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The Resource Piecewise deterministic processes in biological models, Ryszard Rudnicki, Marta Tyran-Kamińska, (electronic book)

Piecewise deterministic processes in biological models, Ryszard Rudnicki, Marta Tyran-Kamińska, (electronic book)

Label
Piecewise deterministic processes in biological models
Title
Piecewise deterministic processes in biological models
Statement of responsibility
Ryszard Rudnicki, Marta Tyran-Kamińska
Creator
Contributor
Subject
Language
eng
Summary
This book presents a concise introduction to piecewise deterministic Markov processes (PDMPs), with particular emphasis on their applications to biological models. Further, it presents examples of biological phenomena, such as gene activity and population growth, where different types of PDMPs appear: continuous time Markov chains, deterministic processes with jumps, processes with switching dynamics, and point processes. Subsequent chapters present the necessary tools from the theory of stochastic processes and semigroups of linear operators, as well as theoretical results concerning the long-time behaviour of stochastic semigroups induced by PDMPs and their applications to biological models. As such, the book offers a valuable resource for mathematicians and biologists alike. The first group will find new biological models that lead to interesting and often new mathematical questions, while the second can observe how to include seemingly disparate biological processes into a unified mathematical theory, and to arrive at revealing biological conclusions. The target audience primarily comprises of researchers in these two fields, but the book will also benefit graduate students.--
Member of
Assigning source
Provided by publisher
Cataloging source
YDX
http://library.link/vocab/creatorName
Rudnicki, Ryszard
Dewey number
  • 519.2/33
  • 510
Index
no index present
LC call number
QA274.7
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
Tyran-Kamińska, Marta
Series statement
SpringerBriefs in applied sciences and technology, Mathematical methods
http://library.link/vocab/subjectName
Markov processes
Label
Piecewise deterministic processes in biological models, Ryszard Rudnicki, Marta Tyran-Kamińska, (electronic book)
Instantiates
Publication
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Preface; Acknowledgements; Contents; 1 Biological Models; 1.1 Introduction; 1.2 Birth-Death Processes; 1.3 Grasshopper and Kangaroo Movement; 1.4 Velocity Jump Process; 1.5 Size of Cells in a Single Line; 1.6 Two-Phase Cell Cycle Model; 1.7 Stochastic Billiard as a Cell Cycle Model; 1.8 Stochastic Gene Expression I; 1.9 Stochastic Gene Expression II; 1.10 Gene Regulatory Models with Bursting; 1.11 Neural Activity; 1.12 Processes with Extra Jumps on a Subspace; 1.13 Size-Structured Population Model; 1.14 Age-Structured Population Model; 1.15 Asexual Phenotype Population Model
  • 1.16 Phenotype Model with a Sexual Reproduction1.17 Coagulation-Fragmentation Process in a Phytoplankton Model; 1.18 Paralog Families; 1.19 Definition of PDMP; 2 Markov Processes; 2.1 Transition Probabilities and Kernels; 2.1.1 Basic Concepts; 2.1.2 Transition Operators; 2.1.3 Substochastic and Stochastic Operators; 2.1.4 Integral Stochastic Operators; 2.1.5 Frobenius -- Perron Operator; 2.1.6 Iterated Function Systems; 2.2 Discrete-Time Markov Processes; 2.2.1 Markov Processes and Transition Probabilities; 2.2.2 Random Mapping Representations; 2.2.3 Canonical Processes
  • 2.3 Continuous-Time Markov Processes2.3.1 Basic Definitions; 2.3.2 Processes with Stationary and Independent Increments; 2.3.3 Markov Jump-Type Processes; 2.3.4 Generators and Martingales; 2.3.5 Existence of PDMPs; 2.3.6 Transition Functions and Generators of PDMPs; 3 Operator Semigroups; 3.1 Generators and Semigroups; 3.1.1 Essentials of Banach Spaces and Operators; 3.1.2 Definitions and Basic Properties; 3.1.3 The Resolvent; 3.2 Basic Examples of Semigroups; 3.2.1 Uniformly Continuous Semigroups; 3.2.2 Multiplication Semigroups; 3.2.3 Translation Semigroups
  • 3.3 Generators of Contraction Semigroups3.3.1 The Hille -- Yosida Theorem; 3.3.2 The Lumer -- Phillips Theorem; 3.3.3 Perturbations of Semigroups; 3.3.4 Perturbing Boundary Conditions; 4 Stochastic Semigroups; 4.1 Aspects of Positivity; 4.1.1 Positive Operators; 4.1.2 Substochastic Semigroups; 4.1.3 Resolvent Positive Operators; 4.1.4 Generation Theorems; 4.1.5 Positive Perturbations; 4.1.6 Positive Unbounded Perturbations; 4.1.7 Adjoint and Transition Semigroups; 4.2 Stochastic Semigroups for PDMPs; 4.2.1 Jump-Type Markov Processes; 4.2.2 Semigroups for Semiflows; 4.2.3 PDMPs Without Boundaries
Dimensions
unknown
Extent
1 online resource.
Form of item
online
Isbn
9783319612959
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Specific material designation
remote
System control number
ocn995013035
Label
Piecewise deterministic processes in biological models, Ryszard Rudnicki, Marta Tyran-Kamińska, (electronic book)
Publication
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Preface; Acknowledgements; Contents; 1 Biological Models; 1.1 Introduction; 1.2 Birth-Death Processes; 1.3 Grasshopper and Kangaroo Movement; 1.4 Velocity Jump Process; 1.5 Size of Cells in a Single Line; 1.6 Two-Phase Cell Cycle Model; 1.7 Stochastic Billiard as a Cell Cycle Model; 1.8 Stochastic Gene Expression I; 1.9 Stochastic Gene Expression II; 1.10 Gene Regulatory Models with Bursting; 1.11 Neural Activity; 1.12 Processes with Extra Jumps on a Subspace; 1.13 Size-Structured Population Model; 1.14 Age-Structured Population Model; 1.15 Asexual Phenotype Population Model
  • 1.16 Phenotype Model with a Sexual Reproduction1.17 Coagulation-Fragmentation Process in a Phytoplankton Model; 1.18 Paralog Families; 1.19 Definition of PDMP; 2 Markov Processes; 2.1 Transition Probabilities and Kernels; 2.1.1 Basic Concepts; 2.1.2 Transition Operators; 2.1.3 Substochastic and Stochastic Operators; 2.1.4 Integral Stochastic Operators; 2.1.5 Frobenius -- Perron Operator; 2.1.6 Iterated Function Systems; 2.2 Discrete-Time Markov Processes; 2.2.1 Markov Processes and Transition Probabilities; 2.2.2 Random Mapping Representations; 2.2.3 Canonical Processes
  • 2.3 Continuous-Time Markov Processes2.3.1 Basic Definitions; 2.3.2 Processes with Stationary and Independent Increments; 2.3.3 Markov Jump-Type Processes; 2.3.4 Generators and Martingales; 2.3.5 Existence of PDMPs; 2.3.6 Transition Functions and Generators of PDMPs; 3 Operator Semigroups; 3.1 Generators and Semigroups; 3.1.1 Essentials of Banach Spaces and Operators; 3.1.2 Definitions and Basic Properties; 3.1.3 The Resolvent; 3.2 Basic Examples of Semigroups; 3.2.1 Uniformly Continuous Semigroups; 3.2.2 Multiplication Semigroups; 3.2.3 Translation Semigroups
  • 3.3 Generators of Contraction Semigroups3.3.1 The Hille -- Yosida Theorem; 3.3.2 The Lumer -- Phillips Theorem; 3.3.3 Perturbations of Semigroups; 3.3.4 Perturbing Boundary Conditions; 4 Stochastic Semigroups; 4.1 Aspects of Positivity; 4.1.1 Positive Operators; 4.1.2 Substochastic Semigroups; 4.1.3 Resolvent Positive Operators; 4.1.4 Generation Theorems; 4.1.5 Positive Perturbations; 4.1.6 Positive Unbounded Perturbations; 4.1.7 Adjoint and Transition Semigroups; 4.2 Stochastic Semigroups for PDMPs; 4.2.1 Jump-Type Markov Processes; 4.2.2 Semigroups for Semiflows; 4.2.3 PDMPs Without Boundaries
Dimensions
unknown
Extent
1 online resource.
Form of item
online
Isbn
9783319612959
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Specific material designation
remote
System control number
ocn995013035

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