Quadrisecants give new lower bounds for the ropelength of a knot

Using the existence of a special quadrisecant line, we show the ropelength of any nontrivial knot is at least 15.66. This improves the previously known lower bound of 12. Numerical experiments have found a trefoil with ropelength less than 16.372, so our new bounds are quite sharp.Comment: v3 is the version published by Geometry & Topology on 25 February 200

Swapping, tempering and equi-energy sampling on a selection of models in statistical mechanics

In dieser Arbeit werden drei Varianten des Metropolis-Hastings Algorithmus betrachtet. Simulated Tempering, Swapping und Equi-Energy Sampling sollen durch Hinzufügen eines Temperaturschritts die Konvergenzgeschwindigkeit dieser Algorithmen gegenüber dem zugrunde liegenden Metropolis-Hastings Algorithmus in Situationen verbessern, in denen dieser langsam gegen das gewünschte Wahrscheinlichkeitsmaß konvergiert. Es wird gezeigt, dass der Swapping Algorithmus im Generalized-Curie-Weiss Modell in polynomiell vielen Schritten konvergiert. Im Blume-Emery-Grifiths Modell ist die Konvergenz in einem Parameterbereich auch schnell, während sie in einem anderen Parameterbereich langsam ist. Auch für die Spingläser Random-Energy-Model und Generalized-Random-Energy-Model benötigen Simulated Tempering und Swapping exponentiell viele Schritte um nahe an die gewünschte Verteilung zu gelangen. Schließlich wird noch gezeigt, dass der Equi-Energy Algorithmus im Potts Modell langsam mischt

Relationship value benefits of membership programs, heterogeneous stakeholders and museum impact beyond fees

In times of decreasing public funding, cultural institutions such as museums increasingly develop new stakeholder management practices to build a different or more diversified support base. Recently, membership programs have especially been gaining popularity. In this paper, we adopt a relationship value approach to study the poorly understood behaviors of members that can benefit museums beyond membership fees. In particular, we focus on the extent to which membership level and the perceived prestige of the museum drive value co-creation through prestige leveraging. We study this by using a sample of 430 members and non-members of the Hermitage Museum in Amsterdam. We find that membership level is positively related with cross-buying behavior at the museum store and restaurant, and recommending the museum. In addition, these value creating behaviors are mediated by members leveraging the museum's prestige in their social environment. In contrast, we find a negative relationship between membership level and recruiting new members into the program, which could be explained by status dilution effects

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

Channel choice complications:Exploring the multiplex nature of citizens' channel choices

Part 2: E-Government Services and Open GovernmentInternational audienceIn spite of massive investment and increased adoption of digital services, citizens continue to use traditional channels to interact with public organizations. The channel choice (CC) field of research tries to understand citizens’ interactions with public authorities to make the interaction more efficient and increase citizen satisfaction. However, most studies have been conducted either as surveys of hypothetical services or in experimental settings, leading to a lack of empirical data from actual use contexts. Therefore, we present the results of a sequential mixed methods study which combines observations of citizen-caseworker interaction in a call center, contextual interviews with callers, and a survey classifying topics from 10,000 telephone calls. We contribute to the CC field and practice with rich empirical data from studies of actual channel choices. Specifically, the study explores the multiplex nature of real-life CC and demonstrate how telephone calls can be part of a process, which occurs across both traditional and digital channels. Moreover, we identify problems, which cause telephone calls related to digital services, and classify these in two groups: information related problems and action related problems

Performance of a diode-end-pumped Yb:YAG laser

Using an end-pumped technology developed at LLNL we have demonstrated a Yb:YAG laser capable of delivering up to 434 W of CW power and 280 W of Q-switched power. In addition, we have frequency doubled the output to 515 nm using a dual crystal scheme to produce 76 W at 10 kHz in a 30 ns pulse length

Nondegenerate Optical Parametric Chirped Pulse Amplification

We present the first recompression of amplified pulses in a highly nondegenerate optical parametric chirped pulse amplifier. 60-fs recompressed pulse width and up to 2 mJ pulses were obtained in our experiments