate of altruistic behavior in a population. Challenging conventional wisdom, we show analytically here that strong altruism evolves in Hamilton’s original model in the case of biparental sexual reproduction. Moreover, when the cost of cooperation is small and the amplified contribution shared by group members is large, cooperation is the only stable strategy in equilibrium. Thus, our results provide a solution to the ‘problem of origination’ of strong altruism, i.e. how cooperation can take off from an initial low frequency of cooperators. We discuss a possible reassessment of cooperation in cases of viral co-infection, as cooperation may even be favored in situations where the prisoner’s dilemma applies.</p></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"595 ","pages":"Article 111946"},"PeriodicalIF":1.9,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142227992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Simple olfactory navigation in air and water 在空气和水中进行简单的嗅觉导航。

IF 1.9 4区数学

Journal of Theoretical Biology Pub Date : 2024-09-11 DOI: 10.1016/j.jtbi.2024.111941

Bowei Ouyang , Aaron C. True , John P. Crimaldi , Bard Ermentrout

{"title":"Simple olfactory navigation in air and water","authors":"Bowei Ouyang , Aaron C. True , John P. Crimaldi , Bard Ermentrout","doi":"10.1016/j.jtbi.2024.111941","DOIUrl":"10.1016/j.jtbi.2024.111941","url":null,"abstract":"<div><p>Two simple algorithms based on combining odor concentration differences across time and space along with information on the flow direction are tested for their ability to locate an odor source in four different odor landscapes. Image data taken from air plumes in three different regimes and a water plume are used as test environments for a bilateral (“stereo sampling”) algorithm using concentration differences across two sensors and a “casting” algorithm that uses successive samples to decide orientation. Agents are started at random locations and orientations in the landscape and allowed to move until they reach the source of the odor (success) or leave the imaged area (failure). Parameters for the algorithm are chosen to optimize success and to minimize path length to the source. Success rates over 90% are consistently obtained with path lengths that can be as low as twice the starting distance from the source in air and four times the distance in the highly turbulent water plumes. We find that parameters that optimize success often lead to more exploratory pathways to the source. Information about the direction from which the odor is coming is necessary for successful navigation in the water plume and reduces the path length in the three tested air plumes.</p></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"595 ","pages":"Article 111941"},"PeriodicalIF":1.9,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022519324002261/pdfft?md5=4baa947541fb13fb4cd0d1e55ea650d5&pid=1-s2.0-S0022519324002261-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142180330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The nasal cavity of the bearded seal: An effective and robust organ for retaining body heat and water 胡须海豹的鼻腔：保持体温和水分的有效而坚固的器官。

IF 1.9 4区数学

Journal of Theoretical Biology Pub Date : 2024-09-10 DOI: 10.1016/j.jtbi.2024.111933

Hyejeong Lee Cheon , Nataliya Kizilova , Eirik G. Flekkøy , Matthew J. Mason , Lars P. Folkow , Signe Kjelstrup

{"title":"The nasal cavity of the bearded seal: An effective and robust organ for retaining body heat and water","authors":"Hyejeong Lee Cheon , Nataliya Kizilova , Eirik G. Flekkøy , Matthew J. Mason , Lars P. Folkow , Signe Kjelstrup","doi":"10.1016/j.jtbi.2024.111933","DOIUrl":"10.1016/j.jtbi.2024.111933","url":null,"abstract":"<div><p>We report the effects of varying physiological and other properties on the heat and water exchange in the maxilloturbinate structure (MT) of the bearded seal (<em>Erignathus barbatus</em> or Eb) in realistic environments, using a computational fluid dynamics (CFD) model. We find that the water retention in percent is very high (about 90 %) and relatively unaffected by either cold (−30 °C) or warm (10 °C) conditions. The retention of heat is also high, around 80 % . Based on a consideration of entropy production by the maxilloturbinate system, we show that anatomical and physiological properties of the seal provide good conditions for heat and water exchange at the mucus lining in the seal’s nasal cavity. At normal values of tidal volume and maxilloturbinate (MT) length, the air temperature in the MT reaches the body temperature before the air has left the MT channels. This confers a safety factor which is expected to be helpful in exercise, when ventilation increases.</p></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"595 ","pages":"Article 111933"},"PeriodicalIF":1.9,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022519324002182/pdfft?md5=8ad7be5d090c3b97f8f54edfd0f34a9f&pid=1-s2.0-S0022519324002182-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142180331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Connectivity between two fishing sites can lead to an emergence phenomenon related to Maximum Sustainable Yield 两个渔场之间的连通性会导致出现与最大持续产量有关的现象。

IF 1.9 4区数学

Journal of Theoretical Biology Pub Date : 2024-09-05 DOI: 10.1016/j.jtbi.2024.111913

Doanh Nguyen-Ngoc , Tri Nguyen-Huu , Pierre Auger

{"title":"Connectivity between two fishing sites can lead to an emergence phenomenon related to Maximum Sustainable Yield","authors":"Doanh Nguyen-Ngoc , Tri Nguyen-Huu , Pierre Auger","doi":"10.1016/j.jtbi.2024.111913","DOIUrl":"10.1016/j.jtbi.2024.111913","url":null,"abstract":"<div><p>In this study, we examine the effects of connectivity on the total catch of a fishery consisting of two fishing sites when the fish population is a predator of a larger prey–predator system. To this end, we analyze a prey–predator fish community model in a two-site environment and compute catch at Maximum Sustainable Yield (MSY). We exhibit some emergence phenomenon: the total catch can be greater than the sum of the catch at two isolated sites due to connectivity. This result is obtained when the two sites are heterogeneous. We show that the increase in capture at MSY is maximal for a certain value of the carrying capacity of the second site, all other parameters remaining constant, including the carrying capacity of the first site. A stronger phenomenon can also be observed: even if none of the sites is viable for fishing, the entire system can be viable. We then study the effects of the heterogeneity of the sites and illustrate our results through simulations. It is shown that the excess yield at MSY can become very significant when the characteristics of the prey and predator in terms of potential growth are opposite at each site.</p></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"595 ","pages":"Article 111913"},"PeriodicalIF":1.9,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142146819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Polymorphic population expansion velocity in a heterogeneous environment 异质环境中的多态种群扩展速度。

IF 1.9 4区数学

Journal of Theoretical Biology Pub Date : 2024-09-05 DOI: 10.1016/j.jtbi.2024.111932

L. Roques , N. Boutillon , P. Zamberletti , J. Papaïx

{"title":"Polymorphic population expansion velocity in a heterogeneous environment","authors":"L. Roques , N. Boutillon , P. Zamberletti , J. Papaïx","doi":"10.1016/j.jtbi.2024.111932","DOIUrl":"10.1016/j.jtbi.2024.111932","url":null,"abstract":"<div><p>How does the spatial heterogeneity of landscapes interact with the adaptive evolution of populations to influence their spreading speed? This question arises in agricultural contexts where a pathogen population spreads in a landscape composed of several types of crops, as well as in epidemiological settings where a virus spreads among individuals with distinct immune profiles. To address it, we introduce an analytical method based on reaction–diffusion models. We focus on spatially periodic environments with two distinct patches, where the dispersing population consists of two specialized morphs, each potentially mutating to the other. We present new formulas for the speed together with criteria for persistence, accounting for both rapidly and slowly varying environments, as well as small and large mutation rates. Altogether, our analytical and numerical results yield a comprehensive understanding of persistence and spreading dynamics. In particular, compared to a situation without mutations or to a single morph spreading in a heterogeneous landscape, the introduction of mutations to a second morph with reverse specialization, while consistently impeding persistence, can significantly increase speed, even if the mutation rate between the two morphs is very small. Additionally, we find that the amplitude of the spatial fragmentation effect is significantly increased in this case. This has implications for agroecology, emphasizing the higher importance of landscape structure in influencing adaptation-driven population dynamics.</p></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"595 ","pages":"Article 111932"},"PeriodicalIF":1.9,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142146820","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An approximate solution of the SLIP model under the regime of linear angular dynamics during stance and the stability of symmetric periodic running gaits 站立期间线性角动力学机制下 SLIP 模型的近似解法以及对称周期性跑步步态的稳定性。

IF 1.9 4区数学

Journal of Theoretical Biology Pub Date : 2024-09-04 DOI: 10.1016/j.jtbi.2024.111934

Alessandro Maria Selvitella , Kathleen Lois Foster

{"title":"An approximate solution of the SLIP model under the regime of linear angular dynamics during stance and the stability of symmetric periodic running gaits","authors":"Alessandro Maria Selvitella , Kathleen Lois Foster","doi":"10.1016/j.jtbi.2024.111934","DOIUrl":"10.1016/j.jtbi.2024.111934","url":null,"abstract":"<div><p>Terrestrial locomotion is a complex phenomenon that is often linked to the survival of an individual and of an animal species. Mathematical models seek to express in quantitative terms how animals move, but this is challenging because the ways in which the nervous and musculoskeletal systems interact to produce body movement is not completely understood. Models with many variables tend to lack biological interpretability and describe the motion of an animal with too many independent degrees of freedom. Instead, reductionist models aim to describe the essential features of a gait with the smallest number of variables, often concentrating on the center of mass dynamics. In particular, spring–mass models have been successful in extracting and describing important characteristics of running. In this paper, we consider the spring loaded inverted pendulum model under the regime of constant angular velocity, small compression, and small angle swept during stance. We provide conditions for the asymptotic stability of periodic trajectories for the full range of parameters. The hypothesis of linear angular dynamics during stance is successfully tested on publicly available human data of individuals running on a treadmill at different velocities. Our analysis highlights a novel bifurcation phenomenon for varying <em>Froude number</em>: there are periodic trajectories of the spring loaded inverted pendulum model that are stable only in a restricted range of <em>Froude numbers</em>, while they become unstable for smaller or larger <em>Froude numbers</em>.</p></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"595 ","pages":"Article 111934"},"PeriodicalIF":1.9,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022519324002194/pdfft?md5=0493b950fcf6e94cd914fad010fbf3ec&pid=1-s2.0-S0022519324002194-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142146818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Identifiability of speciation times under the multispecies coalescent 多物种聚合下物种形成时间的可识别性

IF 1.9 4区数学

Journal of Theoretical Biology Pub Date : 2024-08-30 DOI: 10.1016/j.jtbi.2024.111927

Laura Kubatko , Alexander Leonard , Julia Chifman

{"title":"Identifiability of speciation times under the multispecies coalescent","authors":"Laura Kubatko , Alexander Leonard , Julia Chifman","doi":"10.1016/j.jtbi.2024.111927","DOIUrl":"10.1016/j.jtbi.2024.111927","url":null,"abstract":"<div><p>The advent of rapid and inexpensive sequencing technologies has necessitated the development of computationally efficient methods for analyzing sequence data for many genes simultaneously in a phylogenetic framework. The coalescent process is the most commonly used model for linking the underlying genealogies of individual genes with the global species-level phylogeny, but inference under the coalescent model is computationally daunting in the typical inference frameworks (e.g., the likelihood and Bayesian frameworks) due to the dimensionality of the space of both gene trees and species trees. Here we consider estimation of the branch lengths in fixed species trees with three or four taxa, and show that these branch lengths are identifiable. We also show that for three and four taxa simple estimators for the branch lengths can be derived based on observed site pattern frequencies. Properties of these estimators, such as their asymptotic variances and large-sample distributions, are examined, and performance of the estimators is assessed using simulation. Finally, we use these estimators to develop a hypothesis test that can be used to delimit species under the coalescent model for three or four putative taxa.</p></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"595 ","pages":"Article 111927"},"PeriodicalIF":1.9,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142114874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0