7,634 research outputs found
Generalized modularity matrices
Various modularity matrices appeared in the recent literature on network
analysis and algebraic graph theory. Their purpose is to allow writing as
quadratic forms certain combinatorial functions appearing in the framework of
graph clustering problems. In this paper we put in evidence certain common
traits of various modularity matrices and shed light on their spectral
properties that are at the basis of various theoretical results and practical
spectral-type algorithms for community detection
Quantum information analysis of electronic states at different molecular structures
We have studied transition metal clusters from a quantum information theory
perspective using the density-matrix renormalization group (DMRG) method. We
demonstrate the competition between entanglement and interaction localization.
We also discuss the application of the configuration interaction based
dynamically extended active space procedure which significantly reduces the
effective system size and accelerates the speed of convergence for complicated
molecular electronic structures to a great extent. Our results indicate the
importance of taking entanglement among molecular orbitals into account in
order to devise an optimal orbital ordering and carry out efficient
calculations on transition metal clusters. We propose a recipe to perform DMRG
calculations in a black-box fashion and we point out the connections of our
work to other tensor network state approaches
Analysis of weighted networks
The connections in many networks are not merely binary entities, either
present or not, but have associated weights that record their strengths
relative to one another. Recent studies of networks have, by and large, steered
clear of such weighted networks, which are often perceived as being harder to
analyze than their unweighted counterparts. Here we point out that weighted
networks can in many cases be analyzed using a simple mapping from a weighted
network to an unweighted multigraph, allowing us to apply standard techniques
for unweighted graphs to weighted ones as well. We give a number of examples of
the method, including an algorithm for detecting community structure in
weighted networks and a new and simple proof of the max-flow/min-cut theorem.Comment: 9 pages, 3 figure
A measure of centrality based on the spectrum of the Laplacian
We introduce a family of new centralities, the k-spectral centralities.
k-Spectral centrality is a measurement of importance with respect to the
deformation of the graph Laplacian associated with the graph. Due to this
connection, k-spectral centralities have various interpretations in terms of
spectrally determined information.
We explore this centrality in the context of several examples. While for
sparse unweighted networks 1-spectral centrality behaves similarly to other
standard centralities, for dense weighted networks they show different
properties. In summary, the k-spectral centralities provide a novel and useful
measurement of relevance (for single network elements as well as whole
subnetworks) distinct from other known measures.Comment: 12 pages, 6 figures, 2 table
Identification of optimal investments
Biofortification is regarded as a complement to supplementation, industrial fortification and dietary diversification in the fight against micronutrient deficiencies. It is important therefore to first identify areas where biofortification may have high impact and prioritize these areas for more in-depth analysis. HarvestPlus has developed the Biofortification Prioritization Index (BPI), which ranks countries globally according to their suitability for investment in biofortification interventions. HarvestPlus is also conducting ex ante micronutrient intervention portfolio analyses, designed to simulate the implementation and impact of a biofortification program in countries which have been identified as suitable candidates for investment. Micronutrient intervention portfolio studies offer the ability to distinguish production, consumption and inadequate micronutrient intake at a more disaggregated level and offer a complementary design and planning tool to simulate the implementation of biofortification and examine its potential impact and cost-effectiveness among different approaches. In addition, these studies are designed to examine multiple interventions within a country, to better understand biofortification’s role in reducing micronutrient deficiency when considered among a suite of interventions. This case study of Zambia demonstrates how these tools can be used to assess the potential impact of biofortification, quantify its cost-effectiveness and examine how it interacts with and complements other interventions. Given the long-term nature of biofortification as an intervention investment, future analyses should continue to incorporate various scenarios including continued investment in sustainable development and the effects of climate change which are likely to condition the impact of biofortification and other interventions.Keywords: Biofortification, Biofortification Priority Index (BPI), Cost-effectiveness, Household Consumption and Expenditure Surveys (HCES
Molecular Clock on a Neutral Network
The number of fixed mutations accumulated in an evolving population often
displays a variance that is significantly larger than the mean (the
overdispersed molecular clock). By examining a generic evolutionary process on
a neutral network of high-fitness genotypes, we establish a formalism for
computing all cumulants of the full probability distribution of accumulated
mutations in terms of graph properties of the neutral network, and use the
formalism to prove overdispersion of the molecular clock. We further show that
significant overdispersion arises naturally in evolution when the neutral
network is highly sparse, exhibits large global fluctuations in neutrality, and
small local fluctuations in neutrality. The results are also relevant for
elucidating the topological structure of a neutral network from empirical
measurements of the substitution process.Comment: 10 page
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