Efficient, Optimal kk-Leader Selection for Coherent, One-Dimensional Formations

We study the problem of optimal leader selection in consensus networks with noisy relative information. The objective is to identify the set of $k$ leaders that minimizes the formation's deviation from the desired trajectory established by the leaders. An optimal leader set can be found by an exhaustive search over all possible leader sets; however, this approach is not scalable to large networks. In recent years, several works have proposed approximation algorithms to the $k$-leader selection problem, yet the question of whether there exists an efficient, non-combinatorial method to identify the optimal leader set remains open. This work takes a first step towards answering this question. We show that, in one-dimensional weighted graphs, namely path graphs and ring graphs, the $k$-leader selection problem can be solved in polynomial time (in both $k$ and the network size $n$). We give an $O(n^3)$ solution for optimal $k$-leader selection in path graphs and an $O(kn^3)$ solution for optimal $k$-leader selection in ring graphs.Comment: 7 pages, 5 figures, submitted to ECC1

Generative Models for Rapid Information Propagation

We consider the dynamics of rapid propagation of information in complex social networks focusing on mobile phone networks. We introduce two models for an information propagation process. The first model describes the temporal behavior of people which leads to the emergence of information propagation events and is based on the existence of two types of subscribers: regular subscribers and subscribers that tend to spread information. The second model describes the topology of paths in which the information propagates from one subscriber to another. We further introduce an efficient algorithm for identification of information propagation events. We then apply our algorithm to a large-scale mobile phone network and demonstrate the correspondence between theoretical expectations and the actual results

Factors associated with physicians’ prescriptions for rheumatoid arthritis drugs not filled by patients

Abstract Background This study estimated the extent and predictors of primary nonadherence (i.e., prescriptions made by physicians but not initiated by patients) to methotrexate and to biologics or tofacitinib in rheumatoid arthritis (RA) patients who were newly prescribed these medications. Methods Using administrative claims linked with electronic health records (EHRs) from multiple healthcare provider organizations in the USA, RA patients who received a new prescription for methotrexate or biologics/tofacitinib were identified from EHRs. Claims data were used to ascertain filling or administration status. A logistic regression model for predicting primary nonadherence was developed and tested in training and test samples. Predictors were selected based on clinical judgment and LASSO logistic regression. Results A total of 36.8% of patients newly prescribed methotrexate failed to initiate methotrexate within 2 months; 40.6% of patients newly prescribed biologics/tofacitinib failed to initiate within 3 months. Factors associated with methotrexate primary nonadherence included age, race, region, body mass index, count of active drug ingredients, and certain previously diagnosed and treated conditions at baseline. Factors associated with biologics/tofacitinib primary nonadherence included age, insurance, and certain previously treated conditions at baseline. The area under the receiver operating characteristic curve of the logistic regression model estimated in the training sample and applied to the independent test sample was 0.86 and 0.78 for predicting primary nonadherence to methotrexate and to biologics/tofacitinib, respectively. Conclusions This study confirmed that failure to initiate new prescriptions for methotrexate and biologics/tofacitinib was common in RA patients. It is feasible to predict patients at high risk of primary nonadherence to methotrexate and to biologics/tofacitinib and to target such patients for early interventions to promote adherence