Dynamic Programming for Graphs on Surfaces

We provide a framework for the design and analysis of dynamic programming algorithms for surface-embedded graphs on n vertices and branchwidth at most k. Our technique applies to general families of problems where standard dynamic programming runs in 2^{O(k log k)} n steps. Our approach combines tools from topological graph theory and analytic combinatorics. In particular, we introduce a new type of branch decomposition called "surface cut decomposition", generalizing sphere cut decompositions of planar graphs introduced by Seymour and Thomas, which has nice combinatorial properties. Namely, the number of partial solutions that can be arranged on a surface cut decomposition can be upper-bounded by the number of non-crossing partitions on surfaces with boundary. It follows that partial solutions can be represented by a single-exponential (in the branchwidth k) number of configurations. This proves that, when applied on surface cut decompositions, dynamic programming runs in 2^{O(k)} n steps. That way, we considerably extend the class of problems that can be solved in running times with a single-exponential dependence on branchwidth and unify/improve most previous results in this direction.Comment: 28 pages, 3 figure

Dynamic programming for graphs on surfaces

We provide a framework for the design and analysis of dynamic programming algorithms for surface-embedded graphs on n vertices and branchwidth at most k. Our technique applies to general families of problems where standard dynamic programming runs in 2O(k·log k). Our approach combines tools from topological graph theory and analytic combinatorics.Postprint (updated version

Accurate reference gas mixtures containing tritiated molecules: Their production and raman‐based analysis

Highly accurate, quantitative analyses of mixtures of hydrogen isotopologues—both the stable species, H$_{2}$, D$_{2}$2, and HD, and the radioactive species, T$_{2}$, HT, and DT—are of great importance in fields as diverse as deuterium–tritium fusion, neutrino mass measurements using tritium β-decay, or for photonuclear experiments in which hydrogen–deuterium targets are used. In this publication we describe a production, handling, and analysis facility capable of fabricating well-defined gas samples, which may contain any of the stable and radioactive hydrogen isotopologues, with sub-percent accuracy for the relative species concentrations. The production is based on precise manometric gas mixing of H$_{2}$, D$_{2}$, and T$_{2}$. The heteronuclear isotopologues HD, HT, and DT are generated via controlled, in-line catalytic reaction or by β-induced self-equilibration, respectively. The analysis was carried out using an in-line intensity- and wavelength-calibrated Raman spectroscopy system. This allows for continuous monitoring of the composition of the circulating gas during the self-equilibration or catalytic evolution phases. During all procedures, effects, such as exchange reactions with wall materials, were considered with care. Together with measurement statistics, these and other systematic effects were included in the determination of composition uncertainties of the generated reference gas samples. Measurement and calibration accuracy at the level of 1% was achieved

Effectiveness of the European chromium(vi) directive for cement implementation on occupational allergic contact dermatitis occurrence: assessment in France and the U.K.

International audienc

Frequency Comb Assisted Diode Laser Spectroscopy for Measurement of Microcavity Dispersion

While being invented for precision measurement of single atomic transitions, frequency combs have also become a versatile tool for broadband spectroscopy in the last years. In this paper we present a novel and simple approach for broadband spectroscopy, combining the accuracy of an optical fiber-laser-based frequency comb with the ease-of-use of a tunable external cavity diode laser. This scheme enables broadband and fast spectroscopy of microresonator modes and allows for precise measurements of their dispersion, which is an important precondition for broadband optical frequency comb generation that has recently been demonstrated in these devices. Moreover, we find excellent agreement of measured microresonator dispersion with predicted values from finite element simulations and we show that tailoring microresonator dispersion can be achieved by adjusting their geometrical properties

Monitoring of the operating parameters of the KATRIN Windowless Gaseous Tritium Source

The Karlsruhe Tritium Neutrino (KATRIN) experiment will measure the absolute mass scale of neutrinos with a sensitivity of \m_{\nu} = 200 meV/c$^2$ by high-precision spectroscopy close to the tritium beta-decay endpoint at 18.6 keV. Its Windowless Gaseous Tritium Source (WGTS) is a beta-decay source of high intensity ($10^{11}$/s) and stability, where high-purity molecular tritium at 30 K is circulated in a closed loop with a yearly throughput of 10 kg. To limit systematic effects the column density of the source has to be stabilised at the 0.1% level. This requires extensive sensor instrumentation and dedicated control and monitoring systems for parameters such as the beam tube temperature, injection pressure, gas composition and others. Here we give an overview of these systems including a dedicated Laser-Raman system as well as several beta-decay activity monitors. We also report on results of the WGTS demonstrator and other large-scale test experiments giving proof-of-principle that all parameters relevant to the systematics can be controlled and monitored on the 0.1% level or better. As a result of these works, the WGTS systematics can be controlled within stringent margins, enabling the KATRIN experiment to explore the neutrino mass scale with the design sensitivity.Comment: 32 pages, 13 figures. modification to title, typos correcte

\u201cGive, but Give until It Hurts\u201d: The Modulatory Role of Trait Emotional Intelligence on the Motivation to Help

Two studies investigated the effect of trait Emotional Intelligence (trait EI) on people\u2019s moti- vation to help. In Study 1, we developed a new computer-based paradigm that tested partic- ipants\u2019 motivation to help by measuring their performance on a task in which they could gain a hypothetical amount of money to help children in need. Crucially, we manipulated partici- pants\u2019 perceived efficacy by informing them that they had been either able to save the chil- dren (positive feedback) or unable to save the children (negative feedback). We measured trait EI using the Trait Emotional Intelligence Questionnaire\u2013Short Form (TEIQue-SF) and assessed participants\u2019 affective reactions during the experiment using the PANAS-X. Results showed that high and low trait EI participants performed differently after the presen- tation of feedback on their ineffectiveness in helping others in need. Both groups showed increasing negative affective states during the experiment when the feedback was negative; however, high trait EI participants better managed their affective reactions, modulating the impact of their emotions on performance and maintaining a high level of motivation to help. In Study 2, we used a similar computerized task and tested a control situation to explore the effect of trait EI on participants\u2019 behavior when facing failure or success in a scenario unre- lated to helping others in need. No effect of feedback emerged on participants\u2019 emotional states in the second study. Taken together our results show that trait EI influences the impact of success and failure on behavior only in affect-rich situation like those in which people are asked to help others in need