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

Mechanisms of organelle division and inheritance and their implications regarding the origin of eukaryotic cells

Mitochondria and plastids have their own DNAs and are regarded as descendants of endosymbiotic prokaryotes. Organellar DNAs are not naked in vivo but are associated with basic proteins to form DNA-protein complexes (called organelle nuclei). The concept of organelle nuclei provides a new approach to explain the origin, division, and inheritance of organelles. Organelles divide using organelle division rings (machineries) after organelle-nuclear division. Organelle division machineries are a chimera of the FtsZ (filamentous temperature sensitive Z) ring of bacterial origin and the eukaryotic mechanochemical dynamin ring. Thus, organelle division machineries contain a key to solve the origin of organelles (eukaryotes). The maternal inheritance of organelles developed during sexual reproduction and it is also probably intimately related to the origin of organelles. The aims of this review are to describe the strategies used to reveal the dynamics of organelle division machineries, and the significance of the division machineries and maternal inheritance in the origin and evolution of eukaryotes

Lagrange Duality in Set Optimization

Based on the complete-lattice approach, a new Lagrangian duality theory for set-valued optimization problems is presented. In contrast to previous approaches, set-valued versions for the known scalar formulas involving infimum and supremum are obtained. In particular, a strong duality theorem, which includes the existence of the dual solution, is given under very weak assumptions: The ordering cone may have an empty interior or may not be pointed. "Saddle sets" replace the usual notion of saddle points for the Lagrangian, and this concept is proven to be sufficient to show the equivalence between the existence of primal/dual solutions and strong duality on the one hand and the existence of a saddle set for the Lagrangian on the other hand

Combined fluorescence and reflectance spectroscopy for in vivo quantification of cancer biomarkers in low - and high- grade glioma surgery

Biomarkers are indicators of biological processes and hold promise for the diagnosis and treatment of disease. Gliomas represent a heterogeneous group of brain tumors with marked intra- and inter-tumor variability. The extent of surgical resection is a significant factor influencing post-surgical recurrence and prognosis. Here, we used fluorescence and reflectance spectral signatures for in vivo quantification of multiple biomarkers during glioma surgery, with fluorescence contrast provided by exogenously-induced protoporphyrin IX (PpIX) following administration of 5-aminolevulinic acid. We performed light-transport modeling to quantify multiple biomarkers indicative of tumor biological processes, including the local concentration of PpIX and associated photoproducts, total hemoglobin concentration, oxygen saturation, and optical scattering parameters.We developed a diagnostic algorithm for intra-operative tissue delineation that accounts for the combined tumor-specific predictive capabilities of these quantitative biomarkers. Tumor tissue delineation achieved accuracies of up to 94% (specificity=94%, sensitivity=94%) across a range of glioma histologies beyond current state-of-the-art optical approaches, including state-of-the-art fluorescence image guidance. This multiple biomarker strategy opens the door to optical methods for surgical guidance that use quantification of well-established neoplastic processes. Future work would seek to validate the predictive power of this proof-of-concept study in a separate larger cohort of patients