Scalar Representation and Conjugation of Set-Valued Functions

To a function with values in the power set of a pre-ordered, separated locally convex space a family of scalarizations is given which completely characterizes the original function. A concept of a Legendre-Fenchel conjugate for set-valued functions is introduced and identified with the conjugates of the scalarizations. Using this conjugate, weak and strong duality results are proven.Comment: arXiv admin note: substantial text overlap with arXiv:1012.435

Set-optimization meets variational inequalities

We study necessary and sufficient conditions to attain solutions of set-optimization problems in therms of variational inequalities of Stampacchia and Minty type. The notion of a solution we deal with has been introduced Heyde and Loehne, for convex set-valued objective functions. To define the set-valued variational inequality, we introduce a set-valued directional derivative and we relate it to the Dini derivatives of a family of linearly scalarized problems. The optimality conditions are given by Stampacchia and Minty type Variational inequalities, defined both by the set valued directional derivative and by the Dini derivatives of the scalarizations. The main results allow to obtain known variational characterizations for vector valued optimization problems

Set optimization - a rather short introduction

Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for set- and vector-valued functions, and duality for set optimization problems. Extensive sections with bibliographical comments summarize the state of the art. Applications to vector optimization and financial risk measures are discussed along with algorithmic approaches to set optimization problems

Foot kinematics in patients with two patterns of pathological plantar hyperkeratosis

Background: The Root paradigm of foot function continues to underpin the majority of clinical foot biomechanics practice and foot orthotic therapy. There are great number of assumptions in this popular paradigm, most of which have not been thoroughly tested. One component supposes that patterns of plantar pressure and associated hyperkeratosis lesions should be associated with distinct rearfoot, mid foot, first metatarsal and hallux kinematic patterns. Our aim was to investigate the extent to which this was true. Methods: Twenty-seven subjects with planter pathological hyperkeratosis were recruited into one of two groups. Group 1 displayed pathological plantar hyperkeratosis only under metatarsal heads 2, 3 and 4 (n = 14). Group 2 displayed pathological plantar hyperkeratosis only under the 1st and 5th metatarsal heads (n = 13). Foot kinematics were measured using reflective markers on the leg, heel, midfoot, first metatarsal and hallux. Results: The kinematic data failed to identify distinct differences between these two groups of subjects, however there were several subtle (generally <3°) differences in kinematic data between these groups. Group 1 displayed a less everted heel, a less abducted heel and a more plantarflexed heel compared to group 2, which is contrary to the Root paradigm. Conclusions: There was some evidence of small differences between planter pathological hyperkeratosis groups. Nevertheless, there was too much similarity between the kinematic data displayed in each group to classify them as distinct foot types as the current clinical paradigm proposes

Complexity absorption : A processual strategic approach to corporate entrepreneurship strategy

The author Haina Zhang acknowledges the support of research grant received from the Lancaster University Research Committee (award reference: SGS21/33). The author is also grateful to Professor David Brown for his suggestions on earlier version of this paper.Peer reviewedPublisher PD

Clearance of interstitial fluid (ISF) and CSF (CLIC) group-part of Vascular Professional Interest Area (PIA): Cerebrovascular disease and the failure of elimination of Amyloid-β from the brain and retina with age and Alzheimer's disease-Opportunities for Therapy.

Two of the key functions of arteries in the brain are (1) the well-recognized supply of blood via the vascular lumen and (2) the emerging role for the arterial walls as routes for the elimination of interstitial fluid (ISF) and soluble metabolites, such as amyloid beta (Aβ), from the brain and retina. As the brain and retina possess no conventional lymphatic vessels, fluid drainage toward peripheral lymph nodes is mediated via transport along basement membranes in the walls of capillaries and arteries that form the intramural peri-arterial drainage (IPAD) system. IPAD tends to fail as arteries age but the mechanisms underlying the failure are unclear. In some people this is reflected in the accumulation of Aβ plaques in the brain in Alzheimer's disease (AD) and deposition of Aβ within artery walls as cerebral amyloid angiopathy (CAA). Knowledge of the dynamics of IPAD and why it fails with age is essential for establishing diagnostic tests for the early stages of the disease and for devising therapies that promote the clearance of Aβ in the prevention and treatment of AD and CAA. This editorial is intended to introduce the rationale that has led to the establishment of the Clearance of Interstitial Fluid (ISF) and CSF (CLIC) group, within the Vascular Professional Interest Area of the Alzheimer's Association International Society to Advance Alzheimer's Research and Treatment

Development of a multiplexed bead-based immunoassay for the simultaneous detection of antibodies to 17 pneumococcal proteins

Presently, several pneumococcal proteins are being evaluated as potential vaccine candidates. Here, we gather novel insights in the immunogenicity of PLY, PsaA, PspA, PspC, NanA, Hyl, PpmA, SlrA, Eno, IgA1-protease, PdBD, BVH-3, SP1003, SP1633, SP1651, SP0189 and SP0376. We developed a multiplex bead-based immunoassay (xMAP® Technology, Luminex Corporation) to simultaneously quantify antibodies against these 17 pneumococcal proteins in serum. The median fluorescence intensity (MFI) values obtained for human pooled serum with the multiplex assay were between 82% and 111% (median 94%) of those obtained with the singleplex assays. For IgG, the coefficient of variation (CV) in serum ranged from 2% to 9%, for IgA, the CV ranged from 3% to 14% and for IgM, the CV ranged from 11% to 15%. Using this immunoassay, we showed that anti-pneumococcal antibody levels exhibited extensive inter-individual variability in young children suffering from invasive pneumococcal disease. All proteins, including the proteins with, as yet, unknown function, were immunogenic. In conclusion, the multiplex Streptococcus pneumoniae immunoassay based on proteins is reproducible. This assay can be used to monitor anti-S. pneumoniae antibody responses in a material- and time-saving manner

The Islamic Law in the Historical Study

Dalam kajian tentang sejarah awal Islam dan agama di dunia Barat, Islam dipandang sebagai agama \u27\u27dalam sejarab". Melaiui pandangan ini, para sarjana mempelajari sejarah awal Islam, di antaranya, dengan menggunakan meiode analisa kritik terbadap sumber-sumber sejarah termasuk kepusiakaan selain Islam dijadikan sebagai sumber dan bukti sejarah. Sejak itu pula hukum Islam dikaji melaiui pendekatan yang sama. Melaiui pendekatan ini diyakini bahwa hukum Islam mengandung tradisi-tradisi keagamaan khususnya di wilayab limur dekat yang ada sebeium Islam, dan dipandang sebagai suatu perkembangan yang berkelanjutan. Sebagaimana hasii kajian daripada Patricia Crone dan Gordon D. Newby menunjukkan bahwa di antara tradisi-tradisi keagamaan dimaksud, saiah satunya, adalab hukum Yahudi. Crone memberikan contoh qasama khususnya yang ada pada mazhab Maiiki dan mengktaim bahwa qasama dimaksud merupakan salah satu tradisi hukum yang ada pada orang-orang Yahudi. Sedangkan Newby memberikan contoh tentang penentuan orang band sebagai laki-iaki atau sebagai perempuan dalam hubungannya dengan pembagian kewarisan yang ada pada catatan \u27Amirb. Zarib di daiam sirah Ibnu Ishaq, dan mengktaim juga bahwa catatan tersebut berasai dari hukum Yahudi. Sebaliknya, pendekatan ini merupakan salah satu pendekatan yang ada dalam kajian hukum Islam dan sangat baik dipakai untuk mencari keseimhangan dan menunjukkan bahwa walaupun terdapat kesamaan antara hukum Islam dengan hukum-hukum yang lain, proses sejarab perkembangan hukum Islam itu sendiri sangat berbeda dan mempunyai karakteryang khusu