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We study an overdamped Langevin equation on the $$d$$-dimensional torus with stationary distribution proportional to $$p = e^{-U / \kappa}$$. When $$U$$ has multiple wells the mixing time of the associated process is exponentially large (of size $$e^{O(1/\kappa)}$$). We add a drift to the Langevin dynamics (without changing the stationary distribution) and obtain quantitative estimates on the mixing time. Our main result shows that the mixing time of the Langevin system can be made arbitrarily small by adding a drift that is sufficiently mixing. We provide one construction of a mixing drift, and our main result can be applied by using this drift with a large amplitude. For numerical purposes, it is useful to keep the size of the imposed drift small, and we show that the smallest allowable amplitude ensures that the mixing time is $$O( d/\kappa^2)$$, which is an order of magnitude smaller than $$e^{O(1/\kappa)}$$. 

Differential Privacy (DP) has emerged as a pivotal approach for safeguarding individual privacy in data analysis, yet its practical adoption is often hindered by challenges in the implementation and communication of DP. This paper presents a comprehensive systematization of existing research studies around the usability of DP, synthesizing insights from studies on both the practical use of DP tools and strategies for conveying DP parameters that determine privacy protection levels, such as epsilon. By reviewing and analyzing these studies, we identify core usability challenges, best practices, and critical gaps in current DP tools that affect adoption across diverse user groups, including developers, data analysts, and non-technical stakeholders. Our analysis highlights actionable insights and pathways for future research that emphasizes user-centered design and clear communication, fostering the development of more accessible DP tools that meet practical needs and support broader adoption. 

Understanding and managing data privacy in the digital world can be challenging for sighted users, let alone blind and lowvision (BLV) users. There is limited research on how BLV users, who have special accessibility needs, navigate data privacy, and how potential privacy tools could assist them. We conducted an in-depth qualitative study with 21 US BLV participants to understand their data privacy risk perception and mitigation, as well as their information behaviors related to data privacy. We also explored BLV users’ attitudes towards potential privacy question answering (Q&A) assistants that enable them to better navigate data privacy information. We found that BLV users face heightened security and privacy risks, but their risk mitigation is often insufficient. They do not necessarily seek data privacy information but clearly recognize the benefits of a potential privacy Q&A assistant. They also expect privacy Q&A assistants to possess cross-platform compatibility, support multi-modality, and demonstrate robust functionality. Our study sheds light on BLV users’ expectations when it comes to usability, accessibility, trust and equity issues regarding digital data privacy. 

We establish conditions for shear flows on the d -dimensional torus that give enhanced dissipation for the associated linear advection-diffusion equation for well-prepared data. The diffusion operator can be of fractional or high order and does not need to have constant coefficients. We then construct flows that satisfy these assumptions and obtain a quantitative estimate on the dissipation enhancement. Our examples generalize known examples in two space dimensions to the high-dimensional setting, which is relevant in applications to sampling a distribution and in optimization. 

This repository archives the supplemental materials for the USENIX Security '24 paper of the same title.