资源竞争理论及其研究进展

介绍了国外近20年来发展起来的一种新的竞争理论——资源竞争理论。该理论包含两个主要假说,即R^*-法则和资源比假说。资源竞争理论已在微生物、微藻、高等植物及浮游动物中得到广泛的实验验证。阐述了资源竞争理论形成的基础——Monod竞争模型和Droop竞争模型。对两种模型在稳态及非稳态条件下的预测性能作了比较：对于稳态下的竞争,两种模型皆能做出较好的预测,但使用Monod模型更为简便;对于非稳态下的竞争,使用Droop模型更为合理。对资源竞争理论的发展趋势作了展望。     

二次自催化反应系统的极限环

本文用化学动力学的理论建立了一个二次自催化反应的数学模型,并用定性理论对模型作了定性分析,得到了该模型在大范围内极限环的唯一性的结果．     

土壤水分含量的理论分析及预测模型

本文应用物理学中的电介质和电磁理论,分析和研究土壤的组成成分,得到了反映土壤水分含量的理论表达式,并在自行研制的测试仪器上,对相关变量进行测量,由此建立了土壤水分含量的预测模型,统计检验和国代结果显示了理论模型和预测模型的合理性．     

Cybernetics and biology

Owing to methodical disadvantages, the theory of control still lacks the potential for the analysis of biological systems. To get the full benefit of the method in addition to the algorithmic model of control (as of today the only used model in the theory of control) a parametric model of control is offered to employ. The reasoning for it is explained. The approach suggested provides the possibility to use all potential of the modern theory of control for the analysis of biological systems. The cybernetic approach is shown taking a system of the rise of glucose concentration in blood as an example.     

A model of growth and rupture of abdominal aortic aneurysm

We present here a coupled mathematical model of growth and failure of the abdominal aortic aneurysm (AAA). The failure portion of the model is based on the constitutive theory of softening hyperelasticity where the classical hyperelastic law is enhanced with a new constant indicating the maximum energy that an infinitesimal material volume can accumulate without failure. The new constant controls material failure and it can be interpreted as the average energy of molecular bonds from the microstructural standpoint. The constitutive model is compared to the data from uniaxial tension tests providing an excellent fit to the experiment. The AAA failure model is coupled with a phenomenological theory of soft tissue growth. The unified theory includes both momentum and mass balance laws coupled with the help of the constitutive equations. The microstructural alterations in the production of elastin and remodeling of collagen are reflected in the changing macroscopic parameters characterizing tissue stiffness, strength and density. The coupled theory is used to simulate growth and rupture of an idealized spherical AAA. The results of the simulation showing possible AAA ruptures in growth are reasonable qualitatively while the quantitative calibration of the model will require further clinical observations and in vitro tests. The presented model is the first where growth and rupture are coupled.     

A simple theory of motor protein kinetics and energetics

A simple stochastic theory for kinetics and energetics of the movement of single motor proteins is presented. The model combines the biochemical cycle of nucleotide hydrolysis with the motor protein translocation. Based on the theory of Markov processes, the model provides the force-velocity relationship, the isometric force, and the stochastic stepping of the motor protein along its one-dimensional track. The theoretical model provides a conceptual framework for realistic studies of motor proteins. Relationship between the present theory and other existing models is discussed.     

A theory of natural selection incorporating interaction among individuals. I. The modeling process

Short- and long-term consequences of natural selection, operating in accordance with the classical (non-interaction) model, are reviewed. This review provides the basis for comparisons of the optimum results of the classical model with the results from interaction models. Then as a first step, the simplest interaction modeling system (Model I) is developed subject to the following conditions: (i) The natural selection model is constructed so that it is compatible with the one that already exists for artificial selection theory. This condition ensures that an overall theory is formulated which embraces both natural and artificial selection with a single modeling system and a common notation. (ii) The interaction theory is developed so that it is an extension of the classical theory. This condition ensures that the generalized theory includes the classical results as a special case when interaction is absent.The short- and long-term consequences of selection operating with Model I are determined to be less than optimal when compared with the classical results. Future papers in this series will consider how the interaction model can be modified in order to produce results which tend toward optimality.     

Note on the spread of a state in small social groups

A model is developed for the spread of a state in small social groups. Under suitable assumptions the model exhibits formal identity with Markov chain theory. The basic theorems and classifications of Markov chain theory are stated and interpreted in terms of the model. Finally, some procedures for testing the model are indicated.     

Flutter in collapsible tubes: a theoretical model of wheezes

A mathematical analysis of flow through a flexible channel is examined as a model of flow-induced flutter oscillations that pertain to the production of wheezing breath sounds. The model provides predictions for the critical fluid speed that will initiate flutter waves of the wall, as well as their frequency and wavelength. The mathematical results are separated into linear theory (small oscillations) and nonlinear theory (larger oscillations). Linear theory determines the onset of the flutter, whereas nonlinear theory determines the relationships between the fluid speed and both the wave amplitudes and frequencies. The linear theory predictions correlate well with data taken at the onset of flutter and flow limitation during experiments of airflow in thick-walled collapsible tubes. The nonlinear theory predictions correlate well with data taken as these flows are forced to higher velocities while keeping the flow rate constant. Particular ranges of the parameters are selected to investigate and discuss the applications to airway flows. According to this theory, the mechanism of generation of wheezes is based in the interactions of fluid forces and friction and wall elastic-restoring forces and damping. In particular, a phase delay between the fluid pressure and wall motion is necessary. The wave speed theory of flow limitation is discussed with respect to the specific data and the flutter model.     

ARE WARNING COLORS HANDICAPS?

The handicap theory, in which the cost of waste guarantees honest advertising, is being used increasingly in solutions to the problems of biological signal evolution. However, it is usually applied to systems which are insufficiently understood to allow testing against alternative theories. In particular, the ability of the handicap theory to explain the design of signals has never been properly tested. We test its ability to explain signal design features in an unusually well studied area of biological signalling: warning coloration and mimicry. Since a full handicap model proves immediately unrealistic, we modify the model to incorporate realistic assumptions about predator learning. Using this model we explicitly compare the handicap theory with a purely “conventional” signalling model and with a null model. Predictions relating to three key design features (conspicuousness, pattern similarity, and Batesian mimicry) are compared, and tested against available data. Although many predictions remain to be tested adequately, we conclude that: (i) conspicuousness is most plausibly explained by the conventional signalling theory that ascribes the function of conspicuous coloration to signal efficacy rather than waste; (ii) pattern similarity, within and between species, is unlikely to be the result of the need to produce similar degrees of conspicuousness, as predicted by the handicap theory, but is plausibly explained as the result of pattern generalization amongst discriminating predators, as predicted by the conventional signalling theory; and (iii) Batesian mimicry is predicted by the conventional signalling theory, but not the handicap theory. Therefore the handicap theory fails to provide an adequate explanation of the main design features of at least one major signalling system.     

Robustness of circadian rhythms in the presence of molecular fluctuations: an investigation based on a mechanistic, statistical theory and a simulation algorithm

After a very brief introduction to a mechanistic and statistical theory of molecular fluctuations in chemical reactions developed by Joel Keizer, we explore the robustness of a circadian rhythm model by using the theory and the exact stochastic simulation (ESS). The comparative study shows that the theory reflects the effects of the dynamics of the model on the robustness more than ESS does. Even though the theory is a macroscopic one, the robustness of the model compares well with that computed from the ESS when the system size is larger than 50. The robustness increases nonlinearly with the system size and it reaches an asymptotic value at higher system sizes. As we can expect from the dynamics of the system, the robustness is minimum near the bifurcation point and as the most sensitive parameter increases away from the bifurcation point the robustness according to the theory as well as the ESS increases and then reaches to a steady value.     

Theory of passive permeability through lipid bilayers

Recently measured water permeability through bilayers of different lipids is most strongly correlated with the area per lipid A rather than with other structural quantities such as the thickness. This paper presents a simple three-layer theory that incorporates the area dependence in a physically realistic way and also includes the thickness as a secondary modulating parameter. The theory also includes the well-known strong correlation of permeability upon the partition coefficients of general solutes in hydrocarbon environments (Overton's rule). Two mathematical treatments of the theory are given; one model uses discrete chemical kinetics and one model uses the Nernst-Planck continuum equation. The theory is fit to the recent experiments on water permeability in the accompanying paper.     

Games network and application to PAs system

In this article, we present a game theory based framework, named games network, for modeling biological interactions. After introducing the theory, we more precisely describe the methodology to model biological interactions. Then we apply it to the plasminogen activator system (PAs) which is a signal transduction pathway involved in cancer cell migration. The games network theory extends game theory by including the locality of interactions. Each game in a games network represents local interactions between biological agents. The PAs system is implicated in cytoskeleton modifications via regulation of actin and microtubules, which in turn favors cell migration. The games network model has enabled us a better understanding of the regulation involved in the PAs system.     

Using an Hebbian Learning Rule for Multi-Class SVM Classifiers

Regarding biological visual classification, recent series of experiments have enlighten the fact that data classification can be realized in the human visual cortex with latencies of about 100-150 ms, which, considering the visual pathways latencies, is only compatible with a very specific processing architecture, described by models from Thorpe et al. Surprisingly enough, this experimental evidence is in coherence with algorithms derived from the statistical learning theory. More precisely, there is a double link: on one hand, the so-called Vapnik theory offers tools to evaluate and analyze the biological model performances and on the other hand, this model is an interesting front-end for algorithms derived from the Vapnik theory. The present contribution develops this idea, introducing a model derived from the statistical learning theory and using the biological model of Thorpe et al. We experiment its performances using a restrained sign language recognition experiment. This paper intends to be read by biologist as well as statistician, as a consequence basic material in both fields have been reviewed.     

Poromechanics of compressible charged porous media using the theory of mixtures

Osmotic, electrostatic, and/or hydrational swellings are essential mechanisms in the deformation behavior of porous media, such as biological tissues, synthetic hydrogels, and clay-rich rocks. Present theories are restricted to incompressible constituents. This assumption typically fails for bone, in which electrokinetic effects are closely coupled to deformation. An electrochemomechanical formulation of quasistatic finite deformation of compressible charged porous media is derived from the theory of mixtures. The model consists of a compressible charged porous solid saturated with a compressible ionic solution. Four constituents following different kinematic paths are identified: a charged solid and three streaming constituents carrying either a positive, negative, or no electrical charge, which are the cations, anions, and fluid, respectively. The finite deformation model is reduced to infinitesimal theory. In the limiting case without ionic effects, the presented model is consistent with Blot's theory. Viscous drag compression is computed under closed circuit and open circuit conditions. Viscous drag compression is shown to be independent of the storage modulus. A compressible version of the electrochemomechanical theory is formulated. Using material parameter values for bone, the theory predicts a substantial influence of density changes on a viscous drag compression simulation. In the context of quasistatic deformations, conflicts between poromechanics and mixture theory are only semantic in nature.     

Directionality of evolution at molecular and organismic levels.

The molecular evolution theories of Eigen and Kimura are compared and their difference is explained. In terms of Eigen's theory for the evolution of macromolecules, the selection of genotypes occurs directly. The physical meaning of the neutral theory is the degeneracy of the correlation between a phenotype and a genotype at the molecular level. A model theory of evolution on a fitness landscape is proposed. The theory shows that the constraints of selection determined by the structure and dynamics of previous evolution stages increases its rate strongly.     

Parameterizing a model of Douglas fir water flow using a tracheid-level model

The theory of tree water flow proposed in Aumann & Ford (submitted) is assessed by numerically solving the model developed from this theory under a variety of functional parameterizations. The unknown functions in this nonlinear partial differential equation model are determined using a tracheid-level model of water flow in a block of Douglas fir tracheids. The processes of flow, cavitation, pit aspiration/deaspiration, flow through the cell wall and ray exudation in a block of approximately 79 000 tracheids are modeled. Output from the tracheid model facilitates determination of the hydraulic conductivities in the sapwood as a function of saturation and interfacial area between liquid and gaseous phases of water, the function governing the rate of change in saturation, and the function governing the rate of change in interfacial area. The models show complementary things. The tracheid model shows that capacitance, or the change in saturation per change in pressure, is not constant. When all refilling is stopped, it takes over 180 days for the hydraulic conductivity in the vertical direction to reach 1/4 of its maximal value, showing the robustness of the transpiration stream for conducting water. The shape of the functions determined with the tracheid model change with different tracheid-level assumptions. When these functions are used in the differential equation model, it is shown that cell-wall conductivity plays an important part in the lag in flow observed in many conifers. The flow velocities and rates of change in saturation predicted by the differential equation model agree with those measured in Douglas fir. Both models support the theory of tree water flow presented in Aumann & Ford (submitted) and undermine the theory that water flow in trees is analogous to the flow of current in electric circuits.     

Asymptotics applied to a neural network

A mathematical model of neural processing is proposed which incorporates a theory for the storage of information. The model consists of a network of neurons that linearly processes incoming neural activity. The network stores the input by modifying the synaptic properties of all of its neurons. The model lends support to a distributive theory of memory using synaptic modification. The dynamics of the processing and storage are represented by a discrete system. Asymptotic analysis is applied to the system to show the learning capabilities of the network under constant input. Results are also given to predict the network's ability to learn periodic input, and input subjected to small random fluctuations.