912 research outputs found
Quantum gravity at a large number of dimensions
We consider the large- limit of Einstein gravity. It is observed that a
consistent leading large- graph limit exists, and that it is built up by a
subclass of planar diagrams. The graphs in the effective field theory extension
of Einstein gravity are investigated in the same context, and it is seen that
an effective field theory extension of the basic Einstein-Hilbert theory will
not upset the latter leading large- graph limit, {\it i.e.}, the same
subclass of planar diagrams will dominate at large- in the effective field
theory. The effective field theory description of large- quantum gravity
limit will be renormalizable, and the resulting theory will thus be completely
well defined up to the Planck scale at GeV. The
expansion in gravity is compared to the successful expansion in
gauge theory (the planar diagram limit), and dissimilarities and parallels of
the two expansions are discussed. We consider the expansion of the effective
field theory terms and we make some remarks on explicit calculations of
-point functions.Comment: 18 pages, 23 figures (75 files), format RevTex4, typos corrected,
references adde
Temporal patterns of physical activity and sedentary behavior in 10-14 year-old children on weekdays
Background: An important but often ignored aspect of physical activity (PA) and sedentary behavior (SB) is the chronological succession of activities, or temporal pattern. The main purposes of this study were (1) to investigate when certain types of PA and SB compete against each other during the course of the day and (2) compare intensity-and domain-specific activity levels during different day-segments.
Methods: The study sample consists of 211 children aged 10-14, recruited from 15 primary and 15 secondary schools. PA was assessed combining the SenseWear Mini Armband (SWM) with an electronic activity diary. The intensity-and domain-specific temporal patterns were plotted and PA differences between different day-segments (i.e., morning, school, early evening and late evening) were examined using repeated-measures ANCOVA models.
Results: Physical activity level (PAL) was highest during the early evening (2.51 METSWM) and school hours (2.49 METSWM); the late evening segment was significantly less active (2.21 METSWM) and showed the highest proportion of sedentary time (54 % of total time-use). Throughout the different day-segments, several domains of PA and SB competed with each other. During the critical early-evening segment, screentime (12 % of time-use) and homework (10 %) were dominant compared to activity domains of sports (4 %) and active leisure (3 %). The domain of active travel competed directly with motor travel during the morning (5 % and 6 % respectively) and early-evening segment (both 8 %).
Conclusions: Throughout the day, different aspects of PA and SB go in competition with each other, especially during the time period immediately after school. Detailed information on the temporal patterns of PA and SB of children could help health professionals to develop more effective PA interventions and promotion strategies. By making adaptations to the typical day schedule of children (e.g., through the introduction of extra-curricular PA after school hours), their daily activity levels might improve
Recognizing Treelike k-Dissimilarities
A k-dissimilarity D on a finite set X, |X| >= k, is a map from the set of
size k subsets of X to the real numbers. Such maps naturally arise from
edge-weighted trees T with leaf-set X: Given a subset Y of X of size k, D(Y) is
defined to be the total length of the smallest subtree of T with leaf-set Y .
In case k = 2, it is well-known that 2-dissimilarities arising in this way can
be characterized by the so-called "4-point condition". However, in case k > 2
Pachter and Speyer recently posed the following question: Given an arbitrary
k-dissimilarity, how do we test whether this map comes from a tree? In this
paper, we provide an answer to this question, showing that for k >= 3 a
k-dissimilarity on a set X arises from a tree if and only if its restriction to
every 2k-element subset of X arises from some tree, and that 2k is the least
possible subset size to ensure that this is the case. As a corollary, we show
that there exists a polynomial-time algorithm to determine when a
k-dissimilarity arises from a tree. We also give a 6-point condition for
determining when a 3-dissimilarity arises from a tree, that is similar to the
aforementioned 4-point condition.Comment: 18 pages, 4 figure
An Agent-Based Algorithm exploiting Multiple Local Dissimilarities for Clusters Mining and Knowledge Discovery
We propose a multi-agent algorithm able to automatically discover relevant
regularities in a given dataset, determining at the same time the set of
configurations of the adopted parametric dissimilarity measure yielding compact
and separated clusters. Each agent operates independently by performing a
Markovian random walk on a suitable weighted graph representation of the input
dataset. Such a weighted graph representation is induced by the specific
parameter configuration of the dissimilarity measure adopted by the agent,
which searches and takes decisions autonomously for one cluster at a time.
Results show that the algorithm is able to discover parameter configurations
that yield a consistent and interpretable collection of clusters. Moreover, we
demonstrate that our algorithm shows comparable performances with other similar
state-of-the-art algorithms when facing specific clustering problems
Twin subgraphs and core-semiperiphery-periphery structures
A standard approach to reduce the complexity of very large networks is to
group together sets of nodes into clusters according to some criterion which
reflects certain structural properties of the network. Beyond the well-known
modularity measures defining communities, there are criteria based on the
existence of similar or identical connection patterns of a node or sets of
nodes to the remainder of the network. A key notion in this context is that of
structurally equivalent or twin nodes, displaying exactly the same connection
pattern to the remainder of the network.
The first goal of this paper is to extend this idea to subgraphs of arbitrary
order of a given network, by means of the notions of T-twin and F-twin
subgraphs. This is motivated by the need to provide a systematic approach to
the analysis of core-semiperiphery-periphery (CSP) structures, a notion which
somehow lacks a formal treatment in the literature. The goal is to provide an
analytical framework accommodating and extending the idea that the unique
(ideal) core-periphery (CP) structure is a 2-partitioned K2. We provide a
formal definition of CSP structures in terms of core eccentricities and
periphery degrees, with semiperiphery vertices acting as intermediaries. The
T-twin and F-twin notions then make it possible to reduce the large number of
resulting structures by identifying isomorphic substructures which share the
connection pattern to the remainder of the graph, paving the way for the
decomposition and enumeration of CSP structures. We compute the resulting CSP
structures up to order six.
We illustrate the scope of our results by analyzing a subnetwork of the
network of 1994 metal manufactures trade. Our approach can be further applied
in complex network theory and seems to have many potential extensions
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