scholarly journals Observability and Structural Identifiability of Nonlinear Biological Systems

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Alejandro F. Villaverde
Keyword(s):  
Differential Geometry ◽  
Internal State ◽  
Biological Processes ◽  
State Variables ◽  
Related Property ◽  
Theoretical Possibility ◽  
Structural Identifiability ◽  
Open Problems ◽  
Constant State ◽  
Parameter Values

Observability is a modelling property that describes the possibility of inferring the internal state of a system from observations of its output. A related property, structural identifiability, refers to the theoretical possibility of determining the parameter values from the output. In fact, structural identifiability becomes a particular case of observability if the parameters are considered as constant state variables. It is possible to simultaneously analyse the observability and structural identifiability of a model using the conceptual tools of differential geometry. Many complex biological processes can be described by systems of nonlinear ordinary differential equations and can therefore be analysed with this approach. The purpose of this review article is threefold: (I) to serve as a tutorial on observability and structural identifiability of nonlinear systems, using the differential geometry approach for their analysis; (II) to review recent advances in the field; and (III) to identify open problems and suggest new avenues for research in this area.

scholarly journals An extension of Gronwall inequality in the theory of bodies with voids

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 1161-1167
Author(s):  
Marin Marin ◽  
Praveen Ailawalia ◽  
Ioan Tuns
Keyword(s):  
Boundary Value Problem ◽  
Internal State ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Uniqueness Result ◽  
Internal Variables ◽  
State Variables ◽  
Gronwall’S Inequality ◽  
Initial Boundary Value

Abstract In this paper, we obtain a generalization of the Gronwall’s inequality to cover the study of porous elastic media considering their internal state variables. Based on some estimations obtained in three auxiliary results, we use this form of the Gronwall’s inequality to prove the uniqueness of solution for the mixed initial-boundary value problem considered in this context. Thus, we can conclude that even if we take into account the internal variables, this fact does not affect the uniqueness result regarding the solution of the mixed initial-boundary value problem in this context.

Elastoviscoplastic Models with Relaxed Configurations and Internal State Variables

1990 ◽  
Vol 43 (7) ◽  
pp. 131-151 ◽  
Author(s):  
Sanda Cleja T¸igoiu ◽  
Eugen Soo´s
Keyword(s):  
Experimental Data ◽  
Structural Analysis ◽  
Internal State ◽  
State Variables ◽  
Internal State Variables ◽  
Local Current

We present the microstructural basis, the initial macroscopical formulations, and a possible axiomatic reconstruction of the elastoviscoplastic model for metals based on the use of the local, current, relaxed configurations. Structural analysis and experimental data show that using these configurations offers advantages for the formulation of the material laws when the deformations are small or moderately large. Our review aims to be a concise, historical, and critical exposition of the main stages, contributions and results, which led, during the late sixties and the beginning of seventies, to the formulation of the fundamental ideas lying at the basis of the model. We delineate the role played by Lee, Liu, Teodosiu, Sidoroff, Mandel, and Kratochvil in the first formulation of the theory between 1966 and 1972, as well as the contributions of Dafalias and Loret to the development of the model between 1983 and 1985. Finally, we discuss some results obtained between 1985 and 1988 with models based on local current relaxed configurations.

scholarly journals Design of a biochemical circuit motif for learning linear functions

2014 ◽  
Vol 11 (101) ◽  
pp. 20140902 ◽  
Author(s):  
Matthew R. Lakin ◽  
Amanda Minnich ◽  
Terran Lane ◽  
Darko Stefanovic
Keyword(s):  
Internal State ◽  
Linear Functions ◽  
Learning Performance ◽  
Adaptive Behaviour ◽  
Biological Processes ◽  
Biochemical System ◽  
Biochemical Systems ◽  
Robustness To Noise ◽  
Novel Design

Learning and adaptive behaviour are fundamental biological processes. A key goal in the field of bioengineering is to develop biochemical circuit architectures with the ability to adapt to dynamic chemical environments. Here, we present a novel design for a biomolecular circuit capable of supervised learning of linear functions, using a model based on chemical reactions catalysed by DNAzymes. To achieve this, we propose a novel mechanism of maintaining and modifying internal state in biochemical systems, thereby advancing the state of the art in biomolecular circuit architecture. We use simulations to demonstrate that the circuit is capable of learning behaviour and assess its asymptotic learning performance, scalability and robustness to noise. Such circuits show great potential for building autonomous in vivo nanomedical devices. While such a biochemical system can tell us a great deal about the fundamentals of learning in living systems and may have broad applications in biomedicine (e.g. autonomous and adaptive drugs), it also offers some intriguing challenges and surprising behaviours from a machine learning perspective.

scholarly journals Every laboratory with a fluorescence microscope should consider counting molecules

2014 ◽  
Vol 25 (10) ◽  
pp. 1545-1548 ◽  
Author(s):  
Valerie C. Coffman ◽  
Jian-Qiu Wu
Keyword(s):  
Mathematical Modeling ◽  
Fluorescence Microscopy ◽  
Protein Complexes ◽  
The State ◽  
Fluorescence Microscope ◽  
Cellular Structures ◽  
Biological Processes ◽  
Protein Molecules ◽  
Parameter Values

Protein numbers in cells determine rates of biological processes, influence the architecture of cellular structures, reveal the stoichiometries of protein complexes, guide in vitro biochemical reconstitutions, and provide parameter values for mathematical modeling. The purpose of this essay is to increase awareness of methods for counting protein molecules using fluorescence microscopy and encourage more cell biologists to report these numbers. We address the state of the field in terms of utility and accuracy of the numbers reported and point readers to references for details of specific techniques and applications.

Modeling and Simulation of Microstructure Evolution in Extruded Aluminum Profiles

2009 ◽  
Vol 424 ◽  
pp. 43-50
Author(s):  
Farhad Parvizian ◽  
T. Kayser ◽  
Bob Svendsen
Keyword(s):  
Plastic Deformation ◽  
Aluminum Alloys ◽  
Modeling And Simulation ◽  
Microstructure Evolution ◽  
Internal State ◽  
Extrusion Process ◽  
State Variables ◽  
Cooling Process ◽  
Microstructure Parameters ◽  
Simulation Results

The purpose of this work is to predict the microstructure evolution of aluminum alloys during hot metal forming processes using the Finite Element Method (FEM). Here, the focus will be on the extrusion process of aluminum alloys. Several micromechanical mechanisms such as diffusion, recovery, recrystallization and grain growth are involved in various subsequent stages of the extrusion and the cooling process afterward. The evolution of microstructure parameters is motivated by plastic deformation and temperature. A number of thermomechanical aspects such as plastic deformation, heat transfer between the material and the container, heat generated by friction, and cooling process after the extrusion are involved in the extrusion process and result in changes in temperature and microstructure parameters subsequently. Therefore a thermomechanically coupled modeling and simulation which includes all of these aspects is required for an accurate prediction of the microstructure evolution. A brief explanation of the isotropic thermoelastic viscoplastic material model including some of the simulation results of this model, which is implemented as a user material (UMAT) in the FEM software ABAQUS, will be given. The microstructure variables are thereby modeled as internal state variables. The simulation results are finally compared with some experimental results.

A constitutive model for anisotropic, kinematic hardening materials

1997 ◽  
Vol 32 (3) ◽  
pp. 175-181
Author(s):  
W Deng ◽  
A Asundi ◽  
C W Woo
Keyword(s):  
Inelastic Deformation ◽  
Internal State ◽  
Kinematic Hardening ◽  
Small Deformation ◽  
Inelastic Strain ◽  
State Variables ◽  
Internal State Variables ◽  
Deformation Plasticity ◽  
Independent Variable ◽  
Evolution Laws

Based on previous work by the authors, a model for anisotropic, kinematic hardening materials is constructed to describe constitutive equations and evolution laws in rate-independent, small deformation plasticity on the basis of thermodynamics. Unlike other theories developed earlier wherein only internal state variables are chosen to describe inelastic deformation, the present paper also considers inelastic strain as an independent variable. This can be shown to reduce to the well-known plastic strain in the case of rate-independent plasticity.

The steady two-dimensional reflexion of an oblique partly dispersed shock wave from a plane wall

1973 ◽  
Vol 61 (1) ◽  
pp. 159-172 ◽  
Author(s):  
H. Buggisch
Keyword(s):  
Shock Wave ◽  
Internal State ◽  
Plane Wall ◽  
Plane Shock ◽  
Two Dimensional ◽  
State Variables ◽  
Reflected Shock ◽  
Internal State Variables ◽  
Specific Entropy ◽  
Instantaneous Values

The steady two-dimensional problem of reflexion of an oblique partly dispersed plane shock wave from a plane wall is studied analytically. Viscosity, diffusion and heat conduction are neglected. The thermodynamic state of the gas is assumed to be determined by the instantaneous values of the specific entropy s, pressure p and a finite number of internal state variables. Results for the flow field behind the reflected shock are obtained by a perturbation method which is based on the assumption that the influence of relaxation is relatively weak.

scholarly journals A Unified Constitutive Model for Creep and Cyclic Viscoplasticity Behavior Simulation of Steels Based on the Absolute Reaction Rate Theory

2017 ◽  
Vol 2017 ◽  
pp. 1-13
Author(s):  
Huayan Chen ◽  
Xiangguo Zeng ◽  
Yang Guo ◽  
Fang Wang
Keyword(s):  
Constitutive Model ◽  
Reaction Rate ◽  
Internal State ◽  
Rate Theory ◽  
State Variables ◽  
Absolute Reaction Rate Theory ◽  
Reaction Rate Theory ◽  
Absolute Reaction Rate ◽  
The Absolute ◽  
Absolute Reaction

In this work, the viscoplasticity and creep behavior for modified 9Cr-1Mo and 316 stainless steels were investigated. Based on the absolute reaction rate theory, a unified constitutive model incorporating internal state variables was proposed to characterize the evolution of the back stress. Also, the model was implemented by the ABAQUS system with the semi-implicit stress integration. Compared to the experimental data, the results demonstrated that the proposed approach could effectively simulate the cyclic softening and hardening behavior for such structural steels.

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