On the topological pressure of random bundle transformations in sub-additive case

In this paper, we define the topological pressure for sub-additive potentials via separated sets in random dynamical systems and we give a proof of the relativized variational principle for the topological pressure.Comment: 16page

Graph Analysis in Decentralized Online Social Networks with Fine-Grained Privacy Protection

Graph analysts cannot directly obtain the global structure in decentralized social networks, and analyzing such a network requires collecting local views of the social graph from individual users. Since the edges between users may reveal sensitive social interactions in the local view, applying differential privacy in the data collection process is often desirable, which provides strong and rigorous privacy guarantees. In practical decentralized social graphs, different edges have different privacy requirements due to the distinct sensitivity levels. However, the existing differentially private analysis of social graphs provide the same protection for all edges. To address this issue, this work proposes a fine-grained privacy notion as well as novel algorithms for private graph analysis. We first design a fine-grained relationship differential privacy (FGR-DP) notion for social graph analysis, which enforces different protections for the edges with distinct privacy requirements. Then, we design algorithms for triangle counting and k-stars counting, respectively, which can accurately estimate subgraph counts given fine-grained protection for social edges. We also analyze upper bounds on the estimation error, including k-stars and triangle counts, and show their superior performance compared with the state-of-the-arts. Finally, we perform extensive experiments on two real social graph datasets and demonstrate that the proposed mechanisms satisfying FGR-DP have better utility than the state-of-the-art mechanisms due to the finer-grained protection

NADiffuSE: Noise-aware Diffusion-based Model for Speech Enhancement

The goal of speech enhancement (SE) is to eliminate the background interference from the noisy speech signal. Generative models such as diffusion models (DM) have been applied to the task of SE because of better generalization in unseen noisy scenes. Technical routes for the DM-based SE methods can be summarized into three types: task-adapted diffusion process formulation, generator-plus-conditioner (GPC) structures and the multi-stage frameworks. We focus on the first two approaches, which are constructed under the GPC architecture and use the task-adapted diffusion process to better deal with the real noise. However, the performance of these SE models is limited by the following issues: (a) Non-Gaussian noise estimation in the task-adapted diffusion process. (b) Conditional domain bias caused by the weak conditioner design in the GPC structure. (c) Large amount of residual noise caused by unreasonable interpolation operations during inference. To solve the above problems, we propose a noise-aware diffusion-based SE model (NADiffuSE) to boost the SE performance, where the noise representation is extracted from the noisy speech signal and introduced as a global conditional information for estimating the non-Gaussian components. Furthermore, the anchor-based inference algorithm is employed to achieve a compromise between the speech distortion and noise residual. In order to mitigate the performance degradation caused by the conditional domain bias in the GPC framework, we investigate three model variants, all of which can be viewed as multi-stage SE based on the preprocessing networks for Mel spectrograms. Experimental results show that NADiffuSE outperforms other DM-based SE models under the GPC infrastructure. Audio samples are available at: https://square-of-w.github.io/NADiffuSE-demo/

Applicability of magnetic force models for multi-stable energy harvesters

Multi-stable piezoelectric energy harvesters have been exploited to enhance performance for extracting ambient vibrational energy from a broadband energy source. Since magnetic force plays a significant role in enhancing the dynamic behavior of harvesters, it is necessary to model and understand the significant influencing of structural parameters on magnetic force. Recently, several theoretical modeling methods, including magnetic dipole, improved dipole, magnetic current, and magnetic charge models, have been developed to calculate the magnetic force in multi-stable energy harvesters. However, the influence of structural parameters and magnet dimensions on the accuracy of magnetic force calculation for these methods has not been analyzed. Therefore, it is necessary to investigate the applicability of these methods under a range of operating conditions. New insights into the accuracy and application constraints of these methods are presented in this paper to calculate the impact of magnetic force on multi-stable energy harvesters. From the theoretical derivation of models and numerical results obtained, a quantitative assessment of errors under different structural parameters and magnet sizes is presented and compared to evaluate the application constraints. Moreover, experimental measurements are performed to verify the applicability of these modeling methods for bi-stable and tri-stable energy harvesters with different structural parameters.</p