Extensions to a procedure for generating locally identifiable reparameterisations of unidentifiable systems

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...

Green’s Theorem connects the circulation of a vector field around a closed curve with the behavior of the field across the region enclosed by that curve. It provides a way to replace a line integral around a boundary with a double integral over the interior region, making it especially useful in plane geometry, fluid flow, and vector calculus.Although Green’s Theorem is often introduced using simple regions without gaps, it can also be applied to regions made from several simple parts. This...

Nuclear reprogramming is the process of switching gene expression of one cell type to that of another cell type, usually from a differentiated cell state to an undifferentiated cell state. Differentiation occurs during processes such as development and morphogenesis, tissue regeneration, and malignancy. Cells can also be artificially induced to reprogram their gene expression by techniques such as nuclear transfer, induced pluripotency, and cell fusion. Such techniques have many applications in...

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...

Multiple integrals are often used to evaluate areas, volumes, mass distributions, and other physical quantities over regions in two or three dimensions. In many problems, however, the original region may have complicated curved boundaries when expressed in Cartesian coordinates. These complex boundaries can make the limits of integration difficult to describe and the overall calculation cumbersome. To simplify the evaluation process, a change of variables is introduced that transforms the...

Entropy is a state function, so the standard entropy change for a chemical reaction (ΔS°rxn) can be calculated from the difference in standard entropy between the products and the reactants.