Preface |
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xv | |
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Chapter 1 Environmental interface: definition and introductory comments |
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3 | (8) |
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8 | (3) |
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Chapter 2 Advanced theoretician's tools in the modelling of the environmental interface systems |
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11 | (12) |
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2.1 Modelling Architecture |
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11 | (2) |
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2.2 Basics of Category Theory |
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13 | (2) |
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2.3 Basics of Mathematical Theory of General Systems |
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15 | (1) |
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2.4 Formal Concept Analysis in Modelling the Interaction of Living Systems and Their Environments |
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16 | (4) |
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2.5 Basic Concepts of the Chaos Theory |
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20 | (3) |
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21 | (2) |
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Chapter 3 Approaches and meaning of time in the modelling of the environmental interface systems |
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23 | (8) |
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23 | (3) |
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3.2 Continuous Time Versus Discrete Time in Building the Model |
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26 | (2) |
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3.3 Time in Model Building |
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28 | (3) |
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28 | (3) |
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Chapter 4 Examples of use of the formal complex analysis |
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31 | (12) |
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4.1 Use of Formal Complex Analysis in the Context of Animals: An Example |
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31 | (2) |
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4.2 Use of Formal Complex Analysis in Constructing the Subjective Interface Between Biological Systems and Their Environments |
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33 | (10) |
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39 | (4) |
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PART II TIME IN ENVIRONMENTAL INTERFACES MODELLING |
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Chapter 5 Time in philosophy and physics |
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43 | (8) |
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43 | (3) |
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46 | (5) |
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49 | (2) |
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Chapter 6 Time in biology |
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51 | (6) |
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55 | (2) |
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Chapter 7 Functional time: definition and examples |
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57 | (12) |
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7.1 Mollusk Time Reflex Formation |
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58 | (2) |
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7.2 Prisoner Time Formation in the Cell |
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60 | (1) |
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7.3 Functional Time Formation in Process of Biochemical Substance Exchange in Ring of Cells |
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61 | (8) |
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66 | (3) |
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PART III USE OF DIFFERENT COUPLED MAPS IN THE ENVIRONMENTAL INTERFACES MODELLING |
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Chapter 8 Coupled logistic maps in the environmental interfaces modelling |
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69 | (8) |
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8.1 Coupling of Two Logistic Maps |
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69 | (2) |
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8.2 An Example of Diffusive Coupling: Interaction of Two Environmental Interfaces on the Earth's Surface |
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71 | (2) |
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73 | (4) |
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75 | (2) |
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Chapter 9 Logistic difference equation on extended domain |
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77 | (8) |
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9.1 Logistic Equation on Extended Domain: Mathematical Background |
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77 | (3) |
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9.2 Logistic Equation on Extended Domain in Coupled Maps Serving the Combined Coupling: A Dynamical Analysis |
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80 | (5) |
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83 | (2) |
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Chapter 10 Generalized logistic equation with affinity: its use in modelling heterogeneous environmental interfaces |
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85 | (14) |
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10.1 Generalized Logistic Map With Affinity: Mathematical Background |
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85 | (1) |
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10.2 Uncertainties in Modelling the Turbulent Energy Exchange Over the Heterogeneous Environmental Interfaces - Schmidt's Paradox |
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86 | (7) |
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10.3 Use of the Generalized Logistic Equation With Affinity in Modelling the Turbulent Energy Exchange Over the Heterogeneous Environmental Interfaces |
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93 | (6) |
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97 | (2) |
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Chapter 11 Maps serving the different coupling in the environmental interfaces modelling in the presence of noise |
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99 | (10) |
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11.1 Behavior of a Logistic Map Driven by Fluctuations |
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99 | (2) |
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11.2 Behavior of the Coupled Maps Serving the Combined Coupling in the Presence of Dynamical Noise |
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101 | (8) |
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106 | (3) |
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PART IV HETERARCHY AND EXCHANGE PROCESSES BETWEEN ENVIRONMENTAL INTERFACES |
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Chapter 12 Heterarchy as a concept in environmental interfaces modelling |
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109 | (10) |
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12.1 Hierarchy and Heterarchy |
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109 | (4) |
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12.2 Observational Heterarchy and Formalization of Heterarchical Levels |
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113 | (6) |
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117 | (2) |
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Chapter 13 Heterarchy and biochemical substance exchange in a diffusively coupled ring of cells |
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119 | (12) |
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13.1 Observational Heterarchy and Biochemical Substance Exchange Between Two Cells |
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119 | (5) |
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13.2 Simulations of Active Coupling in a Multicell System |
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124 | (7) |
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128 | (3) |
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Chapter 14 Heterarchy and albedo of the heterogeneous environmental interfaces in environmental modelling |
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131 | (20) |
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14.1 Heterarchy and Aggregation of Albedo Over Heterogeneous Environmental Interfaces |
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131 | (6) |
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14.2 Influence of the Albedo Calculation on the Effective Temperature of the Heterogeneous Grid-Box Consisting of Different Covers |
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137 | (14) |
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145 | (6) |
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PART V COMPLEXITY MEASURES AND TIME SERIES ANALYSIS OF THE PROCESSES AT THE ENVIRONMENTAL INTERFACES |
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Chapter 15 Kolmogorov complexity and the measures based on this complexity |
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151 | (24) |
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15.1 Introductory Comments About Complexity of Environmental Interface Systems |
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151 | (3) |
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15.2 In What Extent Kolmogorov Complexity Enlightens the Physical Complexity? |
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154 | (6) |
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15.3 Novel Measures Based on the Kolmogorov Complexity |
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160 | (7) |
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15.4 Application to Different Dynamical Systems |
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167 | (8) |
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171 | (4) |
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Chapter 16 Complexity analysis of the ionizing and nonionizing radiation time series |
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175 | (32) |
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16.1 A Complexity Analysis of 222Rn Concentration Variation in a Cave |
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175 | (9) |
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16.2 Use of Complexity Analysis in Analyzing the Dependence of 222Rn Concentration Time Series on Indoor Air Temperature and Humidity |
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184 | (7) |
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16.3 Use of the Kolmogorov Complexity and Its Spectrum in Analysis of the UV-B Radiation Time Series |
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191 | (16) |
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201 | (6) |
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Chapter 17 Complexity analysis of the environmental fluid flow time series |
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207 | (28) |
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17.1 Complexity Analysis of the Mountain River Flow Time Series |
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207 | (8) |
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17.2 Randomness Representation in Turbulent Flows with Bed Roughness Elements Using the Kolmogorov Complexity Spectrum |
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215 | (7) |
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17.3 Application of the Complexity Measures Based on the Kolmogorov Complexity on the Analysis of Different River Flow Regimes |
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222 | (13) |
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231 | (4) |
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Chapter 18 How to face the complexity of climate models? |
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235 | (18) |
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18.1 Complexity of the Observed Climate Time Series |
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235 | (5) |
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18.2 Complexity of the Modeled Climate Time Series |
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240 | (13) |
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249 | (4) |
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PART VI PHENOMENON OF CHAOS IN COMPUTING THE ENVIRONMENTAL INTERFACE VARIABLES |
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Chapter 19 Interrelations between mathematics and environmental sciences |
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253 | (12) |
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19.1 The Role of Mathematics in Environmental Sciences |
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253 | (3) |
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19.2 Difference Equations and Occurrence of Chaos in Modelling of Phenomena in the Environmental World |
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256 | (9) |
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262 | (3) |
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Chapter 20 Chaos in modelling the global climate system |
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265 | (20) |
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20.1 Climate Predictability and Climate Models |
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265 | (4) |
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20.2 An Example of the Regional Climate Model Application |
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269 | (9) |
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20.3 Occurrence of Chaos at Environmental Interfaces in Climate Models |
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278 | (7) |
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280 | (5) |
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Chapter 21 Chaos in exchange of vertical turbulent energy fluxes over environmental interfaces in climate models |
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285 | (16) |
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21.1 Chaos in Computing the Environmental Interface Temperature |
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285 | (8) |
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21.2 A Dynamic Analysis of Solutions for the Environmental Interface and Deeper Soil Layer Temperatures Represented by the Coupled Difference Equations |
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293 | (8) |
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299 | (2) |
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Chapter 22 Synchronization and stability of the horizontal energy exchange between environmental interfaces in climate models |
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301 | (20) |
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22.1 Synchronization in Horizontal Energy Exchange Between Environmental Interfaces |
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301 | (3) |
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22.2 Stability of Horizontal Energy Exchange Between Environmental Interfaces |
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304 | (17) |
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316 | (5) |
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PART VII SYNCHRONIZATION AND STABILITY OF THE BIOCHEMICAL SUBSTANCE EXCHANGE BETWEEN CELLS |
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Chapter 23 Environmental interfaces and their stability in biological systems |
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321 | (14) |
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23.1 Building Blocks of Environmental Interfaces |
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321 | (3) |
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23.2 Emergence of Functionality |
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324 | (7) |
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23.3 Functional Stability |
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331 | (4) |
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333 | (2) |
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Chapter 24 Synchronization of the biochemical substance exchange between cells |
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335 | (12) |
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24.1 A Model Representing Biochemical Substance Exchange Between Cells: Model Formalization |
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335 | (5) |
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24.2 Synchronization of the Biochemical Substance Exchange Between Cells: Effect of Fluctuations of Environmental Parameters to Behavior of the Model |
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340 | (7) |
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345 | (2) |
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Chapter 25 Complexity and asymptotic stability in the process of biochemical substance exchange in multicell system |
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347 | (18) |
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25.1 Complexity of the Intercellular Biochemical Substance Exchange |
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347 | (3) |
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25.2 Asymptotic Stability of the Intercellular Biochemical Substance Exchange |
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350 | (7) |
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25.3 Biochemical Substance Exchange in a Multicell System |
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357 | (8) |
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363 | (2) |
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Chapter 26 Use of pseudospectra in analyzing the influence of intercellular nanotubes on cell-to-cell communication integrity |
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365 | (18) |
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26.1 Biological Importance of Tunneling Nanotubes |
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365 | (5) |
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26.2 Computing the Threshold of the Influence of Intercellular Nanotubes on Cell-to-Cell Communication Integrity |
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370 | (3) |
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26.3 Analysis of a Simple Deterministic Model of Intercellular Communication |
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373 | (10) |
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379 | (4) |
Index |
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383 | |