The Bloom filter provides fast approximate set membership while using little memory. Engineers often use these filters to avoid slow operations such as disk or network accesses. As an alternative, a cuckoo filter may need less space than a Bloom filt
er and it is faster. Chazelle et al. proposed a generalization of the Bloom filter called the Bloomier filter. Dietzfelbinger and Pagh described a variation on the Bloomier filter that can be used effectively for approximate membership queries. It has never been tested empirically, to our knowledge. We review an efficient implementation of their approach, which we call the xor filter. We find that xor filters can be faster than Bloom and cuckoo filters while using less memory. We further show that a more compact version of xor filters (xor+) can use even less space than highly compact alternatives (e.g., Golomb-compressed sequences) while providing speeds competitive with Bloom filters.
A minimal perfect hash function bijectively maps a key set $S$ out of a universe $U$ into the first $|S|$ natural numbers. Minimal perfect hash functions are used, for example, to map irregularly-shaped keys, such as string, in a compact space so tha
t metadata can then be simply stored in an array. While it is known that just $1.44$ bits per key are necessary to store a minimal perfect function, no published technique can go below $2$ bits per key in practice. We propose a new technique for storing minimal perfect hash functions with expected linear construction time and expected constant lookup time that makes it possible to build for the first time, for example, structures which need $1.56$ bits per key, that is, within $8.3$% of the lower bound, in less than $2$ ms per key. We show that instances of our construction are able to simultaneously beat the construction time, space usage and lookup time of the state-of-the-art data structure reaching $2$ bits per key. Moreover, we provide parameter choices giving structures which are competitive with alternative, larger-size data structures in terms of space and lookup time. The construction of our data structures can be easily parallelized or mapped on distributed computational units (e.g., within the MapReduce framework), and structures larger than the available RAM can be directly built in mass storage.
Two-dimensional group-VI transition metal dichalcogenide semiconductors, such as MoS2, WSe2 and others, exhibit strong light-matter coupling and possess direct band gaps in the infrared and visible spectral regimes, making them potentially interestin
g candidates for various applications in optics and optoelectronics. Here, we review their optical and optoelectronic properties with emphasis on exciton physics and devices. As excitons are tightly bound in these materials and dominate the optical response even at room-temperature, their properties are examined in depth in the first part of this article. We discuss the remarkably versatile excitonic landscape, including bright, dark, localized and interlayer excitons. In the second part, we provide an overview on the progress in optoelectronic device applications, such as electrically driven light emitters, photovoltaic solar cells, photodetectors and opto-valleytronic devices, again bearing in mind the prominent role of excitonic effects. We conclude with a brief discussion on challenges that remain to be addressed to exploit the full potential of transition metal dichalcogenide semiconductors in possible exciton-based applications.
Recent research in two-dimensional (2D) materials has boosted a renovated interest in the p-n junction, one of the oldest electrical components which can be used in electronics and optoelectronics. 2D materials offer remarkable flexibility to design
novel p-n junction device architectures, not possible with conventional bulk semiconductors. In this Review we thoroughly describe the different 2D p-n junction geometries studied so far, focusing on vertical (out-of-plane) and lateral (in-plane) 2D junctions and on mixed-dimensional junctions. We discuss the assembly methods developed to fabricate 2D p-n junctions making a distinction between top-down and bottom-up approaches. We also revise the literature studying the different applications of these atomically thin p-n junctions in electronic and optoelectronic devices. We discuss experiments on 2D p-n junctions used as current rectifiers, photodetectors, solar cells and light emitting devices. The important electronics and optoelectronics parameters of the discussed devices are listed in a table to facilitate their comparison. We conclude the Review with a critical discussion about the future outlook and challenges of this incipient research field.
A theorem of Dolfi, Herzog, Kaplan, and Lev cite[Thm.~C]{DHKL} asserts that in a finite group with trivial Fitting subgroup, the size of the soluble residual of the group is bounded from below by a certain power of the group order, and that the inequ
ality is sharp. Inspired by this result and some of the arguments in cite{DHKL}, we establish the following generalisation: if $mathfrak{X}$ is a subgroup-closed Fitting formation of full characteristic which does not contain all finite groups and $overline{mathfrak{X}}$ is the extension-closure of $mathfrak{X}$, then there exists an (optimal) constant $gamma$ depending only on $mathfrak{X}$ such that, for all non-trivial finite groups $G$ with trivial $mathfrak{X}$-radical, begin{equation} leftlvert G^{overline{mathfrak{X}}}rightrvert ,>, vert Gvert^gamma, end{equation} where $G^{overline{mathfrak{X}}}$ is the ${overline{mathfrak{X}}}$-residual of $G$. When $mathfrak{X} = mathfrak{N}$, the class of finite nilpotent groups, it follows that $overline{mathfrak{X}} = mathfrak{S}$, the class of finite soluble groups, thus we recover the original theorem of Dolfi, Herzog, Kaplan, and Lev. In the last section of our paper, building on J.,G. Thompsons classification of minimal simple groups, we exhibit a family of subgroup-closed Fitting formations $mathfrak{X}$ of full characteristic such that $mathfrak{S} subset overline{mathfrak{X}} subset mathfrak{E}$, thus providing applications of our main result beyond the reach of cite[Thm.~C]{DHKL}.
Electrically-driven light emission from carbon nanotubes could be exploited in nano-scale lasers and single-photon sources, and has therefore been the focus of much research. However, to date, high electric fields and currents have been either requir
ed for electroluminescence, or have been an undesired side effect, leading to high power requirements and low efficiencies. In addition, electroluminescent linewidths have been broad enough to obscure the contributions of individual optical transitions. Here, we report electrically-induced light emission from individual carbon nanotube p-n diodes. A new level of control over electrical carrier injection is achieved, reducing power dissipation by a factor of up to 1000, and resulting in zero threshold current, negligible self-heating, and high carrier-to- photon conversion efficiencies. Moreover, the electroluminescent spectra are significantly narrower (ca. 35 meV) than in previous studies, allowing the identification of emission from free and localized excitons.
