1,860 research outputs found
Observability and Synchronization of Neuron Models
Observability is the property that enables to distinguish two different
locations in -dimensional state space from a reduced number of measured
variables, usually just one. In high-dimensional systems it is therefore
important to make sure that the variable recorded to perform the analysis
conveys good observability of the system dynamics. In the case of networks
composed of neuron models, the observability of the network depends
nontrivially on the observability of the node dynamics and on the topology of
the network. The aim of this paper is twofold. First, a study of observability
is conducted using four well-known neuron models by computing three different
observability coefficients. This not only clarifies observability properties of
the models but also shows the limitations of applicability of each type of
coefficients in the context of such models. Second, a multivariate singular
spectrum analysis (M-SSA) is performed to detect phase synchronization in
networks composed by neuron models. This tool, to the best of the authors'
knowledge has not been used in the context of networks of neuron models. It is
shown that it is possible to detect phase synchronization i)~without having to
measure all the state variables, but only one from each node, and ii)~without
having to estimate the phase
A new SSI algorithm for LPTV systems: Application to a hinged-bladed helicopter
Many systems such as turbo-generators, wind turbines and helicopters show intrinsic time-periodic behaviors. Usually, these structures are considered to be faithfully modeled as linear time-invariant (LTI). In some cases where the rotor is anisotropic, this modeling does not hold and the equations of motion lead necessarily to a linear periodically time- varying (referred to as LPTV in the control and digital signal field or LTP in the mechanical and nonlinear dynamics world) model. Classical modal analysis methodologies based on the classical time-invariant eigenstructure (frequencies and damping ratios) of the system no more apply. This is the case in particular for subspace methods. For such time-periodic systems, the modal analysis can be described by characteristic exponents called Floquet multipliers. The aim of this paper is to suggest a new subspace-based algorithm that is able to extract these multipliers and the corresponding frequencies and damping ratios. The algorithm is then tested on a numerical model of a hinged-bladed helicopter on the ground
Input-dependent structural identifiability of nonlinear systems
A dynamic model is structurally identifiable if it is possible to infer its unknown parameters by observing its output. Structural identifiability depends on the system dynamics, output, and input, as well as on the specific values of initial conditions and parameters. Here we present a symbolic method that characterizes the input that a model requires to be structurally identifiable. It determines which derivatives must be non-zero in order to have a sufficiently exciting input. Our approach considers structural identifiability as a generalization of nonlinear observability and incorporates extended Lie derivatives. The methodology assesses structural identifiability for time-varying inputs and, additionally, it can be used to determine the input profile that is required to make the parameters structurally locally identifiable. Furthermore, it is sometimes possible to replace an experiment with time-varying input with multiple experiments with constant inputs. We implement the resulting method as a MATLAB toolbox named STRIKE-GOLDD2. This tool can assist in the design of new experiments for the purpose of parameter estimation
A mathematical model for breath gas analysis of volatile organic compounds with special emphasis on acetone
Recommended standardized procedures for determining exhaled lower respiratory
nitric oxide and nasal nitric oxide have been developed by task forces of the
European Respiratory Society and the American Thoracic Society. These
recommendations have paved the way for the measurement of nitric oxide to
become a diagnostic tool for specific clinical applications. It would be
desirable to develop similar guidelines for the sampling of other trace gases
in exhaled breath, especially volatile organic compounds (VOCs) which reflect
ongoing metabolism. The concentrations of water-soluble, blood-borne substances
in exhaled breath are influenced by: (i) breathing patterns affecting gas
exchange in the conducting airways; (ii) the concentrations in the
tracheo-bronchial lining fluid; (iii) the alveolar and systemic concentrations
of the compound. The classical Farhi equation takes only the alveolar
concentrations into account. Real-time measurements of acetone in end-tidal
breath under an ergometer challenge show characteristics which cannot be
explained within the Farhi setting. Here we develop a compartment model that
reliably captures these profiles and is capable of relating breath to the
systemic concentrations of acetone. By comparison with experimental data it is
inferred that the major part of variability in breath acetone concentrations
(e.g., in response to moderate exercise or altered breathing patterns) can be
attributed to airway gas exchange, with minimal changes of the underlying blood
and tissue concentrations. Moreover, it is deduced that measured end-tidal
breath concentrations of acetone determined during resting conditions and free
breathing will be rather poor indicators for endogenous levels. Particularly,
the current formulation includes the classical Farhi and the Scheid series
inhomogeneity model as special limiting cases.Comment: 38 page
Observability of Minimal Cell Models
Identifying and modeling of biological systems is very useful to understand cell's dynamic. To know what really happens inside the cell we need to observe the state of a cell. In fact observability is a structural property of a control system defined as the possibility to deduce the state of the system from observing its input-output behavior. Any complex cell model is a combination of some minimal models which are simpler than complex cell model because they have two dimensions. These models can describe the behavior of the cell. The property of observability for nonlinear systems is very useful in analyzing such systems. This paper deals with the observability of minimal cell models. Based on the fact that the minimal cell models are nonlinear, analyzing the property of these models need nonlinear methods. The method has been used for observability is Lie Derivative. The results indicate observability of minimal cell models
No entailing laws, but enablement in the evolution of the biosphere
Biological evolution is a complex blend of ever changing structural
stability, variability and emergence of new phenotypes, niches, ecosystems. We
wish to argue that the evolution of life marks the end of a physics world view
of law entailed dynamics. Our considerations depend upon discussing the
variability of the very "contexts of life": the interactions between organisms,
biological niches and ecosystems. These are ever changing, intrinsically
indeterminate and even unprestatable: we do not know ahead of time the "niches"
which constitute the boundary conditions on selection. More generally, by the
mathematical unprestatability of the "phase space" (space of possibilities), no
laws of motion can be formulated for evolution. We call this radical emergence,
from life to life. The purpose of this paper is the integration of variation
and diversity in a sound conceptual frame and situate unpredictability at a
novel theoretical level, that of the very phase space. Our argument will be
carried on in close comparisons with physics and the mathematical constructions
of phase spaces in that discipline. The role of (theoretical) symmetries as
invariant preserving transformations will allow us to understand the nature of
physical phase spaces and to stress the differences required for a sound
biological theoretizing. In this frame, we discuss the novel notion of
"enablement". This will restrict causal analyses to differential cases (a
difference that causes a difference). Mutations or other causal differences
will allow us to stress that "non conservation principles" are at the core of
evolution, in contrast to physical dynamics, largely based on conservation
principles as symmetries. Critical transitions, the main locus of symmetry
changes in physics, will be discussed, and lead to "extended criticality" as a
conceptual frame for a better understanding of the living state of matter
Machine learning and mapping algorithms applied to proteomics problems
Proteins provide evidence that a given gene is expressed, and machine learning algorithms can be applied to various proteomics problems in order to gain information about the underlying biology. This dissertation applies machine learning algorithms to proteomics data in order to predict whether or not a given peptide is observable by mass spectrometry, whether a given peptide can serve as a cell penetrating peptide, and then utilizes the peptides observed through mass spectrometry to aid in the structural annotation of the chicken genome. Peptides observed by mass spectrometry are used to identify proteins, and being able to accurately predict which peptides will be seen can allow researchers to analyze to what extent a given protein is observable. Cell penetrating peptides can possibly be utilized to allow targeted small molecule delivery across cellular membranes and possibly serve a role as drug delivery peptides. Peptides and proteins identified through mass spectrometry can help refine computational gene models and improve structural genome annotations
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