7,579 research outputs found
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 maximum flows, admits a
linear time construction of a clustering \C(S) of predominantly connected
communities that contains a given community and is maximum in the sense
that any further clustering of predominantly connected communities that also
contains is hierarchically nested in \C(S). We further generalize this
construction yielding a clustering with similar properties for given
communities in 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 ïŹbres at 15°C and 30°C. Skinned fast type IIa and slow type I ïŹbres 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 ïŹbre force (P0), unloaded shortening velocity (V0), forceâvelocity, and forceâpower relationships determined. Consistent with previous observations, low pH depressed the P0 of both fast and slow ïŹbres, less at 30°C (4â12%) than at 15°C (30%). However, the low pH-induced depressions in slow type I ïŹbre V0 and peak power were both signiïŹcantly greater at 30°C (25% versus 9% for V0 and 34% versus 17% for peak power). For the fast type IIa ïŹbre 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 forceâvelocity relationship was temperature sensitive, and showed a higher a/P0 ratio (less curvature) at 30°C. Importantly, at 30°C low pH signiïŹcantly depressed the ratio of the slow type I ïŹbre, 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 ïŹbres 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 of (simple) Lie algebras
can be completely solved by means of an In\"on\"u-Wigner contraction
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
of a topological space . For the computational version of the
problem, it is well known that there is no algorithm to decide whether the
fundamental group of a given finite simplicial complex is
trivial. On the other hand, there are several algorithms that, given a finite
simplicial complex that is simply connected (i.e., with
trivial), compute the higher homotopy group for any given .
%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 , as an \emph{abstract} finitely generated abelian
group given by generators and relations, but they work with very implicit
representations of the elements of . Converting elements of this
abstract group into explicit geometric maps from the -dimensional sphere
to 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 ,
computes and represents its elements as simplicial maps from a
suitable triangulation of the -sphere to . For fixed , the
algorithm runs in time exponential in , the number of simplices of
. Moreover, we prove that this is optimal: For every fixed , we
construct a family of simply connected spaces such that for any simplicial
map representing a generator of , the size of the triangulation of
on which the map is defined, is exponential in
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