# the calculus of life towards a theory of life springerbriefs in biology

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## The Calculus Of Life

**Author :**Andrés Moya

**ISBN :**9783319169705

**Genre :**Medical

**File Size :**62. 80 MB

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This book explores the exciting world of theoretical biology and is divided into three sections. The first section examines the roles played by renowned scientists such as Jacob, Monod, Rosen, Turing, von Bertalanffy, Waddington and Woodger in developing the field of theoretical biology. The second section, aided with numerous examples, supports the idea that logic and computing are suitable formal languages to describe and understand biological phenomena. The third and final section is, without doubt, the most intellectually challenging and endeavors to show the possible paths we could take to compute a cell - the basic unit of life - or the conditions required for a predictive theory of biological evolution; ultimately, a theory of life in the light of modern Systems Biology. The work aims to show that modern biology is closer than ever to making Goethe's dream come true and that we have reached a point where synthetic and analytical traditions converge to shed light on the living being as a whole.

## Basic Theory

**Author :**Anatoly Kochubei

**ISBN :**9783110571622

**Genre :**Mathematics

**File Size :**82. 10 MB

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This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This first volume collects authoritative chapters covering the mathematical theory of fractional calculus, including fractional-order operators, integral transforms and equations, special functions, calculus of variations, and probabilistic and other aspects.

## Selforganised Criticality And Predictability In Atmospheric Flows

**Author :**Amujuri Mary Selvam

**ISBN :**9783319545462

**Genre :**Science

**File Size :**21. 21 MB

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This book presents a new concept of General Systems Theory and its application to atmospheric physics. It reveals that energy input into the atmospheric eddy continuum, whether natural or manmade, results in enhancement of fluctuations of all scales, manifested immediately in the intensification of high-frequency fluctuations such as the Quasi-Biennial Oscillation and the El-Nino–Southern Oscillation cycles. Atmospheric flows exhibit self-organised criticality, i.e. long-range correlations in space and time manifested as fractal geometry to the spatial pattern concomitant with an inverse power law form for fluctuations of meteorological parameters such as temperature, pressure etc. Traditional meteorological theory cannot satisfactorily explain the observed self-similar space time structure of atmospheric flows. A recently developed general systems theory for fractal space-time fluctuations shows that the larger-scale fluctuation can be visualised to emerge from the space-time averaging of enclosed small-scale fluctuations, thereby generating a hierarchy of self-similar fluctuations manifested as the observed eddy continuum in power spectral analyses of fractal fluctuations. The interconnected network of eddy circulations responds as a unified whole to local perturbations such as global-scale response to El-Nino events. The general systems theory model predicts an inverse power law form incorporating the golden mean τ for the distribution of space-time fluctuation patterns and for the power (variance) spectra of the fluctuations. Since the probability distributions of amplitude and variance are the same, atmospheric flows exhibit quantumlike chaos. Long-range correlations inherent to power law distributions of fluctuations are identified as nonlocal connection or entanglement exhibited by quantum systems such as electrons or photons. The predicted distribution is close to the Gaussian distribution for small-scale fluctuations, but exhibits a fat long tail for large-scale fluctuations. Universal inverse power law for fractal fluctuations rules out unambiguously linear secular trends in climate parameters.

## Fractal Symmetry Of Protein Interior

**Author :**Anirban Banerji

**ISBN :**9783034806510

**Genre :**Science

**File Size :**47. 44 MB

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The essential question that fractal dimensions attempt to answer is about the scales in Nature. For a system as non-idealistic and complex as a protein, studying scale-invariance becomes particularly important. Fractal Symmetry of Protein Interior investigates the diverse facets of the various scales at which we describe protein biophysical and biochemical phenomena. Following a thorough introduction to fractal dimensions, fractal-dimension-based approaches, that have been employed to study protein interior biophysical properties, are described. The focus is on the question “which scales are scale-invariant?” Investigations related to scaling of biophysical and biochemical behaviors may one day help us to formulate a fundamental theory about protein biophysics; which, in turn, may help us to understand fundamental principles of proteins.

## Random Ordinary Differential Equations And Their Numerical Solution

**Author :**Xiaoying Han

**ISBN :**9789811062650

**Genre :**Mathematics

**File Size :**38. 84 MB

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This book is intended to make recent results on the derivation of higher order numerical schemes for random ordinary differential equations (RODEs) available to a broader readership, and to familiarize readers with RODEs themselves as well as the closely associated theory of random dynamical systems. In addition, it demonstrates how RODEs are being used in the biological sciences, where non-Gaussian and bounded noise are often more realistic than the Gaussian white noise in stochastic differential equations (SODEs). RODEs are used in many important applications and play a fundamental role in the theory of random dynamical systems. They can be analyzed pathwise with deterministic calculus, but require further treatment beyond that of classical ODE theory due to the lack of smoothness in their time variable. Although classical numerical schemes for ODEs can be used pathwise for RODEs, they rarely attain their traditional order since the solutions of RODEs do not have sufficient smoothness to have Taylor expansions in the usual sense. However, Taylor-like expansions can be derived for RODEs using an iterated application of the appropriate chain rule in integral form, and represent the starting point for the systematic derivation of consistent higher order numerical schemes for RODEs. The book is directed at a wide range of readers in applied and computational mathematics and related areas as well as readers who are interested in the applications of mathematical models involving random effects, in particular in the biological sciences.The level of this book is suitable for graduate students in applied mathematics and related areas, computational sciences and systems biology. A basic knowledge of ordinary differential equations and numerical analysis is required.