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

Appendiceal Mucocele in an Elderly Patient: How Much Surgery?

Appendiceal mucoceles are rare cystic lesions with an incidence of 0.3–0.7% of all appendectomies. They are divided into four subgroups according to their histology. Even though the symptoms may vary – depending on the level of complication – from right lower quadrant pain, signs of intussusception, gastrointestinal bleeding to an acute abdomen with sepsis, most mucoceles are asymptomatic and found incidentally. We present the case of a 70-year-old patient with an incidentally found appendiceal mucocele. He was seen at the hospital for backache. The CT scan showed a vertebral fracture and a 7-cm appendiceal mass. A preoperative colonoscopy displayed several synchronous adenomas in the transverse and left colon with high-grade dysplasia. In order to lower the cancer risk of this patient, we performed a subtotal colectomy. The appendiceal mass showed no histopathological evidence of malignancy and no sign of perforation. The follow-up was therefore limited to 2 months. In this case, appendectomy would have been sufficient to treat the mucocele alone. The synchronous high-grade dysplastic adenomas were detected in the preoperative colonoscopy and determined the therapeutic approach. Generally, in the presence of positive lymph nodes, a right colectomy is the treatment of choice. In the histological presence of mucinous peritoneal carcinomatosis, cytoreductive surgery with hyperthermic intraperitoneal chemotherapy is indicated. In conclusion, mucoceles of the appendix are detected with high sensitivity by CT scan. If there is no evidence of synchronous tumor preoperatively and no peritoneal spillage, invasion or positive sentinel lymph nodes during surgery, a mucocele is adequately treated by appendectomy

Differentiation of Recently Infarcted Myocardium from Chronic Myocardial Scar: The Value of Contrast-Enhanced SSFP-Based Cine MR Imaging

The purpose of this study is to demonstrate whether the signal intensity (SI) of myocardial infarction (MI) on contrast enhanced (CE)-cine MRI is useful for differentiating recently infarcted myocardium from chronic scar. This study included 24 patients with acute MI (36-84 years, mean age: 57) and 19 patients with chronic MI (44-80 years, mean age: 64). The diagnosis of acute MI was based on the presence of typical symptoms, i.e. elevation of the cardiac enzymes and the absence of any remote infarction history. The diagnosis of chronic MI was based on a history of MI or coronary artery disease of more than one month duration and on the absence of any recent MI within the previous six months. Retrospectively, the ECG-gated breath-hold cine imaging was performed in the short axis plane using a segmented, balanced, turbo-field, echo-pulse sequence two minutes after the administration of Gd-DTPA at a dose of 0.2 mmol/kg body weight. Delayed contrast-enhanced MRI (DCE MRI) in the same plane was performed 10 to 15 minutes after contrast administration, and this was served as the gold standard of reference. The SI of the infarcted myocardium on the CE-cine MRI was compared with that of the normal myocardium on the same image. The area of abnormal SI on the CE-cine MRI was compared with the area of hyperenhancement on the DCE MRI. The area of high SI on the CE-cine MRI was detected in 23 of 24 patients with acute MI (10 with homogenous high SI, 13 high SI with subendocardial low SI, and one with iso SI). The area of high SI on the CE-cine MRI was larger than that seen on the DCE MRI (p < 0.05). In contrast, the areas of chronic MI were seen as iso-SI with thin subendocardial low SI on the CE-cine MR in all the chronic MI patients. The presence of high SI on both the CE-cine MRI and the DCE MRI is more sensitive (95.8%) for determining the age of a MI than the presence of myocardial thinning (66.7%). This study showed the different SI patterns between recently infarcted myocardium and chronic scar on the CE-cine MRI. CE-cine MRI is thought to be quite useful for determining the age of myocardial infarction, in addition to its utility for assessing myocardial contractility

Quantitative X-ray Tomography of the Mouse Cochlea

Imaging with hard X-rays allows visualizing cochlear structures while maintaining intrinsic qualities of the tissue, including structure and size. With coherent X-rays, soft tissues, including membranes, can be imaged as well as cells making use of the so-called in-line phase contrast. In the present experiments, partially coherent synchrotron radiation has been used for micro-tomography. Three-dimensional reconstructions of the mouse cochlea have been created using the EM3D software and the volume has been segmented in the Amira Software Suite. The structures that have been reconstructed include scala tympani, scala media, scala vestibuli, Reissner's membrane, basilar membrane, tectorial membrane, organ of Corti, spiral limbus, spiral ganglion and cochlear nerve. Cross-sectional areas of the scalae were measured. The results provide a realistic and quantitative reconstruction of the cochlea

Resolution of Ultramicroscopy and Field of View Analysis

In a recent publication we described a microscopical technique called Ultramicroscopy, combined with a histological procedure that makes biological samples transparent. With this combination we can gather three-dimensional image data of large biological samples. Here we present the theoretical analysis of the z-resolution. By analyzing the cross-section of the illuminating sheet of light we derive resolution values according to the Rayleigh-criterion. Next we investigate the resolution adjacent to the focal point of the illumination beam, analyze throughout what extend the illumination beam is of acceptable sharpness and investigate the resolution improvements caused by the objective lens. Finally we conclude with a useful rule for the sampling rates. These findings are of practical importance for researchers working with Ultramicroscopy to decide on adequate sampling rates. They are also necessary to modify deconvolution techniques to gain further image improvements

Global nuts and local mangoes: a critical reading of the UNDP Growing Sustainable Business Initiative in Kenya

This article provides a conceptual and empirical assessment of UN brokered partnerships that seek to deepen or create inclusive and sustainable agricultural supply chains in sub-Saharan Africa. More specifically it appraises the decision-making mechanisms, processes of partnership brokerage and project implementation within the UNDP Growing Sustainable Business Initiative (GSB) in Kenya. The paper argues that the lack of bottom-up participation in decision-making mechanisms and the predominantly economic imperatives driving the GSB partnership projects have failed to reach out to the partnerships’ intended beneficiaries—Kenyan small producers of nuts and mangoes. In conclusion it is suggested that opening up the GSB platform might hold the promise of reconciling sustainable business models with (some) poverty reduction

Properties of Graphene: A Theoretical Perspective

In this review, we provide an in-depth description of the physics of monolayer and bilayer graphene from a theorist's perspective. We discuss the physical properties of graphene in an external magnetic field, reflecting the chiral nature of the quasiparticles near the Dirac point with a Landau level at zero energy. We address the unique integer quantum Hall effects, the role of electron correlations, and the recent observation of the fractional quantum Hall effect in the monolayer graphene. The quantum Hall effect in bilayer graphene is fundamentally different from that of a monolayer, reflecting the unique band structure of this system. The theory of transport in the absence of an external magnetic field is discussed in detail, along with the role of disorder studied in various theoretical models. We highlight the differences and similarities between monolayer and bilayer graphene, and focus on thermodynamic properties such as the compressibility, the plasmon spectra, the weak localization correction, quantum Hall effect, and optical properties. Confinement of electrons in graphene is nontrivial due to Klein tunneling. We review various theoretical and experimental studies of quantum confined structures made from graphene. The band structure of graphene nanoribbons and the role of the sublattice symmetry, edge geometry and the size of the nanoribbon on the electronic and magnetic properties are very active areas of research, and a detailed review of these topics is presented. Also, the effects of substrate interactions, adsorbed atoms, lattice defects and doping on the band structure of finite-sized graphene systems are discussed. We also include a brief description of graphane -- gapped material obtained from graphene by attaching hydrogen atoms to each carbon atom in the lattice.Comment: 189 pages. submitted in Advances in Physic