The sensitivity of a multiple eigenvalue of a matrix under perturbations can be measured by its Hölder condition number. Various extensions of this concept are considered. A meaningful notion of structured Hölder condition numbers is introduced and it is shown that many existing results on structured condition numbers for simple eigenvalues carry over to multiple eigenvalues. The structures investigated in more detail include real, Toeplitz, Hankel, symmetric, skew-symmetric, Hamiltonian, and skew-Hamiltonian matrices. Furthermore, unstructured and structured Hölder condition numbers for multiple eigenvalues of matrix pencils are introduced. Particular attention is given to symmetric/skew-symmetric, Hermitian and palindromic pencils. It is also shown how matrix polynomial eigenvalue problems can be covered within this framework.

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a pathogen of immense public health concern. Efforts to control the disease have only proven mildly successful, and the disease will likely continue to cause excessive fatalities until effective preventative measures (such as a vaccine) are developed. To develop disease management strategies, a better understanding of SARS-CoV-2 pathogenesis and population susceptibility to infection are needed. To this end, mathematical modeling can provide a robust in silico tool to understand COVID-19 pathophysiology and the in vivo dynamics of SARS-CoV-2. Guided by ACE2-tropism (ACE2 receptor dependency for infection) of the virus and by incorporating cellular-scale viral dynamics and innate and adaptive immune responses, we have developed a multiscale mechanistic model for simulating the time-dependent evolution of viral load distribution in susceptible organs of the body (respiratory tract, gut, liver, spleen, heart, kidneys, and brain). Following parameter quantification with in vivo and clinical data, we used the model to simulate viral load progression in a virtual patient with varying degrees of compromised immune status. Further, we ranked model parameters through sensitivity analysis for their significance in governing clearance of viral load to understand the effects of physiological factors and underlying conditions on viral load dynamics. Antiviral drug therapy, interferon therapy, and their combination were simulated to study the effects on viral load kinetics of SARS-CoV-2. The model revealed the dominant role of innate immunity (specifically interferons and resident macrophages) in controlling viral load, and the importance of timing when initiating therapy after infection.

While plasma concentration kinetics has traditionally been the predictor of drug pharmacological effects, it can occasionally fail to represent kinetics at the site of action, particularly for solid tumors. This is especially true in the case of delivery of therapeutic macromolecules (drug‐loaded nanomaterials or monoclonal antibodies), which can experience challenges to effective delivery due to particle size‐dependent diffusion barriers at the target site. As a result, disparity between therapeutic plasma kinetics and kinetics at the site of action may exist, highlighting the importance of target site concentration kinetics in determining the pharmacodynamic effects of macromolecular therapeutic agents. Assessment of concentration kinetics at the target site has been facilitated by non‐invasive in vivo imaging modalities. This allows for visualization and quantification of the whole‐body disposition behavior of therapeutics that is essential for a comprehensive understanding of their pharmacokinetics and pharmacodynamics. Quantitative non‐invasive imaging can also help guide the development and parameterization of mathematical models for descriptive and predictive purposes. Here, we present a review of the application of state‐of‐the‐art imaging modalities for quantitative pharmacological evaluation of therapeutic nanoparticles and monoclonal antibodies, with a focus on their integration with mathematical models, and identify challenges and opportunities. This article is categorized under: Therapeutic Approaches and Drug Discovery > Nanomedicine for Oncologic Disease Diagnostic Tools > in vivo Nanodiagnostics and Imaging Nanotechnology Approaches to Biology > Nanoscale Systems in Biology

Artículo de publicación ISIThe Gibbs sampler is an iterative algorithm used to simulate Gaussian random vectors subject to inequality constraints. This algorithm relies on the fact that the distribution of a vector component conditioned by the other components is Gaussian, the mean and variance of which are obtained by solving a kriging system. If the number of components is large, kriging is usually applied with a moving search neighborhood, but this practice can make the simulated vector not reproduce the target correlation matrix. To avoid these problems, variations of the Gibbs sampler are presented. The conditioning to inequality constraints on the vector components can be achieved by simulated annealing or by restricting the transition matrix of the iterative algorithm. Numerical experiments indicate that both approaches provide realizations that reproduce the correlation matrix of the Gaussian random vector, but some conditioning constraints may not be satisfied when using simulated annealing. On the contrary, the restriction of the transition matrix manages to satisfy all the constraints, although at the cost of a large number of iterations.This research was partially funded by the Chilean program MECESUP UCN0711. The authors are grateful to Dr. Christian Lantuéjoul (Mines ParisTech) and to the anonymous reviewers for their insightful comments