Mingjing Liu | Searcharxiv

arXiv2026

Ultrasensitive Terahertz Metasurface Biosensor Based on Quasi-Bound States in the Continuum

The terahertz (THz) spectral regime offers unique opportunities for next-generation biochemical sensing due to its non-destructive, label-free probing capability and strong sensitivity to molecular vibrations. However, conventional THz biosensors remain hampered by intrinsically low-quality factors and limited sensitivity, severely restricting their utility for trace-level biochemical and chemical detection. Here, we report an ultrasensitive THz metasurface biosensor that harnesses quasi-bound states in the continuum (QBICs) with sharp resonances and enhanced light-matter interactions to overcome these limitations. As a proof of concept, the device achieves label-free detection of a sulfur-containing amino acid cysteine, with an ultrahigh sensitivity of 492 GHz/RIU and an ultralow detection limit down to 0.00025 mg/mL. The synergy between QBIC-induced field confinement and meticulous structural optimization of the metasurface underpins this performance, marking a significant advance over conventional THz metasurface biosensing schemes. These results establish QBIC-based metasurfaces as a promising platform for ultrasensitive and high-precision biochemical and chemical sensing, with broad implications for medical diagnostics, food safety, and environmental monitoring.

physics.optics↗

arXiv2013

Some unsolved problems on cycles

Hajos' conjecture that every simple even graph on $n$ vertices can be decomposed into at most $(n-1)/2$ cycles (see L. Lovasz, On covering of graphs, in: P. Erdos, G.O.H. Katona (Eds.), Theory of Graphs, Academic Press, New York, 1968, pp. 231 - 236). Let $f(n)$ be the maximum number of edges in a graph on $n$ vertices in which no two cycles have the same length. P. Erdos raised the problem of determining $f(n)$ (see J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (Macmillan, New York, 1976), p.247, Problem 11). Given a graph $H$, what is the maximum number of edges of a graph with $n$ vertices not containing $H$ as a subgraph? This number is denoted $ex(n,H)$, and is known as the Turan number. P. Erdos conjectured that there exists a positive constant $c$ such that $ex(n,C_{2k})\geq cn^{1+1/k}$(see P. Erdos, Some unsolved problems in graph theory and combinatorial analysis, Combinatorial Mathematics and its Applications (Proc. Conf., Oxford, 1969), pp. 97--109, Academic Press, London, 1971). This paper summarizes some results on these problems and the conjectures that relate to these. We do not think Hajós conjecture is true.

math.CO↗