Counting matroids in minor-closed classes

A flat cover is a collection of flats identifying the non-bases of a matroid. We introduce the notion of cover complexity, the minimal size of such a flat cover, as a measure for the complexity of a matroid, and present bounds on the number of matroids on $n$ elements whose cover complexity is bounded. We apply cover complexity to show that the class of matroids without an $N$-minor is asymptotically small in case $N$ is one of the sparse paving matroids $U_{2,k}$, $U_{3,6}$, $P_6$, $Q_6$, or $R_6$, thus confirming a few special cases of a conjecture due to Mayhew, Newman, Welsh, and Whittle. On the other hand, we show a lower bound on the number of matroids without $M(K_4)$-minor which asymptoticaly matches the best known lower bound on the number of all matroids, due to Knuth.Comment: 13 pages, 3 figure

On the number of matroids

We consider the problem of determining $m_n$, the number of matroids on $n$ elements. The best known lower bound on $m_n$ is due to Knuth (1974) who showed that $\log \log m_n$ is at least $n-3/2\log n-1$. On the other hand, Piff (1973) showed that $\log\log m_n\leq n-\log n+\log\log n +O(1)$, and it has been conjectured since that the right answer is perhaps closer to Knuth's bound. We show that this is indeed the case, and prove an upper bound on $\log\log m_n$ that is within an additive $1+o(1)$ term of Knuth's lower bound. Our proof is based on using some structural properties of non-bases in a matroid together with some properties of independent sets in the Johnson graph to give a compressed representation of matroids.Comment: Final version, 17 page

An entropy argument for counting matroids

We show how a direct application of Shearers' Lemma gives an almost optimum bound on the number of matroids on $n$ elements.Comment: Short note, 4 page

A distributed topology information system for optical networks based on the semantic web

The research networking community has embraced novel network architectures to provide e-Science applications with dedicated connections instead of shared links. IP and optical services converge in these new infrastructures to form hybrid networks. Lightpaths are the services offered to clients in the optical portion of the network. They are chosen because they guarantee the appropriate QoS in terms of bandwidth and latency. NDL-the Network Description Language-is a data model offering users and providers of lightpaths with a common ontology to describe topology information of hybrid optical networks. The strength of NDL is that it supports a wide range of applications, including pathfinding, visualisation and asset management, via the definition of a common data model to exchange network descriptions. Since NDL is based on the Semantic Web techniques, it is straightforward to relate NDL with application-specific ontologies. In this paper we present the current status of the NDL schemas and its use in several applications

Online automatic tuning and control for fed-batch cultivation

Performance of controllers applied in biotechnological production is often below expectation. Online automatic tuning has the capability to improve control performance by adjusting control parameters. This work presents automatic tuning approaches for model reference specific growth rate control during fed-batch cultivation. The approaches are direct methods that use the error between observed specific growth rate and its set point; systematic perturbations of the cultivation are not necessary. Two automatic tuning methods proved to be efficient, in which the adaptation rate is based on a combination of the error, squared error and integral error. These methods are relatively simple and robust against disturbances, parameter uncertainties, and initialization errors. Application of the specific growth rate controller yields a stable system. The controller and automatic tuning methods are qualified by simulations and laboratory experiments with Bordetella pertussis

Willingness to disclose STI status to sex partners among college-age men in the United States

Disclosure of sexually transmitted infections (STIs) to sexual partners is critical to the prevention, treatment and control of STIs. We examine intra- and inter-personal influences on willingness to disclose STI status among college-age males. Participants (n = 1064) were aged 17-24 years and recruited from a variety of university and community venues. Using independent samples t-test, Pearson chi-squares test, and binary logistic regression, we examined the relationship between willingness to disclose a STI and intra- and inter-personal factors, including age, masculinity values, interpersonal violence, partner cell phone monitoring, alcohol and/or drug use, condom use, number and characteristics of sex partners, and previous STI. Results reveal that among college-age males, type of sex partner and masculinity values are significant variables in predicting whether or not an individual is willing to disclose. These data can inform STI control programs to more effectively address the complex issues associated with STI disclosure to sex partners

Oxidation of linear alcohols with hydrogen peroxide over titanium silicate-1

Abatract In this paper different parameters affecting the oxidation of alcohols with hydrogen peroxide are described. The influence of the amount and of the crystallite size of the catalyst, as well as the concentrations of hydrogen peroxide and substrate have been studied. The influence of the reaction temperature, the chain length of the alcohol (C6, C7, C8 and C9 ) and the position of the alcohol group (a, /3 or y) on the reaction rate has also been investigated. As a result of this study it can be reported that the reaction is first order with respect to the amount of catalyst and the hydrogen peroxide concentration, and zero order in alcohol concentration. The activation energy for the oxidation of 2-octanol is 71 kJ/ mol. The particle size has a considerable effect on the reaction rate; larger particles result slower reaction. There is a remarkable effect of the chain length on the reaction rate (C6<C7<C8% C9) and the position of the hydroxyl group has a strong effect on the activity of TS-1 (fl> (Y > y ) . The crystallite size effect can be explained by means of diffusion limitations, as could be illustrated by Weisz modulus calculations. The observed difference in activity between jI and y alcohols can not be related to differences in diffusion (single component diffusion of /I and y alcohols show little difference) and therefore transition state restrictions of the alcohols in the pores of the TS-1 may be a possible explanation for this effect

The exact evaluation of the corner-to-corner resistance of an M x N resistor network: Asymptotic expansion

We study the corner-to-corner resistance of an M x N resistor network with resistors r and s in the two spatial directions, and obtain an asymptotic expansion of its exact expression for large M and N. For M = N, r = s =1, our result is R_{NxN} = (4/pi) log N + 0.077318 + 0.266070/N^2 - 0.534779/N^4 + O(1/N^6).Comment: 12 pages, re-arranged section

Infinite Networks of Identical Capacitors

The capacitance between the origin and any other lattice site in an infinite square lattice of identical capacitors is studied. The method is generalized to infinite Simple Cubic (SC) lattice. We make use of the superposition principle and the symmetry of the infinite gridComment: 16 pages, 5 figures, 2 table