149 research outputs found
Higher rank numerical ranges and low rank perturbations of quantum channels
For a positive integer , the rank- numerical range of an
operator acting on a Hilbert space \cH of dimension at least is the
set of scalars such that for some rank
orthogonal projection . In this paper, a close connection between low rank
perturbation of an operator and is established. In
particular, for it is shown that for any operator with \rank (F) \le r. In quantum
computing, this result implies that a quantum channel with a -dimensional
error correcting code under a perturbation of rank will still have a
-dimensional error correcting code. Moreover, it is shown that if is
normal or if the dimension of is finite, then can be
obtained as the intersection of for a collection of rank
operators . Examples are given to show that the result fails if is a
general operator. The closure and the interior of the convex set
are completely determined. Analogous results are obtained for
defined as the set of scalars such that for an infinite rank orthogonal projection . It is shown that
is the intersection of all for . If is not compact for any \mu \in \IC, then the closure
and the interior of coincide with those of the essential
numerical range of . The situation for the special case when is
compact for some \mu \in \IC is also studied.Comment: 21 page
Effect of SGLT2 inhibitors on stroke and atrial fibrillation in diabetic kidney disease: Results from the CREDENCE trial and meta-analysis
BACKGROUND AND PURPOSE: Chronic kidney disease with reduced estimated glomerular filtration rate or elevated albuminuria increases risk for ischemic and hemorrhagic stroke. This study assessed the effects of sodium glucose cotransporter 2 inhibitors (SGLT2i) on stroke and atrial fibrillation/flutter (AF/AFL) from CREDENCE (Canagliflozin and Renal Events in Diabetes With Established Nephropathy Clinical Evaluation) and a meta-Analysis of large cardiovascular outcome trials (CVOTs) of SGLT2i in type 2 diabetes mellitus. METHODS: CREDENCE randomized 4401 participants with type 2 diabetes mellitus and chronic kidney disease to canagliflozin or placebo. Post hoc, we estimated effects on fatal or nonfatal stroke, stroke subtypes, and intermediate markers of stroke risk including AF/AFL. Stroke and AF/AFL data from 3 other completed large CVOTs and CREDENCE were pooled using random-effects meta-Analysis. RESULTS: In CREDENCE, 142 participants experienced a stroke during follow-up (10.9/1000 patient-years with canagliflozin, 14.2/1000 patient-years with placebo; hazard ratio [HR], 0.77 [95% CI, 0.55-1.08]). Effects by stroke subtypes were: ischemic (HR, 0.88 [95% CI, 0.61-1.28]; n=111), hemorrhagic (HR, 0.50 [95% CI, 0.19-1.32]; n=18), and undetermined (HR, 0.54 [95% CI, 0.20-1.46]; n=17). There was no clear effect on AF/AFL (HR, 0.76 [95% CI, 0.53-1.10]; n=115). The overall effects in the 4 CVOTs combined were: Total stroke (HRpooled, 0.96 [95% CI, 0.82-1.12]), ischemic stroke (HRpooled, 1.01 [95% CI, 0.89-1.14]), hemorrhagic stroke (HRpooled, 0.50 [95% CI, 0.30-0.83]), undetermined stroke (HRpooled, 0.86 [95% CI, 0.49-1.51]), and AF/AFL (HRpooled, 0.81 [95% CI, 0.71-0.93]). There was evidence that SGLT2i effects on total stroke varied by baseline estimated glomerular filtration rate (P=0.01), with protection in the lowest estimated glomerular filtration rate (45 mL/min/1.73 m2]) subgroup (HRpooled, 0.50 [95% CI, 0.31-0.79]). CONCLUSIONS: Although we found no clear effect of SGLT2i on total stroke in CREDENCE or across trials combined, there was some evidence of benefit in preventing hemorrhagic stroke and AF/AFL, as well as total stroke for those with lowest estimated glomerular filtration rate. Future research should focus on confirming these data and exploring potential mechanisms
Erratum: âSearches for Gravitational Waves from Known Pulsars at Two Harmonics in 2015â2017 LIGO Dataâ (2019, ApJ, 879, 10)
Due to an error at the publisher, in the published article the number of pulsars presented in the paper is incorrect in multiple places throughout the text. Specifically, "222" pulsars should be "221." Additionally, the number of pulsars for which we have EM observations that fully overlap with O1 and O2 changes from "168" to "167." Elsewhere, in the machine-readable table of Table 1 and in Table 2, the row corresponding to pulsar J0952-0607 should be excised as well. Finally, in the caption for Table 2 the number of pulsars changes from "188" to "187.
Canagliflozin and Renal Outcomes in Type 2 Diabetes and Nephropathy
BACKGROUND Type 2 diabetes mellitus is the leading cause of kidney failure worldwide, but few effective long-term treatments are available. In cardiovascular trials of inhibitors of sodiumâglucose cotransporter 2 (SGLT2), exploratory results have suggested that such drugs may improve renal outcomes in patients with type 2 diabetes. METHODS In this double-blind, randomized trial, we assigned patients with type 2 diabetes and albuminuric chronic kidney disease to receive canagliflozin, an oral SGLT2 inhibitor, at a dose of 100 mg daily or placebo. All the patients had an estimated glomerular filtration rate (GFR) of 30 to 300 to 5000) and were treated with reninâangiotensin system blockade. The primary outcome was a composite of end-stage kidney disease (dialysis, transplantation, or a sustained estimated GFR of <15 ml per minute per 1.73 m 2), a doubling of the serum creatinine level, or death from renal or cardiovascular causes. Prespecified secondary outcomes were tested hierarchically. RESULTS The trial was stopped early after a planned interim analysis on the recommendation of the data and safety monitoring committee. At that time, 4401 patients had undergone randomization, with a median follow-up of 2.62 years. The relative risk of the primary outcome was 30% lower in the canagliflozin group than in the placebo group, with event rates of 43.2 and 61.2 per 1000 patient-years, respectively (hazard ratio, 0.70; 95% confidence interval [CI], 0.59 to 0.82; P=0.00001). The relative risk of the renal-specific composite of end-stage kidney disease, a doubling of the creatinine level, or death from renal causes was lower by 34% (hazard ratio, 0.66; 95% CI, 0.53 to 0.81; P<0.001), and the relative risk of end-stage kidney disease was lower by 32% (hazard ratio, 0.68; 95% CI, 0.54 to 0.86; P=0.002). The canagliflozin group also had a lower risk of cardiovascular death, myocardial infarction, or stroke (hazard ratio, 0.80; 95% CI, 0.67 to 0.95; P=0.01) and hospitalization for heart failure (hazard ratio, 0.61; 95% CI, 0.47 to 0.80; P<0.001). There were no significant differences in rates of amputation or fracture. CONCLUSIONS In patients with type 2 diabetes and kidney disease, the risk of kidney failure and cardiovascular events was lower in the canagliflozin group than in the placebo group at a median follow-up of 2.62 years
Canagliflozin and renal outcomes in type 2 diabetes and nephropathy
BACKGROUND Type 2 diabetes mellitus is the leading cause of kidney failure worldwide, but few effective long-term treatments are available. In cardiovascular trials of inhibitors of sodiumâglucose cotransporter 2 (SGLT2), exploratory results have suggested that such drugs may improve renal outcomes in patients with type 2 diabetes. METHODS In this double-blind, randomized trial, we assigned patients with type 2 diabetes and albuminuric chronic kidney disease to receive canagliflozin, an oral SGLT2 inhibitor, at a dose of 100 mg daily or placebo. All the patients had an estimated glomerular filtration rate (GFR) of 30 to <90 ml per minute per 1.73 m2 of body-surface area and albuminuria (ratio of albumin [mg] to creatinine [g], >300 to 5000) and were treated with reninâangiotensin system blockade. The primary outcome was a composite of end-stage kidney disease (dialysis, transplantation, or a sustained estimated GFR of <15 ml per minute per 1.73 m2), a doubling of the serum creatinine level, or death from renal or cardiovascular causes. Prespecified secondary outcomes were tested hierarchically. RESULTS The trial was stopped early after a planned interim analysis on the recommendation of the data and safety monitoring committee. At that time, 4401 patients had undergone randomization, with a median follow-up of 2.62 years. The relative risk of the primary outcome was 30% lower in the canagliflozin group than in the placebo group, with event rates of 43.2 and 61.2 per 1000 patient-years, respectively (hazard ratio, 0.70; 95% confidence interval [CI], 0.59 to 0.82; P=0.00001). The relative risk of the renal-specific composite of end-stage kidney disease, a doubling of the creatinine level, or death from renal causes was lower by 34% (hazard ratio, 0.66; 95% CI, 0.53 to 0.81; P<0.001), and the relative risk of end-stage kidney disease was lower by 32% (hazard ratio, 0.68; 95% CI, 0.54 to 0.86; P=0.002). The canagliflozin group also had a lower risk of cardiovascular death, myocardial infarction, or stroke (hazard ratio, 0.80; 95% CI, 0.67 to 0.95; P=0.01) and hospitalization for heart failure (hazard ratio, 0.61; 95% CI, 0.47 to 0.80; P<0.001). There were no significant differences in rates of amputation or fracture. CONCLUSIONS In patients with type 2 diabetes and kidney disease, the risk of kidney failure and cardiovascular events was lower in the canagliflozin group than in the placebo group at a median follow-up of 2.62 years
Search for gravitational waves from Scorpius X-1 in the second Advanced LIGO observing run with an improved hidden Markov model
We present results from a semicoherent search for continuous gravitational waves from the low-mass x-ray binary Scorpius X-1, using a hidden Markov model (HMM) to track spin wandering. This search improves on previous HMM-based searches of LIGO data by using an improved frequency domain matched filter, the J-statistic, and by analyzing data from Advanced LIGO's second observing run. In the frequency range searched, from 60 to 650 Hz, we find no evidence of gravitational radiation. At 194.6 Hz, the most sensitive search frequency, we report an upper limit on gravitational wave strain (at 95% confidence) of h095%=3.47Ă10-25 when marginalizing over source inclination angle. This is the most sensitive search for Scorpius X-1, to date, that is specifically designed to be robust in the presence of spin wandering. © 2019 American Physical Society
Search for gravitational waves from Scorpius X-1 in the second Advanced LIGO observing run with an improved hidden Markov model
We present results from a semicoherent search for continuous gravitational waves from the low-mass x-ray binary Scorpius X-1, using a hidden Markov model (HMM) to track spin wandering. This search improves on previous HMM-based searches of LIGO data by using an improved frequency domain matched filter, the J-statistic, and by analyzing data from Advanced LIGOâs second observing run. In the frequency range searched, from 60 to 650 Hz, we find no evidence of gravitational radiation. At 194.6 Hz, the most sensitive search frequency, we report an upper limit on gravitational wave strain (at 95% confidence) of h95%0=3.47Ă10â25 when marginalizing over source inclination angle. This is the most sensitive search for Scorpius X-1, to date, that is specifically designed to be robust in the presence of spin wandering
GW190412: Observation of a Binary-Black-Hole Coalescence with Asymmetric Masses
We report the observation of gravitational waves from a binary-black-hole coalescence during the first two weeks of LIGOâs and Virgoâs third observing run. The signal was recorded on April 12, 2019 at 05â¶30â¶44 UTC with a network signal-to-noise ratio of 19. The binary is different from observations during the first two observing runs most notably due to its asymmetric masses: a âŒ30âM_â black hole merged with a âŒ8âM_â black hole companion. The more massive black hole rotated with a dimensionless spin magnitude between 0.22 and 0.60 (90% probability). Asymmetric systems are predicted to emit gravitational waves with stronger contributions from higher multipoles, and indeed we find strong evidence for gravitational radiation beyond the leading quadrupolar order in the observed signal. A suite of tests performed on GW190412 indicates consistency with Einsteinâs general theory of relativity. While the mass ratio of this system differs from all previous detections, we show that it is consistent with the population model of stellar binary black holes inferred from the first two observing runs
Searches for gravitational waves from known pulsars at two harmonics in 2015-2017 LIGO data
International audienceWe present a search for gravitational waves from 222 pulsars with rotation frequencies âł10 Hz. We use advanced LIGO data from its first and second observing runs spanning 2015â2017, which provides the highest-sensitivity gravitational-wave data so far obtained. In this search we target emission from both the l = m = 2 mass quadrupole mode, with a frequency at twice that of the pulsarâs rotation, and the l = 2, m = 1 mode, with a frequency at the pulsar rotation frequency. The search finds no evidence for gravitational-wave emission from any pulsar at either frequency. For the l = m = 2 mode search, we provide updated upper limits on the gravitational-wave amplitude, mass quadrupole moment, and fiducial ellipticity for 167 pulsars, and the first such limits for a further 55. For 20 young pulsars these results give limits that are below those inferred from the pulsarsâ spin-down. For the Crab and Vela pulsars our results constrain gravitational-wave emission to account for less than 0.017% and 0.18% of the spin-down luminosity, respectively. For the recycled millisecond pulsar J0711â6830 our limits are only a factor of 1.3 above the spin-down limit, assuming the canonical value of 1038 kg m2 for the starâs moment of inertia, and imply a gravitational-wave-derived upper limit on the starâs ellipticity of 1.2 Ă 10â8. We also place new limits on the emission amplitude at the rotation frequency of the pulsars
- âŠ