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In the present work we apply an augmented Lagrange method to solve pointwise state constrained elliptic optimal control problems. We prove strong convergence of the primal variables as well as weak convergence of the adjoint states and weak-* convergence of the multipliers associated to the state constraint. In addition, we show that the sequence of generated penalty parameters is bounded only in exceptional situations, which is different from classical results in finite-dimensional optimization. In addition, numerical results are presented.

In this paper we apply an augmented Lagrange method to a class of semilinear elliptic optimal control problems with pointwise state constraints. We show strong convergence of subsequences of the primal variables to a local solution of the original problem as well as weak convergence of the adjoint states and weak-* convergence of the multipliers associated to the state constraint. Moreover, we show existence of stationary points in arbitrary small neighborhoods of local solutions of the original problem. Additionally, various numerical results are presented.

In this article we consider a special class of Nash equilibrium problems that cannot be reduced to a single player control problem. Problems of this type can be solved by a semi-smooth Newton method. Applying results from the established convergence analysis we derive superlinear convergence for the associated Newton method and the equivalent active-set method. We also provide detailed finite element discretizations for both methods. Several numerical examples are presented to support the theoretical findings.

We provide a modified augmented Lagrange method coupled with a Tikhonov regularization for solving ill-posed state-constrained elliptic optimal control problems with sparse controls. We consider a linear quadratic optimal control problem without any additional \\(L^2\\) regularization terms. The sparsity is guaranteed by an additional \\(L^1\\) term. Here, the modification of the classical augmented Lagrange method guarantees us uniform boundedness of the multiplier that corresponds to the state constraints. We present a coupling between the regularization parameter introduced by the Tikhonov regularization and the penalty parameter from the augmented Lagrange method, which allows us to prove strong convergence of the controls and their corresponding states. Moreover convergence results proving the weak convergence of the adjoint state and weak*-convergence of the multiplier are provided. Finally, we demonstrate our method in several numerical examples.

In this paper we apply an augmented Lagrange method to a class of semilinear elliptic optimal control problems with pointwise state constraints. We show strong convergence of subsequences of the primal variables to a local solution of the original problem as well as weak convergence of the adjoint states and weak* convergence of the multipliers associated to the state constraint. Moreover, we show existence of stationary points in arbitrary small neighborhoods of local solutions of the original problem. Additionally, various numerical results are presented.

This letter indicates that there is long-lasting skeletal accumulation of bisphosphonate, and ongoing use appears to be the dominant risk factor for rare fractures. To the Editor: Bisphosphonates prevent clinical fractures in women younger than 80 years of age with documented osteoporosis, according to efficacy trials. 1 , 2 However, adverse events related to these agents may affect all patients, including those in groups in which the benefit of these drugs is less well established. We previously found a strong association between bisphosphonate use and atypical fractures in Swedish women. 3 That study of data from 2008 has now been extended to include the period of 2008 through 2010 to investigate the association of potential adverse events with sex, type of bisphosphonate, and timing of use. We . . .

Urbanization can have marked effects on plant and animal populations’ phenology, population size, predator–prey, interactions and reproductive success. These aspects are rarely studied simultaneously in a single system, and some are rarely investigated, e.g., how insect phenology responds to urban development. Here, we study a tri-trophic system of trees, phytophagous insects (caterpillars), and insectivorous birds (Great Tits) to assess how urbanization influences (1) the phenology of each component of this system, (2) insect abundance, and (3) avian reproductive success. We use data from two urban and two forest sites in Hungary, central Europe, collected over four consecutive years. Despite a trend of earlier leaf emergence in urban sites, there is no evidence for an earlier peak in caterpillar abundance. Thus, contrary to the frequently stated prediction in the literature, the earlier breeding of urban bird populations is not associated with an earlier peak in caterpillar availability. Despite this the seasonal dynamics of caterpillar biomass exhibited striking differences between habitat types with a single clear peak in forests, and several much smaller peaks in urban sites. Caterpillar biomass was higher in forests than urban areas across the entire sampling period, and between 8.5 and 24 times higher during the first brood’s chick-rearing period. This higher biomass was not associated with taller trees in forest sites, or with tree species identity, and occurred despite most of our focal trees being native to the study area. Urban Great Tits laid smaller clutches, experienced more frequent nestling mortality from starvation, reared fewer offspring to fledging age, and their fledglings had lower body mass. Our study strongly indicates that food limitation is responsible for lower avian reproductive success in cities, which is driven by reduced availability of the preferred nestling diet, i.e., caterpillars, rather than phenological shifts in the timing of peak food availability.

This study aimed to assess the correlation of temporal muscle thickness (TMT), measured on routine cranial magnetic resonance (MR) images, with lumbar skeletal muscles obtained on computed tomography (CT) images in brain metastasis patients to establish a new parameter estimating skeletal muscle mass on brain MR images. We retrospectively analyzed the cross-sectional area (CSA) of skeletal muscles at the level of the third lumbar vertebra on computed tomography scans and correlated these values with TMT on MR images of the brain in two independent cohorts of 93 lung cancer and 61 melanoma patients (overall: 154 patients) with brain metastases. Pearson correlation revealed a strong association between mean TMT and CSA in lung cancer and melanoma patients with brain metastases (0.733; p<0.001). The two study cohorts did not differ significantly in patient characteristics, including age (p = 0.661), weight (p = 0.787), and height (p = 0.123). However, TMT and CSA measures differed significantly between male and female patients in both lung cancer and melanoma patients with brain metastases (p<0.001). Our data indicate that TMT, measured on routine cranial MR images, is a useful surrogate parameter for the estimation of skeletal muscle mass in patients with brain metastases. Thus, TMT may be useful for prognostic assessment, treatment considerations, and stratification or a selection factor for clinical trials in patients with brain metastases. Further studies are needed to assess the association between TMT and clinical frailty parameters, and the usefulness of TMT in patients with primary brain tumors.

Global increases in population, consumption, and gross domestic product raise concerns about the sustainability of the current and future use of natural resources. The human appropriation of net primary production (HANPP) provides a useful measure of human intervention into the biosphere. The productive capacity of land is appropriated by harvesting or burning biomass and by converting natural ecosystems to managed lands with lower productivity. This work analyzes trends in HANPP from 1910 to 2005 and finds that although human population has grown fourfold and economic output 17-fold, global HANPP has only doubled. Despite this increase in efficiency, HANPP has still risen from 6.9 Gt of carbon per y in 1910 to 14.8 GtC/y in 2005, i.e., from 13% to 25% of the net primary production of potential vegetation. Biomass harvested per capita and year has slightly declined despite growth in consumption because of a decline in reliance on bioenergy and higher conversion efficiencies of primary biomass to products. The rise in efficiency is overwhelmingly due to increased crop yields, albeit frequently associated with substantial ecological costs, such as fossil energy inputs, soil degradation, and biodiversity loss. If humans can maintain the past trend lines in efficiency gains, we estimate that HANPP might only grow to 27–29% by 2050, but providing large amounts of bioenergy could increase global HANPP to 44%. This result calls for caution in refocusing the energy economy on land-based resources and for strategies that foster the continuation of increases in land-use efficiency without excessively increasing ecological costs of intensification.

The micropylar endosperm cap covering the radicle in the mature seeds of most angiosperms acts as a constraint that regulates seed germination. Here, we report on a comparative seed biology study with the close Brassicaceae relatives Lepidium sativum and Arabidopsis thaliana showing that ethylene biosynthesis and signaling regulate seed germination by a mechanism that requires the coordinated action of the radicle and the endosperm cap. The larger seed size of Lepidium allows direct tissue-specific biomechanical, biochemical, and transcriptome analyses. We show that ethylene promotes endosperm cap weakening of Lepidium and endosperm rupture of both species and that it counteracts the inhibitory action of abscisic acid (ABA) on these two processes. Cross-species microarrays of the Lepidium micropylar endosperm cap and the radicle show that the ethylene-ABA antagonism involves both tissues and has the micropylar endosperm cap as a major target. Ethylene counteracts the ABA-induced inhibition without affecting seed ABA levels. The Arabidopsis loss-of-function mutants ACC oxidase2 (aco2; ethylene biosynthesis) and constitutive triple response1 (ethylene signaling) are impaired in the 1-aminocyclopropane-1-carboxylic acid (ACC)-mediated reversion of the ABA-induced inhibition of seed germination. Ethylene production by the ACC oxidase orthologs Lepidium ACO2 and Arabidopsis ACO2 appears to be a key regulatory step. Endosperm cap weakening and rupture are promoted by ethylene and inhibited by ABA to regulate germination in a process conserved across the Brassicaceae.