Correlation Clustering with Low-Rank Matrices

Correlation clustering is a technique for aggregating data based on qualitative information about which pairs of objects are labeled 'similar' or 'dissimilar.' Because the optimization problem is NP-hard, much of the previous literature focuses on finding approximation algorithms. In this paper we explore how to solve the correlation clustering objective exactly when the data to be clustered can be represented by a low-rank matrix. We prove in particular that correlation clustering can be solved in polynomial time when the underlying matrix is positive semidefinite with small constant rank, but that the task remains NP-hard in the presence of even one negative eigenvalue. Based on our theoretical results, we develop an algorithm for efficiently "solving" low-rank positive semidefinite correlation clustering by employing a procedure for zonotope vertex enumeration. We demonstrate the effectiveness and speed of our algorithm by using it to solve several clustering problems on both synthetic and real-world data

Single-photon emitting diode in silicon carbide

Electrically driven single-photon emitting devices have immediate applications in quantum cryptography, quantum computation and single-photon metrology. Mature device fabrication protocols and the recent observations of single defect systems with quantum functionalities make silicon carbide (SiC) an ideal material to build such devices. Here, we demonstrate the fabrication of bright single photon emitting diodes. The electrically driven emitters display fully polarized output, superior photon statistics (with a count rate of $>$300 kHz), and stability in both continuous and pulsed modes, all at room temperature. The atomic origin of the single photon source is proposed. These results provide a foundation for the large scale integration of single photon sources into a broad range of applications, such as quantum cryptography or linear optics quantum computing.Comment: Main: 10 pages, 6 figures. Supplementary Information: 6 pages, 6 figure

Phase transitions and iron-ordered moment form factor in LaFeAsO

Elastic neutron scattering studies of an optimized LaFeAsO single crystal reveal that upon cooling, an onset of the tetragonal (T)-to-orthorhombic (O) structural transition occurs at $T_\texttt{S} \approx 156$ K, and it exhibits a sharp transition at $T_\texttt{P} \approx 148$ K. We argue that in the temperature range $T_\texttt{S}$ to $T_\texttt{P}$, T and O structures may dynamically coexist possibly due to nematic spin correlations recently proposed for the iron pnictides, and we attribute $T_\texttt{P}$ to the formation of long-range O domains from the finite local precursors. The antiferromagnetic structure emerges at $T_\texttt{N} \approx 140$ K, with the iron moment direction along the O \emph{a} axis. We extract the iron magnetic form factor and use the tabulated $\langle j_0\rangle$ of Fe, Fe$^{2+}$ and Fe$^{3+}$ to obtain a magnetic moment size of $\sim$0.8 $\mu_\texttt{B}$ at 9.5 K.Comment: 7 pages, 6 figures, 3 table

Electrically-detected magnetic resonance in ion-implanted Si:P nanostructures

We present the results of electrically-detected magnetic resonance (EDMR) experiments on silicon with ion-implanted phosphorus nanostructures, performed at 5 K. The devices consist of high-dose implanted metallic leads with a square gap, into which Phosphorus is implanted at a non-metallic dose corresponding to 10^17 cm^-3. By restricting this secondary implant to a 100 nm x 100 nm region, the EDMR signal from less than 100 donors is detected. This technique provides a pathway to the study of single donor spins in semiconductors, which is relevant to a number of proposals for quantum information processing.Comment: 9 pages, 3 figure

Optical and electronic properties of sub-surface conducting layers in diamond created by MeV B-implantation at elevated temperatures

Boron implantation with in-situ dynamic annealing is used to produce highly conductive sub-surface layers in type IIa (100) diamond plates for the search of a superconducting phase transition. Here we demonstrate that high-fluence MeV ion-implantation, at elevated temperatures avoids graphitization and can be used to achieve doping densities of 6 at.%. In order to quantify the diamond crystal damage associated with implantation Raman spectroscopy was performed, demonstrating high temperature annealing recovers the lattice. Additionally, low-temperature electronic transport measurements show evidence of charge carrier densities close to the metal-insulator-transition. After electronic characterization, secondary ion mass spectrometry was performed to map out the ion profile of the implanted plates. The analysis shows close agreement with the simulated ion-profile assuming scaling factors that take into account an average change in diamond density due to device fabrication. Finally, the data show that boron diffusion is negligible during the high temperature annealing process.Comment: 22 pages, 6 figures, submitted to JA

Digital support interventions for the self-management of low back pain: a systematic review

Background: Low back pain (LBP) is a common cause of disability and is ranked as the most burdensome health condition globally. Self-management, including components on increased knowledge, monitoring of symptoms, and physical activity, are consistently recommended in clinical guidelines as cost-effective strategies for LBP management and there is increasing interest in the potential role of digital health. Objective: The study aimed to synthesize and critically appraise published evidence concerning the use of interactive digital interventions to support self-management of LBP. The following specific questions were examined: (1) What are the key components of digital self-management interventions for LBP, including theoretical underpinnings? (2) What outcome measures have been used in randomized trials of digital self-management interventions in LBP and what effect, if any, did the intervention have on these? and (3) What specific characteristics or components, if any, of interventions appear to be associated with beneficial outcomes? Methods: Bibliographic databases searched from 2000 to March 2016 included Medline, Embase, CINAHL, PsycINFO, Cochrane Library, DoPHER and TRoPHI, Social Science Citation Index, and Science Citation Index. Reference and citation searching was also undertaken. Search strategy combined the following concepts: (1) back pain, (2) digital intervention, and (3) self-management. Only randomized controlled trial (RCT) protocols or completed RCTs involving adults with LBP published in peer-reviewed journals were included. Two reviewers independently screened titles and abstracts, full-text articles, extracted data, and assessed risk of bias using Cochrane risk of bias tool. An independent third reviewer adjudicated on disagreements. Data were synthesized narratively. Results: Of the total 7014 references identified, 11 were included, describing 9 studies: 6 completed RCTs and 3 protocols for future RCTs. The completed RCTs included a total of 2706 participants (range of 114-1343 participants per study) and varied considerably in the nature and delivery of the interventions, the duration/definition of LBP, the outcomes measured, and the effectiveness of the interventions. Participants were generally white, middle aged, and in 5 of 6 RCT reports, the majority were female and most reported educational level as time at college or higher. Only one study reported between-group differences in favor of the digital intervention. There was considerable variation in the extent of reporting the characteristics, components, and theories underpinning each intervention. None of the studies showed evidence of harm. Conclusions: The literature is extremely heterogeneous, making it difficult to understand what might work best, for whom, and in what circumstances. Participants were predominantly female, white, well educated, and middle aged, and thus the wider applicability of digital self-management interventions remains uncertain. No information on cost-effectiveness was reported. The evidence base for interactive digital interventions to support patient self-management of LBP remains weak

Engineering chromium related single photon emitters in single crystal diamond

Color centers in diamond as single photon emitters, are leading candidates for future quantum devices due to their room temperature operation and photostability. The recently discovered chromium related centers are particularly attractive since they possess narrow bandwidth emission and a very short lifetime. In this paper we investigate the fabrication methodologies to engineer these centers in monolithic diamond. We show that the emitters can be successfully fabricated by ion implantation of chromium in conjunction with oxygen or sulfur. Furthermore, our results indicate that the background nitrogen concentration is an important parameter, which governs the probability of success to generate these centers.Comment: 14 pages, 5 figure

Truth table invariant cylindrical algebraic decomposition

When using cylindrical algebraic decomposition (CAD) to solve a problem with respect to a set of polynomials, it is likely not the signs of those polynomials that are of paramount importance but rather the truth values of certain quantifier free formulae involving them. This observation motivates our article and definition of a Truth Table Invariant CAD (TTICAD). In ISSAC 2013 the current authors presented an algorithm that can efficiently and directly construct a TTICAD for a list of formulae in which each has an equational constraint. This was achieved by generalising McCallum's theory of reduced projection operators. In this paper we present an extended version of our theory which can be applied to an arbitrary list of formulae, achieving savings if at least one has an equational constraint. We also explain how the theory of reduced projection operators can allow for further improvements to the lifting phase of CAD algorithms, even in the context of a single equational constraint. The algorithm is implemented fully in Maple and we present both promising results from experimentation and a complexity analysis showing the benefits of our contributions.Comment: 40 page

Shifting patterns of oil palm driven deforestation in Indonesia and implications for zero-deforestation commitments

Oil palm plantations in Indonesia have been linked to substantial deforestation in the 1990s and 2000s, though recent studies suggest that new plantations are increasingly developed on non-forest land. Without nationwide data to establish recent baseline trends, the impact of commitments to eliminate deforestation from palm oil supply chains could therefore be overestimated. We examine the area and proportion of plantations replacing forests across Sumatra, Kalimantan, and Papua up to 2015, and map biophysically suitable areas for future deforestation-free expansion. We created new maps of oil palm plantations for the years 1995, 2000, 2005, 2010 and 2015, and examined land cover replaced in each period. Nationwide, oil palm plantation expansion occurred at an average rate of 450,000 ha yr−1, and resulted in an average of 117,000 ha yr−1 of deforestation, during 1995–2015. Our analysis of the most recent five-year period (2010–2015) shows that the rate of deforestation due to new plantations has remained relatively stable since 2005, despite large increases in the extent of plantations. As a result, the proportion of plantations replacing forests decreased from 54% during 1995–2000, to 18% during 2010–2015. In addition, we estimate there are 30.2 million hectares of non-forest land nationwide which meet biophysical suitability criteria for oil palm cultivation. Our findings suggest that recent zero-deforestation commitments may not have a large impact on deforestation in Sumatra, where plantations have increasingly expanded onto non-forest land over the past twenty years, and which hosts large potentially suitable areas for future deforestation-free expansion. On the other hand, these pledges could have more influence in Kalimantan, where oil palm driven deforestation increased over our study period, and in Papua, a new frontier of expansion with substantial remaining forest cover