Shinya Inoué: Lighting the way in microscopy

Inoué’s innovations in polarized light microscopy allowed the first documentation of the mitotic spindle in living cells

Epistemic systems and Flagg and Friedman's translation

In 1986, Flagg and Friedman \cite{ff} gave an elegant alternative proof of the faithfulness of G\"{o}del (or Rasiowa-Sikorski) translation $(\cdot)^\Box$ of Heyting arithmetic $\bf HA$ to Shapiro's epistemic arithmetic $\bf EA$. In \S 2, we shall prove the faithfulness of $(\cdot)^\Box$ without using stability, by introducing another translation from an epistemic system to corresponding intuitionistic system which we shall call \it the modified Rasiowa-Sikorski translation\rm . That is, this introduction of the new translation simplifies the original Flagg and Friedman's proof. In \S 3, we shall give some applications of the modified one for the disjunction property ($\mathsf{DP}$) and the numerical existence property ($\mathsf{NEP}$) of Heyting arithmetic. In \S 4, we shall show that epistemic Markov's rule $\mathsf{EMR}$ in $\bf EA$ is proved via $\bf HA$. So $\bf EA$ $\vdash \mathsf{EMR}$ and $\bf HA$ $\vdash \mathsf{MR}$ are equivalent. In \S 5, we shall give some relations among the translations treated in the previous sections. In \S 6, we shall give an alternative proof of Glivenko's theorem. In \S 7, we shall propose several(modal-)epistemic versions of Markov's rule for Horsten's modal-epistemic arithmetic $\bf MEA$. And, as in \S 4, we shall study some meta-implications among those versions of Markov's rules in $\bf MEA$ and one in $\bf HA$. Friedman and Sheard gave a modal analogue $\mathsf{FS}$ (i.e. Theorem in \cite{fs}) of Friedman's theorem $\mathsf{F}$ (i.e. Theorem 1 in \cite {friedman}): \it Any recursively enumerable extension of $\bf HA$ which has $\mathsf{DP}$ also has $\mathsf{NPE}$\rm . In \S 8, we shall give a proof of our \it Fundamental Conjecture \rm $\mathsf{FC}$ proposed in Inou\'{e} \cite{ino90a} as follows: $\mathsf{FC}: \enspace \mathsf{FS} \enspace \Longrightarrow \enspace \mathsf{F}.$ This is a new type of proofs. In \S 9, I shall give discussions.Comment: 33 page

On Bergman's Diamond Lemma for Ring Theory

This expository paper deals with the Diamond Lemma for ring theory, which is proved in the first section of G.M. Bergman, The Diamond Lemma for Ring Theory, Advances in Mathematics, 29 (1978), pp. 178--218. No originality of the present note is claimed on the part of the author, except for some suggestions and figures. Throughout this paper, I shall mostly use Bergman's expressions in his paper.Comment: 15 page

High Resolution Scanning Electron Microscopic Cytology - Specimen Preparation and Intracellular Structures Observed by Scanning Electron Microscopy

With the recent developments of the specimen preparation techniques, intracellular organization has been observed three-dimensionally by scanning electron microscopy (SEM). A suitable preparation method is the most important factor for observing intracellular structures at high resolution. Since intracellular structures are usually hidden in the cytoplasmic matrix, SEM observation of them is impossible merely by cracking the fixed cell. To remove the fixed cytoplasm, an osmic maceration technique is the most effective method which is applicable to almost all kinds of specimen preparation. In our laboratory, we developed some methods for observing intracellular structures. Those are the O-D-O method, the A-O-D-O method, O-D-W method, freeze-polishing method, and so on. Since each specimen preparation method has merits and demerits, it is necessary to select the suitable method for each purpose. To observe the intra-cellular membranous structures such as endoplasmic reticulum and mitochondria, the A-O-D-O method is recommended. An exfoliating method by surface tension is effective to observe submembranous structures. The freeze-polishing method is applied for observing intracellular structures of thin materials such as mesothelial cells or cultured cells. By these methods, some new findings on the three-dimensional architecture of the intracellular organelles were obtained. On the surface of sarcoplasmic reticulum ribosomes were sometimes attached forming spiral polysomes. In Golgi apparatus, the cisternae were composed of compiled cisternae which showed a whorl-like appearance seen from above. Although the newly revealed findings must be investigated further in the near future, it is obvious that three-dimensional cytology by high resolution SEM is emerging

Electron microscopic measurement of the size of the optical focus in laser scanning microscopy

We describe a method for measuring the lateral focal spot size of a multiphoton laser scanning microscope (LSM) with unprecedented accuracy. A specimen consisting of an aluminum film deposited on a glass coverslip was brought into focus in a LSM and the laser intensity was then increased enough to perform nanoablation of the metal film. This process leaves a permanent trace of the raster path usually taken by the beam during the acquisition of an optical image. A scanning electron microscope (SEM) was then used to determine the nanoablated line width to high accuracy, from which the lateral spot size and hence resolution of the LSM can be determined. To demonstrate our method, we performed analysis of a multiphoton LSM at various infrared wavelengths, and we report measurements of optical lateral spot size with an accuracy of 20 nm, limited only by the resolution of the SEM

Microtubule dynamics in cell division : exploring living cells with polarized light microscopy

Author Posting. © The Author(s), 2008. This is the author's version of the work. It is posted here by permission of Annual Reviews for personal use, not for redistribution. The definitive version was published in Annual Review of Cell and Developmental Biology 24 (2008): 1-28, doi:10.1146/annurev.cellbio.24.110707.175323.This Perspective is an account of my early experience while I studied the dynamic organization and behavior of the mitotic spindle and its submicroscopic filaments using polarized light microscopy. The birefringence of spindle filaments in normally dividing plant and animal cells, and those treated by various agents, revealed: A) the reality of spindle fibers and fibrils in healthy living cells; B) the labile, dynamic nature of the molecular filaments making up the spindle fibers; C) the mode of fibrogenesis and action of orienting centers; and D) force-generating properties based on the disassembly and assembly of the fibrils. These studies, which were carried out directly on living cells using improved polarizing microscopes, in fact, predicted the reversible assembly properties of isolated microtubules