Development of a decision analytic model to support decision making and risk communication about thrombolytic treatment

Background Individualised prediction of outcomes can support clinical and shared decision making. This paper describes the building of such a model to predict outcomes with and without intravenous thrombolysis treatment following ischaemic stroke. Methods A decision analytic model (DAM) was constructed to establish the likely balance of benefits and risks of treating acute ischaemic stroke with thrombolysis. Probability of independence, (modified Rankin score mRS ≤ 2), dependence (mRS 3 to 5) and death at three months post-stroke was based on a calibrated version of the Stroke-Thrombolytic Predictive Instrument using data from routinely treated stroke patients in the Safe Implementation of Treatments in Stroke (SITS-UK) registry. Predictions in untreated patients were validated using data from the Virtual International Stroke Trials Archive (VISTA). The probability of symptomatic intracerebral haemorrhage in treated patients was incorporated using a scoring model from Safe Implementation of Thrombolysis in Stroke-Monitoring Study (SITS-MOST) data. Results The model predicts probabilities of haemorrhage, death, independence and dependence at 3-months, with and without thrombolysis, as a function of 13 patient characteristics. Calibration (and inclusion of additional predictors) of the Stroke-Thrombolytic Predictive Instrument (S-TPI) addressed issues of under and over prediction. Validation with VISTA data confirmed that assumptions about treatment effect were just. The C-statistics for independence and death in treated patients in the DAM were 0.793 and 0.771 respectively, and 0.776 for independence in untreated patients from VISTA. Conclusions We have produced a DAM that provides an estimation of the likely benefits and risks of thrombolysis for individual patients, which has subsequently been embedded in a computerised decision aid to support better decision-making and informed consent

Quantum corrections from a path integral over reparametrizations

We study the path integral over reparametrizations that has been proposed as an ansatz for the Wilson loops in the large-$N$ QCD and reproduces the area law in the classical limit of large loops. We show that a semiclassical expansion for a rectangular loop captures the L\"uscher term associated with $d=26$ dimensions and propose a modification of the ansatz which reproduces the L\"uscher term in other dimensions, which is observed in lattice QCD. We repeat the calculation for an outstretched ellipse advocating the emergence of an analog of the L\"uscher term and verify this result by a direct computation of the determinant of the Laplace operator and the conformal anomaly

On the Grothendieck Theorem for jointly completely bounded bilinear forms

We show how the proof of the Grothendieck Theorem for jointly completely bounded bilinear forms on C*-algebras by Haagerup and Musat can be modified in such a way that the method of proof is essentially C*-algebraic. To this purpose, we use Cuntz algebras rather than type III factors. Furthermore, we show that the best constant in Blecher's inequality is strictly greater than one.Comment: 9 pages, minor change

Wilson Loops and QCD/String Scattering Amplitudes

We generalize modern ideas about the duality between Wilson loops and scattering amplitudes in ${\cal N}=4$ SYM to large $N$ QCD by deriving a general relation between QCD meson scattering amplitudes and Wilson loops. We then investigate properties of the open-string disk amplitude integrated over reparametrizations. When the Wilson loop is approximated by the area behavior, we find that the QCD scattering amplitude is a convolution of the standard Koba-Nielsen integrand and a kernel. As usual poles originate from the first factor, whereas no (momentum dependent) poles can arise from the kernel. We show that the kernel becomes a constant when the number of external particles becomes large. The usual Veneziano amplitude then emerges in the kinematical regime where the Wilson loop can be reliably approximated by the area behavior. In this case we obtain a direct duality between Wilson loops and scattering amplitudes when spatial variables and momenta are interchanged, in analogy with the $\cal N$=4 SYM case.Comment: 39pp., Latex, no figures; v2: typos corrected; v3: final, to appear in PR

On the Discrepancies between POD and Fourier Modes on Aperiodic Domains

The application of Fourier analysis in combination with the Proper Orthogonal Decomposition (POD) is investigated. In this approach to turbulence decomposition, which has recently been termed Spectral POD (SPOD), Fourier modes are considered as solutions to the corresponding Fredholm integral equation of the second kind along homogeneous-periodic or homogeneous coordinates. In the present work, the notion that the POD modes formally converge to Fourier modes for increasing domain length is challenged. Numerical results indicate that the discrepancy between POD and Fourier modes along \textit{locally} translationally invariant coordinates is coupled to the Taylor macro/micro scale ratio (MMSR) of the kernel in question. Increasing discrepancies are observed for smaller MMSRs, which are characteristic of low Reynolds number flows. It is observed that the asymptotic convergence rate of the eigenspectrum matches the corresponding convergence rate of the exact analytical Fourier spectrum of the kernel in question - even for extremely small domains and small MMSRs where the corresponding DFT spectra suffer heavily from windowing effects. These results indicate that the accumulated discrepancies between POD and Fourier modes play a role in producing the spectral convergence rates expected from Fourier transforms of translationally invariant kernels on infinite domains

Combined proper orthogonal decompositions of orthogonal subspaces

We present a method for combining proper orthogonal decomposition (POD) bases optimized with respect to different norms into a single complete basis. We produce a basis combining decompositions optimized with respect to turbulent kinetic energy (TKE) and dissipation rate. The method consists of projecting a data set into the subspace spanned by the lowest several TKE optimized POD modes, followed by decomposing the complementary component of the data set using dissipation optimized POD velocity modes. The method can be fine-tuned by varying the number of TKE optimized modes, and may be generalized to accommodate any combination of decompositions. We show that the combined basis reduces the degree of non-orthogonality compared to dissipation optimized velocity modes. The convergence rate of the combined modal reconstruction of the TKE production is shown to exceed that of the energy and dissipation based decompositions. This is achieved by utilizing the different spatial focuses of TKE and dissipation optimized decompositions.Comment: 9 pages, 3 figure

Nucleation of quark matter bubbles in neutron stars

The thermal nucleation of quark matter bubbles inside neutron stars is examined for various temperatures which the star may realistically encounter during its lifetime. It is found that for a bag constant less than a critical value, a very large part of the star will be converted into the quark phase within a fraction of a second. Depending on the equation of state for neutron star matter and strange quark matter, all or some of the outer parts of the star may subsequently be converted by a slower burning or a detonation.Comment: 13 pages, REVTeX, Phys.Rev.D (in press), IFA 93-32. 5 figures (not included) available upon request from [email protected]

Scale Free Cluster Distributions from Conserving Merging-Fragmentation Processes

We propose a dynamical scheme for the combined processes of fragmentation and merging as a model system for cluster dynamics in nature and society displaying scale invariant properties. The clusters merge and fragment with rates proportional to their sizes, conserving the total mass. The total number of clusters grows continuously but the full time-dependent distribution can be rescaled over at least 15 decades onto a universal curve which we derive analytically. This curve includes a scale free solution with a scaling exponent of -3/2 for the cluster sizes.Comment: 4 pages, 3 figure