Showing papers by "University of Cambridge published in 1976"

Simple mathematical models with very complicated dynamics

Abstract: First-order difference equations arise in many contexts in the biological, economic and social sciences. Such equations, even though simple and deterministic, can exhibit a surprising array of dynamical behaviour, from stable points, to a bifurcating hierarchy of stable cycles, to apparently random fluctuations. There are consequently many fascinating problems, some concerned with delicate mathematical aspects of the fine structure of the trajectories, and some concerned with the practical implications and applications. This is an interpretive review of them.

An efficient mRNA-dependent translation system from reticulocyte lysates.

Abstract: A simple method is described for converting a standard rabbit reticulocyte cell-free extract (lysate) into an mRNA-dependent protein synthesis system. The lysate is preincubated with CaCl2 and micrococcal nuclease, and then excess ethyleneglycol-bis(2-aminoethylether)-N,N′-tetraacetic acid is added to chelate the Ca2+ and inactivate the nuclease. Lysates treated in this way have negligible endogenous amino acid incorporation activity, but 75% of the activity of the original lysate can be recovered by the addition of globin mRNA. The efficiency utilisation of added mRNA and the sensitivity of the system are both very high. No residual nuclease activity could be detected, and the tRNA is functionally unimpaired. Several different species of mRNA have been shown to be translated efficiently into full-sized products of the expected molecular weight up to about 200 000, and there is no detectable accumulation of incomplete protein products. The efficient translation of RNA from two plant viruses (tobacco mosaic virus and cowpea mosaic virus) required heterologous tRNA.

Variations in the Earth's Orbit: Pacemaker of the Ice Ages

Abstract: 1) Three indices of global climate have been monitored in the record of the past 450,000 years in Southern Hemisphere ocean-floor sediments. 2) Over the frequency range 10(-4) to 10(-5) cycle per year, climatic variance of these records is concentrated in three discrete spectral peaks at periods of 23,000, 42,000, and approximately 100,000 years. These peaks correspond to the dominant periods of the earth's solar orbit, and contain respectively about 10, 25, and 50 percent of the climatic variance. 3) The 42,000-year climatic component has the same period as variations in the obliquity of the earth's axis and retains a constant phase relationship with it. 4) The 23,000-year portion of the variance displays the same periods (about 23,000 and 19,000 years) as the quasi-periodic precession index. 5) The dominant, 100,000-year climatic [See table in the PDF file] component has an average period close to, and is in phase with, orbital eccentricity. Unlike the correlations between climate and the higher-frequency orbital variations (which can be explained on the assumption that the climate system responds linearly to orbital forcing), an explanation of the correlation between climate and eccentricity probably requires an assumption of nonlinearity. 6) It is concluded that changes in the earth's orbital geometry are the fundamental cause of the succession of Quaternary ice ages. 7) A model of future climate based on the observed orbital-climate relationships, but ignoring anthropogenic effects, predicts that the long-term trend over the next sevem thousand years is toward extensive Northern Hemisphere glaciation.

Relevance weighting of search terms

Abstract: This paper examines statistical techniques for exploiting relevance information to weight search terms. These techniques are presented as a natural extension of weighting methods using information about the distribution of index terms in documents in general. A series of relevance weighting functions is derived and is justified by theoretical considerations. In particular, it is shown that specific weighted search methods are implied by a general probabilistic theory of retrieval. Different applications of relevance weighting are illustrated by experimental results for test collections.

Black Holes and Thermodynamics

Abstract: A black hole of given mass, angular momentum, and charge can have a large number of different unobservable internal configurations which reflect the possible different initial configurations of the matter which collapsed to produce the hole. The logarithm of this number can be regarded as the entropy of the black hole and is a measure of the amount of information about the initial state which was lost in the formation of the black hole. If one makes the hypothesis that the entropy is finite, one can deduce that the black holes must emit thermal radiation at some nonzero temperature. Conversely, the recently derived quantum-mechanical result that black holes do emit thermal radiation at temperature $\frac{\ensuremath{\kappa}\ensuremath{\hbar}}{2\ensuremath{\pi}kc}$, where $\ensuremath{\kappa}$ is the surface gravity, enables one to prove that the entropy is finite and is equal to $\frac{{c}^{3}A}{4G\ensuremath{\hbar}}$, where $A$ is the surface area of the event horizon or boundary of the black hole. Because black holes have negative specific heat, they cannot be in stable thermal equilibrium except when the additional energy available is less than 1/4 the mass of the black hole. This means that the standard statistical-mechanical canonical ensemble cannot be applied when gravitational interactions are important. Black holes behave in a completely random and time-symmetric way and are indistinguishable, for an external observer, from white holes. The irreversibility that appears in the classical limit is merely a statistical effect.

The Deformation of Steep Surface Waves on Water. I. A Numerical Method of Computation

Abstract: Plunging breakers are beyond the reach of all known analytical approximations Previous numerical computations have succeeded only in integrating the equations of motion up to the instant when the surface becomes vertical In this paper we present a new method for following the time-history of space-periodic irrotational surface waves The only independent variables are the coordinates and velocity potential of marked particles at the free surface At each time-step an integral equation is solved for the new normal component of velocity The method is faster and more accurate than previous methods based on a two dimensional grid It has also the advantage that the marked particles become concentrated near regions of sharp curvature Viscosity and surface tension are both neglected The method is tested on a free, steady wave of finite amplitude, and is found to give excellent agreement with independent calculations based on Stokes’s series It is then applied to unsteady waves, produced by initially applying an asymmetric distribution of pressure to a symmetric, progres­sive wave The freely running wave then steepens and overturns It is demonstrated that the surface remains rounded till well after the over­turning takes place

Brownian diffusion of particles with hydrodynamic interaction

Abstract: The classical theory of Brownian motion applies to suspensions which are so dilute that each particle is effectively alone in infinite fluid. We consider here the modifications to the theory that are needed when rigid spherical particles are close enough to interact hydrodynamically. It is first shown that Brownian motion is a diffusion process of the conventional kind provided that the particle configuration does not change significantly during a viscous relaxation time. The original argument due to Einstein, which invokes an equilibrium situation, is generalized to show that the particle flux in probability space due to Brownian motion is the same as that which would be produced by the application of a certain ‘thermodynamic’ force to each particle. We then use this prescription to deduce the Brownian diffusivities in two -different types of situation. The first concerns a dilute homogeneous suspension which is being deformed, and the relative translational diffusivity of two rigid spherical particles with a given separation is calculated from the properties of the low-Reynolds-number flow due to two spheres moving under equal and opposite forces. The second concerns a suspension in which there is a gradient of concentration of particles. The thermodynamic force on each particle in this case is shown to be equal to the gradient of the chemical potential of the particles, which brings considerations of the multi-particle excluded volume into the problem. Determination of the particle flux due to the action of this force is equivalent to determination of the sedimentation velocity of particles falling through fluid under gravity, for which a theoretical result correct to the first order in volume fraction of the particles is available, The diffusivity of the particles is found to increase slowly as the concentration rises from zero. These results are generalized to the case of a (dilute) inhomogeneous suspension of several different species of spherical particle, and expressions are obtained for the diagonal and off-diagonal elements of the diffusivity matrix. Numerical values of all the relevant hydrodynamic functions are given for the case of spheres of uniform size.

Planetary Waves in Horizontal and Vertical Shear: The Generalized Eliassen-Palm Relation and the Mean Zonal Acceleration

Abstract: Using a new generalization of the Eliassen-Palm relations, we discuss the zonal-mean-flow tendency ∂ū/∂t due to waves in a stratified, rotating atmosphere, with particular attention to equatorially trapped modes. Wave transience, forcing and dissipation are taken into account in a very general way. The theory makes it possible to discuss the latitudinal (y) and vertical (z) dependence of ∂ū/∂t qualitatively and calculate it directly from an approximate knowledge of the wave structure. For equatorial modes it reveals that the y profile of ∂ū/∂t is strongly dependent on the nature of the forcing or dissipation mechanism. A by-product of the theory is a far-reaching generalization of the theorems of Charney-Drazin, Dickinson and Holton on the forcing of ∂ū/∂t by conservative linear waves. Implications for the quasi-biennial oscillation in the equatorial stratosphere are discussed. Graphs of y profiles of ∂ū/∂t are given for the equatorial waves considered in the recent analysis of observational data...

The Biological Yield and Harvest Index of Cereals as Agronomic and Plant Breeding Criteria

Abstract: Publisher Summary The chapter discusses the meaning and value of the biological yield and harvest index of cereals in agronomic studies and in cereal breeding. The relationship of biological yield, grain yield, and harvest index to each other and to other plant characteristics is discussed. Various models and actual relationships between biological yields and grain yields within a series of genotypes or agronomic treatments are described. The situation in which a number of varieties have precisely the same biological yield but different grain yields is graphically presented along with the genotypes that are ranked in order of increasing grain yield. Grain yield is proportional to harvest index and their correlation is 1.00, whereas biological yield and harvest index are unrelated. The chapter examines the interaction of biological yield, grain yield, and harvest index with plant density. Biological yield and harvest index are two valuable criteria for the assessment of the performance of cereals.

Oxygen-Isotope and Paleomagnetic Stratigraphy of Pacific Core V28-239 Late Pliocene to Latest Pleistocene

Abstract: V28-239 core from cruis~ 28 of R/V Vema pre-s1!rvo;!~ a detarled ol\\;ygen-isotDpe 3t1!1 paleomagneti<.: record ior a11 of (ho: Pleisl('.:ene E?')Ch. The el'tire 2i-m-iong cme /l-\"ll> been ar.alyzed a l xm inter.·a1s. Glacial stage 22, aoc·ve (he JardllliJIo magileti.:: event, II1:!Y repre,o;!ct the first m?jor N .. xthern HClllisphere cO!ltinental g1aciation of middle P1ei!>tocCile char3cter. Prior 10 this. higher frequcncy glacial events e>.tend to near the leve! of the Olduvai JruigIletic e lent. GJacial evo:nts of less regular freq l.cn::y exteoo t'l the hollom of the core , which rcpresents Iate Pliocene time. AuctLl:itions i!! ::ari-onate dissolution intensity occur lhroughout thc UJI':: with a sirrular frequen...-y to t!te oxygen-isotopc: fluclUations.

Optical Studies of the 1.945 eV Vibronic Band in Diamond

Abstract: The 1945eV band is the dominant end product of annealing radiation damage in diamonds containing isolated substitutional nitrogen atoms In this paper uniaxial stress experiments are described which show the band to be a transition between A 1 (ground) and E (excited) electronic states of a trigonal centre, the E state being coupled predominantly to A 1 modes of vibration Annealing experiments suggest that the centre is either a substitutional nitrogen atom plus an interstitial nitrogen atom, or a substitutional nitrogen atom plus a vacancy Small differences between the luminescence and absorption bands are shown to be consistent with the double minima vibrational potential of the nitrogenvacancy model

Molecular dynamics studies of the vitreous state: Simple ionic systems and silica

Abstract: Some applications of molecular dynamics calculations to the vitreous state have been examined for simple ionic MX and MX2 type glasses. The MX system which corresponds to a hypothetical vitreous and supercooled amorphous KCl is found to undergo an isobaric transition in the region of 0.3 Tf and an isothermal transition at around 35 kbar (T=Tf). The transition is evidenced by a discontinuity in second order thermodynamic properties and may be associated with a virtual disappearance of translational diffusion. By employing a variety of irreversible stress histories, the vitreous state in this case is shown to be insensitive to the thermodynamic stress history up to a maximum computationally permissible relaxation time of around 10−10 sec. Simulations are also reported for some ionic liquids of MX2 stoichiometry which, in contrast with KCl, have glass‐forming ability (BeF2, ZnCl2, and SiO2). Although the relaxation times involved in laboratory glass formation far exceed the long‐time limit of computer ’’expe...

Poles and zeros of linear multivariable systems : a survey of the algebraic, geometric and complex-variable theory

Abstract: This survey is concerned with the definition and main properties of sets of specific values of complex frequency, called poles and zeros, which may be associated with a matrix-valued function of a complex frequency variable. The main emphasis is on the physical interpretation of invariant zeros in terms of the general zero-output behaviour of a linear dynamical system. A discussion is given of the relationship between this definition of a zero and the various other forms adopted in the current literature. The relationship is considered between poles and zeros defined by algebraic means and the standard complex variable theory of algebraic functions. It is shown that the poles and zeros of a square matrix-valued function of a complex variable G(s) are the same as the poles and zeros of an associated algebraic function g(s).

Informant Accuracy in Social Network Data

Abstract: This paper examines the problem of informant accuracy in the production of social network data, through the use of a self-monitoring network. This allows a comparison between cognitive network data and informants' interactive behavior. Against expectations, it turns out that informants are extremely inaccurate. In other words, informants' reports of their behavior bear little resemblance to their behavior. If an informant claimed to have communicated with some person "the most frequently" then, in fact, he communicated with that person between first and fourth most frequently only 52% of the time. The implications of our findings for sociometric and network analysis are: (1) Attempts to filter out noise in a sociometric network matrix by using sophisticated software are likely to be unproductive. This is because such manipulations assume a much lower level of noise than actually occurs. (2) Due to the low level of informant accuracy, theories of social structure built upon presently available network data...

Constitutive equations in suspension mechanics. Part 2. Approximate forms for a suspension of rigid particles affected by Brownian rotations

Abstract: Approximate constitutive equations are derived for a dilute suspension of rigid spheroidal particles with Brownian rotations, and the behaviour of the approximations is explored in various flows. Following the suggestion made in the general formulation in part 1, the approximations take the form of Hand's (1962) fluid model, in which the anisotropic microstructure is described by a single second-order tensor. Limiting forms of the exact constitutive equations are derived for weak flows and for a class of strong flows. In both limits the microstructure is shown to be entirely described by a second-order tensor. The proposed approximations are simple interpolations between the limiting forms of the exact equations. Predictions from the exact and approximate constitutive equations are compared for a variety of flows, including some which are not in the class of strong flows analysed.

Cliques in random graphs

Abstract: Let 0 < p < 1 be fixed and denote by G a random graph with point set , the set of natural numbers, such that each edge occurs with probability p, independently of all other edges. In other words the random variables eij, 1 ≤ i < j, defined byare independent r.v.'s with P(eij = 1) = p, P(eij = 0) = 1 − p. Denote by Gn the subgraph of G spanned by the points 1, 2, …, n. These random graphs G, Gn will be investigated throughout the note. As in (1), denote by Kr a complete graph with r points and denote by kr(H) the number of Kr's in a graph H. A maximal complete subgraph is called a clique. In (1) one of us estimated the minimum of kr(H) provided H has n points and m edges. In this note we shall look at the random variablesthe number of Kr's in Gn, andthe maximal size of a clique in Gn.

Oxygen isotopic evidence for the development of the psychrosphere 38 Myr ago

Abstract: THREE major elements were involved in the evolution of oceanic circulation during the Cainozoic. The first of these was the diminishing role of oceanic meridional circulation in equatorial areas, the second was the development of circum-Antarctic circulation and the third involves the development of the present-day system of bottom waters of the world ocean, the ‘psychrosphere’1,2. Because deep bottom waters are mostly derived from the polar regions, their characteristics, such as temperature, reflect surface conditions at high latitudes3. Past temperature changes of deep oceanic waters, and thus of polar surface waters, can be determined from the oxygen isotopic composition of deep-dwelling benthonic microfossils3,4. A deep-sea palaeo-temperature record has been established4 for the past 54 Myr based on DSDP sites in the sub-Antarctic; detailed arguments4 give evidence that the Antarctic ice sheet developed during the Middle Miocene. Previous to this, however, a significant 5 °C decline in bottom-water temperature is recorded close to the Eocene–Oligocene boundary and is considered4 to represent the onset of Antarctic bottom-water formation at temperatures close to freezing. This heralds the beginning of the modern thermo-haline circulation and is thus one of the most important palaeo-oceanographic events in the Cainozoic. We examine here in more detail the palaeotemperature event near the Eocene-Oligocene boundary, the latter having an age of 38 Myr (ref. 5).

Energy-momentum tensor near an evaporating black hole

Abstract: We calculate the vacuum expectation value, ${T}_{\ensuremath{\mu}\ensuremath{ u}}$, of the energy-momentum tensor of a massless scalar field in a general two-dimensional spacetime and evaluate it in a two-dimensional model of gravitational collapse. In two dimensions, quantum radiation production is incompatible with a conserved and traceless ${T}_{\ensuremath{\mu}\ensuremath{ u}}$. We there-fore resolve an ambiguity in our expression for ${T}_{\ensuremath{\mu}\ensuremath{ u}}$, regularized by a geodesic point-separation procedure, by demanding conservation but allowing a trace. In the collapse model, the results support that picture of black-hole evaporation in which pairs of particles are created outside the horizon (and not entirely in the collapsing matter), one of which carries negative energy into the future horizon of the black hole, while the other contributes to the thermal flux at infinity.

Plasma and brain amino acids in fulminant hepatic failure and their relationship to hepatic encephalopathy.

Abstract: Amino acid concentrations were determined in plasma, whole blood, cerebrospinal fluid and brain tissue of 45 patients with grade 3 or 4 coma due to fulminant hepatic failure. The concentration of 15 of the 19 amino acids determined were significantly increased in blood and the, increases were greatest for the amino acids concerned with neurotransmitter metabolism. There was no correlation, however, between the plasma concentration of these amino acids and changes in the grade of hepatic coma. The plasma concentrations of the branched chain amino acids were normal except in those patients who subsequently recovered in whom levels were slightly decreased. Phenylalanine, tyrosine and methionine were among the 15 out of 18 amino acids which were significantly increased in cerebrospinal fluid and among the 15 out of 21 amino acids which were significantly increased in the brain. The increase in tryptophan was associated with a significant elevation in brain 5-hyroxyindoleacetic acid concentration suggesting an increase in 5-hydroxytryptamine turnover in hepatic coma. Brain to plasma ratios of most amino acids in hepatic coma patients were similar to control subjects suggesting that plasma concentration is the main factor controlling the cerebral concentration. However, for the branched chain amino acids, cerebrospinal fluid and brain concentrations were increased when plasma concentrations were normal suggesting an increase in brain uptake.

Long Term Results of Venesection Therapy in Idiopathic Haemochromatosis

Abstract: Observations on the clinical effects of venesection therapy in 85 treated, as compared with 26 untreated, patients with idiopathic haemochromatosis showed decreased pigmentation and hepatomegaly together with a return to normal tests of liver function in half the patients who had abnormal tests at presentation. Control improved in 28 per cent of those patients with diabetes mellitus, although some patients developed it during the period of observation, despite venesection. Portal hypertension, testicular atrophy and arthropathy were not improved. In only 12 patients was there sufficient reaccumulation of iron after the initial course of venesection to merit further treatment. Rates of iron accumulation in these patients varied between 1-4 mg and 4-8 mg per day and chelatable iron levels were noted to be inappropriately high in relation to body iron stores during the early stages of the reaccumulation period. Life table data shows that the percentage survival five and ten years after diagnosis was 66 and 32 per cent respectively for the treated patients, and 18 and 6 per cent respectively for the untreated patients, both statistically highly significant differences (p less than 0-01). Possible clinical differences such as age of presentation, the presence of diabetes mellitus, cirrhosis, clinical hepatic failure and hepatoma between the treated and untreated groups that might otherwise have weighted survival in favour of the treated group were corrected by the use of covariant analysis. This gave mean log survival values of 4-15 and 2-88 for the treated and untreated patients respectively, equivalent to 63-4 months and 17-8 months, a highly significant difference (p less than 0-01). Ten patients, all of whom had cirrhosis at the time of diagnosis, died of malignant hepatoma between three and 15 years after completing venesection therapy. There was also a high rate of death from neoplasms in a variety of other sites--22 per cent in the venesected group, strikingly higher than that rate predicted for a similarly aged population using national cancer mortality rates.