Quantifying the Dynamics of Coupled Networks of Switches and Oscillators

Complex network dynamics have been analyzed with models of systems of coupled switches or systems of coupled oscillators. However, many complex systems are composed of components with diverse dynamics whose interactions drive the system's evolution. We, therefore, introduce a new modeling framework that describes the dynamics of networks composed of both oscillators and switches. Both oscillator synchronization and switch stability are preserved in these heterogeneous, coupled networks. Furthermore, this model recapitulates the qualitative dynamics for the yeast cell cycle consistent with the hypothesized dynamics resulting from decomposition of the regulatory network into dynamic motifs. Introducing feedback into the cell-cycle network induces qualitative dynamics analogous to limitless replicative potential that is a hallmark of cancer. As a result, the proposed model of switch and oscillator coupling provides the ability to incorporate mechanisms that underlie the synchronized stimulus response ubiquitous in biochemical systems

Emergence of a common generalized synchronization manifold in network motifs of structurally different time-delay systems

We point out the existence of a transition from partial to global generalized synchronization (GS) in symmetrically coupled structurally different time-delay systems of different orders using the auxiliary system approach and the mutual false nearest neighbor method. The present authors have recently reported that there exists a common GS manifold even in an ensemble of structurally nonidentical scalar time-delay systems with different fractal dimensions and shown that GS occurs simultaneously with phase synchronization (PS). In this paper we confirm that the above result is not confined just to scalar one-dimensional time-delay systems alone but there exists a similar type of transition even in the case of time-delay systems with different orders. We calculate the maximal transverse Lyapunov exponent to evaluate the asymptotic stability of the complete synchronization manifold of each of the main and the corresponding auxiliary systems, which in turn ensures the stability of the GS manifold between the main systems. Further we estimate the correlation coefficient and the correlation of probability of recurrence to establish the relation between GS and PS. We also calculate the mutual false nearest neighbor parameter which doubly confirms the occurrence of the global GS manifold.Comment: 17 pages, 11 figures, Accepted for publication in Chaos Solitons Fractal

Sparsity-aware neural user behavior modeling in online interaction platforms

Modern online platforms offer users an opportunity to participate in a variety of content-creation, social networking, and shopping activities. With the rapid proliferation of such online services, learning data-driven user behavior models is indispensable to enable personalized user experiences. Recently, representation learning has emerged as an effective strategy for user modeling, powered by neural networks trained over large volumes of interaction data. Despite their enormous potential, we encounter the unique challenge of data sparsity for a vast majority of entities, e.g., sparsity in ground-truth labels for entities and in entity-level interactions (cold-start users, items in the long-tail, and ephemeral groups). In this dissertation, we develop generalizable neural representation learning frameworks for user behavior modeling designed to address different sparsity challenges across applications. Our problem settings span transductive and inductive learning scenarios, where transductive learning models entities seen during training and inductive learning targets entities that are only observed during inference. We leverage different facets of information reflecting user behavior (e.g., interconnectivity in social networks, temporal and attributed interaction information) to enable personalized inference at scale. Our proposed models are complementary to concurrent advances in neural architectural choices and are adaptive to the rapid addition of new applications in online platforms. First, we examine two transductive learning settings: inference and recommendation in graph-structured and bipartite user-item interactions. In chapter 3, we formulate user profiling in social platforms as semi-supervised learning over graphs given sparse ground-truth labels for node attributes. We present a graph neural network framework that exploits higher-order connectivity structures (network motifs) to learn attributed structural roles of nodes that identify structurally similar nodes with co-varying local attributes. In chapter 4, we design neural collaborative filtering models for few-shot recommendations over user-item interactions. To address item interaction sparsity due to heavy-tailed distributions, our proposed meta-learning framework learns-to-recommend few-shot items by knowledge transfer from arbitrary base recommenders. We show that our framework consistently outperforms state-of-art approaches on overall recommendation (by 5% Recall) while achieving significant gains (of 60-80% Recall) for tail items with fewer than 20 interactions. Next, we explored three inductive learning settings: modeling spread of user-generated content in social networks; item recommendations for ephemeral groups; and friend ranking in large-scale social platforms. In chapter 5, we focus on diffusion prediction in social networks where a vast population of users rarely post content. We introduce a deep generative modeling framework that models users as probability distributions in the latent space with variational priors parameterized by graph neural networks. Our approach enables massive performance gains (over 150% recall) for users with sparse activities while being faster than state-of-the-art neural models by an order of magnitude. In chapter 6, we examine item recommendations for ephemeral groups with limited or no historical interactions together. To overcome group interaction sparsity, we present self-supervised learning strategies that exploit the preference co-variance in observed group memberships for group recommender training. Our framework achieves significant performance gains (over 30% NDCG) over prior state-of-the-art group recommendation models. In chapter 7, we introduce multi-modal inference with graph neural networks that captures knowledge from multiple feature modalities and user interactions for multi-faceted friend ranking. Our approach achieves notable higher performance gains for critical populations of less-active and low degree users