The reverse protraction factor in the induction of bone sarcomas in radium-224 patients

More than 50 bone sarcomas have occurred among a collective of about 800 patients who had been injected in Germany after World War II with large activities of radium-224 for the intended treatment of bone tuberculosis and ankylosing spondylitis.^In an earlier analysis it was concluded that, at equal mean absorbed doses in the skeleton, patients with longer exposure time had a higher incidence of bone sarcomas.^The previous analysis was based on approximations; in particular, it did not account for the varying times at risk of the individual patients.^In view of the implications of a reverse protraction factor for basic considerations in radiation protection, the need was therefore felt to reevaluate the data from the continued follow-up by more rigorous statistical methods.^A first step of the analysis demonstrates the existence of the reverse dose-rate effect in terms of a suitably constructed rank-order test.^In a second step of the analysis it is concluded that the data are consistent with a linear no-threshold dose dependence under the condition of constant exposure time, while there is a steeper than linear dependence on dose when the exposure times increase proportionally to dose.^A maximum likelihood fit of the data is then performed in terms of a proportional hazards model that includes the individual parameters, dose, treatment duration, and age at treatment.^The fit indicates proportionality of the tumor rates to mean skeletal dose with an added factor (1 + 0.18.tau), where tau is the treatment time in months.^This indicates that a protraction of the injections over 15 months instead of 5 months doubles the risk of bone sarcoma

Locating Overlap Information in Quantum Systems

When discussing the black hole information problem the term ``information flow'' is frequently used in a rather loose fashion. In this article I attempt to make this notion more concrete. I consider a Hilbert space which is constructed as a tensor product of two subspaces (representing for example inside and outside the black hole). I discuss how the system has the capacity to contain information which is in NEITHER of the subspaces. I attempt to quantify the amount of information located in each of the two subspaces, and elsewhere, and analyze the extent to which unitary evolution can correspond to ``information flow''. I define the notion of ``overlap information'' which appears to be well suited to the problem.Comment: 25 pages plain LaTeX, no figures. Imperial/TP/93-94/2

Bone sarcoma cumulative tumor rates in patients injected with 224Ra

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An epidemiological assessment of lens opacifications that impaired vision in patients injected with radium-224

The incidence of lens opacifications that impaired vision (cataract) was analyzed among 831 patients who were injected with known dosages of 224Ra in Germany shortly after World War II. The dependence of the incidence on dosage, i.e., injected activity per unit body weight, and on time after treatment was determined. The observations are equally consistent with proportionality of the incidence of cataract to the square of dosage or with a linear dependence beyond a threshold of 0.5 MBq/kg. The possibility of a linear dependence without threshold was strongly rejected (P less than 0.001). The analysis of temporal dependences yielded a component that was correlated with the injected amount of 224Ra and a component that was uncorrelated. The former was inferred by a maximum likelihood analysis to increase approximately as the square of the time after treatment. The component unrelated to the treatment was found to increase steeply with age and to become dominant within the collective of patients between age 50 and 60. The relative magnitudes of the two components were such that a fraction of 55 to 60% of the total of 58 cataracts had to be ascribed to the dose-related incidence. Impaired vision due to cataract was diagnosed before age 54 in 25 cases. In terms of injected activity per unit body weight no dependence of the sensitivity on age was found; specifically there was no indication of a faster occurrence of the treatment-related cataracts in patients treated at older ages

Vector field mediated models of dynamical light velocity

A vector-tensor theory of gravity that was introduced in an earlier publication is analyzed in detail and its consequences for early universe cosmology are examined. The multiple light cone structure of the theory generates different speeds of gravitational and matter wave fronts, and the contraction of these light cones produces acausal, superluminary inflation that can resolve the initial value problems of cosmology.Comment: 16 pages, uses amsar

A Closed-Form Expression for the Gravitational Radiation Rate from Cosmic Strings

We present a new formula for the rate at which cosmic strings lose energy into gravitational radiation, valid for all piecewise-linear cosmic string loops. At any time, such a loop is composed of $N$ straight segments, each of which has constant velocity. Any cosmic string loop can be arbitrarily-well approximated by a piecewise-linear loop with $N$ sufficiently large. The formula is a sum of $O(N^4)$ polynomial and log terms, and is exact when the effects of gravitational back-reaction are neglected. For a given loop, the large number of terms makes evaluation ``by hand" impractical, but a computer or symbolic manipulator yields accurate results. The formula is more accurate and convenient than previous methods for finding the gravitational radiation rate, which require numerical evaluation of a four-dimensional integral for each term in an infinite sum. It also avoids the need to estimate the contribution from the tail of the infinite sum. The formula has been tested against all previously published radiation rates for different loop configurations. In the cases where discrepancies were found, they were due to errors in the published work. We have isolated and corrected both the analytic and numerical errors in these cases. To assist future work in this area, a small catalog of results for some simple loop shapes is provided.Comment: 29 pages TeX, 16 figures and computer C-code available via anonymous ftp from directory pub/pcasper at alpha1.csd.uwm.edu, WISC-MILW-94-TH-10, (section 7 has been expanded, two figures added, and minor grammatical changes made.

The evolution of a network of cosmic string loops

We set up and analyse a model for the non-equilibrium evolution of a network of cosmic strings initially containing only loops and no infinite strings. Due to this particular initial condition, our analytical approach differs significantly from existing ones. We describe the average properties of the network in terms of the distribution function n(l,t) dl, the average number of loops per unit volume with physical length between l and l + dl at time t. The dynamical processes which change the length of loops are then estimated and an equation, which we call the `rate equation', is derived for (dn/dt). In a non-expanding universe, the loops should reach the equilibrium distribution predicted by string statistical mechanics. Analysis of the rate equation gives results consistent with this. We then study the rate equation in an expanding universe and suggest that three different final states are possible for the evolving loop network, each of which may well be realised for some initial conditions. If the initial energy density in loops in the radiation era is low, then the loops rapidly disappear. For large initial energy densities, we expect that either infinite strings are formed or that the loops tend towards a scaling solution in the radiation era and then rapidly disappear in the matter era. Such a scenario may be relevant given recent work highlighting the problems with structure formation from the standard cosmic string scenario.Comment: LaTeX, 27 pages, 10 figures included as .eps file

Characterization of nanometer-sized, mechanically exfoliated graphene on the H-passivated Si(100) surface using scanning tunnelling microscopy

We have developed a method for depositing graphene monolayers and bilayers with minimum lateral dimensions of 2-10 nm by the mechanical exfoliation of graphite onto the Si(100)-2x1:H surface. Room temperature, ultra-high vacuum (UHV) tunnelling spectroscopy measurements of nanometer-sized single-layer graphene reveal a size dependent energy gap ranging from 0.1-1 eV. Furthermore, the number of graphene layers can be directly determined from scanning tunnelling microscopy (STM) topographic contours. This atomistic study provides an experimental basis for probing the electronic structure of nanometer-sized graphene which can assist the development of graphene-based nanoelectronics.Comment: Accepted for publication in Nanotechnolog