Super-resolution community detection for layer-aggregated multilayer networks

Applied network science often involves preprocessing network data before applying a network-analysis method, and there is typically a theoretical disconnect between these steps. For example, it is common to aggregate time-varying network data into windows prior to analysis, and the tradeoffs of this preprocessing are not well understood. Focusing on the problem of detecting small communities in multilayer networks, we study the effects of layer aggregation by developing random-matrix theory for modularity matrices associated with layer-aggregated networks with $N$ nodes and $L$ layers, which are drawn from an ensemble of Erd\H{o}s-R\'enyi networks. We study phase transitions in which eigenvectors localize onto communities (allowing their detection) and which occur for a given community provided its size surpasses a detectability limit $K^*$. When layers are aggregated via a summation, we obtain $K^*\varpropto \mathcal{O}(\sqrt{NL}/T)$, where $T$ is the number of layers across which the community persists. Interestingly, if $T$ is allowed to vary with $L$ then summation-based layer aggregation enhances small-community detection even if the community persists across a vanishing fraction of layers, provided that $T/L$ decays more slowly than $\mathcal{O}(L^{-1/2})$. Moreover, we find that thresholding the summation can in some cases cause $K^*$ to decay exponentially, decreasing by orders of magnitude in a phenomenon we call super-resolution community detection. That is, layer aggregation with thresholding is a nonlinear data filter enabling detection of communities that are otherwise too small to detect. Importantly, different thresholds generally enhance the detectability of communities having different properties, illustrating that community detection can be obscured if one analyzes network data using a single threshold.Comment: 11 pages, 8 figure

Enhanced detectability of community structure in multilayer networks through layer aggregation

Many systems are naturally represented by a multilayer network in which edges exist in multiple layers that encode different, but potentially related, types of interactions, and it is important to understand limitations on the detectability of community structure in these networks. Using random matrix theory, we analyze detectability limitations for multilayer (specifically, multiplex) stochastic block models (SBMs) in which L layers are derived from a common SBM. We study the effect of layer aggregation on detectability for several aggregation methods, including summation of the layers' adjacency matrices for which we show the detectability limit vanishes as O(L^{-1/2}) with increasing number of layers, L. Importantly, we find a similar scaling behavior when the summation is thresholded at an optimal value, providing insight into the common - but not well understood - practice of thresholding pairwise-interaction data to obtain sparse network representations.Comment: 7 pages, 4 figure

Counter-intuitive moral judgement following traumatic brain injury

Several neurological patient populations, including Traumatic Brain Injury (TBI), appear to produce an abnormally ‘utilitarian’ pattern of judgements to moral dilemmas; they tend to make judgements that maximise the welfare of the majority, rather than deontological judgements based on the following of moral rules (e.g., do not harm others). However, this patient research has always used extreme dilemmas with highly valued moral rules (e.g., do not kill). Data from healthy participants, however, suggests that when a wider range of dilemmas are employed, involving less valued moral rules (e.g., do not lie), moral judgements demonstrate sensitivity to the psychological intuitiveness of the judgements, rather than their deontological or utilitarian content (Kahane et al., 2011). We sought the moral judgements of 30 TBI participants and 30 controls on moral dilemmas where content (utilitarian/deontological) and intuition (intuitive/counterintuitive) were measured concurrently. Overall TBI participants made utilitarian judgements in equal proportions to controls; disproportionately favouring utilitarian judgements only when they were counterintuitive, and deontological judgements only when they were counterintuitive. These results speak against the view that TBI causes a specific utilitarian bias, suggesting instead that moral intuition is broadly disrupted following TBI

An Investigation in Oxidative Cation Formation: The Total Synthesis of Lactodehydrothyrsiferol and Synthetic Application for a Bimolecular Carbon–Carbon Bond Forming Reaction

The first total synthesis of lactodehydrothyrsiferol, a selective inhibitor of protein phosphatase 2A, was accomplished through the application of our electron-transfer-initiated cyclization reaction. Other highlights of our synthetic strategy include a novel method for the formation of 1,1-disubstuted vinyl iodides from a terminal alkyne, a Suzuki-Miyaura cross coupling reaction on a iodinated allylic carbonate, a one pot diepoxidation of a diene to generate two epoxides with opposite stereochemical identities, an asymmetric Nozaki-Hiyama-Kishi reaction, and the selective deoxygenation of a triol. This document will focus on the key epoxide cascade and completion of the synthesis. An oxidative method to form Carbon–Carbon bonds through Carbon–Hydrogen bond cleavage is described herein. Chromene and isochromene both form aromatically stabilized oxocarbenium ions in the presence of 2,3-dichloro-5,6-dicyano-1,4-benzoquinone (DDQ). The reactivity of these cations was explored with a variety of nucleophiles. In addition, the electronic properties were altered on the benzopyran ring system to elucidate the substrate scope for this transformation