Solving ill-posed bilevel programs

This paper deals with ill-posed bilevel programs, i.e., problems admitting multiple lower-level solutions for some upper-level parameters. Many publications have been devoted to the standard optimistic case of this problem, where the difficulty is essentially moved from the objective function to the feasible set. This new problem is simpler but there is no guaranty to obtain local optimal solutions for the original optimistic problem by this process. Considering the intrinsic non-convexity of bilevel programs, computing local optimal solutions is the best one can hope to get in most cases. To achieve this goal, we start by establishing an equivalence between the original optimistic problem an a certain set-valued optimization problem. Next, we develop optimality conditions for the latter problem and show that they generalize all the results currently known in the literature on optimistic bilevel optimization. Our approach is then extended to multiobjective bilevel optimization, and completely new results are derived for problems with vector-valued upper- and lower-level objective functions. Numerical implementations of the results of this paper are provided on some examples, in order to demonstrate how the original optimistic problem can be solved in practice, by means of a special set-valued optimization problem

Differential wedging of vertebral body and intervertebral disc in thoracic and lumbar spine in adolescent idiopathic scoliosis – A cross sectional study in 150 patients

<p>Abstract</p> <p>Background</p> <p>Hueter-Volkmann's law regarding growth modulation suggests that increased pressure on the end plate of bone retards the growth (Hueter) and conversely, reduced pressure accelerates the growth (Volkmann). Literature described the same principle in Rat-tail model. Human spine and its deformity i.e. scoliosis has also same kind of pattern during the growth period which causes wedging in disc or vertebral body.</p> <p>Methods</p> <p>This cross sectional study in 150 patients of adolescent idiopathic scoliosis was done to evaluate vertebral body and disc wedging in scoliosis and to compare the extent of differential wedging of body and disc, in thoracic and lumbar area. We measured wedging of vertebral bodies and discs, along with two adjacent vertebrae and disc, above and below the apex and evaluated them according to severity of curve (curve < 30° and curve > 30°) to find the relationship of vertebral body or disc wedging with scoliosis in thoracic and lumbar spine. We also compared the wedging and rotations of vertebrae.</p> <p>Results</p> <p>In both thoracic and lumbar curves, we found that greater the degree of scoliosis, greater the wedging in both disc and body and the degree of wedging was more at apex supporting the theory of growth retardation in stress concentration area. However, the degree of wedging in vertebral body is more than the disc in thoracic spine while the wedging was more in disc than body in lumbar spine. On comparing the wedging with the rotation, we did not find any significant relationship suggesting that it has no relation with rotation.</p> <p>Conclusion</p> <p>From our study, we can conclude that wedging in disc and body are increasing with progression on scoliosis and maximum at apex; however there is differential wedging of body and disc, in thoracic and lumbar area, that is vertebral body wedging is more profound in thoracic area while disc wedging is more profound in lumbar area which possibly form 'vicious cycle' by asymmetric loading to spine for the progression of curve.</p

Descent algorithm for nonsmooth stochastic multiobjective optimization

International audienceAn algorithm for solving the expectation formulation of stochastic nonsmooth multiobjective optimization problems is proposed. The proposed method is an extension of the classical stochastic gradient algorithm to multi-objective optimization using the properties of a common descent vector defined 10 in the deterministic context. The mean square and the almost sure convergence of the algorithm are proven. The algorithm efficiency is illustrated and assessed on an academic example

Synthesis and propagation of complement C3 by microglia/monocytes in the aging retina

INTRODUCTION Complement activation is thought to contribute to the pathogenesis of age-related macular degeneration (AMD), which may be mediated in part by para-inflammatory processes. We aimed to investigate the expression and localization of C3, a crucial component of the complement system, in the retina during the course of aging. METHODS SD rats were born and reared in low-light conditions, and euthanized at post-natal (P) days 100, 450, or 750. Expression of C3, IBA1, and Ccl- and Cxcl- chemokines was assessed by qPCR, and in situ hybridization. Thickness of the ONL was assessed in retinal sections as a measure of photoreceptor loss, and counts were made of C3-expressing monocytes. RESULTS C3 expression increased significantly at P750, and correlated with thinning of the ONL, at P750, and up-regulation of GFAP. In situ hybridization showed that C3 was expressed by microglia/monocytes, mainly from within the retinal vasculature, and occasionally the ONL. The number of C3-expressing microglia increased significantly by P750, and coincided spatiotemporally with thinning of the ONL, and up-regulation of Ccl- and Cxcl- chemokines. CONCLUSIONS Our data suggest that recruited microglia/monocytes contribute to activation of complement in the aging retina, through local expression of C3 mRNA. C3 expression coincides with age-related thinning of the ONL at P750, although it is unclear whether the C3-expressing monocytes are a cause or consequence. These findings provide evidence of activation of complement during natural aging, and may have relevance to cellular events underling the pathogenesis of age-related retinal diseases.Funding provided by Australian Research Council Centres of Excellence Program Grant (CE0561903)

The Disk Wind in the Young Binaries and the Origin of the Cyclic Activity of Young Stars

We present results of numerical modeling of the cyclic brightness modulation in the young binary systems with the eccentric orbits and low-mass secondary components. Brightness variations of the primary is due to the periodical extinction variations on the line-of-sight caused by the disk wind of the secondary and a common envelope it produces. A matter distribution in the envelope has been calculated in the ballistic approach. Calculations showed that for the young binaries with the elliptic orbits parameters of the photometric minima (their depth, duration and the shape of light curves) depend not only on the disk wind parameters and an inclination of the binary orbit to the line-of-sight but also on the longitude of the periastron. A modulation of the scattered radiation of the common envelope with a phase of the orbital period has been investigated in the single scattering approach. It is shown that an amplitude of the modulation is maximal when the system is seen edge-on and has also a non-zero value in the binaries observed pole-on. Possible applications of the theory to the young stellar objects are discussed. In particular, an attention is payed to a resemblance of the light curves in some models with light curves of the objects suspected as candidates to FUORs.Comment: 18 pages, 9 figures, accepted by Astronomy Letter

Multivariate analyses for biomarkers hunting and validation through on-tissue bottom-up or in-source decay in MALDI-MSI: application to prostate cancer.

peer reviewe

Structural Integration in Language and Music: Evidence for a Shared System.

In this study, we investigate whether language and music share cognitive resources for structural processing. We report an experiment that used sung materials and manipulated linguistic complexity (subject-extracted relative clauses, object-extracted relative clauses) and musical complexity (in-key critical note, out-of-key critical note, auditory anomaly on the critical note involving a loudness increase). The auditory-anomaly manipulation was included in order to test whether the difference between in-key and out-of-key conditions might be due to any salient, unexpected acoustic event. The critical dependent measure involved comprehension accuracies to questions about the propositional content of the sentences asked at the end of each trial. The results revealed an interaction between linguistic and musical complexity such that the difference between the subject- and object-extracted relative clause conditions was larger in the out-of-key condition than in the in-key and auditory-anomaly conditions. These results provide evidence for an overlap in structural processing between language and music