Approximation Algorithms for Complex-Valued Ising Models on Bounded Degree Graphs

We study the problem of approximating the Ising model partition function with complex parameters on bounded degree graphs. We establish a deterministic polynomial-time approximation scheme for the partition function when the interactions and external fields are absolutely bounded close to zero. Furthermore, we prove that for this class of Ising models the partition function does not vanish. Our algorithm is based on an approach due to Barvinok for approximating evaluations of a polynomial based on the location of the complex zeros and a technique due to Patel and Regts for efficiently computing the leading coefficients of graph polynomials on bounded degree graphs. Finally, we show how our algorithm can be extended to approximate certain output probability amplitudes of quantum circuits.Comment: 12 pages, 0 figures, published versio

Simulating quantum computations with Tutte polynomials

We establish a classical heuristic algorithm for exactly computing quantum probability amplitudes. Our algorithm is based on mapping output probability amplitudes of quantum circuits to evaluations of the Tutte polynomial of graphic matroids. The algorithm evaluates the Tutte polynomial recursively using the deletion–contraction property while attempting to exploit structural properties of the matroid. We consider several variations of our algorithm and present experimental results comparing their performance on two classes of random quantum circuits. Further, we obtain an explicit form for Clifford circuit amplitudes in terms of matroid invariants and an alternative efficient classical algorithm for computing the output probability amplitudes of Clifford circuits

On the Parameterised Complexity of Induced Multipartite Graph Parameters

We introduce a family of graph parameters, called induced multipartite graph parameters, and study their computational complexity. First, we consider the following decision problem: an instance is an induced multipartite graph parameter $p$ and a given graph $G$, and for natural numbers $k\geq2$ and $\ell$, we must decide whether the maximum value of $p$ over all induced $k$-partite subgraphs of $G$ is at most $\ell$. We prove that this problem is W[1]-hard. Next, we consider a variant of this problem, where we must decide whether the given graph $G$ contains a sufficiently large induced $k$-partite subgraph $H$ such that $p(H)\leq\ell$. We show that for certain parameters this problem is para-NP-hard, while for others it is fixed-parameter tractable

The Melanoma Care Study: Protocol of a randomised controlled trial of a psycho-educational intervention for melanoma survivors at high risk of developing new primary disease

Background: Despite a good prognosis for most melanoma survivors, many experience substantial fear of new or recurrent melanoma, worry and anxiety about the future, and unmet healthcare needs. In this protocol, we outline the design and methods of the Melanoma Care Study for melanoma survivors at high risk of developing new primary disease. The objective of this study is to evaluate the efficacy and cost-effectiveness of a psycho-educational intervention for improving psychological and behavioural adjustment to melanoma risk. Design: The study design is a two-arm randomised controlled trial comparing a psycho-educational intervention to usual care. Methods: The intervention is comprised of a newly-developed psycho-educational booklet and three telephone sessions delivered by a trained psychologist. A total of 154 melanoma survivors at high risk of developing new primary disease who are attending one of three melanoma high risk clinics in New South Wales, Australia, will be recruited. Participants will be assessed at baseline (6 weeks before their high risk clinic dermatological appointment), and then 4 weeks and 6 months after their appointment. If effectiveness of the intervention is demonstrated at 6 months, an additional assessment at 12 months is planned. The primary outcome is fear of new or recurrent melanoma, as assessed by the Fear of Cancer Recurrence Inventory (FCRI). Secondary outcomes include anxiety, depression, unmet supportive care needs, satisfaction with clinical care, knowledge, behavioural adjustment to melanoma risk, quality of life, and cost-effectiveness of the intervention from a health system perspective. Following the intention-to-treat principle, linear mixed models will be used to analyse the data to account for repeated measures. A process evaluation will also be carried out to inform and facilitate potential translation and implementation into clinical practice. Discussion: This study will provide high quality evidence on the efficacy and cost-effectiveness of a psycho-educational intervention aimed at improving psychological and behavioural adjustment amongst melanoma survivors at high risk of new primary disease

Efficient recycling strategies for preparing large Fock states from single-photon sources: Applications to quantum metrology

© 2016 American Physical Society. Fock states are a fundamental resource for many quantum technologies such as quantum metrology. While much progress has been made in single-photon source technologies, preparing Fock states with a large photon number remains challenging. We present and analyze a bootstrapped approach for nondeterministically preparing large photon-number Fock states by iteratively fusing smaller Fock states on a beamsplitter. We show that by employing state recycling we are able to exponentially improve the preparation rate over conventional schemes, allowing the efficient preparation of large Fock states. The scheme requires single-photon sources, beamsplitters, number-resolved photodetectors, fast-feedforward, and an optical quantum memory

Electrostatically gated membrane permeability in inorganic protocells

Although several strategies are now available to produce functional microcompartments analogous to primitive cell-like structures, little progress has been made in generating protocell constructs with self-controlled membrane permeability. Here we describe the preparation of water-dispersible colloidosomes based on silica nanoparticles and delineated by a continuous semipermeable inorganic membrane capable of self-activated, electrostatically gated permeability. We use crosslinking and covalent grafting of a pH-responsive copolymer to generate an ultrathin elastic membrane that exhibits selective release and uptake of small molecules. This behaviour, which depends on the charge of the copolymer coronal layer, serves to trigger enzymatic dephosphorylation reactions specifically within the protocell aqueous interior. This system represents a step towards the design and construction of alternative types of artificial chemical cells and protocell models based on spontaneous processes of inorganic self-organization

Sub-Planckian black holes and the Generalized Uncertainty Principle

The Black Hole Uncertainty Principle correspondence suggests that there could exist black holes with mass beneath the Planck scale but radius of order the Compton scale rather than Schwarzschild scale. We present a modified, self-dual Schwarzschild-like metric that reproduces desirable aspects of a variety of disparate models in the sub-Planckian limit, while remaining Schwarzschild in the large mass limit. The self-dual nature of this solution under $M \leftrightarrow M^{-1}$ naturally implies a Generalized Uncertainty Principle with the linear form $\Delta x \sim \frac{1}{\Delta p} + \Delta p$. We also demonstrate a natural dimensional reduction feature, in that the gravitational radius and thermodynamics of sub-Planckian objects resemble that of $(1+1)$-D gravity. The temperature of sub-Planckian black holes scales as $M$ rather than $M^{-1}$ but the evaporation of those smaller than $10^{-36}$g is suppressed by the cosmic background radiation. This suggests that relics of this mass could provide the dark matter.Comment: 12 pages, 9 figures, version published in J. High En. Phy

Diagnosing the Role of Alfvén Waves in Magnetosphere-Ionosphere Coupling: Swarm Observations of Large Amplitude Nonstationary Magnetic Perturbations During an Interval of Northward IMF

High-resolution multispacecraft Swarm data are used to examine magnetosphere-ionosphere coupling during a period of northward interplanetary magnetic field (IMF) on 31 May 2014. The observations reveal a prevalence of unexpectedly large amplitude (>100 nT) and time-varying magnetic perturbations during the polar passes, with especially large amplitude magnetic perturbations being associated with large-scale downward field-aligned currents. Differences between the magnetic field measurements sampled at 50 Hz from Swarm A and C, approximately 10 s apart along track, and the correspondence between the observed electric and magnetic fields at 16 samples per second, provide significant evidence for an important role for Alfvén waves in magnetosphere-ionosphere coupling even during northward IMF conditions. Spectral comparison between the wave E- and B-fields reveals a frequency-dependent phase difference and amplitude ratio consistent with interference between incident and reflected Alfvén waves. At low frequencies, the E/B ratio is in phase with an amplitude determined by the Pedersen conductance. At higher frequencies, the amplitude and phase change as a function of frequency in good agreement with an ionospheric Alfvén resonator model including Pedersen conductance effects. Indeed, within this Alfvén wave incidence, reflection, and interference paradigm, even quasi-static field-aligned currents might be reasonably interpreted as very low frequency (ω → 0) Alfvén waves. Overall, our results not only indicate the importance of Alfvén waves for magnetosphere-ionosphere coupling but also demonstrate a method for using Swarm data for the innovative experimental diagnosis of Pedersen conductance from low-Earth orbit satellite measurements

Clinical practice guidelines for identification, screening and follow-up of individuals at high risk of primary cutaneous melanoma: a systematic review

Understanding how individuals at high-risk of primary cutaneous melanoma are best identified, screened and followed up will help optimize melanoma prevention strategies and clinical management. We conducted a systematic review of international clinical practice guidelines and documented the quality of supporting evidence for recommendations for clinical management of individuals at high risk of melanoma