Showing papers by "University of California, Santa Cruz published in 1968"

Solution of the Heawood Map-Coloring Problem

Abstract: One of the most fascinating problems in mathematics is the four-color conjecture, and in spite of the fact that we have nothing new to add, a short discussion of the matter is important for our purposes. The fascination of the problem is almost certainly due to the fact that the relevant question may be stated so as to be intelligible to the general public. Are four colors always enough to obtain a coloring of the countries of any map on a sphere? It is only necessary to clarify the italicized words above for the general reader to understand and, if inquisitive, to become interested in the problem. A country must be connected; hence Pakistan, which consists of two disjoined parts, does not qualify. The reader begins to realize that we are considering an abstraction which has little resemblance to political reality. In reference to the term map on a sphere, there are no oceans; every point on the sphere is either inside exactly one country or is on the frontiers of two or more countries. Two countries are adjacent if they have a common line of frontier points. Thus France and Spain are adjacent, but the states of Colorado and Arizona are not, in spite of the fact that they have one frontier point in common. The negating factor is that there is no common line of frontier points. A coloring of a map on a sphere is an assignment of one color to each country so that no pair of adjacent countries is assigned the same color. Thus two countries having the property observed above (Colorado and Arizona) may be assigned the same color, but countries like France and Spain must be assigned different colors. The minimum number of colors which suffices to color a given map is called the chromatic number of the map. The maximum, m, of the chromatic numbers for all maps on the sphere is called the chromatic number of the sphere. Thus we can be assured that any map on the sphere can be colored by using no more than m colors. The question is: \"What is m?\" It is easy to see that there is a map on a sphere that consists of four countries each adjacent to the other three. Hence this map has four as its chromatic number. Consequently, m> 4. This leads to the classical question: \"Does m = 4?\" No one knows the answer. It can be shown, however, that m < 5. M\\any attempts have been made to settle the matter. One of the most notable was made by the English barrister Kempe, who claimed the result in 1880. In 1890 Heawood1 discovered an error in Kempe's proof and went on to consider the problem for surfaces more complicated than a sphere. The simplest in the hierarchy of such surfaces is a torus, or the surface of a tire. The terms \"country,\" \"map,\" \"adjacent,\" etc., have meaning on such a surface, and Heawood showed that the chromatic number of a torus is seven. The standard topological model of a surface (or orientable two-dimensional manifold) S, of genus p is a sphere with p handles attached to it. (One may also think of the surfaces of a Swiss cheese with p holes through it.) Thus a torus is

The in vivo life span of normal and preneoplastic mouse mammary glands: a serial transplantation study

Abstract: It is recognized that organismal death of complex metazoan animals cannot usually be ascribed to the large-scale, simultaneous death or degeneration of their constituent cells. Although age-associated degenerative changes can be identified by both morphological and functional criteria, most cells, tissues, and organs of recently deceased animals are alive and in satisfactory condition at the time of natural death. 1-3 One of the fundamental problems in gerontology is therefore to determine whether such somatic cells have a potentially limited or unlimited lifetime if maintained under conditions which are optimal for growth, survival, and function. Attempts to propagate vertebrate cells serially in vitro have yielded conflicting results, although recent work suggests that most diploid cell types proliferate in culture for a finite and relatively small number of cell generations.4' It is difficult to extend this conclusion to include cells inl vivo because of the necessarily artificial conditions of culture. The corresponding in vivo experiments serial transfer of normal tissue between isogenic animals appear simple but have not yielded definitive answers. When normal tissues are transplanted, it is often impossible to distinguish clearly between host and transplant. Even with skin,

Screened Interionic Potential of the Simple Metals

Abstract: The modified interionic potential which includes both a direct ion-ion interaction and an indirect ion-electron-ion interaction has been studied for twelve simple metals, using Ashcroft's analytic bare-ion pseudopotential form factor and a modified Hartree dielectric function. The direct Coulomb interaction between any pair of ions is demonstrated to be exactly cancelled at distances greater than $2{r}_{c}$, which is around half the nearest-neighbor separation. Therefore, the interionic potential needed for a study of various properties of solids is entirely of a screened nature and has the usual Friedel oscillation in the asymptotic region. In general, however, the simple Friedel form is not a good representation for distances less than the fourth-neighbor separation. The interatomic force constants and the elastic constants derived from the screened interionic potential agreed reasonably well with experiments.

Fur Seals from the Bering Sea breeding in California

Abstract: A colony of northern fur seals has been found breeding on an island off California, and everyone hopes that this will not lead to its disappearance.

Forgetting of dreams in the laboratory.

Abstract: An adult male S slept 45 nights in a laboratory and was awakened at the end of every REM period. He recorded 138 dreams during this time of which he could recall 88 when he awakened in the morning....

Second Positive Phototropism in the Avena Coleoptile

Abstract: A method has been developed whereby the second positive phototropism can be observed separately from the first positive and negative phototropic responses which also occur in oat coleoptiles. Although the second positive phototropic response has often been referred to as the base response, photoreception for it is shown to occur mainly in the apical 3 mm of the coleoptile. The Bunsen-Roscoe reciprocity law, so typical of first positive phototropism, does not apply to the second positive responses, and the amount of curvature increases linearly with the duration of the stimulus. However, although this linear proportionality between stimulus duration and response is the major factor determining response at all intensities tested, the intensity of the stimulus does influence the response somewhat. The action spectrum for the response shows no activity above 510 nm and has peaks at 375 and 450 nm. In all but one particular it closely resembles the action spectrum for the first positive phototropism, and it is concluded that the same, or similar, pigments may well be the photoreceptors for both types of response. The identity of this blue light absorbing pigment is not known.

The Guadalupe Fur Seal: Habitat, Behavior, Population Size, and Field Identification

Abstract: Fur seals, Arctocephalus townsendi Merriam, 1897, at present land and breed regularly only along the precipitous, rocky east shore of Isla de Guadalupe, 256 km west of Baja California, Mexico. They seldom if ever land on open sandy beaches, and many haul out in caves and recesses along the narrow lava shoreline. The restricted range appears related to the near extermination of the species in the last century. Although congeneric with the fur seals of the Southern Hemisphere, which breed in the austral summer, A. townsendi breeds from May to July. Our censuses suggest that the population increased from a few individuals in 1954 to at least 500 in 1967. Form, pelage, vocalizations, certain activities, and habitat provide distinctive features for recognition of A. townsendi in the field.

Sea Urchin Response to Foreign Substances

Abstract: An assessment of the response of Strongylocentrotus purpuratus to substances injected into the coelom shows that (i) foreign molecules are cleared from the coelomic fluid more rapidly than native molecules, (ii) coelomocytes can respond selectively to albumins of human and bovine origin, and (iii) immunization attempts fail to elicit accelerated coelomocyte uptake or accelerated clear-with antigen

The gonads and sexual cycle of the polystyelid ascidian Distomus variolosus gaertner

Abstract: Distomus variolosus from Roscoff, France, comprises two sorts, differing in their branchial and gonadal patterns. Their sexual cycle has been followed histologically and micro-anatomically. Gonads begin as clumps of lymphocytes that persist along germinal tracts. Cavitation of the clump, growth of the gonoduct, maturation of the gametes, and elaboration of accessory structures are described. Oocytes develop in a linear series in each ovary; only one or two reach maturity in each gonad. The released egg and subsequent tadpole may be held to the ovary by a “leash” formed of the partially everted outer follicle of the egg. Post-mature gonads deteriorate. Testes disrupt altogether; ovaries may persist as moribund loci of remnant germinal tissue. The sharp right-left hermaphroditism of the zooid appears to combine with a subtler anterior-posterior gradient of sexual determination.

Nonunilineal Descent and Contextual Definition of Status: The Kwaio Evidence1

Abstract: Despite a decade of concerted attention to nonunilineal descent systems, we are still far from understanding how the problems they pose on paper are resolved on the ground. Here I will present new evidence from the Kwaio of Malaita, British Solomon Islands, a people still strikingly conservative, largely pagan, and cut off from direct European influence, in an island Pacific increasingly pervaded by bicycles and transistor radios. The Kwaio descent system has changed relatively little, and it manifests the features central to debate about nonunilineal descent. The Kwaio evidence on these questions may well have implications reaching beyond the bounds of this debate.2 In nonunilineal or ramage systems, assignment to descent groups is not exclusively through patrilineal or matrilineal links. A crucial question for such a system is whether a man can belong to both his father's and mother's descent groups. If the answer is yes, then how can discrete, corporate groups be formed? Father and mother themselves, through such processes, may each belong to two or more groups; and descent groups could then be little more than overlapping cognatic stocks. If, in such a sysstem, a person can belong to only father's or mother's group, but not both, how is affiliation determined in each generation? Characteristically, in Oceanic ramage systems, the answer lies somewhere in between: membership is neither invariably exclusive and singular, nor is it freely extended and multiple. And in dealing with this middle ground, neither our theories nor the data for most such societies have proven adequate. Here I will argue that many of the problems posed on paper by nonunilineal descent and multiple memberships are resolved by the contextual definition of status: that is, a descent-group membership need not involve "the whole man," and it is neither formally nor pragmatically impossible to maintain and express membership in two or more descent groups. Let me summarize the Kwaio evidence for such an

The fine structure ofPhycomyces: II. Organization of the stage I sporangiophore apex

Abstract: The cytological organization of the apices of sporangiophores and hyphae ofPhycomyces Blakesleeanus was studied by means of light- and electron microscopy. The sporangiophore apex in growth stage I contains a mass of cytoplasm in which is embedded a cluster of lipid globules. Within the plug several zones are differentiated by the grouping of organelles. These zones are not separated by membranes. The most apical zone is low in nuclei and vesicles but rich in mitochondria and dense bodies. Below this zone lies a compact group containing up to several hundred nuclei. Along the midline of the cell, below these nuclei, lies an ovoid region from which vesicles, nuclei and mitochondria are excluded. In this ovoid “exclusion zone” lies the cluster of lipid globules mentioned above. Lateral to the exclusion zone (i.e. in the peripheral region of the cell) the cytoplasm is rich in nuclei, mitochondria, dense bodies, and especially in developing autophagic vesicles. Of these vesicles, the most mature are found farthest from the cell apex. The region between the exclusion zone and the upper end of the cell's large central vacuole is occupied largely by mature, swollen autophagic vesicles. In addition to the zonal organization described above, microtubules are found to run along the cylindrical cell's axis at a distance from the cell wall, and extend to the extreme apex of the cell. Similar tubules occur in growing hyphae, together with dense bodies, and the hyphal apex contains non-autophagic vesicles that increase in size with distance from the hyphal tip. The hyphae lack the zonation shown by sporangiophore apices. Perinuclear masses of cisternae are described and related to the dictyosomes of higher plants. The findings are discussed in relation to the function of the apices in tip growth and sporulation.

Delayed fluorescence in photosynthetic materials: transient response to pulsed light in chlorella

Abstract: — The decay of the delayed fluorescence intensity of Chlorella cells following a brief flash of light is investigated in the region of time from 1 msec to 1 sec with greater accuracy than previous investigations. It is found that the best mathematical description for this decay is the sum of several exponential decays and is thought to be evidence for the existence of several distinct components in the production of delayed fluorescence.

Eye movement during sleep and waking in infant monkeys (Macaca mulatta) deprived of patterned vision

Abstract: Five newborn rhesus monkeys deprived of patterned vision and 4 normal-sighted controls were reared until 18 months of age. There was a significant decrease in frequency of rapid eye movement (REM) in both groups with increasing age. Frequency of REM tended to be lower in experimental monkeys than in controls. Asymmetries in velocity of waking, horizontal eye movement were evident in experimental monkeys, and the velocity of REMs was less in pattern-deprived monkeys than in controls. Nonsequential interval histograms between REMs at 18 months of age differed significantly from a random exponential distribution in both groups. Pattern-deprived monkeys had significantly fewer short intervals between REMs than controls. Visual tests showed the pattern-deprived monkeys to be behaviorally blind on removal of their eye occluders at 18 months of age.

Phase transition in the sliding-filament model of muscular contraction.

Abstract: It was pointed out some time ago' that a first-order phase transition would be particularly suitable in the mechanism of muscular contraction at the molecular level because such a transition could provide a very large change in length from a quite small alteration in the force, or in the concentration of a molecule or ion, or in some other condition (e.g., electric field). The primary object of this paper is to call attention to the fact that the sliding-filament model2 of muscular contraction, which is now well-established experimentally, is indeed, from the statisticalmechanical point of view, a one-dimensional system that exhibits a first-order transition. Hence, it should be expected to have the required \"razor-edge\" sensitivity. Whether the phase transition proves to be a significant feature of the model remains to be seen. But physiologists should at least be aware of the possibility and of some of its implications (see below). Ordinary one-dimensional systems cannot exhibit a first-order transition,3 but in certain rather artificial cases,4' 5 with long-range forces, a transition is found. In contrast, the sliding-filament model is an extremely simple, real (i.e., not artificial) one-dimensional system which virtually has a phase transition built into it. In fact it is difficult to see how nature could select a more elementary thermodynamic device to achieve the sensitivity referred to above. In order to stress the essentials, we shall confine ourselves in this paper to a discussion of the equilibrium properties of a simplified version (Figs. 1 and 2) of the

The XPL compiler generator system

Abstract: The development of the system described here was originally motivated by the need to develop a good student language compiler for a large IBM System/360. An examination of the tools and methods available caused us to establish the subgoal of developing a translator writing system in which we could prepare the student compiler. In our opinion, then and now, the total effort was smaller, and the end product better, for the combined project than for the original project using previously available tools.