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Author: Shen-Shen Zeng Publisher: ISBN: 9783832542801 Category : Differentiable dynamical systems Languages : en Pages : 0
Book Description
In this thesis, the author introduces the concept of ensemble observability of dynamical systems and develop a theoretical framework in which this system property is characterized. An ensemble is a collection of nearly identical copies of one dynamical system, and it is said to be observable if the distribution of the nonidentical initial states can be reconstructed from observing the time evolution of a corresponding distribution of outputs. Similarly, a single dynamical system with output is said to be ensemble observable if a collection of copies of this system, with different initial states, is observable when considered as an ensemble. The consideration of ensemble observability is, in particular, motivated by recent efforts in the study of heterogeneous cell populations. Therein one aims to reconstruct a distribution of states within a population of cells, but is only given the time evolution of the distribution of certain measured quantities within the population. More generally, the motivation for introducing ensemble observability is rooted in the very concept of ensembles itself, in which a collection of individual systems may only be considered as a whole. A main result of this thesis illustrates a fundamental connection between the concept of ensemble observability and mathematical tomography problems. Another main result concerns a natural connection to polynomial systems, which is encountered in the course of a systems theoretic treatment of the ensemble observability problem through the consideration of moments of the distributions. The author also establishes a duality of both approaches for linear systems.
Author: Shen-Shen Zeng Publisher: ISBN: 9783832542801 Category : Differentiable dynamical systems Languages : en Pages : 0
Book Description
In this thesis, the author introduces the concept of ensemble observability of dynamical systems and develop a theoretical framework in which this system property is characterized. An ensemble is a collection of nearly identical copies of one dynamical system, and it is said to be observable if the distribution of the nonidentical initial states can be reconstructed from observing the time evolution of a corresponding distribution of outputs. Similarly, a single dynamical system with output is said to be ensemble observable if a collection of copies of this system, with different initial states, is observable when considered as an ensemble. The consideration of ensemble observability is, in particular, motivated by recent efforts in the study of heterogeneous cell populations. Therein one aims to reconstruct a distribution of states within a population of cells, but is only given the time evolution of the distribution of certain measured quantities within the population. More generally, the motivation for introducing ensemble observability is rooted in the very concept of ensembles itself, in which a collection of individual systems may only be considered as a whole. A main result of this thesis illustrates a fundamental connection between the concept of ensemble observability and mathematical tomography problems. Another main result concerns a natural connection to polynomial systems, which is encountered in the course of a systems theoretic treatment of the ensemble observability problem through the consideration of moments of the distributions. The author also establishes a duality of both approaches for linear systems.
Author: Karsten Kuritz Publisher: Logos Verlag Berlin GmbH ISBN: 383255209X Category : Language Arts & Disciplines Languages : en Pages : 150
Book Description
An ensemble system is a collection of nearly identical dynamical systems which admit a certain degree of heterogeneity, and which are subject to the restriction that they may only be manipulated or observed as a whole. This thesis presents analysis and control methods for cellular ensembles by considering reduced 1-dimensional dynamics of biological processes in high-dimensional single-cell data and models. To be more specific, we address the quest for real-time analysis of biological processes within single-cell data by introducing the measure-preserving map of pseudotime into real-time, in short MAPiT. MAPiT enables the reconstruction of temporal and spatial dynamics from single-cell snapshot experiments. In addition, we propose a PDE-constrained learning algorithm which allows for efficient inference of changes in cell cycle progression from time series single-cell snapshot data. The second part of this thesis, is devoted to controlling a heterogeneous cell population, in the sense, that we aim at achieving a desired distribution of cellular oscillators on their periodic orbit. A systems theoretic approach to the ensemble control problem provides novel necessary and sufficient conditions for the control of phase distributions in terms of the Fourier coefficients of the phase response curve. This thesis establishes a connection between the previously separate areas of single cell analysis and ensemble control. Our holistic view opens new perspectives for theoretic concepts in basic research and therapeutic strategies in precision medicine.
Author: Simon Diner Publisher: World Scientific ISBN: 9789971501501 Category : Mathematics Languages : en Pages : 298
Book Description
This book commemorates the centenary of the birth of Georges David Birhoff, the father of the theory of Dynamical Systems. It consists of a volume of dedicated papers, reflecting the intellectual revolution of his work. This book is divided into four parts: Fundamental Paradigms ? Chaos, Turbulence, Attractors, Bifurcations; Dynamical Systems and Microphysics; Self-Organization and Biological Dynamical Systems; Epistemology and History.
Author: Driss Boutat Publisher: ISBN: 9783030737436 Category : Languages : en Pages : 0
Book Description
This book presents a differential geometric method for designing nonlinear observers for multiple types of nonlinear systems, including single and multiple outputs, fully and partially observable systems, and regular and singular dynamical systems. It is an exposition of achievements in nonlinear observer normal forms. The book begins by discussing linear systems, introducing the concept of observability and observer design, and then explains the difficulty of those problems for nonlinear systems. After providing foundational information on the differential geometric method, the text shows how to use the method to address observer design problems. It presents methods for a variety of systems. The authors employ worked examples to illustrate the ideas presented. Observer Design for Nonlinear Dynamical Systems will be of interest to researchers, graduate students, and industrial professionals working with control of mechanical and dynamical systems. .
Author: S. K. Korovin Publisher: Walter de Gruyter ISBN: 3110218127 Category : Control theory Languages : en Pages : 253
Book Description
This book presents the basic concepts and recent developments of linear control problems with perturbations. The presentation concerns both continuous and discrete dynamical systems. It is self-contained and illustrated by numerous examples. From the contents: Notion of state observers Observability Observers of full-phase vectors for fully determined linear systems Functional observers for fully determined linear systems Asymptotic observers for linear systems with uncertainty Observers for bilinear and discrete systems
Author: Michael J. W. Hall Publisher: Springer ISBN: 3319341669 Category : Science Languages : en Pages : 280
Book Description
This book describes a promising approach to problems in the foundations of quantum mechanics, including the measurement problem. The dynamics of ensembles on configuration space is shown here to be a valuable tool for unifying the formalisms of classical and quantum mechanics, for deriving and extending the latter in various ways, and for addressing the quantum measurement problem. A description of physical systems by means of ensembles on configuration space can be introduced at a very fundamental level: the basic building blocks are a configuration space, probabilities, and Hamiltonian equations of motion for the probabilities. The formalism can describe both classical and quantum systems, and their thermodynamics, with the main difference being the choice of ensemble Hamiltonian. Furthermore, there is a natural way of introducing ensemble Hamiltonians that describe the evolution of hybrid systems; i.e., interacting systems that have distinct classical and quantum sectors, allowing for consistent descriptions of quantum systems interacting with classical measurement devices and quantum matter fields interacting gravitationally with a classical spacetime.
Author: Yasemin Altun Publisher: Springer ISBN: 331971273X Category : Computers Languages : en Pages : 448
Book Description
The three volume proceedings LNAI 10534 – 10536 constitutes the refereed proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases, ECML PKDD 2017, held in Skopje, Macedonia, in September 2017. The total of 101 regular papers presented in part I and part II was carefully reviewed and selected from 364 submissions; there are 47 papers in the applied data science, nectar and demo track. The contributions were organized in topical sections named as follows: Part I: anomaly detection; computer vision; ensembles and meta learning; feature selection and extraction; kernel methods; learning and optimization, matrix and tensor factorization; networks and graphs; neural networks and deep learning. Part II: pattern and sequence mining; privacy and security; probabilistic models and methods; recommendation; regression; reinforcement learning; subgroup discovery; time series and streams; transfer and multi-task learning; unsupervised and semisupervised learning. Part III: applied data science track; nectar track; and demo track.
Author: Tiziana Margaria Publisher: Springer ISBN: 3030034240 Category : Computers Languages : en Pages : 533
Book Description
The four-volume set LNCS 11244, 11245, 11246, and 11247 constitutes the refereed proceedings of the 8th International Symposium on Leveraging Applications of Formal Methods, Verification and Validation, ISoLA 2018, held in Limassol, Cyprus, in October/November 2018. The papers presented were carefully reviewed and selected for inclusion in the proceedings. Each volume focusses on an individual topic with topical section headings within the volume: Part I, Modeling: Towards a unified view of modeling and programming; X-by-construction, STRESS 2018. Part II, Verification: A broader view on verification: from static to runtime and back; evaluating tools for software verification; statistical model checking; RERS 2018; doctoral symposium. Part III, Distributed Systems: rigorous engineering of collective adaptive systems; verification and validation of distributed systems; and cyber-physical systems engineering. Part IV, Industrial Practice: runtime verification from the theory to the industry practice; formal methods in industrial practice - bridging the gap; reliable smart contracts: state-of-the-art, applications, challenges and future directions; and industrial day.
Author: Seon Ki Park Publisher: Springer ISBN: 3319434152 Category : Science Languages : en Pages : 553
Book Description
This book contains the most recent progress in data assimilation in meteorology, oceanography and hydrology including land surface. It spans both theoretical and applicative aspects with various methodologies such as variational, Kalman filter, ensemble, Monte Carlo and artificial intelligence methods. Besides data assimilation, other important topics are also covered including targeting observation, sensitivity analysis, and parameter estimation. The book will be useful to individual researchers as well as graduate students for a reference in the field of data assimilation.
Author: Shen-Shen Zeng
Author: Shen-Shen Zeng
Author: Karsten Kuritz
Author: Simon Diner
Author: Driss Boutat
Author: S. K. Korovin
Author: Michael J. W. Hall
Author: Yasemin Altun
Author: Tiziana Margaria
Author: Seon Ki Park
Author: