Synopsis: This book gives the reader a survey of hundreds results in the field of the cell and cell associated objects modeling. Applications to modeling in the areas of AIDS, cancers and life longevity are investigated in this book. Introduces and proves fundamental properties of evolutionary systems on optimal distribution of their various resources on their internal and external functions Gives detailed analysis of applications to modeling AIDS, cancers, and life longevity Introducing and grounding the respective numerical algorithms and software Detailed analysis of hundreds of scientific works in the field of mathematical modeling of the cell and cell associated objects.

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## Systems Biology: Mathematical Modeling and Model Analysis - CRC Press Book

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Ships with Tracking Number! May not contain Access Codes or Supplements. May be ex-library. Buy with confidence, excellent customer service!. Satisfaction Guaranteed! The choice of these applications is quite deliberate because these are instances where the network structure is intrinsic to the dynamical behaviour of interest. In the case of [ 10 , 13 ] we see two different studies of emergent behaviour in neurophysiological models that are highly dependent on the structure of the network itself.

Starting with simple biologically inspired elements, and a small core network of these elements, they describe a model whereby the elements respond to stimulus to modify their connectivity. This allows the network of neurons to create complex responses to particular stimuli. They characterize this structure in terms of a core network existing within a hypernetwork.

Conversely, in [ 10 ], Li et al. Networks of physiologically inspired neurons have been observed to self-organize into a critical state where the resultant dynamics of the system can exhibit a mixture of ordered and disordered patterns. Curiously, the critical region which may exhibit strongly ordered performance is narrow for systems of spiking neurons. In [ 10 ], we have a study of this problem from the perspective of a liquid state machine. They show that the performance of the liquid state machine is optimal when the neuronal pool is operating at that critical state.

Complex networks appear in a very wide range of applications, and this is demonstrated within this theme issue with our third contribution from this area. Fu et al. There is now a substantial body of literature in the area of diseases and other propagation processes on complex networks. The particular contribution of Chen et al.

They extend the probability generating function approach to the case of necessarily pair-wise approximation across the transmission model. Competing virus strains are, of course, of relevance across a wide range of disease and also treatment.

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Optimization is a basic task in many areas of mathematics, science and technology. For this reason, it has been the subject of much interest and labour over the last centuries. As a result, whole new branches of mathematics such as calculus of variations, convex optimization and operations research emerged.

Nowadays optimization remains a very active research field in which novel techniques are developed to deal with old and new challenges. Christodoulides et al.

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Their paper is a neat example of how classical applied mathematics and in this case dynamical systems theory can be applied to informed personalized medicine. As with many diseases, a patient's response to atopic dermatitis is not constant but behaves as a dynamical system. By characterizing this system they are able to tune the timing and dosage of their treatment to arrive at an optimal solution.

Their example is a neat one because it relies on fairly simple mathematics to obtain an elegant solution to a real-world problem. Time-series analysis is a useful tool in the study of time-evolving phenomena whose governing equations are unknown or too complex to attempt a detailed analysis. In the linear or statistical approach, the usual scope is to find a random process that fits the observations. In nonlinear time-series analysis, the working hypothesis is that the observations are output by a stationary, dissipative nonlinear system.

In the case of multivariate time series, a further scope may be the causal relations also called coupling or information directions between pairs of components. See [ 27 ] for a general introduction to nonlinear time-series analysis with applications. In applications, the scope may actually be more modest. Think of a medical analyst who wishes to distinguish in an electroencephalogram of an epileptic patient the normal health condition from the abnormal condition epileptic seizure. An observable that is up to this task is sometimes called a biomarker in medical applications whatever its mathematical nature.

Thus, one can find in the literature biomarkers ranging from the traditional statistics, several sorts of entropy, the count of some kind of symbols, to even properties of graphs constructed from the data.

### Applied and Computational Mathematics

Concrete implementations of this strategy can be found in [ 16 , 17 ], as we explain in the following. Given L consecutive or, more generally, equidistant data of a time series, one can assign a symbol to them. By repeating this assignment with sliding blocks of data one trades the original time series for a series of permutations which are aptly called ordinal patterns and are being used in time-series analysis, ergodic theory and dynamical systems for a number of purposes [ 28 ].

In [ 16 ], this symbolization procedure is brought a step further to construct an associated ordinal network to the data as follows: the L! This technique makes available the power of network theory to the data analyst.

For example, using entropy-like complexity measures defined from the ordinal network, McCullough et al. Other interesting applications and the numerical issues involved in the analysis are also thoroughly discussed. The paper by Porta et al. Causality analysis provides an ideal framework to assess the strength of the physiological interactions aiming at the maintenance of arterial blood pressure during an orthostatic challenge in the presence of relevant nonlinear relations and confounding factors blurring the causal link from sympathetic neural activity to arterial blood pressure e.

Porta et al. The previous section illustrates the breadth and depth of the mathematical methods currently applied in medicine, specifically in neuroscience, cardiology and pathology, as reflected in the contributions of this theme issue. Thus, differential equations model the action potential of spiking neurons [ 14 ], the treatment effect on a pathogenesis [ 19 ] or the flow of cerebrospinal fluid in the ventricular system [ 20 ].

It also illustrates nicely how different mathematical subject areas usually concur in the modelling and analysis of a specific topic. For example, networks are used in a particular clustering algorithm [ 12 ], represent a symbolic time series [ 16 ], and are the framework of an infection spreading model [ 18 ]. As for the potential implications of the results reported in this issue, they can be classified in the following categories: â€” better data analysis and diagnoses [ 9 , 12 , 16 , 17 ];.

Both authors contributed equally to this Introduction. We declare we have no competing interests. We thank very much all the authors for the high quality of their papers. We are also gratefully indebted to the referees. Without their generous contributions the scope of this theme issue would have not been achieved. Login to your account. Forgot password?

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