Convexity-Increasing Morphs of Planar Graphs

We study the problem of convexifying drawings of planar graphs. Given any planar straight-line drawing of an internally 3-connected graph, we show how to morph the drawing to one with strictly convex faces while maintaining planarity at all times. Our morph is convexity-increasing, meaning that once an angle is convex, it remains convex. We give an efficient algorithm that constructs such a morph as a composition of a linear number of steps where each step either moves vertices along horizontal lines or moves vertices along vertical lines. Moreover, we show that a linear number of steps is worst-case optimal. To obtain our result, we use a well-known technique by Hong and Nagamochi for finding redrawings with convex faces while preserving y-coordinates. Using a variant of Tutte's graph drawing algorithm, we obtain a new proof of Hong and Nagamochi's result which comes with a better running time. This is of independent interest, as Hong and Nagamochi's technique serves as a building block in existing morphing algorithms.Comment: Preliminary version in Proc. WG 201

Diffusion-weighted imaging in oral squamous cell carcinoma using 3 Tesla MRI: is there a chance for preoperative discrimination between benign and malignant lymph nodes in daily clinical routine?

Background Preoperative staging of cervical lymph nodes is important to determine the extent of neck dissection in patients with oral squamous cell carcinoma (OSCC). Purpose To evaluate whether a preoperative discrimination of benign and malignant cervical lymph nodes with diffusion-weighted imaging (DWI) (3T) is feasible for clinical application. Material and Methods Forty-five patients with histological proven OSCC underwent preoperative 3T-MRI. DWI (b=0, 500, and 1000s/mm(2)) was added to the standard magnetic resonance imaging (MRI) protocol. Mean apparent diffusion coefficients (ADC(mean)) were measured for lymph nodes with 3mm or more in short axis by two independent readers. Finally, these results were matched with histology. Results Mean ADC was significantly higher for malignant than for benign nodes (1.1430.188 * 10(-3) mm(2)/s vs. 0.987 +/- 0.215 * 10(-3) mm(2)/s). Using an ADC value of 0.994 * 10(-3) mm(2)/s as threshold results in a sensitivity of 80%, specificity of 65%, positive predictive value of 31%, and negative predictive value of 93%. Conclusion Due to a limited sensitivity and specificity DWI alone is not suitable to reliably discriminate benign from malignant cervical lymph nodes in daily clinical routine. Hence, the preoperative determination of the extent of neck dissection on the basis of ADC measurements is not meaningful

Entanglement in helium

Using a configuration-interaction variational method, we accurately compute the reduced, single-electron von Neumann entropy for several low-energy, singlet and triplet eigenstates of helium atom. We estimate the amount of electron-electron orbital entanglement for such eigenstates and show that it decays with energy.Comment: 5 pages, 2 figures, added references and discussio

Fluctuations in the spectra of open few-body systems

We investigate simple open few-body systems, the spectra of which exhibit fluctuating patterns, and review the conditions for the existence of an Ericson regime in deterministic, open quantum systems. A widely used criterion, the Lorentzian shape of the autocorrelation function of the spectrum, is shown to be insufficient for the occurrence of Ericson fluctuations: integrable systems or open systems that are not in the Ericson regime might display such an autocorrelation function. We also investigate the sensitivity of Ericson fluctuations on simplified models of realistic systems. In particular, we show that a simplified hydrogenic model for alkali atoms in crossed magnetic and electric fields does not yield Ericson fluctuations for a choice of the energy and field parameters where the realistic system is in the Ericson regime

S-wave scattering of a polarizable atom by an absorbing nanowire

We study the scattering of a polarizable atom by a conducting cylindrical wire with incoming boundary conditions, that is, total absorption, near the surface of the wire. Based on the explicit expression given recently [C. Eberlein and R. Zietal, Phys. Rev. A75, 032516 (2007)] for the nonretarded atom-wire potential, we formulate a hierarchy of approximations that enables the numerical determination of this potential to any desired accuracy as economically as possible. We calculate the complex s-wave scattering length for the effectively two-dimensional atom-wire scattering problem. The scattering length a depends on the radius R of the wire and a characteristic length beta related to the polarizability of the atom via a simple scaling relation, a = R (a) over tilde(beta/R). The "scaled scattering length" (a) over tilde tends to unity in the thick-wire limit beta/R -> 0, and it grows almost proportional to 1/R in the opposite thin-wire limit

Interaction of atomic quantum gases with a single carbon nanotube

We study inelastic processes in the hybrid quantum system constituted by a carbon nanotube (CNT) in contact with an ultracold quantum gas, such as a cloud of thermal atoms or a Bose-Einstein condensate (BEC). We present a parameter-free ab initio approach for the loss rate based on the underlying scattering process, considering the two-dimensional character of the system as well as the exact Casimir-Polder potential. The predicted loss rates are in perfect agreement with recent experimental results, obtained both for a thermal cloud of rubidium atoms and for a BEC. For the trap loss of a thermal cloud, we find that retardation effects become important and contribute significantly, which emphasises the crucial role of the exact interaction potential