Related papers: Local identifiability of a parameter function in a…
The formal term-by-term differentiation with respect to parameters is demonstrated to be legitimate for the Mittag-Leffler type functions. The justification of differentiation formulas is made by using the concept of the uniform…
In this paper, we introduce a novel concept for learning of the parameters in a neural network. Our idea is grounded on modeling a learning problem that addresses a trade-off between (i) satisfying local objectives at each node and (ii)…
We consider the identifiability and stable numerical estimation of multiple parameters in a Cahn-Hilliard model for phase separation. Spatially resolved measurements of the phase fraction are assumed to be accessible, with which the…
We consider initial value problems of nonlinear dynamical systems, which include physical parameters. A quantity of interest depending on the solution is observed. A discretisation yields the trajectories of the quantity of interest in many…
We develop a weighted local likelihood estimate for the parameters that govern the local spatial dependency of a locally stationary random field. The advantage of this local likelihood estimate is that it smoothly downweights the influence…
In the framework of an extended phenomenological approach to phase transitions, it is shown that existing nonlinear relation between local critical atomic parameters and phenomenological order parameter induces the corresponding nonlinear…
This note provides a detailed algorithm to the application of local (perturbation) analysis of differential equations which is normally taught at graduate math courses. Exercise books often present more abstract and simplified versions of…
The Euler characteristic, thought of as a function that assigns a numerical value to every finite simplicial complex, is locally determined in both a combinatorial sense and a geometric sense. In this note we show that not every function…
Modelling, parameter identification, and simulation play an important role in systems biology. Usually, the goal is to determine parameter values that minimise the difference between experimental measurement values and model predictions in…
The sensitivity parameter is widely used for quantifying fine tuning. However, examples show it fails to give correct results under certain circumstances. We argue that these problems only occur when calculating the sensitivity of a…
Structural global parameter identifiability indicates whether one can determine a parameter's value from given inputs and outputs in the absence of noise. If a given model has parameters for which there may be infinitely many values, such…
A computation method of algebraic local cohomology with parameters, associated with zero-dimensional ideal with parameter, is introduced. This computation method gives us in particular a decomposition of the parameter space depending on the…
Estimation of parameters in differential equation models can be achieved by applying learning algorithms to quantitative time-series data. However, sometimes it is only possible to measure qualitative changes of a system in response to a…
In several model-based system maintenance problems, parameters are used to represent unknown characteristics of a component, equipment degradation, etc. This allows for modelling constant, slow-varying terms. The identifiability of these…
Identifiability and sloppiness are investigated in this paper for the parameters of a descriptor system based on its frequency response samples. Two metrics are suggested respectively for measuring absolute and relative sloppiness of the…
We study the `local entanglement' remaining after filtering operations corresponding to imperfect measurements performed by one or both parties, such that the parties can only determine whether or not the system is located in some region of…
Ordinary differential equation models have become a standard tool for the mechanistic description of biochemical processes. If parameters are inferred from experimental data, such mechanistic models can provide accurate predictions about…
This paper deals with a unifying approach to the problems of computing the admissible sets of parametrical multi perturbations in appropriate bounded sets such that some fundamental properties of parameter-varying linear dynamic systems are…
In the paper, several concrete examples, as well as their numerical simulations, are given to show that parameter identification based on the so-called adaptive synchronization techniques might be failed if those functions with parameters…
In distributed-parameter inverse problems in computational mechanics, spatially varying fields are inferred from noisy, indirect, and heterogeneous observations. The relevant identifiability question concerns which spatial perturbation…