A simplex-like search method for bi-objective optimization

We describe a new algorithm for bi-objective optimization, similar to the Nelder Mead simplex algorithm, widely used for single objective optimization. For diferentiable bi-objective functions on a continuous search space, internal Pareto optima occur where the two gradient vectors point in opposite directions. So such optima may be located by minimizing the cosine of the angle between these vectors. This requires a complex rather than a simplex, so we term the technique the \cosine seeking complex". An extra beneft of this approach is that a successful search identifes the direction of the effcient curve of Pareto points, expediting further searches. Results are presented for some standard test functions. The method presented is quite complicated and space considerations here preclude complete details. We hope to publish a fuller description in another place

Correlated Confocal and Intermediate Voltage Electron Microscopy Imaging of the Same Cells Using Sequential Fluorescence Labeling, Fixation, and Critical Point Dehydration

Confocal laser scanning microscopy (CLSM) and intermediate voltage transmission electron microscopy (IVEM) each has its own particular advantages. CLSM can examine living cells, but is particularly useful when applied to cells that have been lightly fixed, permeabilized, and stained with fluorescent-labeled antibodies for localization of specific molecular species at the resolution of the light microscope while still in the hydrated state. IVEM provides much higher resolution images, but requires more drastic preparation procedures, including dehydration. This paper presents methods for combining these complementary approaches to examine exactly the same cells sequentially by CLSM and IVEM. Cells are grown in culture on sterile formvar films spread over gold index grids on cover glasses, which are mounted on larger cover glasses or microscope slides with spacers to prevent compression of the cells. Light and epifluorescence microscopy, and CLSM are performed concentrating on cells in grid openings. Then the grids are fixed with aldehydes followed by OsO4, dehydrated and critical point dried (CPD) from liquid CO2. Immediately following CPD, the grids are ready for examination in the IVEM. Low magnification (300-600x) survey images allow correlation of the IVEM images with the light microscopic images. In higher power images, structures that are fluorescent labeled can be related to corresponding regions in the IVEM images