Discovering Communities of Community Discovery

Discovering communities in complex networks means grouping nodes similar to each other, to uncover latent information about them. There are hundreds of different algorithms to solve the community detection task, each with its own understanding and definition of what a "community" is. Dozens of review works attempt to order such a diverse landscape -- classifying community discovery algorithms by the process they employ to detect communities, by their explicitly stated definition of community, or by their performance on a standardized task. In this paper, we classify community discovery algorithms according to a fourth criterion: the similarity of their results. We create an Algorithm Similarity Network (ASN), whose nodes are the community detection approaches, connected if they return similar groupings. We then perform community detection on this network, grouping algorithms that consistently return the same partitions or overlapping coverage over a span of more than one thousand synthetic and real world networks. This paper is an attempt to create a similarity-based classification of community detection algorithms based on empirical data. It improves over the state of the art by comparing more than seventy approaches, discovering that the ASN contains well-separated groups, making it a sensible tool for practitioners, aiding their choice of algorithms fitting their analytic needs

Anomalous quantum-critical scaling corrections in two-dimensional antiferromagnets

We study the N\'eel-paramagnetic quantum phase transition in two-dimensional dimerized $S=1/2$ Heisenberg antiferromagnets using finite-size scaling of quantum Monte Carlo data. We resolve the long standing issue of the role of cubic interactions arising in the bond-operator representation when the dimer pattern lacks a certain symmetry. We find non-monotonic (monotonic) size dependence in the staggered (columnar) dimerized model, where cubic interactions are (are not) present. We conclude that there is an irrelevant field in the staggered model that is not present in the columnar case, but, at variance with previous claims, it is not the leading irrelevant field. The new exponent is $\omega_2 \approx 1.25$ and the prefactor of the correction $L^{-\omega_2}$ is large and comes with a different sign from that of the formally leading conventional correction with exponent $\omega_1 \approx 0.78$. Our study highlights the possibility of competing scaling corrections at quantum critical points.Comment: 6 pages, 6 figure

Cohomologically Full Rings

open3siInspired by a question raised by Eisenbud–Mustaţă–Stillman regarding the injectivity of maps from Ext modules to local cohomology modules and the work by the third author with Pham, we introduce a class of rings, which we call cohomologically full rings. This class of rings includes many well-known singularities: Cohen–Macaulay rings, Stanley–Reisner rings, F-pure rings in positive characteristics, and Du Bois singularities in characteristics 0⁠. We prove many basic properties of cohomologically full rings, including their behavior under flat base change. We show that ideals defining these rings satisfy many desirable properties, in particular they have small cohomological and projective dimension. When R is a standard graded algebra over a field of characteristic 0⁠, we show under certain conditions that being cohomologically full is equivalent to the intermediate local cohomology modules being generated in degree 0⁠. Furthermore, we obtain Kodaira-type vanishing and strong bounds on the regularity of cohomologically full graded algebras.embargoed_20201028Dao, Hailong; De Stefani, Alessandro; Ma, LinquanDao, Hailong; De Stefani, Alessandro; Ma, Linqua

Brain Injury Differences in Frontal Impact Crash Using Different Simulation Strategies

In the real world crashes, brain injury is one of the leading causes of deaths. Using isolated human head finite element (FE) model to study the brain injury patterns and metrics has been a simplified methodology widely adopted, since it costs significantly lower computation resources than a whole human body model does. However, the degree of precision of this simplification remains questionable. This study compared these two kinds of methods: (1) using a whole human body model carried on the sled model and (2) using an isolated head model with prescribed head motions, to study the brain injury. The distribution of the von Mises stress (VMS), maximum principal strain (MPS), and cumulative strain damage measure (CSDM) was used to compare the two methods. The results showed that the VMS of brain mainly concentrated at the lower cerebrum and occipitotemporal region close to the cerebellum. The isolated head modelling strategy predicted higher levels of MPS and CSDM 5%, while the difference is small in CSDM 10% comparison. It suggests that isolated head model may not equivalently reflect the strain levels below the 10% compared to the whole human body model