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Anderson localization transitions are a universal quantum phenomenon sensitive to the disorder and dimensionality of electronic systems. Over the past decades, this intriguing topic has inspired overwhelmingly more theoretical studies than experimental verifications due to the difficulty of controlling a material's disorder or dimensionality without modifying its fundamental electronic properties. Organic crystals with their rich disorders would be terrific playgrounds to investigate such disorder-driven phase transitions except for their low conductivities which usually prohibit low-temperature measurements. Here, we conduct systematic transport experiments in mesoscopic devices made with copper benzenehexathiol thin films across a wide range of thicknesses. We find metal-insulator transitions both among three-dimensional samples with different disorder strengths and between three-dimensional and quasi-two-dimensional samples. Temperature-dependence analysis of the conductivities corroborates the dimensionality crossover. Moreover, our theoretical modeling provides a basis for understanding both types of metal-insulator transitions within the framework of Anderson localization transitions. Our findings establish for the first time that organic crystals such as conductive metal-organic frameworks can exhibit such quantum interference effects. With organic materials' versatile chemical designs and crystalline structures, our work opens new avenues to search for novel quantum phenomena in organic material platforms.

Interlayer sliding ferroelectricity has been discovered in a variety of 2D materials with superb features such as atomic thickness, fast response, and fatigue resistance. So far, research on this phenomenon has been limited to fundamental physics and electronic applications, leaving its potential for electromechanical actuation unexplored. In this work, we design an atomic-scale actuator based on sliding ferroelectricity and field-tunable interfacial friction. With a prototype based on parallelly stacked bilayer h-BN sandwiched between gold contacts, we show how an alternating electric field can drive the bilayer into controlled crawling motions and how uniaxial strain can steer the crawl direction. Using numerical simulations, we demonstrate the actuator's robust operation under a wide range of drive signals, friction scales, and frictional variations. We further provide experimental directions on how to realize field-tunable friction on h-BN interfaces. The wireless-ready actuation mechanism can be generalized to many 2D material systems possessing sliding ferroelectricity and integrated into flexible electronics platforms, opening new avenues in the development of intelligent nanorobotics.

Minimum storage regenerating (MSR) codes, with the MDS property and the optimal repair bandwidth, are widely used in distributed storage systems (DSS) for data recovery. In this paper, we consider the construction of $(n,k,l)$ MSR codes in the centralized model that can repair $h$ failed nodes simultaneously with $e$ out $d$ helper nodes providing erroneous information. We first propose the new repair scheme, and give a complete proof of the lower bound on the amount of symbols downloaded from the helped nodes, provided that some of helper nodes provide erroneous information. Then we focus on two explicit constructions with the repair scheme proposed. For $2\leq h\leq n-k$, $k+2e\leq d \leq n-h$ and $d\equiv k+2e \;(\mod{h})$, the first one has the UER $(h, d)$-optimal repair property, and the second one has the UER $(h, d)$-optimal access property. Compared with the original constructions (Ye and Barg, IEEE Tran. Inf. Theory, Vol. 63, April 2017), our constructions have improvements in three aspects: 1) The proposed repair scheme is more feasible than the one-by-one scheme presented by Ye and Barg in a parallel data system; 2) The sub-packetization is reduced from $\left(\operatorname{lcm}(d-k+1, d-k+2,\cdots, d-k+h)\right)^n$ to $\left((d-2e-k+h)/h\right)^n$, which reduces at least by a factor of $(h(d-k+h))^n$; 3) The field size of the first construction is reduced to $|\mathbb{F}| \geq n(d-2e-k+h)/h$, which reduces at least by a factor of $h(d-k+h)$. Small sub-packetization and small field size are preferred in practice due to the limited storage capacity and low computation complexity in the process of encoding, decoding and repairing.

We derive a lower bound on the amount of information accessed to repair failed nodes within a single rack from any number of helper racks in the rack-aware storage model that allows collective information processing in the nodes that share the same rack. Furthermore, we construct a family of rack-aware minimum-storage regenerating (MSR) codes with the property that the number of symbols accessed for repairing a single failed node attains the bound with equality for all admissible parameters. Constructions of rack-aware optimal-access MSR codes were only known for limited parameters. We also present a family of Reed-Solomon (RS) codes that only require accessing a relatively small number of symbols to repair multiple failed nodes in a single rack. In particular, for certain code parameters, the RS construction attains the bound on the access complexity with equality and thus has optimal access.

BCH codes and their dual codes are two special subclasses of cyclic codes and are the best linear codes in many cases. A lot of progress on the study of BCH cyclic codes has been made, but little is known about the minimum distances of the duals of BCH codes. Recently, a new concept called dually-BCH code was introduced to investigate the duals of BCH codes and the lower bounds on their minimum distances in \cite{GDL21}. For a prime power $q$ and an integer $m \ge 4$, let $n=\frac{q^m-1}{q+1}$ \ ($m$ even), or $n=\frac{q^m-1}{q-1}$ \ ($q>2$). In this paper, some sufficient and necessary conditions in terms of the designed distance will be given to ensure that the narrow-sense BCH codes of length $n$ are dually-BCH codes, which extended the results in \cite{GDL21}. Lower bounds on the minimum distances of their dual codes are developed for $n=\frac{q^m-1}{q+1}$ \ ($m$ even). As byproducts, we present the largest coset leader $\delta_1$ modulo $n$ being of two types, which proves a conjecture in \cite{WLP19} and partially solves an open problem in \cite{Li2017}. We also investigate the parameters of the narrow-sense BCH codes of length $n$ with design distance $\delta_1$. The BCH codes presented in this paper have good parameters in general.

Accurate tooth volume segmentation is a prerequisite for computer-aided dental analysis. Deep learning-based tooth segmentation methods have achieved satisfying performances but require a large quantity of tooth data with ground truth. The dental data publicly available is limited meaning the existing methods can not be reproduced, evaluated and applied in clinical practice. In this paper, we establish a 3D dental CBCT dataset CTooth+, with 22 fully annotated volumes and 146 unlabeled volumes. We further evaluate several state-of-the-art tooth volume segmentation strategies based on fully-supervised learning, semi-supervised learning and active learning, and define the performance principles. This work provides a new benchmark for the tooth volume segmentation task, and the experiment can serve as the baseline for future AI-based dental imaging research and clinical application development.

The minimum storage rack-aware regenerating (MSRR) code is a variation of regenerating codes that achieves the optimal repair bandwidth for a single node failure in the rack-aware model. The authors in~\cite{Chen-Barg2019} and~\cite{Zhou-Zhang2021} provided explicit constructions of MSRR codes for all parameters to repair a single failed node. This paper generalizes the results in~\cite{Chen-Barg2019} to the case of multiple node failures. We propose a class of MDS array codes and scalar Reed-Solomon (RS) codes, and show that these codes have optimal repair bandwidth and error resilient capability for multiple node failures in the rack-aware storage model. Besides, our codes keep the same access level as the low-access constructions in~\cite{Chen-Barg2019} and~\cite{Zhou-Zhang2021}., Comment: Distributed storage; Multiple erasure tolerance; MSRR codes; Universally error-resilient repair