Download or read book Some Problems in Stochastic Dynamics and Statistical Analysis of Single cell Biology of Cancer written by Yue Wang and published by . This book was released on 2018 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: With recent development of instrumentations, data collection capabilities, and computational soft-wares, in cancer biology now one has high-throughput data on individual cells in a population: its heterogeneous genomic makeups and/or phenotypic molecular markers. At this level of description, stochasticity is a significant component of dynamics of single cells. Using purely deterministic representations and mathematical models is no longer realistic nor desirable. In addition, most traditional deterministic models are based on differential equations and dynamical systems with real numbers; single cell data are too discrete to fit a continuous state space. This dissertation consists of three parts: Motivated by laboratory measurements, carried out at Institute for Systems Biology, on the stochastic population growth of Leukemia cells (HL60), Part I, Chapter 2 reports statistical analysis of data and develops dynamic modesl in terms of birth-death processes. It is shown that even in the very earlier stage of ~ 10 cells, there exists already multiple phenotypes in the population: This result invalidates the naive assumption of statistically identical individuals in exponential cell growth. Then in Chapter 3, branching processes are introduced to study the equilibrium of heterogeneous cell population with multiple phenotype switching. A law of large numbers is proven. A proof of mathematical relationship between multi-type branching process and multi-dimensional birth-death process is given in Section 3.8.2. Part II addresses a central issue in data statistics: How to quanitfy the logic casual effect among observations of interdependent random variables. In terms of the notion of Markov boundary, we provide a rather coherent quantification of a class of causal inference. We prove that in certain special cases, quantifying causal effect is not possible. Computational algorithms for determining such scenarios are proposed and implemented. Stochastic processes employed in cancer biology and in statistical physics have a fundamental difference: The latter as models for inanimate matters require detailed balance while the former, as models of living organisms, have positive stationary entropy productions. In Part III (Chapter 5), we investigate a theoretical issue of irreversible Markov processes without detailed balance: How to represent the entropy production in a finite system through a lifting of this stochastic process. We prove that the entropy production rate in the finite system can be represented in terms of a potential function in the limited infinite system with detailed balance. We propose to use this mathematical result to unify the two different statements, due to Clausius and Lord Kelvin, of the Second Law of Thermodynamics.
Download or read book Stochastic Chemical Reaction Systems in Biology written by Hong Qian and published by Springer Nature. This book was released on 2021-10-18 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the analysis of stochastic dynamic models in biology and medicine. The main aim is to offer a coherent set of probabilistic techniques and mathematical tools which can be used for the simulation and analysis of various biological phenomena. These tools are illustrated on a number of examples. For each example, the biological background is described, and mathematical models are developed following a unified set of principles. These models are then analyzed and, finally, the biological implications of the mathematical results are interpreted. The biological topics covered include gene expression, biochemistry, cellular regulation, and cancer biology. The book will be accessible to graduate students who have a strong background in differential equations, the theory of nonlinear dynamical systems, Markovian stochastic processes, and both discrete and continuous state spaces, and who are familiar with the basic concepts of probability theory.
Download or read book Stochastic Models with Applications to Genetics Cancers AIDS and Other Biomedical Systems written by W. Y. Tan and published by World Scientific. This book was released on 2002 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic treatment of Markov chains, diffusion processes and state space models, as well as alternative approaches to Markov chains through stochastic difference equations and stochastic differential equations. It illustrates how these processes and approaches are applied to many problems in genetics, carcinogenesis, AIDS epidemiology and other biomedical systems.One feature of the book is that it describes the basic MCMC (Markov chain and Monte Carlo) procedures and illustrates how to use the Gibbs sampling method and the multilevel Gibbs sampling method to solve many problems in genetics, carcinogenesis, AIDS and other biomedical systems.As another feature, the book develops many state space models for many genetic problems, carcinogenesis, AIDS epidemiology and HIV pathogenesis. It shows in detail how to use the multilevel Gibbs sampling method to estimate (or predict) simultaneously the state variables and the unknown parameters in cancer chemotherapy, carcinogenesis, AIDS epidemiology and HIV pathogenesis. As a matter of fact, this book is the first to develop many state space models for many genetic problems, carcinogenesis and other biomedical problems.
Download or read book Stochastic Models for Carcinogenesis written by Wai-Yuan Tan and published by CRC Press. This book was released on 2020-01-31 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date survey of mathematical models of carcinogenesis, providing the most recent findings of cancer biology as evidence of the models, as well as extensive bibliographies of cancer biology and in-depth mathematical analyses for each of the models. May be used as a reference for biostaticians, biometricians, mathematical and molecular biologists, applied mathematicians, oncologists, cancer and toxicology researchers, environmental scientists, and graduate students in these fields.
Download or read book Stochastic Models of Tumor Latency and Their Biostatistical Applications written by Andrej Yu Yakovlev and published by World Scientific. This book was released on 1996 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research monograph discusses newly developed mathematical models and methods that provide biologically meaningful inferences from data on cancer latency produced by follow-up and discrete surveillance studies. Methods for designing optimal strategies of cancer surveillance are systematically presented for the first time in this book. It offers new approaches to the stochastic description of tumor latency, employs biologically-based models for making statistical inference from data on tumor recurrence and also discusses methods of statistical analysis of data resulting from discrete surveillance strategies. It also offers insight into the role of prognostic factors based on the interpretation of their effects in terms of parameters endowed with biological meaning, as well as methods for designing optimal schedules of cancer screening and surveillance. Last but not least, it discusses survival models allowing for cure rates and the choice of optimal treatment based on covariate information, and presents numerous examples of real data analysis.
Download or read book Dynamics Of Cancer Mathematical Foundations Of Oncology written by Dominik Wodarz and published by World Scientific. This book was released on 2014-04-24 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book aims to provide an introduction to mathematical models that describe the dynamics of tumor growth and the evolution of tumor cells. It can be used as a textbook for advanced undergraduate or graduate courses, and also serves as a reference book for researchers. The book has a strong evolutionary component and reflects the viewpoint that cancer can be understood rationally through a combination of mathematical and biological tools. It can be used both by mathematicians and biologists. Mathematically, the book starts with relatively simple ordinary differential equation models, and subsequently explores more complex stochastic and spatial models. Biologically, the book starts with explorations of the basic dynamics of tumor growth, including competitive interactions among cells, and subsequently moves on to the evolutionary dynamics of cancer cells, including scenarios of cancer initiation, progression, and treatment. The book finishes with a discussion of advanced topics, which describe how some of the mathematical concepts can be used to gain insights into a variety of questions, such as epigenetics, telomeres, gene therapy, and social interactions of cancer cells.
Download or read book Stochastic Methods in Cancer Research Applications to Genomics and Angiogenesis written by Paola M. V. Rancoita and published by Ledizioni. This book was released on 2011 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, I study three stochastic methods that can be applied for the analysis of data in cancer research and, in particular, to cancer genomic data and to images of angiogenic processes. Cancer is a multistep process where the accumulation of genomic lesions alters cell biology. The latter is under control of several pathways and thus, cancer can arise via different mechanisms affecting different pathways. Due to the general complexity of this disease and the different types of tumors, the efforts of cancer research cover several research areas such as, for example, immunology, genetics, cell biology, angiogenesis.
Download or read book Statistics and Informatics in Molecular Cancer Research written by Carsten Wiuf and published by OUP Oxford. This book was released on 2009-06-18 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Molecular understanding of cancer and cancer progression is at the forefront of many research programs today. High-throughput array technologies and other modern molecular techniques produce a wealth of molecular data about the structure, and function of cells, tissues, and organisms. Correctly analyzed and interpreted these data hold the promise of bringing new markers for prognostic and diagnostic use, for new treatment schemes, and of gaining new biological insight into the evolution of cancer and its molecular, pathological, and clinical consequences. Aimed at graduates and researchers, this book discusses novel advances in informatics and statistics in molecular cancer research. Through eight chapters from carefully chosen experts it brings the reader up to date with specific topics in cancer research, how the topics give rise to development of new informatics and statistics tools, and how the tools can be applied. The focus of the book is to give the reader an understanding of key concepts and tools, rather than focusing on technical issues. A main theme is the extensive use of array technologies in modern cancer research - gene expression and exon arrays, SNP and copy number arrays, and methylation arrays - to derive quantitative and qualitative statements about cancer, its progression and aetiology, and to understand how these technologies on one hand allow us learn about cancer tissue as a complex system and on the other hand allow us to pinpoint key genes and events as crucial for the development of the disease.
Download or read book Handbook Of Cancer Models With Applications written by Wai-yuan Tan and published by World Scientific. This book was released on 2008-06-02 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: Composed of contributions from an international team of leading researchers, this book pulls together the most recent research results in the field of cancer modeling to provide readers with the most advanced mathematical models of cancer and their applications.Topics included in the book cover oncogenetic trees, stochastic multistage models of carcinogenesis, effects of ionizing radiation on cell cycle and genomic instability, induction of DNA damage by ionizing radiation and its repair, epigenetic cancer models, bystander effects of radiation, multiple pathway models of human colon cancer, and stochastic models of metastasis. The book also provides some important applications of cancer models to the assessment of cancer risk associated with various hazardous environmental agents, to cancer screening by MRI, and to drug resistance in cancer chemotherapy. An updated statistical design and analysis of xenograft experiments as well as a statistical analysis of cancer occult clinical data are also provided.The book will serve as a useful source of reference for researchers in biomathematics, biostatistics and bioinformatics; for clinical investigators and medical doctors employing quantitative methods to develop procedures for cancer diagnosis, prevention, control and treatment; and for graduate students.
Download or read book An Integrated Approach to Model Cancer Cell Growth and Treatment Response with Multimodal Data Sources written by Kaitlyn Elizabeth Johnson and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical modeling and computational biology have been used to understand, describe, and predict critical behaviors of cancer progression. Recent technological advancements in the acquisition of single cell resolution data by high-throughput micrographic imaging and by single cell genomics now enable new analyses of cancer cells at the individual cell and cell population levels. This dissertation focuses on the development of math modeling frameworks capable of integrating and improving our utilization of these novel data types. First, we investigate the relevance of deviations from the conventional exponential growth model via an ecological principle known as the Allee effect, in which cancer cells exhibit cooperative growth dynamics at low population densities relevant in tumor initiation and metastases. Using a large number of single cell resolution growth trajectories acquired at low cell densities, we apply a stochastic parameter estimation framework to systematically evaluate the relevance of an Allee effect in a controlled experimental setting. Our findings reveal evidence for cooperative growth even in the presence of optimal space and nutrients, giving us motivation to consider Allee effects in making predictions regarding treatment response and tumor initiation. The remainder of our work focuses on utilizing multimodal data sources to better understand the dynamics of resistance to chemotherapy. We utilize a mathematical model describing the effects of a treatment-induced resistance on a population of cancer cells and seek to utilize available snapshot and longitudinal data to identify the model parameters. Using lineage tracing technologies developed in the Brock lab, the transcriptomic data set is made actionable by developing a classifier capable of predicting whether a cell in a sample is sensitive or resistant to chemotherapy. We apply this to estimate the composition of the population at a few snapshots in time during treatment response and combine this with longitudinal data directly into our model calibration. The explicit incorporation of molecular level data with population-size dynamics data improves the identifiability and predictive power of the mathematical model. We intend this work to be exemplary of ways in which novel methods can improve the use of data to describe, evaluate, predict, and optimize cancer treatments
Download or read book The Evolution of the Use of Mathematics in Cancer Research written by Pedro Jose Gutiérrez Diez and published by Springer Science & Business Media. This book was released on 2012-02-17 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book will provide an exhaustive and clear explanation of how Statistics, Mathematics and Informatics have been used in cancer research, and seeks to help cancer researchers in achieving their objectives. To do so, state-of-the-art Biostatistics, Biomathematics and Bioinformatics methods will be described and discussed in detail through illustrative and capital examples taken from cancer research work already published. The book will provide a guide for cancer researchers in using Statistics, Mathematics and Informatics, clarifying the contribution of these logical sciences to the study of cancer, thoroughly explaining their procedures and methods, and providing criteria to their appropriate use.
Download or read book Stochastic Processes Multiscale Modeling and Numerical Methods for Computational Cellular Biology written by David Holcman and published by Springer. This book was released on 2017-10-04 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the modeling and mathematical analysis of stochastic dynamical systems along with their simulations. The collected chapters will review fundamental and current topics and approaches to dynamical systems in cellular biology. This text aims to develop improved mathematical and computational methods with which to study biological processes. At the scale of a single cell, stochasticity becomes important due to low copy numbers of biological molecules, such as mRNA and proteins that take part in biochemical reactions driving cellular processes. When trying to describe such biological processes, the traditional deterministic models are often inadequate, precisely because of these low copy numbers. This book presents stochastic models, which are necessary to account for small particle numbers and extrinsic noise sources. The complexity of these models depend upon whether the biochemical reactions are diffusion-limited or reaction-limited. In the former case, one needs to adopt the framework of stochastic reaction-diffusion models, while in the latter, one can describe the processes by adopting the framework of Markov jump processes and stochastic differential equations. Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology will appeal to graduate students and researchers in the fields of applied mathematics, biophysics, and cellular biology.
Download or read book Stochastic Narrow Escape in Molecular and Cellular Biology written by David Holcman and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers recent developments in the non-standard asymptotics of the mathematical narrow escape problem in stochastic theory, as well as applications of the narrow escape problem in cell biology. The first part of the book concentrates on mathematical methods, including advanced asymptotic methods in partial equations, and is aimed primarily at applied mathematicians and theoretical physicists who are interested in biological applications. The second part of the book is intended for computational biologists, theoretical chemists, biochemists, biophysicists, and physiologists. It includes a summary of output formulas from the mathematical portion of the book and concentrates on their applications in modeling specific problems in theoretical molecular and cellular biology. Critical biological processes, such as synaptic plasticity and transmission, activation of genes by transcription factors, or double-strained DNA break repair, are controlled by diffusion in structures that have both large and small spatial scales. These may be small binding sites inside or on the surface of the cell, or narrow passages between subcellular compartments. The great disparity in spatial scales is the key to controlling cell function by structure. This volume reports recent progress on resolving analytical and numerical difficulties in extracting properties from experimental data, biophysical models, and from Brownian dynamics simulations of diffusion in multi-scale structures.
Download or read book Graph Representation Learning written by William L. William L. Hamilton and published by Springer Nature. This book was released on 2022-06-01 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph-structured data is ubiquitous throughout the natural and social sciences, from telecommunication networks to quantum chemistry. Building relational inductive biases into deep learning architectures is crucial for creating systems that can learn, reason, and generalize from this kind of data. Recent years have seen a surge in research on graph representation learning, including techniques for deep graph embeddings, generalizations of convolutional neural networks to graph-structured data, and neural message-passing approaches inspired by belief propagation. These advances in graph representation learning have led to new state-of-the-art results in numerous domains, including chemical synthesis, 3D vision, recommender systems, question answering, and social network analysis. This book provides a synthesis and overview of graph representation learning. It begins with a discussion of the goals of graph representation learning as well as key methodological foundations in graph theory and network analysis. Following this, the book introduces and reviews methods for learning node embeddings, including random-walk-based methods and applications to knowledge graphs. It then provides a technical synthesis and introduction to the highly successful graph neural network (GNN) formalism, which has become a dominant and fast-growing paradigm for deep learning with graph data. The book concludes with a synthesis of recent advancements in deep generative models for graphs—a nascent but quickly growing subset of graph representation learning.
Download or read book Statistical Methods for Cancer Studies written by Richard G. Cornell and published by CRC Press. This book was released on 1984-02-28 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on public health and epidemiologic aspects of cancer, and explores the sources of information concerning the frequency of occurrence of human cancer. It describes statistical methods useful in studying problems arising in the field of cancer and its concurrent development.
Download or read book Systems Biology of Cancer written by Sam Thiagalingam and published by Cambridge University Press. This book was released on 2015-04-09 with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt: An overview of the current systems biology-based knowledge and the experimental approaches for deciphering the biological basis of cancer.
Download or read book The Cancer Problem written by Charles Edward Green and published by . This book was released on 1914 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
