*Thomas S. Bianchi and Elizabeth A. Canuel*

- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691134147
- eISBN:
- 9781400839100
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691134147.003.0001
- Subject:
- Biology, Ecology

This chapter provides a general background on the synthesis of chemical biomarkers and their association with key metabolic pathways in organisms, as related to differences in cellular structure and ...
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This chapter provides a general background on the synthesis of chemical biomarkers and their association with key metabolic pathways in organisms, as related to differences in cellular structure and function across the three domains of life. It discusses photosynthesis, the dominant pathway by which biomass is synthesized. It also presents information about chemoautotrophic and microbial heterotrophic processes. The holistic view of biosynthetic pathways of chemical biomarkers provides a roadmap for other chapters in the book, where more specific details on chemical pathways are presented for each of the respective biomarker groups. While other organic geochemistry books have generally introduced the concepts of chemical biomarkers in the context of physical and chemical gradients found in natural ecosystems (e.g., anaerobic, aerobic), this book begins by examining biosynthetic pathways at the cellular level of differentiation.Less

This chapter provides a general background on the synthesis of chemical biomarkers and their association with key metabolic pathways in organisms, as related to differences in cellular structure and function across the three domains of life. It discusses photosynthesis, the dominant pathway by which biomass is synthesized. It also presents information about chemoautotrophic and microbial heterotrophic processes. The holistic view of biosynthetic pathways of chemical biomarkers provides a roadmap for other chapters in the book, where more specific details on chemical pathways are presented for each of the respective biomarker groups. While other organic geochemistry books have generally introduced the concepts of chemical biomarkers in the context of physical and chemical gradients found in natural ecosystems (e.g., anaerobic, aerobic), this book begins by examining biosynthetic pathways at the cellular level of differentiation.

*Pierre Calka*

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199232574
- eISBN:
- 9780191716393
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199232574.003.0005
- Subject:
- Mathematics, Geometry / Topology

Random tessellations and cellular structures occur in many domains of application, such as astrophysics, ecology, telecommunications, biochemistry and naturally cellular biology (see Stoyan, Kendall ...
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Random tessellations and cellular structures occur in many domains of application, such as astrophysics, ecology, telecommunications, biochemistry and naturally cellular biology (see Stoyan, Kendall and Mecke 1987 or Okabe, Boots, Sugihara and Chiu 2000 for complete surveys). The theoretical study of these objects was initiated in the second half of the twentieth century by D. G. Kendall, J. L. Meijering, E. N. Gilbert and R. E. Miles, notably. Two isotropic and stationary models have emerged as the most basic and useful: the Poisson hyperplane tessellation and the Poisson–Voronoi tessellation. Since then, a large majority of questions raised about random tessellations have concerned statistics of the population of cells (‘how many cells are triangles in the plane?’, ‘how many cells have a volume greater than one?’) or properties of a specific cell (typically the one containing the origin). Two types of results are presented below: exact distributional calculations and asymptotic estimations. In the first part, we describe the two basic constructions of random tessellations (i.e. by throwing random hyperplanes or by constructing Voronoi cells around random nuclei) and we introduce the fundamental notion of typical cell of a stationary tessellation. The second part is devoted to the presentation of exact distributional results on basic geometrical characteristics (number of hyperfaces, typical k‐face, etc.). The following part concerns asymptotic properties of the cells. It concentrates in particular on the well‐known D. G. Kendall conjecture which states that large planar cells in a Poisson line tessellation are close to the circular shape. In the last part, we present some recent models of iterated tessellations which appear naturally in applied fields (study of crack structures, telecommunications). Intentionally, this chapter does not contain an exhaustive presentation of all the models of random tessellations existing in the literature (in particular, dynamical constructions such as Johnson‐Mehl tessellations will be omitted). The aim of the text below is to provide a selective view of recent selected methods and results on a few specific models.Less

Random tessellations and cellular structures occur in many domains of application, such as astrophysics, ecology, telecommunications, biochemistry and naturally cellular biology (see Stoyan, Kendall and Mecke 1987 or Okabe, Boots, Sugihara and Chiu 2000 for complete surveys). The theoretical study of these objects was initiated in the second half of the twentieth century by D. G. Kendall, J. L. Meijering, E. N. Gilbert and R. E. Miles, notably. Two isotropic and stationary models have emerged as the most basic and useful: the Poisson hyperplane tessellation and the Poisson–Voronoi tessellation. Since then, a large majority of questions raised about random tessellations have concerned statistics of the population of cells (‘how many cells are triangles in the plane?’, ‘how many cells have a volume greater than one?’) or properties of a specific cell (typically the one containing the origin). Two types of results are presented below: exact distributional calculations and asymptotic estimations. In the first part, we describe the two basic constructions of random tessellations (i.e. by throwing random hyperplanes or by constructing Voronoi cells around random nuclei) and we introduce the fundamental notion of typical cell of a stationary tessellation. The second part is devoted to the presentation of exact distributional results on basic geometrical characteristics (number of hyperfaces, typical k‐face, etc.). The following part concerns asymptotic properties of the cells. It concentrates in particular on the well‐known D. G. Kendall conjecture which states that large planar cells in a Poisson line tessellation are close to the circular shape. In the last part, we present some recent models of iterated tessellations which appear naturally in applied fields (study of crack structures, telecommunications). Intentionally, this chapter does not contain an exhaustive presentation of all the models of random tessellations existing in the literature (in particular, dynamical constructions such as Johnson‐Mehl tessellations will be omitted). The aim of the text below is to provide a selective view of recent selected methods and results on a few specific models.

*Habib Ammari, Elie Bretin, Josselin Garnier, Hyeonbae Kang, Hyundae Lee, and Abdul Wahab*

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691165318
- eISBN:
- 9781400866625
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691165318.001.0001
- Subject:
- Mathematics, Applied Mathematics

This book comprehensively explores elasticity imaging and examines recent, important developments in asymptotic imaging, modeling, and analysis of deterministic and stochastic elastic wave ...
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This book comprehensively explores elasticity imaging and examines recent, important developments in asymptotic imaging, modeling, and analysis of deterministic and stochastic elastic wave propagation phenomena. It derives the best possible functional images for small inclusions and cracks within the context of stability and resolution, and introduces a topological derivative-based imaging framework for detecting elastic inclusions in the time-harmonic regime. For imaging extended elastic inclusions, accurate optimal control methodologies are designed and the effects of uncertainties of the geometric or physical parameters on stability and resolution properties are evaluated. In particular, the book shows how localized damage to a mechanical structure affects its dynamic characteristics, and how measured eigenparameters are linked to elastic inclusion or crack location, orientation, and size. Demonstrating a novel method for identifying, locating, and estimating inclusions and cracks in elastic structures, the book opens possibilities for a mathematical and numerical framework for elasticity imaging of nanoparticles and cellular structures.Less

This book comprehensively explores elasticity imaging and examines recent, important developments in asymptotic imaging, modeling, and analysis of deterministic and stochastic elastic wave propagation phenomena. It derives the best possible functional images for small inclusions and cracks within the context of stability and resolution, and introduces a topological derivative-based imaging framework for detecting elastic inclusions in the time-harmonic regime. For imaging extended elastic inclusions, accurate optimal control methodologies are designed and the effects of uncertainties of the geometric or physical parameters on stability and resolution properties are evaluated. In particular, the book shows how localized damage to a mechanical structure affects its dynamic characteristics, and how measured eigenparameters are linked to elastic inclusion or crack location, orientation, and size. Demonstrating a novel method for identifying, locating, and estimating inclusions and cracks in elastic structures, the book opens possibilities for a mathematical and numerical framework for elasticity imaging of nanoparticles and cellular structures.