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In this paper, we present a model that explains the prepatterning of lymphatic vessel morphology in collagen gels. This model is derived using the theory of two phase rubber material due to Flory and coworkers and it consists of t...
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In this paper, we present a model that explains the prepatterning of lymphatic vessel morphology in collagen gels. This model is derived using the theory of two phase rubber material due to Flory and coworkers and it consists of two coupled fourth order partial differential equations describing the evolution of the collagen volume fraction, and the evolution of the proton concentration in a collagen implant; as described in experiments of Boardman and Swartz (Circ. Res. 92, 801–808, 2003). Using linear stability analysis, we find that above a critical level of proton concentration, spatial patterns form due to small perturbations in the initially uniform steady state. Using a long wavelength reduction, we can reduce the two coupled partial differential equations to one fourth order equation that is very similar to the Cahn–Hilliard equation; however, it has more complex nonlinearities and degeneracies. We present the results of numerical simulations and discuss the biological implications of our model.
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Mathematics anxiety is one of the influential factors on students' mathematical performance as a negative relationship between students' mathematics anxiety and mathematical performances has been frequently reported. Predicting st...
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Mathematics anxiety is one of the influential factors on students' mathematical performance as a negative relationship between students' mathematics anxiety and mathematical performances has been frequently reported. Predicting students' mathematics anxiety can help educators to have a better understanding of students, and potentially could help them to know if specific interventions are needed to design to control students' anxiety level. Epidemiology is the study of the distribution of diseases and other health matters. Recently, epidemiological modeling has been widely used as a tool to predict future behaviors in social sciences, economics, and disease progression. In the present study, an epidemiological model is designed to predict undergraduate students' mathematics anxiety level. The findings show that a high percentage of students, approximately 70%, will suffer from high mathematics anxiety in near future.
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Duchenne Muscular Dystrophy (DMD) is a common X-linked disease, caused by mutations in the gene encoding dystrophin and characterized by widespread muscle damage that invariably leads to paralysis and death. Lack of dystrophin in ...
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Duchenne Muscular Dystrophy (DMD) is a common X-linked disease, caused by mutations in the gene encoding dystrophin and characterized by widespread muscle damage that invariably leads to paralysis and death. Lack of dystrophin in the muscles of DMD patients determines an increased fragility of muscle fibers, leading to repeated cycles of necrosis and regeneration that result in failed regeneration, increased fibrosis and progressive loss of muscle function.In this work, we propose a three-dimensional chemo-mechanical mathematical model of skeletal muscle in DMD. This model is based on stress-strain mechanical data of the muscle and studies of changes in fiber structure and interaction aiming to shade light into the biophysical mechanisms regulating muscle contraction. The results show that the model is able to reproduce the experimental data of maximum isometric force, maximum contraction velocity and concentric normalized F-V curve for the healthy and dystrophic muscle. Furthermore, the model is capable of predicting the force-velocity response of the muscle to eccentric loading without explicitly imposing its functional form in the formulation, and it is able to reproduce the concentric normalized F-V curve of the healthy fiber, as an additional proof of the predictive capabilities of the model. The resulting model represents a novel approach to study DMD pathogenesis by providing insights into the underlying mechanisms of muscle response to force associated with the impaired muscle functionality. Moreover, it could be an innovative tool for researchers to predict muscle response under conditions that are not possible to explore in the laboratory and an important step towards a new paradigm of in-silico trials that could allow identifying novel therapies bypassing the use of animal models. (C) 2019 Elsevier Ltd. All rights reserved.
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Question: How does selection mediated by a spatially spreading disturbance affect individual-level dispersal and population-level spatial structure? Model features: We start with a birth-death process on a lattice and introduce a ...
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Question: How does selection mediated by a spatially spreading disturbance affect individual-level dispersal and population-level spatial structure? Model features: We start with a birth-death process on a lattice and introduce a spatially spreading disturbance. We consider three different scenarios affecting whether an individual recovers from disturbance, corresponding to different trade-offs between short- and longdistance dispersal. Analytic methods: In addition to computer simulation, we use a pair approximation to conduct an invasion analysis of different dispersal strategies. Conclusions: Of the trade-offs we examined, only a context-sensitive recovery, in which an individual's survival probability is enhanced by the presence of weaker neighbours, results in a mixed dispersal strategy.
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Tumors are complex multicellular heterogeneous systems comprised of components that interact with and modify one another. Tumor development depends on multiple factors: intrinsic, such as genetic mutations, altered signaling pathw...
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Tumors are complex multicellular heterogeneous systems comprised of components that interact with and modify one another. Tumor development depends on multiple factors: intrinsic, such as genetic mutations, altered signaling pathways, or variable receptor expression; and extrinsic, such as differences in nutrient supply, crosstalk with stromal or immune cells, or variable composition of the surrounding extracellular matrix. Tumors are also characterized by high cellular heterogeneity and dynamically changing tumor microenvironments. The complexity increases when this multiscale, multicomponent system is perturbed by anticancer treatments. Modeling such complex systems and predicting how tumors will respond to therapies require mathematical models that can handle various types of information and combine diverse theoretical methods on multiple temporal and spatial scales, that is, hybrid models. In this update, we discuss the progress that has been achieved during the last 10 years in the area of the hybrid modeling of tumors. The classical definition of hybrid models refers to the coupling of discrete descriptions of cells with continuous descriptions of microenvironmental factors. To reflect on the direction that the modeling field has taken, we propose extending the definition of hybrid models to include of coupling two or more different mathematical frameworks. Thus, in addition to discussing recent advances in discrete/continuous modeling, we also discuss how these two mathematical descriptions can be coupled with theoretical frameworks of optimal control, optimization, fluid dynamics, game theory, and machine learning. All these methods will be illustrated with applications to tumor development and various anticancer treatments. This article is characterized under: Analytical and Computational Methods > Computational Methods Translational, Genomic, and Systems Medicine > Therapeutic Methods Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models
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Consumer-resource interactions with intraguild predation (IGP) were studied in a spatial setting (i.e., predators catch prey and individuals reproduce within local neighborhoods only). Pair approximation (a method for deriving ord...
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Consumer-resource interactions with intraguild predation (IGP) were studied in a spatial setting (i.e., predators catch prey and individuals reproduce within local neighborhoods only). Pair approximation (a method for deriving ordinary differential equations that approximate the dynamics of a community that interacts in a lattice environment) was used to study the effect of spatially structured species interactions. An individual-based computer simulation was used to extend the study to a case with spatially variable resource densities. The qualitative results of the pair approximation model were similar to those of the corresponding non-spatial model. However, the spatial model predicted coex((istence over a wider range of parameters than the non-spatial model when intraguild prey are nutritionally valuable to intraguild predators. Spatially heterogeneous resource distributions and spatially structured interaction could overturn the qualitative predictions of non-spatial models.
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It is well-known that the classical SIR model is unable to make accurate predictions on the course of illnesses such as COVID-19. In this paper, we show that the official data released by the authorities of several countries (Ital...
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It is well-known that the classical SIR model is unable to make accurate predictions on the course of illnesses such as COVID-19. In this paper, we show that the official data released by the authorities of several countries (Italy, Spain and The USA) regarding the expansion of COVID-19 are compatible with a non-autonomous SIR type model with vital dynamics and non-constant population, calibrated according to exponentially decaying infection and death rates. Using this calibration we construct a model whose outcomes for most relevant epidemiological paramenters, such as the number of active cases, cumulative deaths, daily new deaths and daily new cases (among others) fit available real data about the first and successive waves of COVID-19. In addition to this, we also provide predictions on the evolution of this pandemic in Italy and the USA in several plausible scenarios. (c) 2021 Elsevier Ltd. All rights reserved.
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During disasters and emergencies (earthquakes, pandemics, economic crises etc.), we also face a second challenge, pollution of information. The transmitted information may be false, potentially harmful and speculative. Today, the ...
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During disasters and emergencies (earthquakes, pandemics, economic crises etc.), we also face a second challenge, pollution of information. The transmitted information may be false, potentially harmful and speculative. Today, the main source of information seems to be the social media, which behaves as a vector via sharing news. In this manuscript, the concept of the transmission dynamics of vector-borne diseases is adapted to the transmission dynamics of vector-borne disinformation. The dynamical behavior of the model is analyzed, the disinformation-free and disinformation endemic equilibria of the model are found and both their local and global stabilities are presented. Finally, numerical simulations are carried out to support the analytical results of the dynamical transmission of disinformation.(C) 2022 Elsevier B.V. All rights reserved.
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В связи с развитием мировой торговли у металлургических комбинатов появилась большая вариативность при составлении произво...
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В связи с развитием мировой торговли у металлургических комбинатов появилась большая вариативность при составлении производственного плана. На АО ?ЕВРАЗ Западно-Сибирский металлургический комбинат? (АО ?ЕВРАЗ ЗСМК?) шихту оптимизируют из 110 компонентов только в части агломерационного и доменного производств. Номенклатура выпускаемой продукции состоит более чем из 2000 единиц и меняется от месяца к месяцу. Обычно производственный план оптимизируют только внутри отдельных переделов. Целью оптимизации является минимизация себестоимости передела и максимизация производства. В работе представлены разработка и внедрение системы математического моделирования производства всего металлургического комбината на примере АО ?ЕВРАЗ ЗСМК?. В отличие от существующих систем моделирования переделов целью системы является единовременная сквозная оптимизация всех переделов комбината. Конечная цель - максимизация прибыли всего комбината. В процессе эксплуатации новой системы в 2019-2020 гг. были обнаружены высокие трудозатраты при работе пользователей. Например, совершается более 10 000 те
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