Granular Partitions Research Articles

Vague Reference and Approximating Judgments

"Mount Everest" is a vague name. That is (on the account here defended) there are many portions of reality all of which have equal claims to serve as its referent. We propose a new account of such vagueness in terms of a theory of what we shall call granular partitions. We distinguish different kinds of crisp and non-crisp granular partitions and we describe the relations between them, concentrating especially on spatial examples. In addition, we describe the practice whereby subjects use systems of reference grids as a means for tempering the vagueness of their judgments for example when they say that Libya straddles the Equator or that the meeting will take place between 2 and 3pm. We then demonstrate how the theory of reference partitions can yield a natural account of this practice, which is referred to in the literature as 'approximation'.

Quantum Mereotopology

While mereotopology – the theory of boundaries, contact and separation built up on a mereological foundation – has found fruitful applications in the realm of qualitative spatial reasoning, it faces problems when its methods are extended to deal with those varieties of spatial and non-spatial reasoning which involve a factor of granularity. This is because granularity cannot easily be represented within a mereology-based framework. We sketch how this problem can be solved by means of a theory of i>granular partitions, a theory general enough to comprehend not only the familiar sorts of spatial partitions but also a range of coarse-grained partitions of other, non-spatial sorts. We then show how these same methods can be extended to apply to finite sequences of granular partitions evolving over time, or to what we shall call coarse- and fine-grained i>histories.

ULTRAVIOLET AND PHASE MICROSCOPY OF SPORULATING SACCHAROMYCES.

Miller, Glendon R. (Southern Illinois University, Carbondale), Dan O. McClary, and Wilbert D. Bowers, Jr. Ultraviolet and phase microscopy of sporulating Saccharomyces. J. Bacteriol. 85:725-731. 1963.-During active growth, the cytoplasm of yeast cells is densely absorbent to ultraviolet light at 260 mmu, whereas the nucleus is only faintly so, and the vacuole is nonabsorbent. After 24 hr on presporulation medium (about the age of transfer to acetate sporulation medium), the cells manifest many characteristics of starvation. The cytoplasm is weakly absorbent to ultraviolet light except for a dense zone immediately surrounding the vacuole and one or two groups of highly refractile granules clustered on one or both sides of the juncture of the nucleus and the vacuole. After several hours on the acetate sporulation medium, the cells undergo a progressive vacuolation until four or more large vacuoles appear, separated by granular cytoplasm. The nucleus is obscured to ultraviolet light during the vacuolation stage, at which time previous studies have shown its division to occur, and remains so during the rest of the cycle. Photographs of densely granulated cells, at various wavelengths of ultraviolet and visible light, indicated several different types of granules with respect to their absorption spectra. With continued development of the ascus, the granules increase in number until they fill the entire cell and obscure the vacuoles, after which they condense into a compact mass, leaving much of the cell empty. Spores emerge from the granular mass as separate, ultraviolet-absorbent regions without distinguishable cell walls, which seem to be the last structures formed. The rudimentary spores contain a central cluster of dense granules and are separated within the ascus by optically dense, granular partitions which diminish as spore walls are laid down. With the maturing of the ascus, the granules and epiplasm disappear, and the ascus wall is drawn tightly around the more or less homogeneously absorbent spores.