Concentration for Poisson U-statistics: Subgraph counts in random geometric graphs

Concentration bounds for the probabilities $\mathbb{P}(N\ge M+r)$ and $\mathbb{P}(N\le M?r)$ are proved, where $M$ is a median or the expectation of a subgraph count $N$ associated with a random geometric graph built over a Poisson process. The lower tail bounds have a Gaussian decay and the upper tail inequalities satisfy an optimality condition. A remarkable feature is that the underlying Poisson process can have a.s. infinitely many points.The estimates for subgraph counts follow from tail inequalities for more general local Poisson U-statistics. These bounds are proved using recent general concentration results for Poisson U-statistics and techniques involving the convex distance for Poisson processes.     

Group activity selection problem with approval preferences

We consider a setting where one has to organize one or several group activities for a set of agents. Each agent will participate in at most one activity, and her preferences over activities depend on the number of participants in the activity. The goal is to assign agents to activities based on their preferences in a way that is socially optimal and/or stable. We put forward a general model for this setting, which is a natural generalization of anonymous hedonic games. We then focus on a special case of our model where agents’ preferences are binary, i.e., each agent classifies all pairs of the form ‘(activity, group size)’ into ones that are acceptable and ones that are not. We formulate several solution concepts for this scenario, and study them from the computational point of view, providing hardness results for the general case as well as efficient algorithms for settings where agents’ preferences satisfy certain natural constraints.     

Dependence of the zero shear-rate viscosity and the viscosity function of linear high-density polyethylenes on the mass-average molar mass and polydispersity

Linear high-density polyethylenes with molar masses M _w between 240 and 1,000,000 g/mol, obtained by metallocene catalysts, were characterized in shear using oscillatory and creep tests. The polydispersities of the molar mass distributions (MMDs) lay between 1 and 16. The resulting zero shear-rate viscosities η₀ covered a range from 2.5×10⁻³ to around 10⁸ Pas. Above a critical molar mass of M _c≈2,900 g/mol, the experimental results can be described by the relation η₀ ∼ M _w^3.6, independently of the MMD. The oscillatory data were fitted with a Carreau–Yasuda equation. The resulting parameters were correlated to molecular structure. The parameter a, being a quantity for the width of the transition between the Newtonian and the non-Newtonian regime, showed a dependence on the molar mass M _w but not on M _w/M _n. The parameter λ of the Carreau-Yasuda equation was found to be the reciprocal crossover frequency for all samples with a log-Gaussian MMD. λ depends on the molar mass M _w and also on M _w/M _n.

Open Sets Avoiding Integral Distances

We study open point sets in Euclidean spaces $\mathbb{R }^d$ R d without a pair of points an integral distance apart. By a result of Furstenberg, Katznelson, and Weiss such sets must be of Lebesgue upper density $0$ 0 . We are interested in how large such sets can be in $d$ d -dimensional volume. We determine the exact values for the maximum volumes of the sets in terms of the number of their connected components and dimension. Here techniques from diophantine approximation, algebra and the theory of convex bodies come into play. Our problem can be viewed as a counterpart to known problems on sets with pairwise rational or integral distances. It possibly opens a new research direction with strong links to topology and measure theory.     

Experimental demonstration of a quantum protocol for byzantine agreement and liar detection

We introduce a new quantum protocol for solving detectable Byzantine agreement (also called detectable broadcast) between three parties, and also for solving the detectable liar detection problem. The protocol is suggested by the properties of a four-qubit entangled state, and the classical part of the protocol is simpler than that of previous proposals. In addition, we present an experimental implementation of the protocol using four-photon entanglement.     

Passively mode-locked Yb:YAG thin-disk laser with pulse energies exceeding 13 microJ by use of an active multipass geometry

We demonstrate the generation of high-energy picosecond pulses directly from a thin-disk laser oscillator by employing a self-imaging active multipass geometry. Stable single-pulse operation has been obtained with an average output power in excess of 50 W, excluding a cw background of 8%, at a repetition rate of 3.8 MHz. Self-starting passive mode locking was accomplished using a semiconductor saturable absorber mirror. The maximum pulse energy was 13.4 microJ at a pulse duration of 1.36 ps with a time-bandwidth product of 0.34. Single-pass external frequency doubling with a conversion efficiency of 60% yielded >28 W of average power at 515 nm.     

Few-boson dynamics in double wells: from single-atom to correlated pair tunneling

We investigate few-boson tunneling in a one-dimensional double well, covering the full crossover from weak interactions to the fermionization limit of strong correlations. Based on exact quantum-dynamical calculations, it is found that the tunneling dynamics of two atoms evolves from Rabi oscillations to correlated pair tunneling as we increase the interaction strength. Near the fermionization limit, fragmented-pair tunneling is observed and analyzed in terms of the population imbalance and two-body correlations. For more atoms, the tunneling dynamics near fermionization is shown to be sensitive to both atom number and initial configuration.     

Volatile organic compounds in head and neck squamous cell carcinoma—An in vitro pilot study

Owing to the lack of specific symptoms, diagnosis of head and neck squamous cell carcinoma (HNSCC) may be delayed. We evaluated volatile organic compounds in tumor samples from patients suffering from HNSCC and tested the hypothesis that there is a characteristic altered composition in the headspace of HNSCC compared with control samples from the same patient with normal squamous epithelium. These results provide the basis for future noninvasive breath analysis in HNSCC. Headspace air of suspected tumor and contralateral control samples in 20 patients were analyzed using ion-mobility spectrometry. Squamous cell carcinoma was diagnosed in 16 patients. In total, we observed 93 different signals in headspace measurements. Squamous cell carcinomas revealed significantly higher levels of volatile cyclohexanol (0.54 ppb_v, 25th to 75th percentiles 0.35–0.86) compared with healthy squamous epithelium (0.24 ppb_v, 25th to 75th percentiles 0.12–0.3; p < 0.001). In conclusion, head and neck squamous cell carcinoma emitted significantly higher levels of volatile cyclohexanol in headspace compared with normal squamous epithelium. These findings form the basis for future breath analysis for diagnosis, therapy control and the follow-up of HNSSC to improve therapy and aftercare.     

Soret effect of nonionic surfactants in water studied by different transient grating setups

We studied the thermal diffusion behavior of the nonionic surfactant solutions C 12E 6/water and C 12E 5/water at different concentrations and temperatures using thermal diffusion forced Rayleigh scattering (TDFRS). Two different types of TDFRS setups have been applied. In the classical TDFRS, we use an argon laser to write the optical grating into the sample by using a small amount of ionic dye to convert the optical grating into a temperature grating. In the other setup, called IR-TDFRS, we use an infrared laser as the writing beam, which utilizes the water absorption band to convert the optical grating into a temperature grating. The measurements by IR-TDFRS show a one-mode signal for all concentrations and temperatures, while the signal in the classical TDFRS consists of two modes for higher temperatures and lower surfactant concentrations (Ning, H.; et al. J. Phys. Chem. B 2006, 110, 10746). We find good agreement between the Soret coefficient determined in the IR-TDFRS and the one derived from the first fast mode in the previous studies. The Soret coefficient of the nonionic solutions is positive and enhanced at the critical point. In general, the Soret coefficient of the micelles tends to increase with temperature. We found that the presence of the second mode observed in the classical TDFRS is related to the addition of the ionic dye, but even with the ionic dye it is not possible to observe a second mode in the IR-TDFRS. The origin of the second mode is discussed in terms of charged micelles and an inhomogenous dye distribution in the temperature gradient.