Some basics on tolerances

In this note we deal with sensitivity analysis of combinatorial optimization problems and its fundamental term, the tolerance. For three classes of objective functions (?, ?, MAX) we prove some basic properties on upper and lower tolerances. We show that the upper tolerance of an element is well defined, how to compute the upper tolerance of an element, and give equivalent formulations when the upper tolerance is +? or > 0. Analogous results are proven for the lower tolerance and some results on the relationship between lower and upper tolerances are given.

Quantum capacitance and density of states of graphene

We report on measurements of the quantum capacitance in graphene as a function of charge carrier density. A resonant LC-circuit giving high sensitivity to small capacitance changes is employed. The density of states, which is directly proportional to the quantum capacitance, is found to be significantly larger than zero at and around the charge neutrality point. This finding is interpreted to be a result of potential fluctuations with amplitudes of the order of 100 meV in good agreement with scanning single-electron transistor measurements on bulk graphene and transport studies on nanoribbons

Generalization of Hasimoto's transformation

In this paper, we generalize the famous Hasimoto's transformation by showing that the dynamics of a closed unidimensional vortex filament embedded in a three-dimensional manifold of constant curvature gives rise under Hasimoto's transformation to the non-linear Schrodinger equation. We also give a natural interpretation of the function \psi introduced by Hasimoto in terms of moving frames associated to a natural complex bundle over the filament

Coulomb oscillations in three-layer graphene nanostructures

We present transport measurements on a tunable three-layer graphene single electron transistor (SET). The device consists of an etched three-layer graphene flake with two narrow constrictions separating the island from source and drain contacts. Three lateral graphene gates are used to electrostatically tune the device. An individual three-layer graphene constriction has been investigated separately showing a transport gap near the charge neutrality point. The graphene tunneling barriers show a strongly nonmonotonic coupling as function of gate voltage indicating the presence of localized states in the constrictions. We show Coulomb oscillations and Coulomb diamond measurements proving the functionality of the graphene SET. A charging energy of $\approx 0.6$ meV is extracted.Comment: 10 pages, 6 figure

Topological Influence and Locality in Swap Schelling Games

Residential segregation is a wide-spread phenomenon that can be observed in almost every major city. In these urban areas residents with different racial or socioeconomic background tend to form homogeneous clusters. Schelling’s famous agent-based model for residential segregation explains how such clusters can form even if all agents are tolerant, i.e., if they agree to live in mixed neighborhoods. For segregation to occur, all it needs is a slight bias towards agents preferring similar neighbors. Very recently, Schelling’s model has been investigated from a game-theoretic point of view with selfish agents that strategically select their residential location. In these games, agents can improve on their current location by performing a location swap with another agent who is willing to swap. We significantly deepen these investigations by studying the influence of the underlying topology modeling the residential area on the existence of equilibria, the Price of Anarchy and on the dynamic properties of the resulting strategic multi-agent system. Moreover, as a new conceptual contribution, we also consider the influence of locality, i.e., if the location swaps are restricted to swaps of neighboring agents. We give improved almost tight bounds on the Price of Anarchy for arbitrary underlying graphs and we present (almost) tight bounds for regular graphs, paths and cycles. Moreover, we give almost tight bounds for grids, which are commonly used in empirical studies. For grids we also show that locality has a severe impact on the game dynamics

Observation of excited states in a graphene quantum dot

We demonstrate that excited states in single-layer graphene quantum dots can be detected via direct transport experiments. Coulomb diamond measurements show distinct features of sequential tunneling through an excited state. Moreover, the onset of inelastic cotunneling in the diamond region could be detected. For low magnetic fields, the positions of the single-particle energy levels fluctuate on the scale of a flux quantum penetrating the dot area. For higher magnetic fields, the transition to the formation of Landau levels is observed. Estimates based on the linear energy-momentum relation of graphene give carrier numbers of the order of 10 for our device.Comment: 3 pages, 3 figure