Simultaneously recovering running cost and Hamiltonian in Mean Field Games system

We propose and study several inverse problems for the mean field games (MFG) system in a bounded domain. Our focus is on simultaneously recovering the running cost and the Hamiltonian within the MFG system by the associated boundary observation. There are several technical novelties that make the study intriguing and challenging. First, the MFG system couples two nonlinear parabolic PDEs with one moving forward and the other one moving backward in time. Second, there is a probability density constraint on the population distribution of the agents. Third, the simultaneous recovery of two coupling factors within the MFG system is technically far from being trivial. Fourth, we consider both cases that the running cost depends on the population density locally and non-locally, and the two cases present different technical challenges for the inverse problem study. We develop two mathematical strategies that can ensure the probability constraint as well as effectively tackle the inverse problems, which are respectively termed as high-order variation and successive linearisation. In particular, the high-order variation method is new to the literature, which demonstrates a novel concept to examine the inverse problems by non-negative inputs only. We believe the methods developed can find applications to inverse problems in other contexts

A Dynamic Grouping Strategy for Beyond Diagonal Reconfigurable Intelligent Surfaces with Hybrid Transmitting and Reflecting Mode

Beyond diagonal reconfigurable intelligent surface (BD-RIS) is a novel branch of RIS which breaks through the limitation of traditional RIS with diagonal scattering matrices. However, the existing research focuses on BD-RIS with fixed architectures regardless of channel state information (CSI), which limit the achievable performance of BD-RIS. To solve this issue, in this paper, we propose a novel dynamically group-connected BD-RIS based on a dynamic grouping strategy. Specifically, RIS antennas are dynamically divided into several subsets adapting to the CSI, yielding a permuted block-diagonal scattering matrix. To verify the effectiveness of the proposed dynamically group-connected BD-RIS, we propose an efficient algorithm to optimize the BD-RIS with dynamic grouping for a BD-RIS-assisted multi-user multiple-input single-output system. Simulation results show that the proposed dynamically group-connected architecture outperforms fixed group-connected architectures.Comment: 6 pages, 6 figures, accepted by IEEE Trans. Veh. Techno

Beyond Diagonal Reconfigurable Intelligent Surfaces: A Multi-Sector Mode Enabling Highly Directional Full-Space Wireless Coverage

Reconfigurable intelligent surface (RIS) has gained much traction due to its potential to manipulate the propagation environment via nearly-passive reconfigurable elements. In our previous work, we have analyzed and proposed a beyond diagonal RIS (BD-RIS) model, which is not limited to traditional diagonal phase shift matrices, to unify different RIS modes/architectures. In this paper, we create a new branch of BD-RIS supporting a multi-sector mode. A multi-sector BD-RIS is modeled as multiple antennas connected to a multi-port group-connected reconfigurable impedance network. More specifically, antennas are divided into $L$ ($L \ge 2$) sectors and arranged as a polygon prism with each sector covering $1/L$ space. Different from the recently introduced concept of intelligent omni-surface (or simultaneously transmitting and reflecting RIS), the multi-sector BD-RIS not only achieves a full-space coverage, but also has significant performance gains thanks to the highly directional beam of each sector.We derive the constraint of the multi-sector BD-RIS and the corresponding channel model taking into account the relationship between antenna beamwidth and gain. With the proposed model, we first derive the scaling law of the received signal power for a multi-sector BD-RIS-assisted single-user system. We then propose efficient beamforming design algorithms to maximize the sum-rate of the multi-sector BD-RIS-assisted multiuser system. Simulation results verify the effectiveness of the proposed design and demonstrate the performance enhancement of the proposed multi-sector BD-RIS.Comment: 14 pages, 10 figures, submitted to IEEE journa

DeepDRK: Deep Dependency Regularized Knockoff for Feature Selection

Model-X knockoff, among various feature selection methods, received much attention recently due to its guarantee on false discovery rate (FDR) control. Subsequent to its introduction in parametric design, knockoff is advanced to handle arbitrary data distributions using deep learning-based generative modeling. However, we observed that current implementations of the deep Model-X knockoff framework exhibit limitations. Notably, the "swap property" that knockoffs necessitate frequently encounter challenges on sample level, leading to a diminished selection power. To overcome, we develop "Deep Dependency Regularized Knockoff (DeepDRK)", a distribution-free deep learning method that strikes a balance between FDR and power. In DeepDRK, a generative model grounded in a transformer architecture is introduced to better achieve the "swap property". Novel efficient regularization techniques are also proposed to reach higher power. Our model outperforms other benchmarks in synthetic, semi-synthetic, and real-world data, especially when sample size is small and data distribution is complex.Comment: 23 pages, 14 figures, 7 table

Credit Information in Earnings Calls

We develop a novel technique to extract credit-relevant information from the text of quarterly earnings calls. This information is not spanned by fundamental or market variables and forecasts future credit spread changes. One reason for such forecastability is that our text-based measure predicts future credit spread risk and firm profitability. More firm- and call-level complexity increase the forecasting power of our measure for spread changes. Out-of-sample portfolio tests show the information in our measure is valuable for investors. Both results suggest that investors do not fully internalize the credit-relevant information contained in earnings calls

Diet Code Is Healthy: Simplifying Programs for Pre-trained Models of Code

Pre-trained code representation models such as CodeBERT have demonstrated superior performance in a variety of software engineering tasks, yet they are often heavy in complexity, quadratically with the length of the input sequence. Our empirical analysis of CodeBERT's attention reveals that CodeBERT pays more attention to certain types of tokens and statements such as keywords and data-relevant statements. Based on these findings, we propose DietCode, which aims at lightweight leverage of large pre-trained models for source code. DietCode simplifies the input program of CodeBERT with three strategies, namely, word dropout, frequency filtering, and an attention-based strategy which selects statements and tokens that receive the most attention weights during pre-training. Hence, it gives a substantial reduction in the computational cost without hampering the model performance. Experimental results on two downstream tasks show that DietCodeBERT provides comparable results to CodeBERT with 40% less computational cost in fine-tuning and testing.Comment: Accepted to be published in ESEC/FSE 202

Reconfigurable Intelligent Surfaces 2.0: Beyond Diagonal Phase Shift Matrices

Reconfigurable intelligent surface (RIS) has been envisioned as a promising technique to enable and enhance future wireless communications due to its potential to engineer the wireless channels in a cost-effective manner. Extensive research attention has been drawn to the use of conventional RIS 1.0 with diagonal phase shift matrices, where each RIS element is connected to its own load to ground but not connected to other elements. However, the simple architecture of RIS 1.0 limits its flexibility of manipulating passive beamforming. To fully exploit the benefits of RIS, in this paper, we introduce RIS 2.0 beyond diagonal phase shift matrices, namely beyond diagonal RIS (BD-RIS). We first explain the modeling of BD-RIS based on the scattering parameter network analysis and classify BD-RIS by the mathematical characteristics of the scattering matrix, supported modes, and architectures. Then, we provide simulations to evaluate the sum-rate performance with different modes/architectures of BD-RIS. We summarize the benefits of BD-RIS in providing high flexibility in wave manipulation, enlarging coverage, facilitating the deployment, and requiring low complexity in resolution bit and element numbers. Inspired by the benefits of BD-RIS, we also discuss potential applications of BD-RIS in various wireless systems. Finally, we list key challenges in modeling, designing, and implementing BD-RIS in practice and point to possible future research directions for BD-RIS.Comment: 7 pages, 5 figures, submitted to IEEE journal for possible publicatio