On Density-Critical Matroids

For a matroid $M$ having $m$ rank-one flats, the density $d(M)$ is $\tfrac{m}{r(M)}$ unless $m = 0$, in which case $d(M)= 0$. A matroid is density-critical if all of its proper minors of non-zero rank have lower density. By a 1965 theorem of Edmonds, a matroid that is minor-minimal among simple matroids that cannot be covered by $k$ independent sets is density-critical. It is straightforward to show that $U_{1,k+1}$ is the only minor-minimal loopless matroid with no covering by $k$ independent sets. We prove that there are exactly ten minor-minimal simple obstructions to a matroid being able to be covered by two independent sets. These ten matroids are precisely the density-critical matroids $M$ such that $d(M) > 2$ but $d(N) \le 2$ for all proper minors $N$ of $M$. All density-critical matroids of density less than $2$ are series-parallel networks. For $k \ge 2$, although finding all density-critical matroids of density at most $k$ does not seem straightforward, we do solve this problem for $k=\tfrac{9}{4}$.Comment: 16 page

Fabrication and deterministic transfer of high quality quantum emitter in hexagonal boron nitride

Color centers in solid state crystals have become a frequently used system for single photon generation, advancing the development of integrated photonic devices for quantum optics and quantum communication applications. In particular, defects hosted by two-dimensional (2D) hexagonal boron nitride (hBN) are a promising candidate for next-generation single photon sources, due to its chemical and thermal robustness and high brightness at room temperature. The 2D crystal lattice of hBN allows for a high extraction efficiency and easy integration into photonic circuits. Here we develop plasma etching techniques with subsequent high temperature annealing to reliably create defects. We show how different fabrication parameters influence the defect formation probability and the emitter brightness. A full optical characterization reveals the higher quality of the created quantum emitters, represented by a narrow spectrum, short excited state lifetime and high single photon purity. We also investigated the photostability on short and very long timescales. We utilize a wet chemically-assisted transfer process to reliably transfer the single photon sources onto arbitrary substrates, demonstrating the feasibility for the integration into scalable photonic quantum information processing networks.Comment: revised versio

Land capability study for horticulture in the Swan Valley

The Swan Valley is an important agricultural, recreational, tourist and heritage area in which there are a number of competing land uses because of its location close to Perth. The traditional agricultural use, mainly centred around the viticulture industry, has to compete with tourist development, urban encroachment, hobby farms and clay extraction. The major objective of this report was to identify any areas of prime horticultural land which should be retained for that purpose. A land capability study was done using the existing soil series map of the Swan Valley (Pym 1955), which covers most of the Swan Valley Policy Area. The map units were assessed for 11 land qualities (e.g. site drainage, rooting conditions) which were then related to the land use requirements to derive the land capability ratings. The ratings for six horticultural crops: table grapes, wine grapes, dried vine fruit, stone fruit, citrus and market gardening were determined. Map production was done by the Department of Agriculture\u27s Geographic Information System (digital data base) to enable interpretative analysis and reproduction of special purpose maps. A corridor of prime horticultural land for table grape production has been identified adjacent to the Swan River and corresponds to the Swan, Belhus, Houghton, Pyrton, Herne and Cruse soil series. This corridor would be suitable for a special horticultural zone within the Swan Valley, with the boundaries corresponding to the existing Swan Valley Rural Zone. Tight control over alternative land uses would be needed to protect the prime agricultural land and ensure the long term prosperity of the table grape industry. The competing land uses include subdivision, tourism and clay extraction. Included with the report are maps showing the soil types (1:25,000) (Pym 1955) and the land capability for table grapes (1:50,000). Land capability maps for the other land uses assessed are available from the Department of Agriculture on request

A mirrorless spinwave resonator

Optical resonance is central to a wide range of optical devices and techniques. In an optical cavity, the round-trip length and mirror reflectivity can be chosen to optimize the circulating optical power, linewidth, and free-spectral range (FSR) for a given application. In this paper we show how an atomic spinwave system, with no physical mirrors, can behave in a manner that is analogous to an optical cavity. We demonstrate this similarity by characterising the build-up and decay of the resonance in the time domain, and measuring the effective optical linewidth and FSR in the frequency domain. Our spinwave is generated in a 20 cm long Rb gas cell, yet it facilitates an effective FSR of 83 kHz, which would require a round-trip path of 3.6 km in a free-space optical cavity. Furthermore, the spinwave coupling is controllable enabling dynamic tuning of the effective cavity parameters.Comment: 13 pages, 4 figure

Nano-Kelvin thermometry and temperature control: beyond the thermal noise limit

We demonstrate thermometry with a resolution of 80 $\mathrm{nK} / \sqrt{\mathrm{Hz}}$ using an isotropic crystalline whispering-gallery mode resonator based on a dichroic dual-mode technique. We simultaneously excite two modes that have a mode frequency ratio very close to two ($\pm0.3$ppm). The wavelength- and temperature-dependence of the refractive index means that the frequency difference between these modes is an ultra-sensitive proxy of the resonator temperature. This approach to temperature sensing automatically suppresses sensitivity to thermal expansion and vibrationally induced changes of the resonator. We also demonstrate active suppression of temperature fluctuations in the resonator by controlling the intensity of the driving laser. The residual temperature fluctuations are shown to be below the limits set by fundamental thermodynamic fluctuations of the resonator material

MCMC-driven learning

This paper is intended to appear as a chapter for the Handbook of Markov Chain Monte Carlo. The goal of this chapter is to unify various problems at the intersection of Markov chain Monte Carlo (MCMC) and machine learning\unicode{x2014}which includes black-box variational inference, adaptive MCMC, normalizing flow construction and transport-assisted MCMC, surrogate-likelihood MCMC, coreset construction for MCMC with big data, Markov chain gradient descent, Markovian score climbing, and more\unicode{x2014}within one common framework. By doing so, the theory and methods developed for each may be translated and generalized