Equilibrium states of the pressure function for products of matrices

Let $\{M_i\}_{i=1}^\ell$ be a non-trivial family of $d\times d$ complex matrices, in the sense that for any $n\in \N$, there exists $i_1... i_n\in \{1,..., \ell\}^n$ such that $M_{i_1}... M_{i_n}\neq {\bf 0}$. Let $P \colon (0,\infty)\to \R$ be the pressure function of $\{M_i\}_{i=1}^\ell$. We show that for each $q>0$, there are at most $d$ ergodic $q$-equilibrium states of $P$, and each of them satisfies certain Gibbs property.Comment: 12 pages. To appear in DCD

Omnidirectionally Bending to the Normal in epsilon-near-Zero Metamaterials

Contrary to conventional wisdom that light bends away from the normal at the interface when it passes from high to low refractive index media, here we demonstrate an exotic phenomenon that the direction of electromagnetic power bends towards the normal when light is incident from arbitrary high refractive index medium to \epsilon-near-zero metamaterial. Moreover, the direction of the transmitted beam is close to the normal for all angles of incidence. In other words, the electromagnetic power coming from different directions in air or arbitrary high refractive index medium can be redirected to the direction almost parallel to the normal upon entering the \epsilon-near-zero metamaterial. This phenomenon is counterintuitive to the behavior described by conventional Snell's law and resulted from the interplay between \epsilon-near-zero and material loss. This property has potential applications in communications to increase acceptance angle and energy delivery without using optical lenses and mechanical gimbals

A machine learning approach to explore the spectra intensity pattern of peptides using tandem mass spectrometry data

Background: A better understanding of the mechanisms involved in gas-phase fragmentation of peptides is essential for the development of more reliable algorithms for high-throughput protein identification using mass spectrometry (MS). Current methodologies depend predominantly on the use of derived m/z values of fragment ions, and, the knowledge provided by the intensity information present in MS/MS spectra has not been fully exploited. Indeed spectrum intensity information is very rarely utilized in the algorithms currently in use for high-throughput protein identification. Results: In this work, a Bayesian neural network approach is employed to analyze ion intensity information present in 13878 different MS/MS spectra. The influence of a library of 35 features on peptide fragmentation is examined under different proton mobility conditions. Useful rules involved in peptide fragmentation are found and subsets of features which have significant influence on fragmentation pathway of peptides are characterised. An intensity model is built based on the selected features and the model can make an accurate prediction of the intensity patterns for given MS/MS spectra. The predictions include not only the mean values of spectra intensity but also the variances that can be used to tolerate noises and system biases within experimental MS/MS spectra. Conclusion: The intensity patterns of fragmentation spectra are informative and can be used to analyze the influence of various characteristics of fragmented peptides on their fragmentation pathway. The features with significant influence can be used in turn to predict spectra intensities. Such information can help develop more reliable algorithms for peptide and protein identification

Resonant Transmission of Electromagnetic Fields through Subwavelength Zero-ϵ\epsilon Slits

We theoretically investigate the transmission of electromagnetic radiation through a metal plate with a zero-$\epsilon$ metamaterial slit, where the permittivity tends towards zero over a given bandwidth. Our analytic results demonstrate that the transmission coefficient can be substantial for a broad range of slit geometries, including subwavelength widths that are many wavelengths long. This novel resonant effect has features quite unlike the Fabry-P\'{e}rot-like resonances that have been observed in conductors with deep channels. We further reveal that these high impedance ultranarrow zero-$\epsilon$ channels can have significantly {\it greater} transmission compared to slits with no wave impedance difference across them