Functions tiling simultaneously with two arithmetic progressions

We consider measurable functions $f$ on $\mathbb{R}$ that tile simultaneously by two arithmetic progressions $\alpha \mathbb{Z}$ and $\beta \mathbb{Z}$ at respective tiling levels $p$ and $q$. We are interested in two main questions: what are the possible values of the tiling levels $p,q$, and what is the least possible measure of the support of $f$? We obtain sharp results which show that the answers depend on arithmetic properties of $\alpha, \beta$ and $p,q$, and in particular, on whether the numbers $\alpha, \beta$ are rationally independent or not.Comment: To appear in the Proceedings of the London Mathematical Societ

Prefect Klein tunneling in anisotropic graphene-like photonic lattices

We study the scattering of waves off a potential step in deformed honeycomb lattices. For small deformations below a critical value, perfect Klein tunneling is obtained. This means that a potential step in any direction transmits waves at normal incidence with unit transmission probability, irrespective of the details of the potential. Beyond the critical deformation, a gap in the spectrum is formed, and a potential step in the deformation direction reflects all normal-incidence waves, exhibiting a dramatic transition form unit transmission to total reflection. These phenomena are generic to honeycomb lattice systems, and apply to electromagnetic waves in photonic lattices, quasi-particles in graphene, cold atoms in optical lattices

Probing topological invariants in the bulk of a non-Hermitian optical system

Topological insulators are insulating in the bulk but feature conducting states on their surfaces. Standard methods for probing their topological properties largely involve probing the surface, even though topological invariants are defined via the bulk band structure. Here, we utilize non-hermiticy to experimentally demonstrate a topological transition in an optical system, using bulk behavior only, without recourse to surface properties. This concept is relevant for a wide range of systems beyond optics, where the surface physics is difficult to probe

Introductory programming: a systematic literature review

As computing becomes a mainstream discipline embedded in the school curriculum and acts as an enabler for an increasing range of academic disciplines in higher education, the literature on introductory programming is growing. Although there have been several reviews that focus on specific aspects of introductory programming, there has been no broad overview of the literature exploring recent trends across the breadth of introductory programming. This paper is the report of an ITiCSE working group that conducted a systematic review in order to gain an overview of the introductory programming literature. Partitioning the literature into papers addressing the student, teaching, the curriculum, and assessment, we explore trends, highlight advances in knowledge over the past 15 years, and indicate possible directions for future research

Correlation of p16INK4A Expression and HPV Copy Number with Cellular FTIR Spectroscopic Signatures of Cervical Cancer Cells

Cervical cancer, a potentially preventable disease, has its main aetiology in infection by high risk human papillomavirus (HR-HPV). Approaches to improving cervical cancer screening and diagnostic methodologies include molecular biological analysis, targeting of biomarker proteins, but also exploration and implementation of new techniques such as vibrational spectroscopy. This study correlates the biomarker protein p16INK4A expression levels dependent on HPV copy number with the infrared absorption spectral signatures of the cervical cancer cell lines, HPV negative C33A, HPV-16 positive SiHa and CaSki and HPV-18 positive HeLa. Confocal fluorescence microscopy demonstrated that p16INK4A is expressed in all investigated cell lines in both nuclear and cytoplasmic regions, although predominantly in the cytoplasm. Flow cytometry was used to quantify the p16INK4A expression levels and demonstrated a correlation, albeit nonlinear, between the reported number of integrated HPV copies and p16INK4A expression levels. CaSki cells were found to have the highest level of expression, HeLa intermediate levels, and SiHa and C33A the lowest levels. FTIR spectra revealed differences in nucleic acid, lipid and protein signatures between the cell lines with varying HPV copy number. Peak intensities exhibited increasing tendency in nucleic acid levels and decreasing tendency in lipid levels with increasing HPV copy number, and although they were found to be nonlinearly correlated with the HPV copy number, their dependence on p16INK4A levels was found to be close to linear. Principal Component Analysis (PCA) of the Infrared absorption spectra revealed differences between nuclear and cytoplasmic spectroscopic signatures for all cell lines, and furthermore clearly differentiated the groups of spectra representing each cell line. Finally, Partial Least Squares (PLS) analysis was employed to construct a model which can predict the p16INK4A expression level based on a spectral fingerprint of a cell line, demonstrating the diagnostic potential of spectroscopic techniques