Metric Dimension for Gabriel Unit Disk Graphs is NP-Complete

We show that finding a minimal number of landmark nodes for a unique virtual addressing by hop-distances in wireless ad-hoc sensor networks is NP-complete even if the networks are unit disk graphs that contain only Gabriel edges. This problem is equivalent to Metric Dimension for Gabriel unit disk graphs. The Gabriel edges of a unit disc graph induce a planar O(\sqrt{n}) distance and an optimal energy spanner. This is one of the most interesting restrictions of Metric Dimension in the context of wireless multi-hop networks.Comment: A brief announcement of this result has been published in the proceedings of ALGOSENSORS 201

Lower bounds on the dilation of plane spanners

(I) We exhibit a set of 23 points in the plane that has dilation at least $1.4308$, improving the previously best lower bound of $1.4161$ for the worst-case dilation of plane spanners. (II) For every integer $n\geq13$, there exists an $n$-element point set $S$ such that the degree 3 dilation of $S$ denoted by $\delta_0(S,3) \text{ equals } 1+\sqrt{3}=2.7321\ldots$ in the domain of plane geometric spanners. In the same domain, we show that for every integer $n\geq6$, there exists a an $n$-element point set $S$ such that the degree 4 dilation of $S$ denoted by $\delta_0(S,4) \text{ equals } 1 + \sqrt{(5-\sqrt{5})/2}=2.1755\ldots$ The previous best lower bound of $1.4161$ holds for any degree. (III) For every integer $n\geq6$, there exists an $n$-element point set $S$ such that the stretch factor of the greedy triangulation of $S$ is at least $2.0268$.Comment: Revised definitions in the introduction; 23 pages, 15 figures; 2 table

Size induced metal insulator transition in nanostructured Niobium thin films: Intragranular and intergranular contributions

With a reduction in the average grain size in nanostructured films of elemental Nb, we observe a systematic crossover from metallic to weakly-insulating behavior. An analysis of the temperature dependence of the resistivity in the insulating phase clearly indicates the existence of two distinct activation energies corresponding to inter-granular and intra-granular mechanisms of transport. While the high temperature behavior is dominated by grain boundary scattering of the conduction electrons, the effect of discretization of energy levels due to quantum confinement shows up at low temperatures. We show that the energy barrier at the grain boundary is proportional to the width of the largely disordered inter-granular region, which increases with a decrease in the grain size. For a metal-insulator transition to occur in nano-Nb due to the opening up of an energy gap at the grain boundary, the critical grain size is ~ 8nm and the corresponding grain boundary width is ~ 1.1nm

A Universal Point Set for 2-Outerplanar Graphs

A point set $S \subseteq \mathbb{R}^2$ is universal for a class $\cal G$ if every graph of ${\cal G}$ has a planar straight-line embedding on $S$. It is well-known that the integer grid is a quadratic-size universal point set for planar graphs, while the existence of a sub-quadratic universal point set for them is one of the most fascinating open problems in Graph Drawing. Motivated by the fact that outerplanarity is a key property for the existence of small universal point sets, we study 2-outerplanar graphs and provide for them a universal point set of size $O(n \log n)$.Comment: 23 pages, 11 figures, conference version at GD 201

Scalable solid-state quantum processor using subradiant two-atom states

We propose a realization of a scalable, high-performance quantum processor whose qubits are represented by the ground and subradiant states of effective dimers formed by pairs of two-level systems coupled by resonant dipole-dipole interaction. The dimers are implanted in low-temperature solid host material at controllable nanoscale separations. The two-qubit entanglement either relies on the coherent excitation exchange between the dimers or is mediated by external laser fields.Comment: 4 pages, 3 figure

Quantum Fields with Noncommutative Target Spaces

Quantum field theories (QFT's) on noncommutative spacetimes are currently under intensive study. Usually such theories have world sheet noncommutativity. In the present work, instead, we study QFT's with commutative world sheet and noncommutative target space. Such noncommutativity can be interpreted in terms of twisted statistics and is related to earlier work of Oeckl [1], and others [2,3,4,5,6,7,8]. The twisted spectra of their free Hamiltonians has been found earlier by Carmona et al [9,10]. We review their derivation and then compute the partition function of one such typical theory. It leads to a deformed black body spectrum, which is analysed in detail. The difference between the usual and the deformed black body spectrum appears in the region of high frequencies. Therefore we expect that the deformed black body radiation may potentially be used to compute a GZK cut-off which will depend on the noncommutative parameter $\theta$.Comment: 20 pages, 5 figures; Abstract changed. Changes and corrections in the text. References adde

A History of Flips in Combinatorial Triangulations

Given two combinatorial triangulations, how many edge flips are necessary and sufficient to convert one into the other? This question has occupied researchers for over 75 years. We provide a comprehensive survey, including full proofs, of the various attempts to answer it.Comment: Added a paragraph referencing earlier work in the vertex-labelled setting that has implications for the unlabeled settin

Strong influence of the complex bandstructure on the tunneling electroresistance: A combined model and ab-initio study

The tunneling electroresistance (TER) for ferroelectric tunnel junctions (FTJs) with BaTiO_{3} (BTO) and PbTiO}_{3} (PTO) barriers is calculated by combining the microscopic electronic structure of the barrier material with a macroscopic model for the electrostatic potential which is caused by the ferroelectric polarization. The TER ratio is investigated in dependence on the intrinsic polarization, the chemical potential, and the screening properties of the electrodes. A change of sign in the TER ratio is obtained for both barrier materials in dependence on the chemical potential. The inverse imaginary Fermi velocity describes the microscopic origin of this effect; it qualitatively reflects the variation and the sign reversal of the TER. The quantity of the imaginary Fermi velocity allows to obtain detailed information on the transport properties of FTJs by analyzing the complex bandstructure of the barrier material.Comment: quality of figures reduce

Entanglement Concentration Using Quantum Statistics

We propose an entanglement concentration scheme which uses only the effects of quantum statistics of indistinguishable particles. This establishes the fact that useful quantum information processing can be accomplished by quantum statistics alone. Due to the basis independence of statistical effects, our protocol requires less knowledge of the initial state than most entanglement concentration schemes. Moreover, no explicit controlled operation is required at any stage.Comment: 2 figure