Slepian Wavelets for the Analysis of Incomplete Data on Manifolds

Many fields in science and engineering measure data that inherently live on non-Euclidean geometries, such as the sphere. Techniques developed in the Euclidean setting must be extended to other geometries. Due to recent interest in geometric deep learning, analogues of Euclidean techniques must also handle general manifolds or graphs. Often, data are only observed over partial regions of manifolds, and thus standard whole-manifold techniques may not yield accurate predictions. In this thesis, a new wavelet basis is designed for datasets like these. Although many definitions of spherical convolutions exist, none fully emulate the Euclidean definition. A novel spherical convolution is developed, designed to tackle the shortcomings of existing methods. The so-called sifting convolution exploits the sifting property of the Dirac delta and follows by the inner product of a function with the translated version of another. This translation operator is analogous to the Euclidean translation in harmonic space and exhibits some useful properties. In particular, the sifting convolution supports directional kernels; has an output that remains on the sphere; and is efficient to compute. The convolution is entirely generic and thus may be used with any set of basis functions. An application of the sifting convolution with a topographic map of the Earth demonstrates that it supports directional kernels to perform anisotropic filtering. Slepian wavelets are built upon the eigenfunctions of the Slepian concentration problem of the manifold - a set of bandlimited functions which are maximally concentrated within a given region. Wavelets are constructed through a tiling of the Slepian harmonic line by leveraging the existing scale-discretised framework. A straightforward denoising formalism demonstrates a boost in signal-to-noise for both a spherical and general manifold example. Whilst these wavelets were inspired by spherical datasets, like in cosmology, the wavelet construction may be utilised for manifold or graph data

Developing Capacitated p-median Location-allocation Model in the spopt Library to Allow UCL Student Teacher Placements Using Public Transport

Location-allocation is a key tool within the GIS and network analysis toolbox. In this paper we discuss the real world application of a location-allocation case study (approx 800 students, 500 schools) from UCL using public transport. The use of public transportation is key for this case study, as many location-allocation approaches only make use of drive-time or walking-time distances, but the location of UCL in Greater London, UK makes the inclusion of public transport vital for this case study. The location-allocation is implemented as a capacitated p-median location-allocation model, using the spopt library, part of the Python Spatial Analysis Library (PySAL). The capacitated variation of the p-median location-allocation problem is a new addition to the spopt library, which this work will present. The results from the initial version of the capacitated p-median location-allocation problem has shown a marked improvement on public transport travel time, with public transport travel time reduced by 891 minutes overall for an initial sample of 93 students (9.58 minutes per student). Results will be presented below and plans for further improvement shared

Quantum state preparation and macroscopic entanglement in gravitational-wave detectors

Long-baseline laser-interferometer gravitational-wave detectors are operating at a factor of 10 (in amplitude) above the standard quantum limit (SQL) within a broad frequency band. Such a low classical noise budget has already allowed the creation of a controlled 2.7 kg macroscopic oscillator with an effective eigenfrequency of 150 Hz and an occupation number of 200. This result, along with the prospect for further improvements, heralds the new possibility of experimentally probing macroscopic quantum mechanics (MQM) - quantum mechanical behavior of objects in the realm of everyday experience - using gravitational-wave detectors. In this paper, we provide the mathematical foundation for the first step of a MQM experiment: the preparation of a macroscopic test mass into a nearly minimum-Heisenberg-limited Gaussian quantum state, which is possible if the interferometer's classical noise beats the SQL in a broad frequency band. Our formalism, based on Wiener filtering, allows a straightforward conversion from the classical noise budget of a laser interferometer, in terms of noise spectra, into the strategy for quantum state preparation, and the quality of the prepared state. Using this formalism, we consider how Gaussian entanglement can be built among two macroscopic test masses, and the performance of the planned Advanced LIGO interferometers in quantum-state preparation

Searching for a Stochastic Background of Gravitational Waves with LIGO

The Laser Interferometer Gravitational-wave Observatory (LIGO) has performed the fourth science run, S4, with significantly improved interferometer sensitivities with respect to previous runs. Using data acquired during this science run, we place a limit on the amplitude of a stochastic background of gravitational waves. For a frequency independent spectrum, the new limit is $\Omega_{\rm GW} < 6.5 \times 10^{-5}$. This is currently the most sensitive result in the frequency range 51-150 Hz, with a factor of 13 improvement over the previous LIGO result. We discuss complementarity of the new result with other constraints on a stochastic background of gravitational waves, and we investigate implications of the new result for different models of this background.Comment: 37 pages, 16 figure

Case Reports1. A Late Presentation of Loeys-Dietz Syndrome: Beware of TGFβ Receptor Mutations in Benign Joint Hypermobility

Background: Thoracic aortic aneurysms (TAA) and dissections are not uncommon causes of sudden death in young adults. Loeys-Dietz syndrome (LDS) is a rare, recently described, autosomal dominant, connective tissue disease characterized by aggressive arterial aneurysms, resulting from mutations in the transforming growth factor beta (TGFβ) receptor genes TGFBR1 and TGFBR2. Mean age at death is 26.1 years, most often due to aortic dissection. We report an unusually late presentation of LDS, diagnosed following elective surgery in a female with a long history of joint hypermobility. Methods: A 51-year-old Caucasian lady complained of chest pain and headache following a dural leak from spinal anaesthesia for an elective ankle arthroscopy. CT scan and echocardiography demonstrated a dilated aortic root and significant aortic regurgitation. MRA demonstrated aortic tortuosity, an infrarenal aortic aneurysm and aneurysms in the left renal and right internal mammary arteries. She underwent aortic root repair and aortic valve replacement. She had a background of long-standing joint pains secondary to hypermobility, easy bruising, unusual fracture susceptibility and mild bronchiectasis. She had one healthy child age 32, after which she suffered a uterine prolapse. Examination revealed mild Marfanoid features. Uvula, skin and ophthalmological examination was normal. Results: Fibrillin-1 testing for Marfan syndrome (MFS) was negative. Detection of a c.1270G > C (p.Gly424Arg) TGFBR2 mutation confirmed the diagnosis of LDS. Losartan was started for vascular protection. Conclusions: LDS is a severe inherited vasculopathy that usually presents in childhood. It is characterized by aortic root dilatation and ascending aneurysms. There is a higher risk of aortic dissection compared with MFS. Clinical features overlap with MFS and Ehlers Danlos syndrome Type IV, but differentiating dysmorphogenic features include ocular hypertelorism, bifid uvula and cleft palate. Echocardiography and MRA or CT scanning from head to pelvis is recommended to establish the extent of vascular involvement. Management involves early surgical intervention, including early valve-sparing aortic root replacement, genetic counselling and close monitoring in pregnancy. Despite being caused by loss of function mutations in either TGFβ receptor, paradoxical activation of TGFβ signalling is seen, suggesting that TGFβ antagonism may confer disease modifying effects similar to those observed in MFS. TGFβ antagonism can be achieved with angiotensin antagonists, such as Losartan, which is able to delay aortic aneurysm development in preclinical models and in patients with MFS. Our case emphasizes the importance of timely recognition of vasculopathy syndromes in patients with hypermobility and the need for early surgical intervention. It also highlights their heterogeneity and the potential for late presentation. Disclosures: The authors have declared no conflicts of interes

TRY plant trait database – enhanced coverage and open access

Plant traits - the morphological, anatomical, physiological, biochemical and phenological characteristics of plants - determine how plants respond to environmental factors, affect other trophic levels, and influence ecosystem properties and their benefits and detriments to people. Plant trait data thus represent the basis for a vast area of research spanning from evolutionary biology, community and functional ecology, to biodiversity conservation, ecosystem and landscape management, restoration, biogeography and earth system modelling. Since its foundation in 2007, the TRY database of plant traits has grown continuously. It now provides unprecedented data coverage under an open access data policy and is the main plant trait database used by the research community worldwide. Increasingly, the TRY database also supports new frontiers of trait‐based plant research, including the identification of data gaps and the subsequent mobilization or measurement of new data. To support this development, in this article we evaluate the extent of the trait data compiled in TRY and analyse emerging patterns of data coverage and representativeness. Best species coverage is achieved for categorical traits - almost complete coverage for ‘plant growth form’. However, most traits relevant for ecology and vegetation modelling are characterized by continuous intraspecific variation and trait–environmental relationships. These traits have to be measured on individual plants in their respective environment. Despite unprecedented data coverage, we observe a humbling lack of completeness and representativeness of these continuous traits in many aspects. We, therefore, conclude that reducing data gaps and biases in the TRY database remains a key challenge and requires a coordinated approach to data mobilization and trait measurements. This can only be achieved in collaboration with other initiatives

Measurement of b hadron lifetimes in exclusive decays containing a J/psi in p-pbar collisions at sqrt(s)=1.96TeV

We report on a measurement of $b$-hadron lifetimes in the fully reconstructed decay modes B^+ -->J/Psi K+, B^0 --> J/Psi K*, B^0 --> J/Psi Ks, and Lambda_b --> J/Psi Lambda using data corresponding to an integrated luminosity of 4.3 ${\rm fb}^{-1}$, collected by the CDF II detector at the Fermilab Tevatron. The measured lifetimes are $\tau$B^+ = $1.639 \pm 0.009 ({\rm stat}) \pm 0.009 {\rm (syst) ~ ps}$, $\tau$B^0 = $1.507 \pm 0.010 ({\rm stat}) \pm 0.008 {\rm (syst) ~ ps}$ and $\tau$Lambda_b = $1.537 \pm 0.045 ({\rm stat}) \pm 0.014 {\rm (syst) ~ ps}$. The lifetime ratios are $\tau$B^+/$\tau$B^0 = $1.088 \pm 0.009 ({\rm stat})\pm 0.004 ({\rm syst})$ and $\tau$Lambda_b/$\tau$B^0 = $1.020 \pm 0.030 ({\rm stat})\pm 0.008 ({\rm syst})$. These are the most precise determinations of these quantities from a single experiment.Comment: revised version. accepted for PRL publicatio

Enhancing rare variant interpretation in inherited arrhythmias through quantitative analysis of consortium disease cohorts and population controls.

PURPOSE: Stringent variant interpretation guidelines can lead to high rates of variants of uncertain significance (VUS) for genetically heterogeneous disease like long QT syndrome (LQTS) and Brugada syndrome (BrS). Quantitative and disease-specific customization of American College of Medical Genetics and Genomics/Association for Molecular Pathology (ACMG/AMP) guidelines can address this false negative rate. METHODS: We compared rare variant frequencies from 1847 LQTS (KCNQ1/KCNH2/SCN5A) and 3335 BrS (SCN5A) cases from the International LQTS/BrS Genetics Consortia to population-specific gnomAD data and developed disease-specific criteria for ACMG/AMP evidence classes-rarity (PM2/BS1 rules) and case enrichment of individual (PS4) and domain-specific (PM1) variants. RESULTS: Rare SCN5A variant prevalence differed between European (20.8%) and Japanese (8.9%) BrS patients (p = 5.7 × 10-18) and diagnosis with spontaneous (28.7%) versus induced (15.8%) Brugada type 1 electrocardiogram (ECG) (p = 1.3 × 10-13). Ion channel transmembrane regions and specific N-terminus (KCNH2) and C-terminus (KCNQ1/KCNH2) domains were characterized by high enrichment of case variants and >95% probability of pathogenicity. Applying the customized rules, 17.4% of European BrS and 74.8% of European LQTS cases had (likely) pathogenic variants, compared with estimated diagnostic yields (case excess over gnomAD) of 19.2%/82.1%, reducing VUS prevalence to close to background rare variant frequency. CONCLUSION: Large case-control data sets enable quantitative implementation of ACMG/AMP guidelines and increased sensitivity for inherited arrhythmia genetic testing

Searching for stochastic gravitational waves using data from the two colocated LIGO Hanford detectors

Searches for a stochastic gravitational-wave background (SGWB) using terrestrial detectors typically involve cross-correlating data from pairs of detectors. The sensitivity of such cross-correlation analyses depends, among other things, on the separation between the two detectors: the smaller the separation, the better the sensitivity. Hence, a colocated detector pair is more sensitive to a gravitational-wave background than a noncolocated detector pair. However, colocated detectors are also expected to suffer from correlated noise from instrumental and environmental effects that could contaminate the measurement of the background. Hence, methods to identify and mitigate the effects of correlated noise are necessary to achieve the potential increase in sensitivity of colocated detectors. Here we report on the first SGWB analysis using the two LIGO Hanford detectors and address the complications arising from correlated environmental noise. We apply correlated noise identification and mitigation techniques to data taken by the two LIGO Hanford detectors, H1 and H2, during LIGO’s fifth science run. At low frequencies, 40–460 Hz, we are unable to sufficiently mitigate the correlated noise to a level where we may confidently measure or bound the stochastic gravitational-wave signal. However, at high frequencies, 460–1000 Hz, these techniques are sufficient to set a 95% confidence level upper limit on the gravitational-wave energy density of Ω(f) < 7.7 × 10[superscript -4](f/900  Hz)[superscript 3], which improves on the previous upper limit by a factor of ~180. In doing so, we demonstrate techniques that will be useful for future searches using advanced detectors, where correlated noise (e.g., from global magnetic fields) may affect even widely separated detectors.National Science Foundation (U.S.)United States. National Aeronautics and Space AdministrationCarnegie TrustDavid & Lucile Packard FoundationAlfred P. Sloan Foundatio

Measurement of b Hadron Lifetimes in Exclusive Decays Containing a J/Psi in p(p)over-bar Collisions at root s=1.96 TeV

We report on a measurement of b-hadron lifetimes in the fully reconstructed decay modes B+-> J/psi K+, B-0 -> J/psi K*(892)(0), B-0 -> J/psi K-s(0), and Lambda(0)(b)-> J/psi Lambda(0) using data corresponding to an integrated luminosity of 4.3 fb(-1), collected by the CDF II detector at the Fermilab Tevatron. The measured lifetimes are tau(B+)=[1.639 +/- 0.009(stat)+/- 0.009(syst)]ps, tau(B-0)=[1.507 +/- 0.010(stat)+/- 0.008(syst)]ps, and tau(Lambda(0)(b))=[1.537 +/- 0.045(stat)+/- 0.014(syst)]ps. The lifetime ratios are tau(B+)/tau(B-0)=[1.088 +/- 0.009(stat)+/- 0.004(syst)] and tau(Lambda(0)(b))/tau(B-0)=[1.020 +/- 0.030(stat)+/- 0.008(syst)]. These are the most precise determinations of these quantities from a single experiment