Experimental and numerical studies of terahertz surface waves on a thin metamaterial film

We present experimental and numerical studies of localized terahertz surface waves on a subwavelength-thick metamaterial film consisting of in-plane split-ring resonators. A simple and intuitive model is derived that describes the propagation of surface waves as guided modes in a waveguide filled with a Lorentz-like medium. The effective medium model allows to deduce the dispersion relation of the surface waves in excellent agreement with the numerical data obtained from 3-D full-wave calculations. Both the accuracy of the analytical model and the numerical calculations are confirmed by spectroscopic terahertz time domain measurements.Comment: 3 pages, 3 figure

Gradient Index Metamaterial Based on Slot Elements

We present a gradient-index (GRIN) metamaterial based on an array of annular slots. The structure allows a large variation of the effective refractive index under normal-to-plane incidence and thus enables the construction of GRIN devices consisting of only a small number of functional layers. Using full-wave simulations, we demonstrate the annular slot concept by means of a 3-unit-cell thin GRIN lens for the terahertz (THz) range. In the presented realizations, we achieved an index contrast of Delta n = 1.5 resulting in a highly refractive lens suitable for focusing THz radiation to a spot size smaller than the wavelength.Comment: 4 pages, 5 figure

In-Plane Focusing of Terahertz Surface Waves on a Gradient Index Metamaterial Film

We designed and implemented a gradient index metasurface for the in-plane focusing of confined terahertz surface waves. We measured the spatial propagation of the surface waves by two-dimensional mapping of the complex electric field using a terahertz near-field spectroscope. The surface waves were focused to a diameter of 500 \micro m after a focal length of approx. 2 mm. In the focus, we measured a field amplitude enhancement of a factor of 3.Comment: 6 pages, 4 figure

Metamaterial near-field sensor for deep-subwavelength thickness measurements and sensitive refractometry in the terahertz frequency range

We present a metamaterial-based terahertz (THz) sensor for thickness measurements of subwavelength-thin materials and refractometry of liquids and liquid mixtures. The sensor operates in reflection geometry and exploits the frequency shift of a sharp Fano resonance minimum in the presence of dielectric materials. We obtained a minimum thickness resolution of 12.5 nm (1/16000 times the wavelength of the THz radiation) and a refractive index sensitivity of 0.43 THz per refractive index unit. We support the experimental results by an analytical model that describes the dependence of the resonance frequency on the sample material thickness and the refractive index.Comment: 10 pages, 5 figure

Collectively canalizing Boolean functions

This paper studies the mathematical properties of collectively canalizing Boolean functions, a class of functions that has arisen from applications in systems biology. Boolean networks are an increasingly popular modeling framework for regulatory networks, and the class of functions studied here captures a key feature of biological network dynamics, namely that a subset of one or more variables, under certain conditions, can dominate the value of a Boolean function, to the exclusion of all others. These functions have rich mathematical properties to be explored. The paper shows how the number and type of such sets influence a function's behavior and define a new measure for the canalizing strength of any Boolean function. We further connect the concept of collective canalization with the well-studied concept of the average sensitivity of a Boolean function. The relationship between Boolean functions and the dynamics of the networks they form is important in a wide range of applications beyond biology, such as computer science, and has been studied with statistical and simulation-based methods. But the rich relationship between structure and dynamics remains largely unexplored, and this paper is intended as a contribution to its mathematical foundation.Comment: 15 pages, 2 figure

Immobilized stem–loop structured probes as conformational switches for enzymatic detection of microbial 16S rRNA

We have designed and evaluated novel DNA stem–loop structured probes for enzymatic detection of nucleic acid targets. These probes constitute a novel class of conformational switches for enzymatic activity, which in the absence of a target sterically shield an affinity label and upon hybridization of the target to the recognition sequence that forms the loop of the probe restore accessibility of the label for the binding of a reporter enzyme. Analysis of probe characteristics revealed stem stability as the most important parameter governing detection functionality, while other factors such as the length of linker molecules attaching the label to the stem–loop structure and the nature of the solid support proved to be less critical. Apparently, the bulky nature of the reporter enzyme facilitates shielding of the label in the absence of the target, thereby conferring considerable structural tolerance to the conformational switch system. The stem–loop structured probes allow sensitive detection of unlabeled nucleic acid targets. Employing a microtiter assay format, 4 ng of bacterial 16S ribosomal RNA corresponding to 8 fmol could be detected, which can be compared favorably with current immobilized molecular beacon concepts based on fluorescence detection

Inference in receiver operating characteristic surface analysis via a trinormal model‐based testing approach

Receiver operating characteristic (ROC) analysis is the methodological framework of choice for the assessment of diagnostic markers and classification procedures in general, in both two‐class and multiple‐class classification problems. We focus on the three‐class problem for which inference usually involves formal hypothesis testing using a proxy metric such as the volume under the ROC surface (VUS). In this article, we develop an existing approach from the two‐class ROC framework. We define a hypothesis‐testing procedure that directly compares two ROC surfaces under the assumption of the trinormal model. In the case of the assessment of a single marker, the corresponding ROC surface is compared with the chance plane, that is, to an uninformative marker. A simulation study investigating the proposed tests with existing ones on the basis of the VUS metric follows. Finally, the proposed methodology is applied to a dataset of a panel of pancreatic cancer diagnostic markers. The described testing procedures along with related graphical tools are supported in the corresponding R‐package trinROC, which we have developed for this purpose

Inference in receiver operating characteristic surface analysis via a trinormal model‐based testing approach

Receiver operating characteristic (ROC) analysis is the methodological framework of choice for the assessment of diagnostic markers and classification procedures in general, in both two‐class and multiple‐class classification problems. We focus on the three‐class problem for which inference usually involves formal hypothesis testing using a proxy metric such as the volume under the ROC surface (VUS). In this article, we develop an existing approach from the two‐class ROC framework. We define a hypothesis‐testing procedure that directly compares two ROC surfaces under the assumption of the trinormal model. In the case of the assessment of a single marker, the corresponding ROC surface is compared with the chance plane, that is, to an uninformative marker. A simulation study investigating the proposed tests with existing ones on the basis of the VUS metric follows. Finally, the proposed methodology is applied to a dataset of a panel of pancreatic cancer diagnostic markers. The described testing procedures along with related graphical tools are supported in the corresponding R‐package trinROC, which we have developed for this purpose