Showing papers by "University of Oxford published in 1974"

The theory and properties of randomly disordered crystals and related physical systems

Abstract: We review the methods which have been developed over the past several years to determine the behavior of solids whose properties vary randomly at the microscopic level, with principal attention to systems having composition variation on a well-defined structure (random "alloys"). We begin with a survey of the various elementary excitations and put the dynamics of electrons, phonons, magnons, and excitons into one common descriptive Hamiltonian; we then review the use of double-time thermodynamic Green's functions to determine the experimental properties of systems. Next we discuss these aspects of the problem which derive from the statistical specification of the microscopic parameters; we examine what information can and cannot be obtained from averaged Green's functions. The central portion of the review concerns methods for calculating the averaged Green's function to successively better approximation, including various self-consistent methods, and higher-order cluster effects. The last part of the review presents a comparison of theory with the experimental results of a variety of properties---optical, electronic, magnetic, and neutron scattering. An epilogue calls attention to the similarity between these problems and those of other fields where random material heterogeneity has played an essential role.

Growth with Exhaustible Natural Resources: Efficient and Optimal Growth Paths

Abstract: The proposition that limited natural resources provide a limit to growth and to the sustainable size of population is an old one. The natural resource that was the centre of the discussion in Malthus' day was land; more recently, some concern has been expressed over the limitations imposed by the supplies of oil, or more generally, energy sources, of phosphorus, and of other materials required for production. Those who predicted imminent doom in the nineteenth century were obviously wrong. Were they simply wrong about the immediacy of catastrophe, or did they leave out something fundamental from their calculations? There are at least three economic forces offsetting the limitations imposed by natural resources: technical change, the substitution of man-made factors of production (capital) for natural resources, and returns to scale. This study is an attempt to determine more precisely under what conditions a sustainable level of per capita consumption is feasible, to characterize steady state paths in economies with natural resources, and to describe the optimal growth path of the economy, in particular to derive the optimal rate of extraction and the optimal savings rate in the presence of exhaustible natural resouces. One of the interesting problems posed by the presence of exhaustible natural resources is that some of the basic concepts of growth theory, such as " steady state " and " natural rate of growth ", need to be re-examined. If, for instance, there are two unproduced factors, labour and natural resources, one of which is growing exponentially, the other of which is not growing at all, what is the " natural rate of growth "? In conventional economic discussions, the long-run growth rate of the economy is determined simply by the natural rate of growth and is independent of the savings rate. We shall show that in economies with natural resources, efficient growth paths which differ with respect to savings rate also differ, even asymptotically, with respect to the rate of growth. The analysis of optimal growth paths presents certain technical difficulties, because there are two state variables (the stock of capital per man and the stock of natural resources per man) and two control variables (the rate of extraction of natural resources and the savings rate). Fortunately, by the appropriate choice of variables, the qualitative properties of the path can be completely described. Optimal growth paths for economies with only capital or with just natural resources have been examined elsewhere. Typically, a country begins with little capital and hence, in the former models, optimal growth is characterized by increasing consumption per capita. On the other hand, natural resources act much like a capital good; since the stock

Markovian master equations

Abstract: We give a rigorous proof that under certain technical conditions the memory effects in a quantum-mechanical master equation become negligible in the weak coupling limit. This is sufficient to show that a number of open systems obey an exponential decay law in the weak coupling limit for a rescaled time variable. The theory is applied to a fairly general finite dimensional system weakly coupled to an infinite free heat bath.

Pigou, taxation and public goods

Abstract: The results of Samuelson [5-7] in the theory of public goods have provided the basis for most subsequent discussion of the optimum provision of public goods. Samuelson showed that a necessary condition for Pareto Optimality (and hence for maximizing a social welfare function which responds positively to individual utilities) is that the sum of the marginal rates of substitution (E MRS) between a public good and a private good be equal to the marginal rate of transformation (MRT). The sole constraint is that production is in the aggregate production set. This optimum can be achieved as a competitive equilibrium with the government supplying the public good up to the point where I MRS = MRT and financing its production by lump-sum taxation. Lump-sum transfers may also be employed to achieve the appropriate income distribution. The achievement of the " full " optimum described above depends on lump-sum taxes and transfers being feasible. If the taxation tools available exclude lump-sum taxation, then the optimization problem must be modified to include explicitly the means by which government revenue is raised. The importance of this point was clearly recognized by Pigou [3], who argued that the cost to consumers of the public good would be larger than just the necessary resources on account of the " indirect " damage caused by taxation:

Observation of tissue metabolites using 31P nuclear magnetic resonance.

Abstract: 31P NMR spectra of intact biological tissues can now be observed. The use of the spectra to study the course of reactions within the tissues is illustrated by experiments on muscle and its glycogen particle fraction.

Experiments on whether schooling by their prey affects the hunting behaviour of cephalopods and fish predators

Abstract: The experiments investigated the effects of a school of live prey fish on the hunting behaviour of squid, cuttlefish and pike (ambush predators) and perch (a chasing predator). The hunting behaviour of all species is described, including some previously unrecorded actions. For all species the increasing shoal size from one fish to six, to 20, decreased the success of the predators' attacks per encounter with a prey. This was partly because attacks on larger shoals lasted longer, and fish became increasingly difficult to catch as a hunt went on. However, for some of the species there was a clear effect of the shoals at the start of the hunt. For other species it was less conclusive. The disruptive effect of the shoals was shown to act for the ambush predators by interfering with the “optimal” sequence of an attack and causing avoidance actions together with so-called irrelevant behaviour. For the perch, shoals seemed to disrupt by forcing the predator continually to switch targets during his pursuit. The artificiality of the experiments is discussed in relation to field observations. The relatively high incidence of avoidance and irrelevant behaviour seems to be an artefact, but the main results are quite compatible with field studies. In nature fish predators may be able to get sufficient food by restricting their attacks to individuals which are conspicuous either by an abnormal appearance or by becoming separated from the school. An individual prey fish no doubt gains a considerable advantage from the school by burying itself in the crowd. Our experiments show that a shoal can provide further protection in hampering the attack of a predator.

Nonparametric Estimation of a Survivorship Function with Doubly Censored Data

Abstract: A simple iterative procedure is proposed for obtaining estimates of a response time distribution when some of the data are censored on the left and some on the right. The procedure is based on the product-limit method of Kaplan and Meier [15], and it also uses the idea of self-consistency due to Efron [8]. Under fairly general assumptions, the method is shown to yield unique consistent maximum likelihood estimators. Asymptotic expressions for their variances and covariances are derived and an extension to the case of arbitrary censoring is suggested.

Regulation of the pentose phosphate cycle

Abstract: 1. A search was made for mechanisms which may exert a ;fine' control of the glucose 6-phosphate dehydrogenase reaction in rat liver, the rate-limiting step of the oxidative pentose phosphate cycle. 2. The glucose 6-phosphate dehydrogenase reaction is expected to go virtually to completion because the primary product (6-phosphogluconate lactone) is rapidly hydrolysed and the equilibrium of the joint dehydrogenase and lactonase reactions is in favour of virtually complete formation of phosphogluconate. However, the reaction does not go to completion, because glucose 6-phosphate dehydrogenase is inhibited by NADPH (Neglein & Haas, 1935). 3. Measurements of the inhibition (which is competitive with NADP(+)) show that at physiological concentrations of free NADP(+) and free NADPH the enzyme is almost completely inhibited. This indicates that the regulation of the enzyme activity is a matter of de-inhibition. 4. Among over 100 cell constituents tested only GSSG and AMP counteracted the inhibition by NADPH; only GSSG was highly effective at concentrations that may be taken to occur physiologically. 5. The effect of GSSG was not due to the GSSG reductase activity of liver extracts, because under the test conditions the activity of this enzyme was very weak, and complete inhibition of the reductase by Zn(2+) did not abolish the GSSG effect. 6. Preincubation of the enzyme preparation with GSSG in the presence of Mg(2+) and NADP(+) before the addition of glucose 6-phosphate and NADPH much increased the GSSG effect. 7. Dialysis of liver extracts and purification of glucose 6-phosphate dehydrogenase abolished the GSSG effect, indicating the participation of a cofactor in the action of GSSG. 8. The cofactor removed by dialysis or purification is very unstable. The cofactor could be separated from glucose 6-phosphate dehydrogenase by ultrafiltration of liver homogenates. Some properties of the cofactor are described. 9. The hypothesis that GSSG exerts a fine control of the pentose phosphate cycle by counteracting the NADPH inhibition of glucose 6-phosphate dehydrogenase is discussed.

Phase zone plates for x rays and the extreme uv

Abstract: Phase-reversal zone plates can be designed even for regions of the electromagnetic spectrum where the index of refraction is complex, with a real part close to 1.0. These devices are superior to Fresnel zone plates both in their light collection, and in their signal-to-noise characteristics. Materials with suitable optical and mechanical properties exist throughout most of the 1–800-A wavelength range for their construction. Imperfections in fabrication, such as incorrect plate thickness, sloping zone edges, or an error in the width of alternate zones result in only moderate deterioration in optical performance.

Gangliosides as membrane receptors for tetanus toxin, cholera toxin and serotonin

Abstract: Tetanus toxin is bound by a sialidase-labile disialosyl ganglioside, serotonin by another, and cholera toxin by a sialidase-stable monosialosyl ganglioside. There is good evidence that the monosialosyl ganglioside may be the receptor for cholera toxin in cell membranes; what of the disialosyl ganglioside and tetanus toxin?

Gauge invariance and relativistic radiative transitions

Abstract: The gauge invariance of the matrix elements of electromagnetic interaction is a property that is usually taken for granted. The author describes a unified derivation in which the dependence of the matrix elements on the gauge in which the electromagnetic potentials are written is exhibited explicitly. The necessary and sufficient condition for the transition matrices for all multipoles to be gauge invariant is that the transition matrix for longitudinal photons should vanish identically. This imposes conditions on the initial and final wavefunctions which are automatically satisfied for a single-particle model but may not necessarily hold in, say, the Hartree-Fock model. For electric dipole transitions, it is shown that the Coulomb gauge leads to the dipole velocity form of the matrix element in the nonrelativistic limit and that a different choice is needed to give the dipole length form. Arguments are advanced suggesting that the dipole velocity form should be given a privileged position in approximate calculations of atomic and molecular transition probabilities.

Human cortical magnification factor and its relation to visual acuity

Abstract: The magnification factor (M) of the retina is the linear extent of visual striate cortex to which each degree of the retina projects. It has been suggested that magnification factor is directly proportional to visual acuity, but magnification factor measured in monkeys was compared with visual acuity in man. Here we first describe calculation of the magnification factor in man, and then compare it to human visual acuity. We calculated M for the first 30 degrees of the lower visual field by using infor mation provided by Brindley and Lewin (1968), who plotted the distribution of phosphenes evoked by stimulation of visual cortex in a human patient with electrodes implanted on the visual cortex. Since the inter-electrode distance was specified it was possible to calculate M for each of many pairs of electrodes by measuring the angular separation and mean eccentricity of the corresponding pairs of phosphenes. For the lower visual field, M was approximately 4 mm/degree at 2 degrees eccentricity and declined monotonically to 0.5 mm/degree at 25 degrees eccentricity. The results indicated that the reciprocal of M is directly proportional to the minimum angle of resolution and, correspondingly, that the magnification factor is directly proportional to visual acuity in man. By extrapolating this function for the whole of the visual field it was possible to estimate the area of striate cortex. The total extent of striate cortex estimated in this way agreed closely with previous direct measurements, suggesting that the measurements of M are accurate.

Trace anomalies in dimensional regularization

Abstract: An unusual perturbation theory anomaly is pointed out. If there exists a trace identity valid in an arbitrary number of dimensions, then employing dimensional regularization can result in an amplitude satisfying the identity in an arbitrary number of dimensions, but the finite part of the amplitude violating it in four dimensions. An example given here is the one-loop neutrino contribution to the graviton propagator. Anomalous behaviour, of a different origin, also occurs in the one-loop photon contribution. Both kinds of anomaly can be removed at the expense of introducingn-dimensional, rather than 4-dimensional, counterterms.

The Food Searching Behaviour of Two European Thrushes. Ii: the Adaptiveness of the Search Patterns

Abstract: 1) This study describes the searching behaviour of two thrushes foraging for both naturally occurring and artificial foods. I have paid particular attention to temporal and spatial changes in searching behaviour and have attempted to answer the question of whether the changes in searching behaviour were adaptive ones. 2) When thrushes captured an earthworm and continued searching, they showed a net change in patterning of the twelve turns following capture so that they probably searched the area surrounding the capture point more thoroughly than an area covering the same number of moves units before capture (Figs 4, 5; Table 1). This confirms N. TINBERGEN'S (1967) hypothesis that path changes sometimes follow prey capture in bird predators. Since earthworms on the study meadow were aggregated in distribution, the net change in path may have been of adaptive value to the thrushes, by concentrating their search where further prey items were most likely to occur. It was not, however, possible to relate the increased searching effort quantitatively to the size of the earthworm aggregates. (3) The thrushes were then presented with populations of cryptically-coloured artificial prey in random, regular and aggregated distributions at each of two densities (Fig. 7). The movements of the thrushes (mainly blackbirds) feeding on these prey were recorded as described by SMITH (1974). (4) The overall distribution of the search paths of the thrushes showed a correspondence with the distributions of the artificial food populations (Fig. 9). The thrushes made larger turns and showed less tendency to alternate left and right turns at the higher density (Tables 8, 11), thus helping them to maintain their search paths within the smaller confines of the high density populations. (5) The capture rates of the thrushes at the two prey densities were roughly proportional to the differences in prey density (Table 4). Although there were suggestions of differing capture rates, unforeseen errors in experimental procedure did not allow firm conclusions on the effects of thrush predation on the different prey distributions within each density. (6) The presentation of the cryptic artificial prey led to an increase in the average length of moves made by blackbirds (Fig. 10; Table 5). Further increases in move length followed the cutting of the grass on the study meadow (Fig. 13) and the introduction of more conspicuous artificial prey (Figs 11, 12). It is suggested that the increases in move lengths were an adaptive reaction by the blackbirds to increases in prey detectability. (7) Captures of single artificial prey were preceded by larger than average turns and were followed by larger than average turns in the opposite direction (Table 9). (8) The presentation of the artificial food led to an overall increase in the speed of movement of the blackbirds (Table 10). (9) After the capture of prey in the low density random and aggregated populations thrushes showed a net tendency to concentrate their searching in the area surrounding the site of prey capture (Fig. 16; Table 12), similar to that shown after the capture of earthworms. This was not shown after the capture of regularly distributed prey (Figs 16, 17 ; Table 12), nor was it clearly shown after the capture of prey in the high density random and aggregated distributions (Fig. 17; Table 12). (10) The overall speed of movement was greater over the ten moves preceding capture than over the ten moves following capture in the low density regular distribution (Table 13). (11) The changes in searching behaviour following capture are discussed with reference to N. TINBERGEN'S (1967) hypothesis that predators select for 'spacing out' in prey. (12) A method is presented which allowed the measurement of the wild blackbirds' abilities to detect the artificial prey supplied (Figs 18-20). The 'risk' to the artificial prey was high when the blackbirds were within 20 cm of the prey, but fell to near zero at a distance of 120 cm. (Fig. 21). The square root of the risk was linearly related to the distance between predator and prey (Fig. 22). The measures of the detection ability of the blackbirds are discussed in relation to their movement patterns. (13) The results are discussed in light of the general problem of whether predatory animals show adaptive flexibility in response to spatial and temporal variations in food supply. I have argued that at least some aspects of the thrushes' behaviour provide evidence for such flexibility. I have emphasised that the basic 'unpredictability' of the environment, which generates the need for behavioural plasticity, also makes it unrealistic to expect to find predators making optimally adapted responses to all variations in the environment.

Cholera Toxin: Interaction of Subunits with Ganglioside GM1

Abstract: Vibrio cholerae exotoxin is an aggregate of two different noninterconvertible subunits (molecular weights about 15,000 and about 25,000). Only the smaller subunit reacts with ganglioside G(M1), a possible biological receptor. The larger subunit, found only in active toxin molecules, can be eluted with 8 molar urea from insoluble complexes of toxin, ganglioside, and cerebroside.

A spectrophotometric assay of beta-lactamase action on penicillins.

Abstract: A new method for measuring the enzymic hydrolysis of the beta-lactam ring in penicillins is described. The change in extinction in the u.v. region is determined. The method is sensitive (50mum-benzylpenicillin can be used) and convenient.

The locust jump

Abstract: The locust jumps by a rapid extension of its metathoracic tibiae. The comparatively slow rate of rise of tension of the extensor tibia muscle means that if it is to shorten rapidly, it must develop tension isometrically prior to the jump by co-contracting with the flexor muscle. The extensor muscle is far stronger than the flexor and thus there has to be considerable structural specialisation of the joint to enable the flexor to prevent the tibia moving under the extensor tension. The geometry of the joint gives the flexor muscle a very large mechanical advantage over the extensor in the fully flexed position. This mechanical advantage decreases rapidly as the joint extends so that the residual flexor tension does not slow down the movement (Fig. 4). There is also a locking device associated with the flexor tendon which is engaged when the tibia is fully flexed and which holds it in this position against the developing extensor force (Fig. 5).

Which graphs have integral spectra

Abstract: The spectrum S(G) of a graph G of order p is defined as the non-increasing sequence of the p real eigenvalues of the adjacency matrix of G. It has been found that certain graphs have an integral spectrum, i.e., every eigenvalue is an integer. Thus, it is natural to ask just which graphs have this property. We develop a systematic approach to this question based on operations on graphs. The general problem appears intractable.