Subgraph covers -- An information theoretic approach to motif analysis in networks

Many real world networks contain a statistically surprising number of certain subgraphs, called network motifs. In the prevalent approach to motif analysis, network motifs are detected by comparing subgraph frequencies in the original network with a statistical null model. In this paper we propose an alternative approach to motif analysis where network motifs are defined to be connectivity patterns that occur in a subgraph cover that represents the network using minimal total information. A subgraph cover is defined to be a set of subgraphs such that every edge of the graph is contained in at least one of the subgraphs in the cover. Some recently introduced random graph models that can incorporate significant densities of motifs have natural formulations in terms of subgraph covers and the presented approach can be used to match networks with such models. To prove the practical value of our approach we also present a heuristic for the resulting NP-hard optimization problem and give results for several real world networks.Comment: 10 pages, 7 tables, 1 Figur

Flow Equations and Normal Ordering

In this paper we consider flow-equations where we allow a normal ordering which is adjusted to the one-particle energy of the Hamiltonian. We show that this flow converges nearly always to the stable phase. Starting out from the symmetric Hamiltonian and symmetry-broken normal ordering nearly always yields symmetry breaking below the critical temperature.Comment: 7 page

Bias in Perceptions of Parenting Roles: Analysis of Gender and Socioeconomic Status

After industrialization in the United States, men primarily moved from the farm to the workplace, leaving women responsible for the children and maintaining the household alone. This arrangement contributed to the so called tender years doctrine, which suggested that mothers were better caretakers of the children and should therefore receive sole custody. The preference for mothers continued until the 1960\u27s, after the women\u27s liberation movement, when a large portion of women moved from the home into the workforce. State statutes were later changed to establish gender-neutrality for the purposes of determining custody decisions and suggested the custody of children should be in their best interests. However, the change of language in the statutes did not change the results of most custody decisions; custody continued to be granted to the mother in most cases. Research suggests there has been a small increase in sharing custody of children but no increase in the number of fathers being awarded sole custody. A prior notion of who should get custody and what defines a good parent is likely wrought with gender stereotypes and bias. This study examined gender stereotypes related to parenting by sampling three occupational groups: judges, psychologists and college students. The significant discrepancy in the ratings of mothers versus fathers varied based on which occupational group was rating the vignette parent and what aspects of parenting were being rated. All three groups rated the vignette mother higher on overall parenting skills and empathic parenting behaviors, as compared to the father in the vignette. Also, as the age of the respondent increased, overall parenting skills ratings declined, indicating a more critical evaluation of parents. Evaluating parenting skills appears complex, individualized and partially influenced by sex-role stereotyping. Gender differences that are likely due to vignette characteristics were found, suggesting bias exists in the evaluation of parenting. However, it may not be an intentional bias for or against one gender, instead it is more likely personal perceptions entering into the decision-making process

Identifying networks with common organizational principles

Many complex systems can be represented as networks, and the problem of network comparison is becoming increasingly relevant. There are many techniques for network comparison, from simply comparing network summary statistics to sophisticated but computationally costly alignment-based approaches. Yet it remains challenging to accurately cluster networks that are of a different size and density, but hypothesized to be structurally similar. In this paper, we address this problem by introducing a new network comparison methodology that is aimed at identifying common organizational principles in networks. The methodology is simple, intuitive and applicable in a wide variety of settings ranging from the functional classification of proteins to tracking the evolution of a world trade network.Comment: 26 pages, 7 figure