Purdue University

About: Purdue University is a education organization based out in West Lafayette, Indiana, United States. It is known for research contribution in the topics: Population & Heat transfer. The organization has 73219 authors who have published 163563 publications receiving 5775236 citations. The organization is also known as: Purdue & Purdue-West Lafayette.

Higher-order organization of complex networks

Abstract: Networks are a fundamental tool for understanding and modeling complex systems in physics, biology, neuroscience, engineering, and social science. Many networks are known to exhibit rich, lower-order connectivity patterns that can be captured at the level of individual nodes and edges. However, higher-order organization of complex networks—at the level of small network subgraphs—remains largely unknown. Here, we develop a generalized framework for clustering networks on the basis of higher-order connectivity patterns. This framework provides mathematical guarantees on the optimality of obtained clusters and scales to networks with billions of edges. The framework reveals higher-order organization in a number of networks, including information propagation units in neuronal networks and hub structure in transportation networks. Results show that networks exhibit rich higher-order organizational structures that are exposed by clustering based on higher-order connectivity patterns.

A Representation and Economic Interpretation of a Two-Level Programming Problem

Abstract: This paper first presents a formulation for a class of hierarchial problems that show a two-stage decision making process; this formulation is termed multilevel programming and could be defined, in...

Testing a Point Null Hypothesis: The Irreconcilability of P Values and Evidence

Abstract: The problem of testing a point null hypothesis (or a “small interval” null hypothesis) is considered. Of interest is the relationship between the P value (or observed significance level) and conditional and Bayesian measures of evidence against the null hypothesis. Although one might presume that a small P value indicates the presence of strong evidence against the null, such is not necessarily the case. Expanding on earlier work [especially Edwards, Lindman, and Savage (1963) and Dickey (1977)], it is shown that actual evidence against a null (as measured, say, by posterior probability or comparative likelihood) can differ by an order of magnitude from the P value. For instance, data that yield a P value of .05, when testing a normal mean, result in a posterior probability of the null of at least .30 for any objective prior distribution. (“Objective” here means that equal prior weight is given the two hypotheses and that the prior is symmetric and nonincreasing away from the null; other definiti...