Global regularity of three-dimensional Ricci limit spaces

In their recent work [ST17], Miles Simon and the second author established a local bi-Hölder correspondence between weakly noncollapsed Ricci limit spaces in three dimensions and smooth manifolds. In particular, any open ball of finite radius in such a limit space must be bi-Hölder homeomorphic to some open subset of a complete smooth Riemannian three-manifold. In this work we build on the technology from [ST16, ST17] to improve this local correspondence to a global-local correspondence. That is, we construct a smooth three-manifold M, and prove that the entire (weakly) noncollapsed three-dimensional Ricci limit space is homeomorphic to M via a globally-defined homeomorphism that is bi-Hölder once restricted to any compact subset. Here the bi-Hölder regularity is with respect to the distance dg on M, where g is any smooth complete metric on M. A key step in our proof is the construction of local pyramid Ricci flows, existing on uniform regions of spacetime, that are inspired by Hochard’s partial Ricci flows [Hoc16]. Suppose (M, g0, x0) is a complete smooth pointed Riemannian three-manifold that is (weakly) noncollapsed and satisfies a lower Ricci bound. Then, given any k ∈ N, we construct a smooth Ricci flow g(t) living on a subset of spacetime that contains, for each j ∈ {1, . . . , k}, a cylinder Bg0 (x0, j) × [0, Tj ], where Tj is dependent only on the Ricci lower bound, the (weakly) noncollapsed volume lower bound and the radius j (in particular independent of k) and with the property that g(0) = g0 throughout Bg0 (x0, k).</p

Improved Pseudolocality on Large Hyperbolic Balls

We obtain an improved pseudolocality result for Ricci flows on two-dimensional surfaces that are initially almost-hyperbolic on large hyperbolic balls. We prove that, at the central point of the hyperbolic ball, the Gauss curvature remains close to the hyperbolic value for a time that grows exponentially in the radius of the ball. This two-dimensional result allows us to precisely conjecture how the phenomenon should appear in the higher dimensional setting.Comment: 15 page

Generalised Recombination Interpolation Method (GRIM)

In this paper we develop the Generalised Recombination Interpolation Method (GRIM) for finding sparse approximations of functions initially given as linear combinations of some (large) number of simpler functions. GRIM is a hybrid of dynamic growth-based interpolation techniques and thinning-based reduction techniques. We establish that the number of non-zero coefficients in the approximation returned by GRIM is controlled by the concentration of the data. In the case that the functions involved are Lip$(\gamma)$ for some $\gamma > 0$ in the sense of Stein, we obtain improved convergence properties for GRIM. In particular, we prove that the level of data concentration required to guarantee that GRIM finds a good sparse approximation is decreasing with respect to the regularity parameter $\gamma > 0$

Model for quantitative tip-enhanced spectroscopy and the extraction of nanoscale-resolved optical constants

Near-field infrared spectroscopy by elastic scattering of light from a probe tip resolves optical contrasts in materials at dramatically sub-wavelength scales across a broad energy range, with the demonstrated capacity for chemical identification at the nanoscale. However, current models of probe-sample near-field interactions still cannot provide a sufficiently quantitatively interpretation of measured near-field contrasts, especially in the case of materials supporting strong surface phonons. We present a model of near-field spectroscopy derived from basic principles and verified by finite-element simulations, demonstrating superb predictive agreement both with tunable quantum cascade laser near-field spectroscopy of SiO$_2$ thin films and with newly presented nanoscale Fourier transform infrared (nanoFTIR) spectroscopy of crystalline SiC. We discuss the role of probe geometry, field retardation, and surface mode dispersion in shaping the measured near-field response. This treatment enables a route to quantitatively determine nano-resolved optical constants, as we demonstrate by inverting newly presented nanoFTIR spectra of an SiO$_2$ thin film into the frequency dependent dielectric function of its mid-infrared optical phonon. Our formalism further enables tip-enhanced spectroscopy as a potent diagnostic tool for quantitative nano-scale spectroscopy.Comment: 19 pages, 9 figure

Nanoscale infrared spectroscopy as a non-destructive probe of extraterrestrial samples

Advances in the spatial resolution of modern analytical techniques have tremendously augmented the scientific insight gained from the analysis of natural samples. Yet, while techniques for the elemental and structural characterization of samples have achieved sub-nanometre spatial resolution, infrared spectral mapping of geochemical samples at vibrational 'fingerprint' wavelengths has remained restricted to spatial scales >10 mu m. Nevertheless, infrared spectroscopy remains an invaluable contactless probe of chemical structure, details of which offer clues to the formation history of minerals. Here we report on the successful implementation of infrared near-field imaging, spectroscopy and analysis techniques capable of sub-micron scale mineral identification within natural samples, including a chondrule from the Murchison meteorite and a cometary dust grain (Iris) from NASA's Stardust mission. Complementary to scanning electron microscopy, energy-dispersive X-ray spectroscopy and transmission electron microscopy probes, this work evidences a similarity between chondritic and cometary materials, and inaugurates a new era of infrared nano-spectroscopy applied to small and invaluable extraterrestrial samples

Nanoscale infrared spectroscopy as a non-destructive probe of extraterrestrial samples

Advances in the spatial resolution of modern analytical techniques have tremendously augmented the scientific insight gained from the analysis of natural samples. Yet, while techniques for the elemental and structural characterization of samples have achieved sub-nanometre spatial resolution, infrared spectral mapping of geochemical samples at vibrational 'fingerprint' wavelengths has remained restricted to spatial scales >10 mu m. Nevertheless, infrared spectroscopy remains an invaluable contactless probe of chemical structure, details of which offer clues to the formation history of minerals. Here we report on the successful implementation of infrared near-field imaging, spectroscopy and analysis techniques capable of sub-micron scale mineral identification within natural samples, including a chondrule from the Murchison meteorite and a cometary dust grain (Iris) from NASA's Stardust mission. Complementary to scanning electron microscopy, energy-dispersive X-ray spectroscopy and transmission electron microscopy probes, this work evidences a similarity between chondritic and cometary materials, and inaugurates a new era of infrared nano-spectroscopy applied to small and invaluable extraterrestrial samples

The metabolism of anabolic-androgenic steroids in the greyhound

BACKGROUND Effective control of the use of anabolic-androgenic steroids (AASs) in animal sports is essential in order to ensure both animal welfare and integrity. In order to better police their use in Australian and New Zealand greyhound racing, thorough metabolic studies have been carried out on a range of registered human and veterinary AASs available in the region. RESULTS Canine metabolic data are presented for the AASs boldenone, danazol, ethylestrenol, mesterolone, methandriol, nandrolone and norethandrolone. The principal Phase I metabolic processes observed were the reduction of A-ring unsaturations and/or 3-ketones with either 3α,5β- or 3β,5α-stereochemistry, the oxidation of secondary 17β-hydroxyl groups and 16α-hydroxylation. The Phase II β-glucuronylation of sterol metabolites was extensive. CONCLUSION The presented data have enabled the effective analysis of AASs and their metabolites in competition greyhound urine samples.Australian Research Council LP077483

Identification of pre-leukaemic haematopoietic stem cells in acute leukaemia.

In acute myeloid leukaemia (AML), the cell of origin, nature and biological consequences of initiating lesions, and order of subsequent mutations remain poorly understood, as AML is typically diagnosed without observation of a pre-leukaemic phase. Here, highly purified haematopoietic stem cells (HSCs), progenitor and mature cell fractions from the blood of AML patients were found to contain recurrent DNMT3A mutations (DNMT3A(mut)) at high allele frequency, but without coincident NPM1 mutations (NPM1c) present in AML blasts. DNMT3A(mut)-bearing HSCs showed a multilineage repopulation advantage over non-mutated HSCs in xenografts, establishing their identity as pre-leukaemic HSCs. Pre-leukaemic HSCs were found in remission samples, indicating that they survive chemotherapy. Therefore DNMT3A(mut) arises early in AML evolution, probably in HSCs, leading to a clonally expanded pool of pre-leukaemic HSCs from which AML evolves. Our findings provide a paradigm for the detection and treatment of pre-leukaemic clones before the acquisition of additional genetic lesions engenders greater therapeutic resistance

Real-world outcomes of sipuleucel-T treatment in PROCEED, a prospective registry of men with metastatic castration-resistant prostate cancer.

BackgroundThe large registry, PROVENGE Registry for the Observation, Collection, and Evaluation of Experience Data (PROCEED)(NCT01306890), evaluated sipuleucel-T immunotherapy for asymptomatic/minimally symptomatic metastatic castration-resistant prostate cancer (mCRPC).MethodsPROCEED enrolled patients with mCRPC receiving 3 biweekly sipuleucel-T infusions. Assessments included overall survival (OS), serious adverse events (SAEs), cerebrovascular events (CVEs), and anticancer interventions (ACIs). Follow-up was for ≥3&nbsp;years or until death or study withdrawal.ResultsIn 2011-2017, 1976 patients were followed for 46.6&nbsp;months (median). The median age was 72&nbsp;years, and the baseline median prostate-specific antigen level was 15.0&nbsp;ng/mL; 86.7% were white, and 11.6% were African American. Among the patients, 1902 had 1 or more sipuleucel-T infusions. The median OS was 30.7&nbsp;months (95% confidence interval [CI], 28.6-32.2&nbsp;months). Known prognostic factors were independently associated with OS in a multivariable analysis. Among the 1255 patients who died, 964 (76.8%) died of prostate cancer (PC) progression. The median time from the first infusion to PC death was 42.7&nbsp;months (95% CI, 39.4-46.2&nbsp;months). The incidence of sipuleucel-T-related SAEs was 3.9%. The incidence of CVEs was 2.8%, and the rate per 100 person-years was 1.2 (95% CI, 0.9-1.6). The CVE incidence among 11,972 patients with mCRPC from the Surveillance, Epidemiology, and End Results-Medicare database was 2.8%; the rate per 100 person-years was 1.5 (95% CI, 1.4-1.7). One or more ACIs (abiraterone, enzalutamide, docetaxel, cabazitaxel, or radium 223) were received by 77.1% of the patients after sipuleucel-T; 32.5% and 17.4% of the patients experienced 1- and 2-year treatment-free intervals, respectively.ConclusionsPROCEED provides contemporary survival data for sipuleucel-T-treated men in a real-world setting of new life-prolonging agents, which will be useful in discussing treatment options with patients and in powering future trials with sipuleucel-T. The safety and tolerability of sipuleucel-T in PROCEED were consistent with previous findings