Algorithm for linear least squares problems with equality and nonnegativity constraints

A new algorithm for solving a linear least-squares problem with linear constraints is presented. The constraints can be equality constraint equations and nonnegativity constraints on selected variables. This problem, while appearing to be quite special, is the core problem arising in the solution of the general linearly constrained linear least-squares problem. The reduction process of the general problem to the core problem can be done in many ways. Three such techniques are discussed. The method employed for solving the core problem is based on combining the equality constraints with differentially weighted least-squares equations to form an augmented least-squares system. This weighted least-squares system is solved with nonnegativity constraints on selected variables. Seven small examples, including a constrained least-squares curve fitting example, are presented. A reference to user instructions for subprograms to compute solutions of constrained least-squares problems is included. 3 figures, 9 tables

Association of Accelerometry-Measured Physical Activity and Cardiovascular Events in Mobility-Limited Older Adults: The LIFE (Lifestyle Interventions and Independence for Elders) Study.

BACKGROUND:Data are sparse regarding the value of physical activity (PA) surveillance among older adults-particularly among those with mobility limitations. The objective of this study was to examine longitudinal associations between objectively measured daily PA and the incidence of cardiovascular events among older adults in the LIFE (Lifestyle Interventions and Independence for Elders) study. METHODS AND RESULTS:Cardiovascular events were adjudicated based on medical records review, and cardiovascular risk factors were controlled for in the analysis. Home-based activity data were collected by hip-worn accelerometers at baseline and at 6, 12, and 24 months postrandomization to either a physical activity or health education intervention. LIFE study participants (n=1590; age 78.9±5.2 [SD] years; 67.2% women) at baseline had an 11% lower incidence of experiencing a subsequent cardiovascular event per 500 steps taken per day based on activity data (hazard ratio, 0.89; 95% confidence interval, 0.84-0.96; P=0.001). At baseline, every 30 minutes spent performing activities ≥500 counts per minute (hazard ratio, 0.75; confidence interval, 0.65-0.89 [P=0.001]) were also associated with a lower incidence of cardiovascular events. Throughout follow-up (6, 12, and 24 months), both the number of steps per day (per 500 steps; hazard ratio, 0.90, confidence interval, 0.85-0.96 [P=0.001]) and duration of activity ≥500 counts per minute (per 30 minutes; hazard ratio, 0.76; confidence interval, 0.63-0.90 [P=0.002]) were significantly associated with lower cardiovascular event rates. CONCLUSIONS:Objective measurements of physical activity via accelerometry were associated with cardiovascular events among older adults with limited mobility (summary score >10 on the Short Physical Performance Battery) both using baseline and longitudinal data. CLINICAL TRIAL REGISTRATION:URL: http://www.clinicaltrials.gov. Unique identifier: NCT01072500

Breast Tumor Cells with PI3K Mutation or HER2 Amplification Are Selectively Addicted to Akt Signaling

Dysregulated PI3K/Akt signaling occurs commonly in breast cancers and is due to HER2 amplification, PI3K mutation or PTEN inactivation. The objective of this study was to determine the role of Akt activation in breast cancer as a function of mechanism of activation and whether inhibition of Akt signaling is a feasible approach to therapy.A selective allosteric inhibitor of Akt kinase was used to interrogate a panel of breast cancer cell lines characterized for genetic lesions that activate PI3K/Akt signaling: HER2 amplification or PI3K or PTEN mutations in order to determine the biochemical and biologic consequences of inhibition of this pathway. A variety of molecular techniques and tissue culture and in vivo xenograft models revealed that tumors with mutational activation of Akt signaling were selectively dependent on the pathway. In sensitive cells, pathway inhibition resulted in D-cyclin loss, G1 arrest and induction of apoptosis, whereas cells without pathway activation were unaffected. Most importantly, the drug effectively inhibited Akt kinase and its downstream effectors in vivo and caused complete suppression of the growth of breast cancer xenografts with PI3K mutation or HER2 amplification, including models of the latter selected for resistance to Herceptin. Furthermore, chronic administration of the drug was well-tolerated, causing only transient hyperglycemia without gross toxicity to the host despite the pleiotropic normal functions of Akt.These data demonstrate that breast cancers with PI3K mutation or HER2 amplification are selectively dependent on Akt signaling, and that effective inhibition of Akt in tumors is feasible and effective in vivo. These findings suggest that direct inhibition of Akt may represent a therapeutic strategy for breast and other cancers that are addicted to the pathway including tumors with resistant to Herceptin

Retinoic Acid-Dependent Signaling Pathways and Lineage Events in the Developing Mouse Spinal Cord

Studies in avian models have demonstrated an involvement of retinoid signaling in early neural tube patterning. The roles of this signaling pathway at later stages of spinal cord development are only partly characterized. Here we use Raldh2-null mouse mutants rescued from early embryonic lethality to study the consequences of lack of endogenous retinoic acid (RA) in the differentiating spinal cord. Mid-gestation RA deficiency produces prominent structural and molecular deficiencies in dorsal regions of the spinal cord. While targets of Wnt signaling in the dorsal neuronal lineage are unaltered, reductions in Fibroblast Growth Factor (FGF) and Notch signaling are clearly observed. We further provide evidence that endogenous RA is capable of driving stem cell differentiation. Raldh2 deficiency results in a decreased number of spinal cord derived neurospheres, which exhibit a reduced differentiation potential. Raldh2-null neurospheres have a decreased number of cells expressing the neuronal marker β-III-tubulin, while the nestin-positive cell population is increased. Hence, in vivo retinoid deficiency impaired neural stem cell growth. We propose that RA has separable functions in the developing spinal cord to (i) maintain high levels of FGF and Notch signaling and (ii) drive stem cell differentiation, thus restricting both the numbers and the pluripotent character of neural stem cells

Search for gravitational-lensing signatures in the full third observing run of the LIGO-Virgo network

Gravitational lensing by massive objects along the line of sight to the source causes distortions of gravitational wave-signals; such distortions may reveal information about fundamental physics, cosmology and astrophysics. In this work, we have extended the search for lensing signatures to all binary black hole events from the third observing run of the LIGO--Virgo network. We search for repeated signals from strong lensing by 1) performing targeted searches for subthreshold signals, 2) calculating the degree of overlap amongst the intrinsic parameters and sky location of pairs of signals, 3) comparing the similarities of the spectrograms amongst pairs of signals, and 4) performing dual-signal Bayesian analysis that takes into account selection effects and astrophysical knowledge. We also search for distortions to the gravitational waveform caused by 1) frequency-independent phase shifts in strongly lensed images, and 2) frequency-dependent modulation of the amplitude and phase due to point masses. None of these searches yields significant evidence for lensing. Finally, we use the non-detection of gravitational-wave lensing to constrain the lensing rate based on the latest merger-rate estimates and the fraction of dark matter composed of compact objects

Search for eccentric black hole coalescences during the third observing run of LIGO and Virgo

Despite the growing number of confident binary black hole coalescences observed through gravitational waves so far, the astrophysical origin of these binaries remains uncertain. Orbital eccentricity is one of the clearest tracers of binary formation channels. Identifying binary eccentricity, however, remains challenging due to the limited availability of gravitational waveforms that include effects of eccentricity. Here, we present observational results for a waveform-independent search sensitive to eccentric black hole coalescences, covering the third observing run (O3) of the LIGO and Virgo detectors. We identified no new high-significance candidates beyond those that were already identified with searches focusing on quasi-circular binaries. We determine the sensitivity of our search to high-mass (total mass M>70 M⊙) binaries covering eccentricities up to 0.3 at 15 Hz orbital frequency, and use this to compare model predictions to search results. Assuming all detections are indeed quasi-circular, for our fiducial population model, we place an upper limit for the merger rate density of high-mass binaries with eccentricities 0<e≤0.3 at 0.33 Gpc−3 yr−1 at 90\% confidence level

Ultralight vector dark matter search using data from the KAGRA O3GK run

Among the various candidates for dark matter (DM), ultralight vector DM can be probed by laser interferometric gravitational wave detectors through the measurement of oscillating length changes in the arm cavities. In this context, KAGRA has a unique feature due to differing compositions of its mirrors, enhancing the signal of vector DM in the length change in the auxiliary channels. Here we present the result of a search for U(1)B−L gauge boson DM using the KAGRA data from auxiliary length channels during the first joint observation run together with GEO600. By applying our search pipeline, which takes into account the stochastic nature of ultralight DM, upper bounds on the coupling strength between the U(1)B−L gauge boson and ordinary matter are obtained for a range of DM masses. While our constraints are less stringent than those derived from previous experiments, this study demonstrates the applicability of our method to the lower-mass vector DM search, which is made difficult in this measurement by the short observation time compared to the auto-correlation time scale of DM