Applying Formal Methods to Gossiping Networks with mCRL and Groove

In this paper we explore the practical possibilities of using formal methods to analyze gossiping networks. In particular, we use mCRL and Groove to model the peer sampling service, and analyze it through a series of model transformations to CTMCs and finally MRMs. Our tools compute the expected value of various network quality indicators, such as average path lengths, over all possible system runs. Both transient and steady state analysis are supported. We compare our results with the simulation and emulation results found in [10]

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

Forelimb muscle and joint actions in Archosauria: insights from Crocodylus johnstoni (Pseudosuchia) and Mussaurus patagonicus (Sauropodomorpha)

Many of the major locomotor transitions during the evolution of Archosauria, the lineage including crocodiles and birds as well as extinct Dinosauria, were shifts from quadrupedalism to bipedalism (and vice versa). Those occurred within a continuum between more sprawling and erect modes of locomotion and involved drastic changes of limb anatomy and function in several lineages, including sauropodomorph dinosaurs. We present biomechanical computer models of two locomotor extremes within Archosauria in an analysis of joint ranges of motion and the moment arms of the major forelimb muscles in order to quantify biomechanical differences between more sprawling, pseudosuchian (represented the crocodile Crocodylus johnstoni) and more erect, dinosaurian (represented by the sauropodomorph Mussaurus patagonicus) modes of forelimb function. We compare these two locomotor extremes in terms of the reconstructed musculoskeletal anatomy, ranges of motion of the forelimb joints and the moment arm patterns of muscles across those ranges of joint motion. We reconstructed the three-dimensional paths of 30 muscles acting around the shoulder, elbow and wrist joints. We explicitly evaluate how forelimb joint mobility and muscle actions may have changed with postural and anatomical alterations from basal archosaurs to early sauropodomorphs. We thus evaluate in which ways forelimb posture was correlated with muscle leverage, and how such differences fit into a broader evolutionary context (i.e. transition from sprawling quadrupedalism to erect bipedalism and then shifting to graviportal quadrupedalism). Our analysis reveals major differences of muscle actions between the more sprawling and erect models at the shoulder joint. These differences are related not only to the articular surfaces but also to the orientation of the scapula, in which extension/flexion movements in Crocodylus (e.g. protraction of the humerus) correspond to elevation/depression in Mussaurus. Muscle action is highly influenced by limb posture, more so than morphology. Habitual quadrupedalism in Mussaurus is not supported by our analysis of joint range of motion, which indicates that glenohumeral protraction was severely restricted. Additionally, some active pronation of the manus may have been possible in Mussaurus, allowing semi-pronation by a rearranging of the whole antebrachium (not the radius against the ulna, as previously thought) via long-axis rotation at the elbow joint. However, the muscles acting around this joint to actively pronate it may have been too weak to drive or maintain such orientations as opposed to a neutral position in between pronation and supination. Regardless, the origin of quadrupedalism in Sauropoda is not only linked to manus pronation but also to multiple shifts of forelimb morphology, allowing greater flexion movements of the glenohumeral joint and a more columnar forelimb posture

SYM N=4 in light-cone gauge and the "bridge" identities

The light-cone gauge allows to single out a set of ``transverse'' fields (TF), whose Green functions are free from UV divergences in SYM N=4. Green functions with external lines involving the remaining fields do instead exhibit divergences: indeed those fields can be expressed, by solving their equations of motion, as composite operators in terms of ``transverse'' fields. A set of exact identities (bridge identities) automatically realize their insertions in a path-integral formulation.Comment: 12 pages, LaTeX, uses cernrep, axodraw, cancel; figures included; minor improvements, references added, version accepted for publication in Phys. Rev.

In vivo testing of crosslinked polyethers. II. Weight loss, IR analysis, and swelling behavior after implantation

As reported in Part I (In vivo testing of crosslinked polyethers. I. Tissue reactions and biodegradation, J. Biomed. Mater. Res., this issue, pp. 307-320), microscopical evaluation after implantation of crosslinked (co)polyethers in rats showed differences in the rate of biodegradation, depending on the presence of tertiary hydrogen atoms in the main chain and the hydrophilicity of the polyether system. In this article (Part II) the biostability will be discussed in terms of weight loss, the swelling behavior, and changes in the chemical structure of the crosslinked polyethers after implantation. The biostability increased in the order poly(POx) < poly(THF-co-OX) < poly(THF) for the relatively hydrophobic polyethers. This confirmed our hypothesis that the absence of tertiary hydrogen atoms would improve the biostability. On the other hand, signs of biodegradation were observed for all polyether system studied. Infrared surface analysis showed that biodegradation was triggered by oxidative attack on the polymeric chain, leading to the formation of carboxylic ester and acid groups. It also was found that in the THF-based (co)polyethers, α-methylene groups were more sensitive than β-methylene groups. For a hydrophilic poly(THF)/PEO blend, an increase in surface PEO content was found, which might be due to preferential degradation of the PEO domains

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