Hierarchies of Predominantly Connected Communities

We consider communities whose vertices are predominantly connected, i.e., the vertices in each community are stronger connected to other community members of the same community than to vertices outside the community. Flake et al. introduced a hierarchical clustering algorithm that finds such predominantly connected communities of different coarseness depending on an input parameter. We present a simple and efficient method for constructing a clustering hierarchy according to Flake et al. that supersedes the necessity of choosing feasible parameter values and guarantees the completeness of the resulting hierarchy, i.e., the hierarchy contains all clusterings that can be constructed by the original algorithm for any parameter value. However, predominantly connected communities are not organized in a single hierarchy. Thus, we develop a framework that, after precomputing at most $2(n-1)$ maximum flows, admits a linear time construction of a clustering \C(S) of predominantly connected communities that contains a given community $S$ and is maximum in the sense that any further clustering of predominantly connected communities that also contains $S$ is hierarchically nested in \C(S). We further generalize this construction yielding a clustering with similar properties for $k$ given communities in $O(kn)$ time. This admits the analysis of a network's structure with respect to various communities in different hierarchies.Comment: to appear (WADS 2013

Low Cell pH Depresses Peak Power in Rat Skeletal Muscle Fibres at Both 30°C and 15°C: Implications for Muscle Fatigue

Historically, an increase in intracellular H+ (decrease in cell pH) was thought to contribute to muscle fatigue by direct inhibition of the cross-bridge leading to a reduction in velocity and force. More recently, due to the observation that the effects were less at temperatures closer to those observed in vivo, the importance of H+ as a fatigue agent has been questioned. The purpose of this work was to re-evaluate the role of H+ in muscle fatigue by studying the effect of low pH (6.2) on force, velocity and peak power in rat fast-and slow-twitch muscle fibres at 15°C and 30°C. Skinned fast type IIa and slow type I fibres were prepared from the gastrocnemius and soleus, respectively, mounted between a force transducer and position motor, and studied at 15°C and 30°C and pH 7.0 and 6.2, and fibre force (P0), unloaded shortening velocity (V0), force–velocity, and force–power relationships determined. Consistent with previous observations, low pH depressed the P0 of both fast and slow fibres, less at 30°C (4–12%) than at 15°C (30%). However, the low pH-induced depressions in slow type I fibre V0 and peak power were both significantly greater at 30°C (25% versus 9% for V0 and 34% versus 17% for peak power). For the fast type IIa fibre type, the inhibitory effect of low pH on V0 was unaltered by temperature, while for peak power the inhibition was reduced at 30°C (37% versus 18%). The curvature of the force–velocity relationship was temperature sensitive, and showed a higher a/P0 ratio (less curvature) at 30°C. Importantly, at 30°C low pH significantly depressed the ratio of the slow type I fibre, leading to less force and velocity at peak power. These data demonstrate that the direct effect of low pH on peak power in both slow-and fast-twitch fibres at near-in vivo temperatures (30°C) is greater than would be predicted based on changes in P0, and that the fatigue-inducing effects of low pH on cross-bridge function are still substantial and important at temperatures approaching those observed in vivo

Exploring the Evolution of Node Neighborhoods in Dynamic Networks

Dynamic Networks are a popular way of modeling and studying the behavior of evolving systems. However, their analysis constitutes a relatively recent subfield of Network Science, and the number of available tools is consequently much smaller than for static networks. In this work, we propose a method specifically designed to take advantage of the longitudinal nature of dynamic networks. It characterizes each individual node by studying the evolution of its direct neighborhood, based on the assumption that the way this neighborhood changes reflects the role and position of the node in the whole network. For this purpose, we define the concept of \textit{neighborhood event}, which corresponds to the various transformations such groups of nodes can undergo, and describe an algorithm for detecting such events. We demonstrate the interest of our method on three real-world networks: DBLP, LastFM and Enron. We apply frequent pattern mining to extract meaningful information from temporal sequences of neighborhood events. This results in the identification of behavioral trends emerging in the whole network, as well as the individual characterization of specific nodes. We also perform a cluster analysis, which reveals that, in all three networks, one can distinguish two types of nodes exhibiting different behaviors: a very small group of active nodes, whose neighborhood undergo diverse and frequent events, and a very large group of stable nodes

Internal labelling operators and contractions of Lie algebras

We analyze under which conditions the missing label problem associated to a reduction chain $\frak{s}^{\prime}\subset \frak{s}$ of (simple) Lie algebras can be completely solved by means of an In\"on\"u-Wigner contraction $\frak{g}$ naturally related to the embedding. This provides a new interpretation of the missing label operators in terms of the Casimir operators of the contracted algebra, and shows that the available labeling operators are not completely equivalent. Further, the procedure is used to obtain upper bounds for the number of invariants of affine Lie algebras arising as contractions of semisimple algebras.Comment: 20 pages, 2 table

Physical Activity Modulates Corticospinal Excitability of the Lower Limb in Young and Old Adults

Aging is associated with reduced neuromuscular function, which may be due in part to altered corticospinal excitability. Regular physical activity (PA) may ameliorate these age-related declines, but the influence of PA on corticospinal excitability is unknown. The purpose of this study was to determine the influence of age, sex, and PA on corticospinal excitability by comparing the stimulus-response curves of motor evoked potentials (MEP) in 28 young (22.4 ± 2.2 yr; 14 women and 14 men) and 50 old adults (70.2 ± 6.1 yr; 22 women and 28 men) who varied in activity levels. Transcranial magnetic stimulation was used to elicit MEPs in the active vastus lateralis muscle (10% maximal voluntary contraction) with 5% increments in stimulator intensity until the maximum MEP amplitude. Stimulus-response curves of MEP amplitudes were fit with a four-parameter sigmoidal curve and the maximal slope calculated (slopemax). Habitual PA was assessed with tri-axial accelerometry and participants categorized into either those meeting the recommended PA guidelines for optimal health benefits (\u3e10,000 steps/day, high-PA; n = 21) or those not meeting the guidelines (n = 41). The MEP amplitudes and slopemax were greater in the low-PA compared with the high-PA group (P \u3c 0.05). Neither age nor sex influenced the stimulus-response curve parameters (P \u3e 0.05), suggesting that habitual PA influenced the excitability of the corticospinal tract projecting to the lower limb similarly in both young and old adults. These findings provide evidence that achieving the recommended PA guidelines for optimal health may mediate its effects on the nervous system by decreasing corticospinal excitability

Computing simplicial representatives of homotopy group elements

A central problem of algebraic topology is to understand the homotopy groups $\pi_d(X)$ of a topological space $X$. For the computational version of the problem, it is well known that there is no algorithm to decide whether the fundamental group $\pi_1(X)$ of a given finite simplicial complex $X$ is trivial. On the other hand, there are several algorithms that, given a finite simplicial complex $X$ that is simply connected (i.e., with $\pi_1(X)$ trivial), compute the higher homotopy group $\pi_d(X)$ for any given $d\geq 2$. %The first such algorithm was given by Brown, and more recently, \v{C}adek et al. However, these algorithms come with a caveat: They compute the isomorphism type of $\pi_d(X)$, $d\geq 2$ as an \emph{abstract} finitely generated abelian group given by generators and relations, but they work with very implicit representations of the elements of $\pi_d(X)$. Converting elements of this abstract group into explicit geometric maps from the $d$-dimensional sphere $S^d$ to $X$ has been one of the main unsolved problems in the emerging field of computational homotopy theory. Here we present an algorithm that, given a~simply connected space $X$, computes $\pi_d(X)$ and represents its elements as simplicial maps from a suitable triangulation of the $d$-sphere $S^d$ to $X$. For fixed $d$, the algorithm runs in time exponential in $size(X)$, the number of simplices of $X$. Moreover, we prove that this is optimal: For every fixed $d\geq 2$, we construct a family of simply connected spaces $X$ such that for any simplicial map representing a generator of $\pi_d(X)$, the size of the triangulation of $S^d$ on which the map is defined, is exponential in $size(X)$