Peter Gardner | Searcharxiv

arXiv2026

Infrared photonics for healthcare: A roadmap for proactive and predictive health management

The field of infrared (IR) photonics is currently undergoing remarkable progress, moving rapidly towards practical sensing applications demanded by medical therapy and diagnostics (theranostics). The Developments can be divided into three main categories: (i) novel devices and measurement concepts including advanced updates of classical approaches that push medical sensing into the spotlight; (ii) new demonstrations of photonic integrated circuit (PIC-)based IR devices enabling highly miniaturized sensors for point-of-care application as well as medical and wellness wearables; and (iii) technologically-mature IR demonstrators that enable first medical sensing and treatment applications. This roadmap paper provides a consolidated overview of this highly dynamic and interdisciplinary research field with a focus on the major roadblocks that limit the widespread adoption of IR photonics in large-scale medical diagnostics. Special attention is given to the ambivalence between the molecular-level spectroscopic interpretation and a broader health-state assessment, highlighting the need for a common framework. Additionally, the paper discusses the critical importance of unified measurement standards, calibration protocols, and medical certification processes to ensure the validity of experimental results, reproducibility, and clinical trust, particularly when novel experimental techniques and AI algorithms are involved. Perspectives from major past and current contributors to application-oriented IR photonics will be provided.

physics.app-ph↗

arXiv2018

On the Domination Number of Permutation Graphs and an Application to Strong Fixed Points

A permutation graph $G_\pi$ is a simple graph with vertices corresponding to the elements of $\pi$ and an edge between $i$ and $j$ when $i$ and $j$ are inverted in $\pi$. A set of vertices $D$ is said to dominate a graph $G$ when every vertex in $G$ is either an element of $D$, or adjacent to an element of $D$. The domination number $\gamma(G)$ is defined as the cardinality of a minimum dominating set of $G$. A strong fixed point of a permutation $\pi$ of order $n$ is an element $k$ such that $\pi^{-1}(j)<\pi^{-1}(k)$ for all $j \pi^{-1}(k)$ for all $i>k$. In this article, we count the number of connected permutation graphs on $n$ vertices with domination number $1$ and domination number $\frac{n}{2}$. We further show that for a natural number $k\leq \frac{n}{2}$, there exists a connected permutation graph on $n$ vertices with domination number $k$. We find a closed expression for the number of permutation graphs dominated by a set with two elements, and we find a closed expression for the number of permutation graphs efficiently dominated by any set of vertices. We conclude by providing an application of these results to strong fixed points, proving some conjectures posed on the OEIS.

math.CO↗