Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization

The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and collaborative filtering. Although specific instances can often be solved with specialized algorithms, the general affine rank minimization problem is NP-hard. In this paper, we show that if a certain restricted isometry property holds for the linear transformation defining the constraints, the minimum rank solution can be recovered by solving a convex optimization problem, namely the minimization of the nuclear norm over the given affine space. We present several random ensembles of equations where the restricted isometry property holds with overwhelming probability. The techniques used in our analysis have strong parallels in the compressed sensing framework. We discuss how affine rank minimization generalizes this pre-existing concept and outline a dictionary relating concepts from cardinality minimization to those of rank minimization

Biodistribution and PET Imaging of pharmacokinetics of manganese in mice using Manganese-52

<div><p>Manganese is essential to life, and humans typically absorb sufficient quantities of this element from a normal healthy diet; however, chronic, elevated ingestion or inhalation of manganese can be neurotoxic, potentially leading to <i>manganism</i>. Although imaging of large amounts of accumulated Mn(II) is possible by MRI, quantitative measurement of the biodistribution of manganese, particularly at the trace level, can be challenging. In this study, we produced the positron-emitting radionuclide ⁵²Mn (<i>t</i>_<i>1/2</i> = 5.6 d) by proton bombardment (<i>E</i>_<i>p</i><15 MeV) of chromium metal, followed by solid-phase isolation by cation-exchange chromatography. An aqueous solution of [⁵²Mn]MnCl₂ was nebulized into a closed chamber with openings through which mice inhaled the aerosol, and a separate cohort of mice received intravenous (IV) injections of [⁵²Mn]MnCl₂. <i>Ex vivo</i> biodistribution was performed at 1 h and 1 d post-injection/inhalation (p.i.). In both trials, we observed uptake in lungs and thyroid at 1 d p.i. Manganese is known to cross the blood-brain barrier, as confirmed in our studies following IV injection (0.86%ID/g, 1 d p.i.) and following inhalation of aerosol, (0.31%ID/g, 1 d p.i.). Uptake in salivary gland and pancreas were observed at 1 d p.i. (0.5 and 0.8%ID/g), but to a much greater degree from IV injection (6.8 and 10%ID/g). In a separate study, mice received IV injection of an imaging dose of [⁵²Mn]MnCl₂, followed by <i>in vivo</i> imaging by positron emission tomography (PET) and <i>ex vivo</i> biodistribution. The results from this study supported many of the results from the biodistribution-only studies. In this work, we have confirmed results in the literature and contributed new results for the biodistribution of inhaled radiomanganese for several organs. Our results could serve as supporting information for environmental and occupational regulations, for designing PET studies utilizing ⁵²Mn, and/or for predicting the biodistribution of manganese-based MR contrast agents.</p></div

Lewisian quidditism, humility, and diffidence

In ‘Ramseyan Humility’ Lewis presents the Permutation Argument for quidditism. As he presents it the argument is simple enough, but once one digs beneath its surface, and attempts to understand it in strictly Lewisian terms, difficulties arise. The fundamental difficulty is that, as he presents it, the argument only seems to be sound if one rejects views that Lewis explicitly holds. One aim of this paper is to clarify the argument to show that one can make sense of it in strictly Lewisian terms. In so doing I clarify Lewis’s view, clearly lay out the commitments that Lewis has, and define quidditism in strictly Lewisian terms. However, I also have a secondary aim. Lewis accepts that quidditism entails a form of scepticism, that he calls ‘Humility’. However, by an extension of the permutation argument I show that quidditism entails a form of scepticism, that I call ‘Diffidence’, that is far more wide-reaching than Humility

Constraints on the Atmospheric Circulation and Variability of the Eccentric Hot Jupiter XO-3b

We report secondary eclipse photometry of the hot Jupiter XO-3b in the 4.5~$\mu$m band taken with the Infrared Array Camera (IRAC) on the Spitzer Space Telescope. We measure individual eclipse depths and center of eclipse times for a total of twelve secondary eclipses. We fit these data simultaneously with two transits observed in the same band in order to obtain a global best-fit secondary eclipse depth of $0.1580\pm 0.0036\%$ and a center of eclipse phase of $0.67004\pm 0.00013$. We assess the relative magnitude of variations in the dayside brightness of the planet by measuring the size of the residuals during ingress and egress from fitting the combined eclipse light curve with a uniform disk model and place an upper limit of 0.05$\%$. The new secondary eclipse observations extend the total baseline from one and a half years to nearly three years, allowing us to place an upper limit on the periastron precession rate of $2.9\times 10^{-3}$ degrees/day the tightest constraint to date on the periastron precession rate of a hot Jupiter. We use the new transit observations to calculate improved estimates for the system properties, including an updated orbital ephemeris. We also use the large number of secondary eclipses to obtain the most stringent limits to date on the orbit-to-orbit variability of an eccentric hot Jupiter and demonstrate the consistency of multiple-epoch Spitzer observations.Comment: 14 pages, 11 figures, published by Ap

Observational Results of a Multi-Telescope Campaign in Search of Interstellar Urea [(NH2_2)2_2CO]

In this paper, we present the results of an observational search for gas phase urea [(NH$_2$)$_2$CO] observed towards the Sgr B2(N-LMH) region. We show data covering urea transitions from $\sim$100 GHz to 250 GHz from five different observational facilities: BIMA, CARMA, the NRAO 12 m telescope, the IRAM 30 m telescope, and SEST. The results show that the features ascribed to urea can be reproduced across the entire observed bandwidth and all facilities by best fit column density, temperature, and source size parameters which vary by less than a factor of 2 between observations merely by adjusting for telescope-specific parameters. Interferometric observations show that the emission arising from these transitions is cospatial and compact, consistent with the derived source sizes and emission from a single species. Despite this evidence, the spectral complexity, both of (NH$_2$)$_2$CO and of Sgr B2(N), makes the definitive identification of this molecule challenging. We present observational spectra, laboratory data, and models, and discuss our results in the context of a possible molecular detection of urea.Comment: 38 pages, 9 Figures, accepted in the Astrophysical Journa

Estimation of cardiac output and pulmonary vascular resistance by contrast echocardiography transit time measurement: a prospective pilot study

Background Studies with other imaging modalities have demonstrated a relationship between contrast transit and cardiac output (CO) and pulmonary vascular resistance (PVR). We tested the hypothesis that the transit time during contrast echocardiography could accurately estimate both CO and PVR compared to right heart catheterization (RHC). Methods 27 patients scheduled for RHC had 2D-echocardiogram immediately prior to RHC. 3 ml of DEFINITY contrast followed by a 10 ml saline flush was injected, and a multi-cycle echo clip was acquired from the beginning of injection to opacification of the left ventricle. 2D-echo based calculations of CO and PVR along with the DEFINITY-based transit time calculations were subsequently correlated with the RHC-determined CO and PVR. Results The transit time from full opacification of the right ventricle to full opacification of the left ventricle inversely correlated with CO (r = -0.61, p \u3c 0.001). The transit time from peak opacification of the right ventricle to first appearance in the left ventricle moderately correlated with PVR (r = 0.46, p \u3c 0.01). Previously described echocardiographic methods for the determination of CO (Huntsman method) and PVR (Abbas and Haddad methods) did not correlate with RHC-determined values (p = 0.20 for CO, p = 0.18 and p = 0.22 for PVR, respectively). The contrast transit time method demonstrated reliable intra- (p \u3c 0.0001) and inter-observer correlation (p \u3c 0.001). Conclusions We describe a novel method for the quantification of CO and estimation of PVR using contrast echocardiography transit time. This technique adds to the methodologies used for noninvasive hemodynamic assessment, but requires further validation to determine overall applicability

Use of angiotensin receptor blockers and risk of dementia in a predominantly male population: prospective cohort analysis

Objective To investigate whether angiotensin receptor blockers protect against Alzheimer’s disease and dementia or reduce the progression of both diseases