Deterministic global optimization using space-filling curves and multiple estimates of Lipschitz and Holder constants

In this paper, the global optimization problem $\min_{y\in S} F(y)$ with $S$ being a hyperinterval in $\Re^N$ and $F(y)$ satisfying the Lipschitz condition with an unknown Lipschitz constant is considered. It is supposed that the function $F(y)$ can be multiextremal, non-differentiable, and given as a `black-box'. To attack the problem, a new global optimization algorithm based on the following two ideas is proposed and studied both theoretically and numerically. First, the new algorithm uses numerical approximations to space-filling curves to reduce the original Lipschitz multi-dimensional problem to a univariate one satisfying the H\"{o}lder condition. Second, the algorithm at each iteration applies a new geometric technique working with a number of possible H\"{o}lder constants chosen from a set of values varying from zero to infinity showing so that ideas introduced in a popular DIRECT method can be used in the H\"{o}lder global optimization. Convergence conditions of the resulting deterministic global optimization method are established. Numerical experiments carried out on several hundreds of test functions show quite a promising performance of the new algorithm in comparison with its direct competitors.Comment: 26 pages, 10 figures, 4 table

Effectiveness of the National Program of Complementary Feeding for older adults in Chile on vitamin B12 status in older adults; secondary outcome analysis from the CENEX Study (ISRCTN48153354).

BACKGROUND: Older people are at increased risk of vitamin B12 deficiency and the provision of fortified foods may be an effective way to ensure good vitamin B12 status in later life. AIM: To evaluate the effectiveness of a vitamin B12 fortified food provided by a national program of complementary food for older people on plasma vitamin B12 levels. SUBJECTS AND METHODS: A random sub-sample of 351 subjects aged 65-67 y from a large cluster randomised controlled trial provided blood samples at baseline and after 24 months of intervention. The intervention arm (10 clusters 186 participants) received a vitamin B12 fortified food designed to deliver 1.4 μg/day, while the control arm did not receive complementary food (10 clusters, 165 participants). Serum vitamin B12 and folate levels determined by radioimmunoassay were used to estimate the effect of intervention on vitamin B12 levels, adjusting for baseline levels and sex. RESULTS: Attrition at 24 months was 16.7% and 23.6% in the intervention and control arms respectively (p = 0.07). Over 24 months of intervention, mean (95% CI) serum vitamin B12 decreased from 392 (359-425) pmol/dL to 357 (300-414) pmol/dL (p < 0.07) in the intervention arm and from 395 (350-440) pmol/dL to 351 (308-395) pmol/dL in the control arm. There was no significant effect of the intervention on folate status. DISCUSSION: Our findings suggest that foods fortified with 1.4 μg/daily vitamin B12 as provided by Chile's national programme for older people are insufficient to ensure adequate vitamin B12 levels in this population. Chile has a long and successful experience with nutrition intervention programs; however, the country's changing demographic and nutritional profiles require a constant adjustment of the programs

Thermogravimetry and neutron thermodiffractometry studies of the H-YBa2Cu3O7 system.

The high Tc superconducting oxide YBa2Cu3O7¿x reacts with hydrogen gas. Thermogravimetric, X-ray and neutron scattering experiments allow us to propose a two-step type of hydrogen bonding. Firstly, a few hydrogen atoms fill some oxygen vacancies and may favourably modify the electron state, giving rise to a slight increase in the critical temperature. Secondly, after a prolonged heating period, the collapse of the YBa2Cu3O7¿x type framework and of superconductivity were observed, and a new, highly hydrogenated material appeared

Numerical methods using two different approximations of space-filling curves for black-box global optimization

In this paper, multi-dimensional global optimization problems are considered, where the objective function is supposed to be Lipschitz continuous, multiextremal, and without a known analytic expression. Two different approximations of Peano-Hilbert curve to reduce the problem to a univariate one satisfying the Hölder condition are dis- cussed. The first of them, piecewise-linear approximation, is broadly used in global optimization and not only whereas the second one, non- univalent approximation, is less known. Multi-dimensional geomet- ric algorithms employing these Peano curve approximations are intro- duced and their convergence conditions are established. Numerical experiments executed on 800 randomly generated test functions taken from the literature show a promising performance of algorithms em- ploying Peano curve approximations w.r.t. their direct competitors

Securing tropical forest carbon: the contribution of protected areas to REDD

Forest loss and degradation in the tropics contribute 6-17% of all greenhouse gas emissions. Protected areas cover 217.2 million ha (19.6%) of the world's humid tropical forests and contain c. 70.3 petagrams of carbon (Pg C) in biomass and soil to 1 m depth. Between 2000 and 2005, we estimate that 1.75 million ha of forest were lost from protected areas in humid tropical forests, causing the emission of 0.25-0.33 Pg C. Protected areas lost about half as much carbon as the same area of unprotected forest. We estimate that the reduction of these carbon emissions from ongoing deforestation in protected sites in humid tropical forests could be valued at USD 6,200-7,400 million depending on the land use after clearance. This is >1.5 times the estimated spending on protected area management in these regions. Improving management of protected areas to retain forest cover better may be an important, although certainly not sufficient, component of an overall strategy for reducing emissions from deforestation and forest degradation (REDD

The role of gender in the association between self-rated health and mortality among older adults in Santiago, Chile: A cohort study.

BACKGROUND: Previous studies on the role of gender in the association between self-rated health and mortality have shown contrasting results. This study was aimed to determine the importance of gender in the association between self-rated health and mortality among older people in Santiago, Chile. METHODS: A 10 year follow-up of 1066 people aged 60 or more, from the Chilean cohort of the Study of Health, Ageing and Well-Being. Self-rated health was assessed in face to face interviews through a single general question, along with socio-demographic and health status information. Cox proportional hazards and flexible parametric models for survival analyses were employed. RESULTS: By the end of follow-up, 30.7% of women and 39.4% of men died. Adjusted hazard ratio of poor self-rated health, compared to good self-rated health, was 1.92(95% CI 1.29-2.86). In models stratified by gender, an increased risk of mortality was observed among women who rated their health as poor (HR = 2.21, 95% CI 1.43-3.40), but not among men (HR = 1.04, 95% CI 0.58-1.86). Age was associated with mortality in both groups; for men, functional limitation and underweight were also risk factors and obesity was a protective factor. CONCLUSIONS: Compared to older women who rated their health as good, older women who rated their health as poor had a 2 fold increased risk of mortality over the subsequent 10 years. These findings stress the importance of considering a gender perspective into health programmes, including those focused on older people, in order to address the different elements that increase, on the long run, the risk of dying among older women and men

Analysis of the left-handed corrugated circular waveguide

Infinite circular corrugated waveguide is analysed to investigate its ability to support modes with backward wave behaviour. Such waveguides provide an alternative structure, easier to manufacture than those already reported based on rectangular symmetry with corrugated walls or filled with frequency selective surfaces. The corrugations if sufficiently deep provide a guiding structure with the required series capacitance and shunt inductance to allow left-handed propagation within some frequency bands. These backward waves are analysed using the surface impedance model of propagation in corrugated waveguides to predict their properties. Interpreting the physical meaning of the analysis, the authors discuss how backward waves are related to resonances in corrugated structures. The relationship between power flows in the guide and the behaviour of the group velocity for such guides is shown. A full wave simulator is also applied to validate these results and the case of a dielectric filled waveguide is considered showing the improved ability to support left-handed modes. The authors present the results of a parametric study of how left-handed propagation depends on the corrugation depth. Potential applications of backward waves in corrugated circular waveguides are proposed