The Internet of Things (IoT) plays a crucial role in the construction and maintenance of modern civilization. Currently, for computation-intensive analyses, IoT relies heavily on cloud servers and a stable Internet connection. Recent research aims to reduce this dependency through collaborative computation at the edge of IoT networks. Specifically, these studies break down computation-intensive tasks into smaller components, each managed by resource-constrained edge devices. Inter-component data sharing is essential for these solutions. However, while existing research demonstrates the feasibility of computation using such a split-mode approach (known as splitexecution), it does not address how the overall system performs in low-power IoT environments, where communication between devices may be limited due to energy constraints. In this work, we propose a framework called PIEdge, designed to efficiently implement split-execution in low-power wireless networks through the collaborative processing of the task components across edge devices. The design of PIEdge emphasizes flexibility and fault tolerance while leveraging the strengths of edge computing. We evaluate PIEdge by applying split-execution to Principal Component Analysis (PCA) for outlier detection, as well as for multiplying a series of matrices, which serve as examples of data parallelism and model parallelism, respectively. Additionally, PIEdge demonstrates resilience under a substantial degree of random node failures.

Metastases are the main reason for cancer-related deaths. Initiation of metastases, where newly seeded tumor cells expand into colonies, presents a tremendous bottleneck to metastasis formation. Despite its importance, a quantitative description of metastasis initiation and its clinical implications is lacking. Here, we set theoretical grounds for the metastatic bottleneck with a simple stochastic model. The model assumes that the proliferation-to-death rate ratio for the initiating metastatic cells increases when they are surrounded by more of their kind. For a total of 159,191 patients across 13 cancer types, we found that a single cell has an extremely low median probability of successful seeding of the order of 10-8. With increasing colony size, a sharp transition from very unlikely to very likely successful metastasis initiation occurs. The median metastatic bottleneck, defined as the critical colony size that marks this transition, was between 10 and 21 cells. We derived the probability of metastasis occurrence and patient outcome based on primary tumor size at diagnosis and tumor type. The model predicts that the efficacy of patient treatment depends on the primary tumor size but even more so on the severity of the metastatic bottleneck, which is estimated to largely vary between patients. We find that medical interventions aiming at tightening the bottleneck, such as immunotherapy, can be much more efficient than therapies that decrease overall tumor burden, such as chemotherapy.

In online social systems, users with common affiliations or interests form social groups for discussing various topical issues. We study the relationships among these social groups, which manifest through users who are common members of multiple groups, and the evolution of these relationships as new users join the groups. Focusing on a certain number of the most popular groups, we model the group memberships of users as a subclass of bipartite networks, known as Alphabetic Bipartite Networks (α-BiNs), where one of the partitions contains a fixed number of nodes (the popular groups) while the other grows unboundedly with time (new users joining the groups). Specifically, we consider the evolution of the thresholded projection of the user-group bipartite network onto the set of groups, which accurately represents the inter-group relationships. We propose and solve a preferential attachment based growth model for evolution of α-BiNs, and analytically compute the degree distribution of the thresholded projection. We further investigate whether the predictions of this model can explain the projection degree distributions of user-group networks derived from several real social systems (Livejournal, Youtube and Flickr). The study also shows that the inter-group network is tightly knit, and there is an implicit semantic hierarchy within its structure, that is clearly identified by the method of thresholding. To the best of our knowledge, this is the first attempt to analytically model the dynamical relationships among groups in online social systems.