The Radius of Metric Subregularity

There is a basic paradigm, called here the radius of well-posedness, which quantifies the "distance" from a given well-posed problem to the set of ill-posed problems of the same kind. In variational analysis, well-posedness is often understood as a regularity property, which is usually employed to measure the effect of perturbations and approximations of a problem on its solutions. In this paper we focus on evaluating the radius of the property of metric subregularity which, in contrast to its siblings, metric regularity, strong regularity and strong subregularity, exhibits a more complicated behavior under various perturbations. We consider three kinds of perturbations: by Lipschitz continuous functions, by semismooth functions, and by smooth functions, obtaining different expressions/bounds for the radius of subregularity, which involve generalized derivatives of set-valued mappings. We also obtain different expressions when using either Frobenius or Euclidean norm to measure the radius. As an application, we evaluate the radius of subregularity of a general constraint system. Examples illustrate the theoretical findings.Comment: 20 page

Constraints on Nucleon Decay via "Invisible" Modes from the Sudbury Neutrino Observatory

Data from the Sudbury Neutrino Observatory have been used to constrain the lifetime for nucleon decay to ``invisible'' modes, such as n -> 3 nu. The analysis was based on a search for gamma-rays from the de-excitation of the residual nucleus that would result from the disappearance of either a proton or neutron from O16. A limit of tau_inv > 2 x 10^{29} years is obtained at 90% confidence for either neutron or proton decay modes. This is about an order of magnitude more stringent than previous constraints on invisible proton decay modes and 400 times more stringent than similar neutron modes.Comment: Update includes missing efficiency factor (limits change by factor of 2) Submitted to Physical Review Letter

Electron Antineutrino Search at the Sudbury Neutrino Observatory

Upper limits on the \nuebar flux at the Sudbury Neutrino Observatory have been set based on the \nuebar charged-current reaction on deuterium. The reaction produces a positron and two neutrons in coincidence. This distinctive signature allows a search with very low background for \nuebar's from the Sun and other potential sources. Both differential and integral limits on the \nuebar flux have been placed in the energy range from 4 -- 14.8 MeV. For an energy-independent \nu_e --> \nuebar conversion mechanism, the integral limit on the flux of solar \nuebar's in the energy range from 4 -- 14.8 MeV is found to be \Phi_\nuebar <= 3.4 x 10^4 cm^{-2} s^{-1} (90% C.L.), which corresponds to 0.81% of the standard solar model 8B \nu_e flux of 5.05 x 10^6 cm^{-2} s^{-1}, and is consistent with the more sensitive limit from KamLAND in the 8.3 -- 14.8 MeV range of 3.7 x 10^2 cm^{-2} s^{-1} (90% C.L.). In the energy range from 4 -- 8 MeV, a search for \nuebar's is conducted using coincidences in which only the two neutrons are detected. Assuming a \nuebar spectrum for the neutron induced fission of naturally occurring elements, a flux limit of Phi_\nuebar <= 2.0 x 10^6 cm^{-2} s^{-1}(90% C.L.) is obtained.Comment: submitted to Phys. Rev.

Postprandial Insulin and Triglyceride Concentrations Are Suppressed in Response to Breaking Up Prolonged Sitting in Qatari Females

Funding for this study was received from Qatar University Centre for Health Sciences SEED interdisciplinary grant (CHSS-SF-16-2). The publication of this article was funded by the Qatar National Library

EFSA Panel on Dietetic Products, Nutrition and Allergies (NDA); Scientific Opinion on Dietary Reference Values for energy

Following a request from the European Commission, the Panel on Dietetic Products, Nutrition and Allergies (NDA) derived dietary reference values for energy, which are provided as average requirements (ARs) of specified age and sex groups. For children and adults, total energy expenditure (TEE) was determined factorially from estimates of resting energy expenditure (REE) plus the energy needed for various levels of physical activity (PAL) associated with sustainable lifestyles in healthy individuals. To account for uncertainties inherent in the prediction of energy expenditure, ranges of the AR for energy were calculated with several equations for predicting REE in children (1-17 years) and adults. For practical reasons, only the REE estimated by the equations of Henry (2005) was used in the setting of the AR and multiplied with PAL values of 1.4, 1.6, 1.8 and 2.0, which approximately reflect low active (sedentary), moderately active, active and very active lifestyles. For estimating REE in adults, body heights measured in representative national surveys in 13 EU Member States and body masses calculated from heights assuming a body mass index of 22 kg/m2 were used. For children, median body masses and heights from the WHO Growth Standards or from harmonised growth curves of children in the EU were used. Energy expenditure for growth was accounted for by a 1 % increase of PAL values for each age group. For infants (7-11 months), the AR was derived from TEE estimated by regression equation based on doubly labelled water (DLW) data, plus the energy needs for growth. For pregnant and lactating women, the additional energy for the deposition of newly formed tissue, and for milk output, was derived from data obtained by the DLW method and from factorial estimates, respectively. The proposed ARs for energy may need to be adapted depending on specific objectives and target populations

Enhancing Abiotic Stress Tolerance in Cereals Through Breeding and Transgenic Interventions

The success of plant breeding in the 20th century led to new cultivars that, to date, have provided enough food for an increasing world population (Conway and Toenniessen 1999; Mifflin 2000). The results of the Green Revolution-led in the 1960s by Henry M. Beachell andNormanE. Dotlaug—resulted in a dramatic increase in rice and wheal grain yields (Milford and Runge 2007; Ortiz et al. 2007). However, abiotic stresses and climate change are becoming increasingly serious threats to crop production worldwide at a time when food staple supply will need to be significantly higher to meet the demand of the growing human population. Water scarcity (Rockstrom et al. 2007], salinity (Rengasamy 2006). and low soil fertility (Sanchez and Swaminathan 2005) rank among the moat important abiotic stresses worldwide. Similarly, increased climatic disturbances due to global warming are causing the major stresses that necessitate crop improvements to safeguard grain supply, particularly in the developing world (Kumar 2006). Hence, genetic enhancement of cereal crops with respect to abiotic stress tolerance will be essential far ensuring grain yields in water-limited, increasingly hotter agricultural zones, particularly If these conditions combine with poor and saline soils, conditions that prevail in parts of the developing world. Crop breeding for adaptation to abiotic stress-prone environments remains a challenging task, not least because of the complexity of the stress-adaptive mechanisms in plants and particularly cereal crops, which are the staple of most of the world's population (Reynolds et al. 2005}