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of South Florida , Tampa, FL , USA
1 School of Medicine, Western Sydney University , Locked Bag 1797, Campbelltown, NSW 2751 , Australia
2 **David** **Simmons**
RCTs of whether screening asymptomatic

We construct a self-affine sponge in \(\mathbb {R}^3\) whose dynamical dimension, i.e. the supremum of the Hausdorff dimensions of its invariant measures, is strictly less than its Hausdorff dimension. This resolves a long-standing open problem in the dimension theory of dynamical systems, namely whether every expanding repeller has an ergodic invariant measure of full Hausdorff ...

We compute numerically the dimensions and OPE coefficients of several operators in the 3d Ising CFT, and then try to reverse-engineer the solution to crossing symmetry analytically. Our key tool is a set of new techniques for computing infinite sums of SL(2, \( \mathrm{\mathbb{R}} \)) conformal blocks. Using these techniques, we solve the lightcone bootstrap to all orders in an ...

Simultaneous Diophantine approximation is concerned with the approximation of a point \(\mathbf x\in \mathbb R^d\) by points \(\mathbf r\in \mathbb Q^d\), with a view towards jointly minimizing the quantities \(\Vert \mathbf x - \mathbf r\Vert \) and \(H(\mathbf r)\). Here \(H(\mathbf r)\) is the so-called “standard height” of the rational point \(\mathbf r\). In this paper the ...

We present a new method of proving the Diophantine extremality of various dynamically defined measures, vastly expanding the class of measures known to be extremal. This generalizes and improves the celebrated theorem of Kleinbock and Margulis (’98) resolving Sprindžuk’s conjecture, as well as its extension by Kleinbock, Lindenstrauss, and Weiss (’04), hereafter abbreviated KLW. As ...

We consider Lorentzian correlators of local operators. In perturbation theory, singularities occur when we can draw a position-space Landau diagram with null lines. In theories with gravity duals, we can also draw Landau diagrams in the bulk. We argue that certain singularities can arise only from bulk diagrams, not from boundary diagrams. As has been previously observed, these ...

We study two-dimensional (4, 4) superconformal field theories of central charge c = 6, corresponding to nonlinear sigma models on K3 surfaces, using the superconformal bootstrap. This is made possible through a surprising relation between the BPS \( \mathcal{N} \) = 4 superconformal blocks with c = 6 and bosonic Virasoro conformal blocks with c = 28, and an exact result on the ...

We make precise determinations of the leading scaling dimensions and operator product expansion (OPE) coefficients in the 3d Ising, O(2), and O(3) models from the conformal bootstrap with mixed correlators. We improve on previous studies by scanning over possible relative values of the leading OPE coefficients, which incorporates the physical information that there is only a single ...

We introduce SDPB: an open-source, parallelized, arbitrary-precision semidefinite program solver, designed for the conformal bootstrap. SDPB significantly outperforms less specialized solvers and should enable many new computations. As an example application, we compute a new rigorous high-precision bound on operator dimensions in the 3d Ising CFT, Δ σ = 0.518151(6), Δ ϵ = ...

Objective To develop and recalibrate an Australian 5-year cardiovascular disease (CVD) mortality risk score to produce contemporary predictions of risk. Methods Data were pooled from six Australian cohort studies (n = 54,829), with baseline data collected between 1989 and 2003. Participants included were aged 40–74 years and free of CVD at baseline. Variables were harmonised across ...

Aims/hypothesis Asymptomatic pregnant women are screened for gestational diabetes (GDM) at 24–28 weeks’ gestation. Recent guidelines also recommend screening early in gestation to identify undiagnosed pre-existing overt diabetes. We assessed the performance of random plasma glucose (RPG) testing at antenatal booking in predicting GDM diagnosis later in pregnancy. Methods Data from ...

We study 3d CFTs with an O(N) global symmetry using the conformal bootstrap for a system of mixed correlators. Specifically, we consider all nonvanishing scalar four-point functions containing the lowest dimension O(N) vector ϕ i and the lowest dimension O(N) singlet s, assumed to be the only relevant operators in their symmetry representations. The constraints of crossing symmetry ...

We compute the conformal blocks associated with scalar-scalar-fermion-fermion 4-point functions in 3D CFTs. Together with the known scalar conformal blocks, our result completes the task of determining the so-called ‘seed blocks’ in three dimensions. Conformal blocks associated with 4-point functions of operators with arbitrary spins can now be determined from these seed blocks by ...

**David** **Simmons**-Duffin
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Open Access
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c The Authors. Article funded by SCOAP
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0
Jefferson Physical Laboratory, Harvard University
,
Cambridge, MA 02138 U.S.A
We introduce a method for computing

We study the conformal bootstrap for a 4-point function of fermions 〈ψψψψ〉 in 3D. We first introduce an embedding formalism for 3D spinors and compute the conformal blocks appearing in fermion 4-point functions. Using these results, we find general bounds on the dimensions of operators appearing in the ψ × ψ OPE, and also on the central charge C T . We observe features in our ...

We study the conformal bootstrap for systems of correlators involving nonidentical operators. The constraints of crossing symmetry and unitarity for such mixed correlators can be phrased in the language of semidefinite programming. We apply this formalism to the simplest system of mixed correlators in 3D CFTs with a ℤ2 global symmetry. For the leading ℤ2-odd operator σ and ℤ2-even ...

We study the conformal bootstrap for 3D CFTs with O(N ) global symmetry. We obtain rigorous upper bounds on the scaling dimensions of the first O(N ) singlet and symmetric tensor operators appearing in the ϕ i × ϕ j OPE, where ϕ i is a fundamental of O(N ). Comparing these bounds to previous determinations of critical exponents in the O(N ) vector models, we find strong numerical ...

Melbourne, Shepparton,
Victoria, Australia; and the 3Illawarra Shoalhaven
Local Health District, Wollongong, New South
Wales, Australia.
Corresponding author: **David** **Simmons**, david
..
DOI: 10.2337/dc13

Aims/hypothesis Gestational diabetes mellitus (GDM) is associated with increased risks to mother and child, but globally agreed diagnostic criteria remain elusive. Identification of women with GDM is important, as treatment reduces adverse outcomes such as perinatal death, shoulder dystocia and neonatal hypoglycaemia. Recently, the UK’s National Institute for Health and Care ...

We use supershadow methods to derive new expressions for superconformal blocks in 4d \( \mathcal{N} \) = 1 superconformal field theories. We analyze the four-point function \( \left\langle {\mathcal{A}}_1{\mathcal{A}}_2^{\dagger }{\mathrm{\mathcal{B}}}_1{\mathrm{\mathcal{B}}}_2^{\dagger}\right\rangle \), where \( \mathcal{A} \) i and ℬ i are scalar superconformal primary operators ...