Journal of Theoretical Biology最新文献

{"title":"Uncertainty quantification for the random HIV dynamical model driven by drug adherence","authors":"Dingding Yan ,&nbsp;Mengqi He ,&nbsp;Sanyi Tang","doi":"10.1016/j.jtbi.2024.111895","DOIUrl":"10.1016/j.jtbi.2024.111895","url":null,"abstract":"<div><p>In HIV drug therapy, the high variability of CD<span><math><msup><mrow><mn>4</mn></mrow><mrow><mo>+</mo></mrow></msup></math></span> T cells and viral loads brings uncertainty to the determination of treatment options and the ultimate treatment efficacy, which may be the result of poor drug adherence. We develop a dynamical HIV model coupled with pharmacokinetics, driven by drug adherence as a random variable, and systematically study the uncertainty quantification, aiming to construct the relationship between drug adherence and therapeutic effect. Using adaptive generalized polynomial chaos, stochastic solutions are approximated as polynomials of input random parameters. Numerical simulations show that results obtained by this method are in good agreement, compared with results obtained through Monte Carlo sampling, which helps to verify the accuracy of approximation. Based on these expansions, we calculate the time-dependent probability density functions of this system theoretically and numerically. To verify the applicability of this model, we fit clinical data of four HIV patients, and the goodness of fit results demonstrate that the proposed random model depicts the dynamics of HIV well. Sensitivity analyses based on the Sobol index indicate that the randomness of drug effect has the greatest impact on both CD<span><math><msup><mrow><mn>4</mn></mrow><mrow><mo>+</mo></mrow></msup></math></span> T cells and viral loads, compared to random initial values, which further highlights the significance of drug adherence. The proposed models and qualitative analysis results, along with monitoring CD<span><math><msup><mrow><mn>4</mn></mrow><mrow><mo>+</mo></mrow></msup></math></span> T cells counts and viral loads, evaluate the influence of drug adherence on HIV treatment, which helps to better interpret clinical data with fluctuations and makes several contributions to the design of individual-based optimal antiretroviral strategies.</p></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"592 ","pages":"Article 111895"},"PeriodicalIF":1.9,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141538944","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}

{"title":"Evolution of cooperation in social dilemmas with assortment in finite populations","authors":"Éloi Martin,&nbsp;Sabin Lessard","doi":"10.1016/j.jtbi.2024.111891","DOIUrl":"10.1016/j.jtbi.2024.111891","url":null,"abstract":"<div><p>We investigate conditions for the evolution of cooperation in social dilemmas in finite populations with assortment of players by group founders and general payoff functions for cooperation and defection within groups. Using a diffusion approximation in the limit of a large population size that does not depend on the precise updating rule, we show that the first-order effect of selection on the fixation probability of cooperation when represented once can be expressed as the difference between time-averaged payoffs with respect to effective time that cooperators and defectors spend in direct competition in the different group states. Comparing this fixation probability to its value under neutrality and to the corresponding fixation probability for defection, we deduce conditions for the evolution of cooperation. We show that these conditions are generally less stringent as the level of assortment increases under a wide range of assumptions on the payoffs such as additive, synergetic or discounted benefits for cooperation, fixed cost for cooperation and threshold benefit functions. This is not necessarily the case, however, when payoffs in pairwise interactions are multiplicatively compounded within groups.</p></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"592 ","pages":"Article 111891"},"PeriodicalIF":1.9,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022519324001759/pdfft?md5=6a416d397b4df0af395652ea8a795f62&pid=1-s2.0-S0022519324001759-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141472739","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}

{"title":"Data-driven mathematical modeling of sleep consolidation in early childhood","authors":"","doi":"10.1016/j.jtbi.2024.111892","DOIUrl":"10.1016/j.jtbi.2024.111892","url":null,"abstract":"<div><p>Across early childhood development, sleep behavior transitions from a biphasic pattern (a daytime nap and nighttime sleep) to a monophasic pattern (only nighttime sleep). The transition to consolidated nighttime sleep, which occurs in most children between 2- and 5-years-old, is a major developmental milestone and reflects interactions between the developing homeostatic sleep drive and circadian system. Using a physiologically-based mathematical model of the sleep-wake regulatory network constrained by observational and experimental data from preschool-aged participants, we analyze how developmentally-mediated changes in the homeostatic sleep drive may contribute to the transition from napping to non-napping sleep patterns. We establish baseline behavior by identifying parameter sets that model typical 2-year-old napping behavior and 5-year-old non-napping behavior. Then we vary six model parameters associated with the dynamics of and sensitivity to the homeostatic sleep drive between the 2-year-old and 5-year-old parameter values to induce the transition from biphasic to monophasic sleep. We analyze the individual contributions of these parameters to sleep patterning by independently varying their age-dependent developmental trajectories. Parameters vary according to distinct evolution curves and produce bifurcation sequences representing various ages of transition onset, transition durations, and transitional sleep patterns. Finally, we consider the ability of napping and non-napping light schedules to reinforce napping or promote a transition to consolidated sleep, respectively. These modeling results provide insight into the role of the homeostatic sleep drive in promoting interindividual variability in developmentally-mediated transitions in sleep behavior and lay foundations for the identification of light- or behavior-based interventions that promote healthy sleep consolidation in early childhood.</p></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"593 ","pages":"Article 111892"},"PeriodicalIF":1.9,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022519324001760/pdfft?md5=7deec2791c33f05f7c1c56c9503f77f4&pid=1-s2.0-S0022519324001760-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141472738","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}

{"title":"Computational model of the cancer necrotic core formation in a tumor-on-a-chip device","authors":"Elton Diêgo Bonifácio ,&nbsp;Cleudmar Amaral Araújo ,&nbsp;Marcília Valéria Guimarães ,&nbsp;Márcio Peres de Souza ,&nbsp;Thiago Parente Lima ,&nbsp;Bethânia Alves de Avelar Freitas ,&nbsp;Libardo Andrés González-Torres","doi":"10.1016/j.jtbi.2024.111893","DOIUrl":"10.1016/j.jtbi.2024.111893","url":null,"abstract":"<div><p>The mechanisms underlying the formation of necrotic regions within avascular tumors are complex and poorly understood. In this paper, we investigate the formation of a necrotic core in a 3D tumor cell culture within a microfluidic device, considering oxygen, nutrients, and the microenvironment acidification by means of a computational-mathematical model. Our objective is to simulate cell processes, including proliferation and death inside a microfluidic device, according to the microenvironmental conditions. We employed approximation utilizing finite element models taking into account glucose, oxygen, and hydrogen ions diffusion, consumption and production, as well as cell proliferation, migration and death, addressing how tumor cells evolve under different conditions. The resulting mathematical model was examined under different scenarios, being capable of reproducing cell death and proliferation under different cell concentrations, and the formation of a necrotic core, in good agreement with experimental data reported in the literature. This approach not only advances our fundamental understanding of necrotic core formation but also provides a robust computational platform to study personalized therapeutic strategies, offering an important tool in cancer research and treatment design.</p></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"592 ","pages":"Article 111893"},"PeriodicalIF":1.9,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141472737","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}

{"title":"Minimal cellular automaton model with heterogeneous cell sizes predicts epithelial colony growth","authors":"Steffen Lange ,&nbsp;Jannik Schmied ,&nbsp;Paul Willam ,&nbsp;Anja Voss-Böhme","doi":"10.1016/j.jtbi.2024.111882","DOIUrl":"10.1016/j.jtbi.2024.111882","url":null,"abstract":"<div><p>Regulation of cell proliferation is a crucial aspect of tissue development and homeostasis and plays a major role in morphogenesis, wound healing, and tumor invasion. A phenomenon of such regulation is contact inhibition, which describes the dramatic slowing of proliferation, cell migration and individual cell growth when multiple cells are in contact with each other. While many physiological, molecular and genetic factors are known, the mechanism of contact inhibition is still not fully understood. In particular, the relevance of cellular signaling due to interfacial contact for contact inhibition is still debated. Cellular automata (CA) have been employed in the past as numerically efficient mathematical models to study the dynamics of cell ensembles, but they are not suitable to explore the origins of contact inhibition as such agent-based models assume fixed cell sizes. We develop a minimal, data-driven model to simulate the dynamics of planar cell cultures by extending a probabilistic CA to incorporate size changes of individual cells during growth and cell division. We successfully apply this model to previous in-vitro experiments on contact inhibition in epithelial tissue: After a systematic calibration of the model parameters to measurements of single-cell dynamics, our CA model quantitatively reproduces independent measurements of emergent, culture-wide features, like colony size, cell density and collective cell migration. In particular, the dynamics of the CA model also exhibit the transition from a low-density confluent regime to a stationary postconfluent regime with a rapid decrease in cell size and motion. This implies that the volume exclusion principle, a mechanical constraint which is the only inter-cellular interaction incorporated in the model, paired with a size-dependent proliferation rate is sufficient to generate the observed contact inhibition. We discuss how our approach enables the introduction of effective bio-mechanical interactions in a CA framework for future studies.</p></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"592 ","pages":"Article 111882"},"PeriodicalIF":1.9,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022519324001668/pdfft?md5=99b3e3ab9d3771b9d069c7b542e30ddd&pid=1-s2.0-S0022519324001668-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141472766","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}

{"title":"Leading edge of the a-wave of the electroretinogram and sodium iodate-induced age-related macular degeneration: A model","authors":"Deepak K. Pattanaik ,&nbsp;Vasudevan Lakshminarayanan ,&nbsp;Nachieketa K Sharma ,&nbsp;Amir Prasad Sahu","doi":"10.1016/j.jtbi.2024.111879","DOIUrl":"10.1016/j.jtbi.2024.111879","url":null,"abstract":"<div><h3>Background</h3><p>Iron-induced oxidative stress was thought to be the reason why the <em>a</em>-wave amplitude of the electroretinogram (ERG) dropped when iron ions were present.</p><p>It is assumed that reactive oxygen species (ROS) are generated in the presence of iron ions, and this leads to a decrease in hyperpolarization of the photoreceptor. It is known that in age-related macular degeneration (AMD), sodium iodate can induce oxidative stress, apoptosis, and retinal damage, which mimic the effects of clinical AMD. Here, the reduction of the <em>a</em>-wave amplitude in mice with sodium iodate-induced age-related macular degeneration is explained.</p></div><div><h3>Methods</h3><p>The leading edge of the <em>a</em>-wave is divided into voltages developed by cones and rods. The same oxidative stress model is applied here since sodium iodate causes the creation of ROS in a manner similar to that caused by iron ions, with the exception that the retina is treated as a circuit of various resistances when computing the photoresponse. Moreover, sodium iodate also leads to apoptosis and, hence, may cause misalignment in cones (not in rods) during the initial stage of apoptosis in AMD. To include the effects of apoptosis and shortening in cones and rods, we have used a factor representing the fraction of total cones and rods that are alive. To include the effect of misalignment of cones on the reduction of the <em>a</em>-wave amplitude, we have used the Stiles-Crawford function to calculate the number of photoisomerizations occurring in a photoreceptor misaligned at an angle θ. The results are compared with experimental data.</p></div><div><h3>Results</h3><p>In sodium iodate-treated eyes, the ROS produced can attract calcium ions in the photoreceptor, which increases the calcium influx. In the case of the cones, the inclusion of the misalignment angle in the phototransduction process helps in determining the voltage and slope of the voltage vs. time graph.<!--> <!-->The smaller the fraction of active photoreceptors, the smaller the amplitude of the <em>a</em>-wave. The calcium influx, misaligned photoreceptors, and total photoreceptor loss all cause the amplitude of the <span><math><mi>a</mi></math></span>-wave to decrease, and at any time from the beginning of phototransduction cascade, the calcium influx causes the slope of the <em>a</em>-wave to increase.</p></div><div><h3>Conclusion</h3><p>The reduction in the <em>a</em>-wave amplitude in the eyes of sodium iodate-treated mice is attributed to oxidative stress in both cones and rods and cone misalignment, which ultimately lead to apoptosis and vision loss in AMD.</p></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"592 ","pages":"Article 111879"},"PeriodicalIF":1.9,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141443775","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}

{"title":"A model of time-dependent macromolecular and elemental composition of phytoplankton","authors":"Anne Willem Omta ,&nbsp;Justin D. Liefer ,&nbsp;Zoe V. Finkel ,&nbsp;Andrew J. Irwin ,&nbsp;Daniel Sher ,&nbsp;Michael J. Follows","doi":"10.1016/j.jtbi.2024.111883","DOIUrl":"10.1016/j.jtbi.2024.111883","url":null,"abstract":"<div><p>Phytoplankton Chl:C:N:P ratios are important from both an ecological and a biogeochemical perspective. We show that these elemental ratios can be represented by a phytoplankton physiological model of low complexity that includes major cellular macromolecular pools. In particular, our model resolves time-dependent intracellular pools of chlorophyll, proteins, nucleic acids, carbohydrates/lipids, and N and P storage. Batch culture data for two diatom and two prasinophyte species are used to constrain parameters that represent specific allocation traits and strategies. A key novelty is the simultaneous estimation of physiological parameters for two phytoplankton groups of such different sizes. The number of free parameters is reduced by assuming (i) allometric scaling for maximum uptake rates, (ii) shared half-saturation constants for synthesis of functional macromolecules, (iii) shared exudation rates of functional macromolecules across the species. The rationale behind this assumption is that across the different species, the same or similar processes, enzymes, and metabolites play a role in key physiological processes. For the turnover numbers of macromolecular synthesis and storage exudation rates, differences between diatoms and prasinophytes need to be taken into account to obtain a good fit. Our model fits suggest that the parameters related to storage dynamics dominate the differences in the C:N:P ratios between the different phytoplankton groups. Since descriptions of storage dynamics are still incomplete and imprecise, predictions of C:N:P ratios by phytoplankton models likely have a large uncertainty.</p></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"592 ","pages":"Article 111883"},"PeriodicalIF":1.9,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S002251932400167X/pdfft?md5=c44ef3b5f6ed41769ed8403d0f1dc0b2&pid=1-s2.0-S002251932400167X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141441160","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}

{"title":"A mathematical model of signalling molecule-mediated processes during regeneration of osteochondral defects after chondrocyte implantation","authors":"Kelly Campbell ,&nbsp;Shailesh Naire ,&nbsp;Jan Herman Kuiper","doi":"10.1016/j.jtbi.2024.111874","DOIUrl":"10.1016/j.jtbi.2024.111874","url":null,"abstract":"<div><p>Treating bone-cartilage defects is a fundamental clinical problem. The ability of damaged cartilage to self-repair is limited due to its avascularity. Left untreated, these defects can lead to osteoarthritis. Details of osteochondral defect repair are elusive, but animal models indicate healing occurs via an endochondral ossification-like process, similar to that in the growth plate. In the growth plate, the signalling molecules parathyroid hormone-related protein (PTHrP) and Indian Hedgehog (Ihh) form a feedback loop regulating chondrocyte hypertrophy, with Ihh inducing and PTHrP suppressing hypertrophy. To better understand this repair process and to explore the regulatory role of signalling molecules on the regeneration process, we formulate a reaction–diffusion mathematical model of osteochondral defect regeneration after chondrocyte implantation. The drivers of healing are assumed to be chondrocytes and osteoblasts, and their interaction via signalling molecules. We model cell proliferation, migration and chondrocyte hypertrophy, and matrix production and conversion, spatially and temporally. We further model nutrient and signalling molecule diffusion and their interaction with the cells. We consider the PTHrP-Ihh feedback loop as the backbone mechanisms but the model is flexible to incorporate extra signalling mechanisms if needed. Our mathematical model is able to represent repair of osteochondral defects, starting with cartilage formation throughout the defect. This is followed by chondrocyte hypertrophy, matrix calcification and bone formation deep inside the defect, while cartilage at the surface is maintained and eventually separated from the deeper bone by a thin layer of calcified cartilage. The complete process requires around 48 months. A key highlight of the model demonstrates that the PTHrP-Ihh loop alone is insufficient and an extra mechanism is required to initiate chondrocyte hypertrophy, represented by a critical cartilage density. A parameter sensitivity study reveals that the timing of the repair process crucially depends on parameters, such as the critical cartilage density, and those describing the actions of PTHrP to suppress hypertrophy, such as its diffusion coefficient, threshold concentration and degradation rate.</p></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"592 ","pages":"Article 111874"},"PeriodicalIF":1.9,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022519324001589/pdfft?md5=3edc20bc97ae2fa4e3e89f60731d2445&pid=1-s2.0-S0022519324001589-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141441159","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}

{"title":"Range-limited Heaps’ law for functional DNA words in the human genome","authors":"Wentian Li ,&nbsp;Yannis Almirantis ,&nbsp;Astero Provata","doi":"10.1016/j.jtbi.2024.111878","DOIUrl":"10.1016/j.jtbi.2024.111878","url":null,"abstract":"<div><p>Heaps’ or Herdan-Heaps’ law is a linguistic law describing the relationship between the vocabulary/dictionary size (type) and word counts (token) to be a power-law function. Its existence in genomes with certain definition of DNA words is unclear partly because the dictionary size in genome could be much smaller than that in a human language. We define a DNA word as a coding region in a genome that codes for a protein domain. Using human chromosomes and chromosome arms as individual samples, we establish the existence of Heaps’ law in the human genome within limited range. Our definition of words in a genomic or proteomic context is different from other definitions such as over-represented k-mers which are much shorter in length. Although an approximate power-law distribution of protein domain sizes due to gene duplication and the related Zipf’s law is well known, their translation to the Heaps’ law in DNA words is not automatic. Several other animal genomes are shown herein also to exhibit range-limited Heaps’ law with our definition of DNA words, though with various exponents. When tokens were randomly sampled and sample sizes reach to the maximum level, a deviation from the Heaps’ law was observed, but a quadratic regression in log–log type-token plot fits the data perfectly. Investigation of type-token plot and its regression coefficients could provide an alternative narrative of reusage and redundancy of protein domains as well as creation of new protein domains from a linguistic perspective.</p></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"592 ","pages":"Article 111878"},"PeriodicalIF":1.9,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141433402","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}

{"title":"Corrigendum to “From the Price equation to the selection gradient in class-structured populations: A quasi-equilibrium route” [J. Theor. Biol. 447 (2018) 178–189]","authors":"Sébastien Lion","doi":"10.1016/j.jtbi.2024.111873","DOIUrl":"https://doi.org/10.1016/j.jtbi.2024.111873","url":null,"abstract":"","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":"591 ","pages":"Article 111873"},"PeriodicalIF":2.0,"publicationDate":"2024-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022519324001577/pdfft?md5=dfad351749022dd305140874fde4741a&pid=1-s2.0-S0022519324001577-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141322912","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}