arXiv subjects

Peizhi Liu

Publications and source records attributed to Peizhi Liu.

3 recordsLinked to original sources

arXiv2026

Box dimension prints

We study lower and upper box dimension prints for bounded subsets of $\mathbb R^n$, defined by weighted covering numbers for independently oriented rectangular boxes with prescribed ordered side-length bounds. The limits range over all eccentricities, including unbounded aspect ratios. For every non-empty bounded set, we identify the closure of the lower print with the intersection of the half-spaces determined by its lower eccentricity profile, without any uniformity assumption. The profile equals the support function of this closure if and only if it is subadditive. A planar product example has distinct lower and upper profiles on every ray and an explicitly computable lower-print closure. We also prove that both prints are invariant under nonsingular projective transformations on compact sets avoiding the pole hyperplane. Uniform anisotropic covering estimates determine both prints, including their boundary points, for non-degenerate curves of type $(1,\ldots,n)$, their Ahlfors regular parameter subsets, and higher-dimensional spheres. Finally, local covering-count and product-measure criteria identify the lower box print with the Hausdorff dimension print, while a reciprocal-sequence example shows that this inclusion can be strict.

math.MG↗

arXiv2025

Collusion Resistant DNS With Private Information Retrieval

There has been a growing interest in Internet user privacy, demonstrated by the popularity of privacy-preserving products such as Telegram and Brave, and the widespread adoption of HTTPS. The Domain Name System (DNS) is a key component of Internet-based communication and its privacy has been neglected for years. Recently, DNS over HTTPS (DoH) has improved the situation by fixing the issue of in-path middleboxes. Further progress has been made with proxy-based solutions such as Oblivious DoH (ODoH), which separate a user's identity from their DNS queries. However, these solutions rely on non-collusion assumptions between DNS resolvers and proxies -- an assumption difficult to guarantee in practice. To address this, we explore integrating single-server Private Information Retrieval (PIR) into DNS to enable encrypted query processing without relying on trust assumptions. However, applying PIR to DNS is challenging due to its hierarchical nature -- particularly, interactions with recursive resolvers can still leak information. Navigating performance and privacy trade-offs, we propose PDNS, a DNS extension leveraging single-server PIR to strengthen privacy guarantees. We have implemented a prototype of PDNS and compared its performance against state-of-the-art solutions via trace-driven experiments. The results show that PDNS achieves acceptable performance (2x faster than DoH over Tor with similar privacy guarantees) and strong privacy guarantees today, mainly at the cost of its scalability, which specialized hardware for PIR can address in the near future.

cs.NI↗

arXiv2017

Gate-controlled reversible rectifying behaviour in tunnel contacted atomically-thin MoS$_{2}$ transistor

Atomically-thin 2D semiconducting materials integrated into van der Waals heterostructures have enabled architectures that hold great promise for next generation nanoelectronics. However, challenges still remain to enable their full acceptance as compliant materials for integration in logic devices. Two key-components to master are the barriers at metal/semiconductor interfaces and the mobility of the semiconducting channel, which endow the building-blocks of ${pn}$ diode and field effect transistor. Here, we have devised a reverted stacking technique to intercalate a wrinkle-free h-BN tunnel layer between MoS$_{2}$ channel and contacting electrodes. Vertical tunnelling of electrons therefore makes it possible to suppress the Schottky barriers and Fermi level pinning, leading to homogeneous gate-control of the channel chemical potential across the bandgap edges. The observed unprecedented features of ambipolar ${pn}$ to ${np}$ diode, which can be reversibly gate tuned, paves the way for future logic applications and high performance switches based on atomically thin semiconducting channel.

physics.app-ph↗