Accurately Modeling Biased Random Walks on Weighted Graphs Using $textit{Node2vec+}$

Node embedding is a powerful approach for representing the structural role of each node in a graph. $textit{Node2vec}$ is a widely used method for node embedding that works by exploring the local neighborhoods via biased random walks on the graph. However, $textit{node2vec}$ does not consider edge weights when computing walk biases. This intrinsic limitation prevents $textit{node2vec}$ from leveraging all the information in weighted graphs and, in turn, limits its application to many real-world networks that are weighted and dense. Here, we naturally extend $textit{node2vec}$ to $textit{node2vec+}$ in a way that accounts for edge weights when calculating walk biases, but which reduces to $textit{node2vec}$ in the cases of unweighted graphs or unbiased walks. We empirically show that $textit{node2vec+}$ is more robust to additive noise than $textit{node2vec}$ in weighted graphs using two synthetic datasets. We also demonstrate that $textit{node2vec+}$ significantly outperforms $textit{node2vec}$ on a commonly benchmarked multi-label dataset (Wikipedia). Furthermore, we test $textit{node2vec+}$ against GCN and GraphSAGE using various challenging gene classification tasks on two protein-protein interaction networks. Despite some clear advantages of GCN and GraphSAGE, they show comparable performance with $textit{node2vec+}$. Finally, $textit{node2vec+}$ can be used as a general approach for generating biased random walks, benefiting all existing methods built on top of $textit{node2vec}$. $textit{Node2vec+}$ is implemented as part of $texttt{PecanPy}$, which is available at https://github.com/krishnanlab/PecanPy .

Bayesian Optimization of Area-based Road Pricing

This study presents a Bayesian Optimization framework for area- and distance-based time-of-day pricing (TODP) for urban networks. The road pricing optimization problem can reach high level of complexity depending on the pricing scheme considered, its associated detailed network properties and the affected heterogeneous demand features. We consider heterogeneous travellers with individual-specific trip attributes and departure-time choice parameters together with a Macroscopic Fundamental Diagram (MFD) model for the urban network. Its mathematical formulation is presented and an agent-based simulation framework is constructed as evaluation function for the TODP optimization problem. The latter becomes highly nonlinear and relying on an expensive-to-evaluate objective function. We then present and test a Bayesian Optimization approach to compute different time-of-day pricing schemes by maximizing social welfare. Our proposed method learns the relationship between the prices and welfare within a few iterations and is able to find good solutions even in scenarios with high dimensionality in the decision variables space, setting a path for complexity reduction in more realistic road pricing optimization problems. Furthermore and as expected, the simulation results show that TODP improves the social welfare against the no-pricing case.

Managing network congestion with a tradable credit scheme: a trip-based MFD approach

This study investigates the efficiency and effectiveness of an area-based tradable credit scheme (TCS) using the trip-based Macroscopic Fundamental Diagram model for the morning commute problem. In the proposed TCS, the regulator distributes initial credits to all travelers and designs a time-varying and trip length specific credit tariff. Credits are traded between travelers and the regulator via a credit market, and the credit price is determined by the demand and supply of credits. The heterogeneity of travelers is considered in terms of desired arrival time, trip length and departure-time choice preferences. The TCS is incorporated into a day-to-day modelling framework to examine the travelers learning process, the evolution of network, and the properties of the credit market. The existence of an equilibrium solution and the uniqueness of the credit price at the equilibrium state are established analytically. Furthermore, an open-source simulation framework is developed to validate the analytical properties of the proposed TCS and compare it with alternative control strategies in terms of mobility, network performance, and social welfare. Bayesian optimization is then adopted to optimize the credit toll scheme. The numerical results demonstrate that the proposed TCS outperforms the no-control case and matches the performance of the time-of-day pricing strategy, while maintaining revenue-neutral nature.

Relativity and Diversity of Strong Coupling to Measured Subsystems

The strong coupling between two subsystems consisting of quantum emitters and photonic modes, at which the level splitting of mixed quantum states occurs, has been a central subject of quantum physics and nanophotonics due to various important applications. The spectral Rabi-splitting of photon emission or absorption has been adopted to experimentally characterize the strong coupling under the equality assumption that it is identical to the level splitting. Here, we for the first time reveal that the equality assumption is not valid. It is the invalidity that results in the relativity and diversity of the strong coupling characterized by the spectral Rabi-splitting to the measured subsystems, highly correlated with their dissipative decays. The strong coupling is easier to be observed from the subsystem with larger decay, and can be classified into pseudo-, dark-, middle-, and super-strong interaction regimes. We also suggest a prototype of coupled plasmon-exciton system for possibly future experiment observations on these novel predictions. Our work brings new fundamental insight to the light-matter interaction in nanostructures, which will stimulate further researches in this field.