The order of large random permutations with cycle weights

The order $O_n(\sigma)$ of a permutation $\sigma$ of $n$ objects is the smallest integer $k \geq 1$ such that the $k$-th iterate of $\sigma$ gives the identity. A remarkable result about the order of a uniformly chosen permutation is due to Erd\"os and Tur\'an who proved in 1965 that $\log O_n$ satisfies a central limit theorem. We extend this result to the so-called \textit{generalized Ewens measure} in a previous paper. In this paper, we establish a local limit theorem as well as, under some extra moment condition, a precise large deviations estimate. These properties are new even for the uniform measure. Furthermore, we provide precise large deviations estimates for random permutations with polynomial cycle weights.Comment: 41 pages, 5 figure

Large cycles and a functional central limit theorem for generalized weighted random permutations

The objects of our interest are the so-called $A$-permutations, which are permutations whose cycle length lie in a fixed set $A$. They have been extensively studied with respect to the uniform or the Ewens measure. In this paper, we extend some classical results to a more general weighted probability measure which is a natural extension of the Ewens measure and which in particular allows to consider sets $A_n$ depending on the degree $n$ of the permutation. By means of complex analysis arguments and under reasonable conditions on generating functions we study the asymptotic behaviour of classical statistics. More precisely, we generalize results concerning large cycles of random permutations by Vershik, Shmidt and Kingman, namely the weak convergence of the size ordered cycle length to a Poisson-Dirichlet distribution. Furthermore, we apply our tools to the cycle counts and obtain a Brownian motion central limit theorem which extends results by DeLaurentis, Pittel and Hansen.Comment: 24 pages, 3 Figure

Energy awareness displays: motivating conservation at the workplace through feedback

Börner, D., Storm, J., Kalz, M., & Specht, M. (2012). Energy awareness displays: motivating conservation at the workplace through feedback. International Journal of Mobile Learning and Organisation, 6(3/4), 189–203.The paper presents a project that sets up to make energy consumption data visible and accessible to employees by providing dynamic situated consumption feedback at the workplace. Therefore a supporting infrastructure as well as two example applications have been implemented and evaluated. The resulting prototype fosters a ubiquitous learning process among the employees with the goal to change their consumption behaviour as well as the attitudes towards energy conservation. The paper presents the approach, the requirements, the infrastructure and applications, as well as the evaluation results of the conducted informative study, comparative study, user evaluation, and design study

Energy Awareness Displays - Prototype for personalised energy consumption feedback

Börner, D., Storm, J., Kalz, M., & Specht, M. (2012). Energy Awareness Displays - Prototype for personalised energy consumption feedback. In A. Ravencroft, S. Lindstaedt, C. D. Kloos, & D. Hernández-Leo (Eds.), 21st Century Learning for 21st Century Skills - 7th European Conference on Technology Enhanced Learning (EC-TEL 2012), LNCS 7563 (pp. 471-476). September, 18-21, 2012, Saarbrücken, Germany: Springer.The paper presents the “Energy Awareness Displays” project that makes hidden energy consumption data visible and accessible for people working in office buildings. Besides raising awareness on the topic and introducing relevant conservation strategies, the main goal is to provide dynamic situated feedback when taking individual consumption actions at the workplace. Therefore a supporting infrastructure as well as two example applications to access and explore the consumption information have been implemented and evaluated. The paper presents and discusses the approach, the developed infrastructure and applications, as well as the evaluation results

Total variation distance and the Erdős-Turán law for random permutations with polynomially growing cycle weights

We study the model of random permutations of $n$ objects with polynomially growing cycle weights, which was recently considered by Ercolani and Ueltschi, among others. Using saddle-point analysis, we prove that the total variation distance between the process which counts the cycles of size $1, 2, ..., b$ and a process $(Z_1, Z_2, ..., Z_b)$ of independent Poisson random variables converges to $0$ if and only if $b=o(\ell)$ where $\ell$ denotes the length of a typical cycle in this model. By means of this result, we prove a central limit theorem for the order of a permutation and thus extend the Erd\H{o}s-Tur\'an Law to this measure. Furthermore, we prove a Brownian motion limit theorem for the small cycles

Tangible Interactive Ambient Display Prototypes to Support Learning Scenarios

This paper describes the research and development of tangible interactive ambient display prototypes to support learning scenarios. Therefore a prototypical system design called the Feedback Cube is presented. The prototypes combine motion sensors, visual and auditive actuators, as well as wireless communication capabilities in a cubic layout. An initial formative study underpins the prototypes’ potential to facilitate interaction and/or indicate feedback. Based on the presented results possible applications scenarios in a learning context are outlined.METALOGUE. Seventh Framework Programme collaborative project funded by the European Commission under grant agreement number: 611073 (http://www.metalogue.eu)

Engineering of Aspergillus niger for the production of secondary metabolites

Background: Filamentous fungi can each produce dozens of secondary metabolites which are attractive as therapeutics, drugs, antimicrobials, flavour compounds and other high-value chemicals. Furthermore, they can be used as an expression system for eukaryotic proteins. Application of most fungal secondary metabolites is, however, so far hampered by the lack of suitable fermentation protocols for the producing strain and/or by low product titers. To overcome these limitations, we report here the engineering of the industrial fungus Aspergillus niger to produce high titers (up to 4,500 mg • l-1) of secondary metabolites belonging to the class of nonribosomal peptides. Results: For a proof-of-concept study, we heterologously expressed the 351 kDa nonribosomal peptide synthetase ESYN from Fusarium oxysporum in A. niger. ESYN catalyzes the formation of cyclic depsipeptides of the enniatin family, which exhibit antimicrobial, antiviral and anticancer activities. The encoding gene esyn1 was put under control of a tunable bacterial-fungal hybrid promoter (Tet-on) which was switched on during early-exponential growth phase of A. niger cultures. The enniatins were isolated and purified by means of reverse phase chromatography and their identity and purity proven by tandem MS, NMR spectroscopy and X-ray crystallography. The initial yields of 1 mg • l-1 of enniatin were increased about 950 fold by optimizing feeding conditions and the morphology of A. niger in liquid shake flask cultures. Further yield optimization (about 4.5 fold) was accomplished by cultivating A. niger in 5 l fed batch fermentations. Finally, an autonomous A. niger expression host was established, which was independent from feeding with the enniatin precursor D-2-hydroxyvaleric acid D-Hiv. This was achieved by constitutively expressing a fungal D-Hiv dehydrogenase in the esyn1-expressing A. niger strain, which used the intracellular ɑ-ketovaleric acid pool to generate D-Hiv. Conclusions: This is the first report demonstrating that A. niger is a potent and promising expression host for nonribosomal peptides with titers high enough to become industrially attractive. Application of the Tet-on system in A. niger allows precise control on the timing of product formation, thereby ensuring high yields and purity of the peptides produced.EC/FP7/607332/EU/Quantitative Biology for Fungal Secondary Metabolite Producers/QuantFungDFG, EXC 314, Unifying Concepts in Catalysi

High cell density cultivation and recombinant protein production with Escherichia coli in a rocking-motion-type bioreactor

<p>Abstract</p> <p>Background</p> <p>Single-use rocking-motion-type bag bioreactors provide advantages compared to standard stirred tank bioreactors by decreased contamination risks, reduction of cleaning and sterilization time, lower investment costs, and simple and cheaper validation. Currently, they are widely used for cell cultures although their use for small and medium scale production of recombinant proteins with microbial hosts might be very attractive. However, the utilization of rocking- or wave-induced motion-type bioreactors for fast growing aerobic microbes is limited because of their lower oxygen mass transfer rate. A conventional approach to reduce the oxygen demand of a culture is the fed-batch technology. New developments, such as the BIOSTAT^®CultiBag RM system pave the way for applying advanced fed-batch control strategies also in rocking-motion-type bioreactors. Alternatively, internal substrate delivery systems such as EnBase^®Flo provide an opportunity for adopting simple to use fed-batch-type strategies to shaken cultures. Here, we investigate the possibilities which both strategies offer in view of high cell density cultivation of <it>E. coli </it>and recombinant protein production.</p> <p>Results</p> <p>Cultivation of <it>E. coli </it>in the BIOSTAT^®CultiBag RM system in a conventional batch mode without control yielded an optical density (OD₆₀₀) of 3 to 4 which is comparable to shake flasks. The culture runs into oxygen limitation. In a glucose limited fed-batch culture with an exponential feed and oxygen pulsing, the culture grew fully aerobically to an OD₆₀₀of 60 (20 g L^-1cell dry weight). By the use of an internal controlled glucose delivery system, EnBase^®Flo, OD₆₀₀of 30 (10 g L^-1cell dry weight) is obtained without the demand of computer controlled external nutrient supply. EnBase^®Flo also worked well in the CultiBag RM system with a recombinant <it>E. coli </it>RB791 strain expressing a heterologous alcohol dehydrogenase (ADH) to very high levels, indicating that the enzyme based feed supply strategy functions well for recombinant protein production also in a rocking-motion-type bioreactor.</p> <p>Conclusions</p> <p>Rocking-motion-type bioreactors may provide an interesting alternative to standard cultivation in bioreactors for cultivation of bacteria and recombinant protein production. The BIOSTAT^®Cultibag RM system with the single-use sensors and advanced control system paves the way for the fed-batch technology also to rocking-motion-type bioreactors. It is possible to reach cell densities which are far above shake flasks and typical for stirred tank reactors with the improved oxygen transfer rate. For more simple applications the EnBase^®Flo method offers an easy and robust solution for rocking-motion-systems which do not have such advanced control possibilities.</p

Emergency vaccination of rabies under limited resources – combating or containing?

BACKGROUND: Rabies is the most important viral zoonosis from a global perspective. Worldwide efforts to combat the disease by oral vaccination of reservoirs have managed to eradicate wildlife rabies in large areas of central Europe and North-America. Thus, repeated vaccination has been discontinued recently on a geographical scale. However, as rabies has not yet been eradicated globally, a serious risk of re-introduction remains. What is the best spatial design for an emergency vaccination program – particularly if resources are limited? Either, we treat a circular area around the detected case and run the risk of infected hosts leaving the limited control area, because a sufficient immunisation level has not yet been built up. Or, initially concentrate the SAME resources in order to establish a protective ring which is more distant from the infected local area, and which then holds out against the challenge of the approaching epidemic. METHODS: We developed a simulation model to contrast the two strategies for emergency vaccination. The spatial-explicit model is based on fox group home-ranges, which facilitates the simulation of rabies spread to larger areas relevant to management. We used individual-based fox groups to follow up the effects of vaccination in a detailed manner. Thus, regionally – bait distribution orientates itself to standard schemes of oral immunisation programs and locally – baits are assigned to individual foxes. RESULTS: Surprisingly, putting the controlled area ring-like around the outbreak does not outperform the circular area of the same size centred on the outbreak. Only during the very first baitings, does the ring area result in fewer breakouts. But then as rabies is eliminated within the circle area, the respective ring area fails, due to the non-controlled inner part. We attempt to take advantage of the initially fewer breakouts beyond the ring when applying a mixed strategy. Therefore, after a certain number of baitings, the area under control was increased for both strategies towards the same larger circular area. The circle-circle strategy still outperforms the ring-circle strategy and analysis of the spatial-temporal disease spread reveals why: improving control efficacy by means of a mixed strategy is impossible in the field, due to the build-up time of population immunity. CONCLUSION: For practical emergency management of a new outbreak of rabies, the ring-like application of oral vaccination is not a favourable strategy at all. Even if initial resources are substantially low and there is a serious risk of rabies cases outside the limited control area, our results suggest circular application instead of ring vaccination