Understanding the coevolution of mask wearing and epidemics:A network perspective

Nonpharmaceutical interventions (NPIs) such as mask wearing can be effective in mitigating the spread of infectious diseases. Therefore, understanding the behavioral dynamics of NPIs is critical for characterizing the dynamics of disease spread. Nevertheless, standard infection models tend to focus only on disease states, overlooking the dynamics of "beneficial contagions," e.g., compliance with NPIs. In this work, we investigate the concurrent spread of disease and mask-wearing behavior over multiplex networks. Our proposed framework captures both the competing and complementary relationships between the dueling contagion processes. Further, the model accounts for various behavioral mechanisms that influence mask wearing, such as peer pressure and fear of infection. Our results reveal that under the coupled disease-behavior dynamics, the attack rate of a disease-as a function of transition probability-exhibits a critical transition. Specifically, as the transmission probability exceeds a critical threshold, the attack rate decreases abruptly due to sustained mask-wearing responses. We empirically explore the causes of the critical transition and demonstrate the robustness of the observed phenomena. Our results highlight that without proper enforcement of NPIs, reductions in the disease transmission probability via other interventions may not be sufficient to reduce the final epidemic size.</p

Approximation Schemes for Multi-Budgeted Independence Systems

A natural way to deal with multiple, partially conflicting objectives is turning all the objectives but one into budget constraints. Some classical optimization problems, such as spanning tree and forest, shortest path, (perfect) matching, independent set (basis) in a matroid or in the intersection of two matroids, become NP-hard even with one budget constraint. Still, for most of these problems efficient deterministic and randomized approximation schemes are known. For two or more bud-gets, typically only multi-criteria approximation schemes are available, which return slightly infeasible solutions. Not much is known however for strict budget constraints: filling this gap is the main goal of this paper. It is not hard to see that the above-mentioned problems whose solution sets do not correspond to independence systems are inapproximable al-ready for two budget constraints. For the remaining problems, we present approximation schemes for a constant number k of budget constraints using a variety of techniques: i) we present a simple and powerful mech-anism to transform multi-criteria approximation schemes into pure ap-proximation schemes. This leads to deterministic and randomized ap-proximation schemes for various of the above-mentioned problems; ii) we show that points in low-dimensional faces of any matroid polytope are almost integral, an interesting result on its own. This gives a de-terministic approximation scheme for k-budgeted matroid independent set; iii) we present a deterministic approximation scheme for 2-budgeted matching. The backbone of this result is a purely topological property of curves in R2

A Coloring Based Backbone Construction Algorithm in Wireless Ad Hoc Network

A wireless ad hoc network consists of many mobile hosts communicating with each other without any infrastructure. Virtual backbone plays a key role in a wireless ad hoc network for routing optimization, energy conservation and resource allocation. To construct virtual backbones efficiently, a new distributed method based on coloring algorithm is proposed in this paper. Because the proposed algorithm uses only 1-hop neighbors information, it is proven that this coloring based method can cluster into groups with O(Δ) time complexity and O(nΔ2) message complexity, which are better than referenced work in this paper

Strong edge coloring for channel assignment in wireless radio networks

We give efficient sequential and distributed approximation algorithms for strong edge coloring graphs modeling wireless networks. Strong edge coloring is equivalent to computing a conflict-free assignment of channels or frequencies to pairwise links between transceivers in the network