@article{jiang_huang_panahi_yu_krim_smith_2021, title={Dynamic Graph Learning: A Structure-Driven Approach}, volume={9}, ISSN={["2227-7390"]}, DOI={10.3390/math9020168}, abstractNote={The purpose of this paper is to infer a dynamic graph as a global (collective) model of time-varying measurements at a set of network nodes. This model captures both pairwise as well as higher order interactions (i.e., more than two nodes) among the nodes. The motivation of this work lies in the search for a connectome model which properly captures brain functionality across all regions of the brain, and possibly at individual neurons. We formulate it as an optimization problem, a quadratic objective functional and tensor information of observed node signals over short time intervals. The proper regularization constraints reflect the graph smoothness and other dynamics involving the underlying graph’s Laplacian, as well as the time evolution smoothness of the underlying graph. The resulting joint optimization is solved by a continuous relaxation of the weight parameters and an introduced novel gradient-projection scheme. While the work may be applicable to any time-evolving data set (e.g., fMRI), we apply our algorithm to a real-world dataset comprising recorded activities of individual brain cells. The resulting model is shown to be not only viable but also efficiently computable.}, number={2}, journal={MATHEMATICS}, author={Jiang, Bo and Huang, Yuming and Panahi, Ashkan and Yu, Yiyi and Krim, Hamid and Smith, Spencer L.}, year={2021}, month={Jan} }
 @article{huang_panahi_krim_dai_2020, title={Community Detection and Improved Detectability in Multiplex Networks}, volume={7}, ISSN={["2327-4697"]}, DOI={10.1109/TNSE.2019.2949036}, abstractNote={We investigate the widely encountered problem of detecting communities in multiplex networks, such as social networks, with an unknown arbitrary heterogeneous structure. To improve detectability, we propose a generative model that leverages the multiplicity of a single community in multiple layers, with no prior assumption on the relation of communities among different layers. Our model relies on a novel idea of incorporating a large set of generic localized community label constraints across the layers, in conjunction with the celebrated Stochastic Block Model (SBM) in each layer. Accordingly, we build a probabilistic graphical model over the entire multiplex network by treating the constraints as Bayesian priors. We mathematically prove that these constraints/priors promote existence of identical communities across layers without introducing further correlation between individual communities. The constraints are further tailored to render a sparse graphical model and the numerically efficient Belief Propagation algorithm is subsequently employed. We further demonstrate by numerical experiments that in the presence of consistent communities between different layers, consistent communities are matched, and the detectability is improved over a single layer. We compare our model with a “correlated model” which exploits the prior knowledge of community correlation between layers. Similar detectability improvement is obtained under such a correlation, even though our model relies on much milder assumptions than the correlated model. Our model even shows a better detection performance over a certain correlation and signal to noise ratio (SNR) range. In the absence of community correlation, the correlation model naturally fails, while ours maintains its performance.}, number={3}, journal={IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING}, author={Huang, Yuming and Panahi, Ashkan and Krim, Hamid and Dai, Liyi}, year={2020}, pages={1697–1709} }
 @article{huang_daniels_2016, title={Friction and pressure-dependence of force chain communities in granular materials}, volume={18}, ISSN={["1434-7636"]}, url={https://doi.org/10.1007/s10035-016-0681-6}, DOI={10.1007/s10035-016-0681-6}, abstractNote={Granular materials transmit stress via a network of force chains. Despite the importance of these chains in characterizing the stress state and dynamics of the system, there is no common framework for quantifying their properties. Recently, attention has turned to the tools of network science as a promising route to such a description. In this paper, we apply a common network-science technique, community detection, to the force network of numerically-generated packings of spheres over a range of interparticle friction coefficients and confining pressures. In order to extract chain-like features, we use a modularity maximization with a recently-developed geographical null model (Bassett et al. in Soft Matter 11:2731–2744, 2015), and optimize the technique to detect sparse structures by minimizing the normalized convex hull ratio of the detected communities. We characterize the force chain communities by their size (number of particles), network force (interparticle forces), and normalized convex hull ratio (sparseness). We find that the first two are highly correlated and are therefore largely redundant. For both pressure P and interparticle friction $$\mu $$ , we observe two distinct transitions in behavior. One, for $$\mu \lesssim 0.1$$ the packings exhibit more distinguishability to pressure than at higher $$\mu $$ . Two, we identify a transition pressure $$P^*$$ at which the frictional dependence switches behaviors. Below $$P^*$$ there are more large/strong communities at low $$\mu $$ , while above $$P^*$$ there are more large/strong communities at high $$\mu $$ . We explain these phenomena by comparison to the spatial distribution of communities along the vertical axis of the system. These results provide new tools for considering the mesoscale structure of a granular system and pave the way for reduced descriptions based on the force chain structure.}, number={4}, journal={GRANULAR MATTER}, publisher={Springer Science and Business Media LLC}, author={Huang, Yuming and Daniels, Karen E.}, year={2016}, month={Nov} }