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