Pole Dancing: 3D Morphs for Tree Drawings

We study the question whether a crossing-free 3D morph between two straight-line drawings of an $n$-vertex tree can be constructed consisting of a small number of linear morphing steps. We look both at the case in which the two given drawings are two-dimensional and at the one in which they are three-dimensional. In the former setting we prove that a crossing-free 3D morph always exists with $O(\log n)$ steps, while for the latter $\Theta(n)$ steps are always sufficient and sometimes necessary.Comment: Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018

Shock waves in strongly coupled plasmas

Shock waves are supersonic disturbances propagating in a fluid and giving rise to dissipation and drag. Weak shocks, i.e., those of small amplitude, can be well described within the hydrodynamic approximation. On the other hand, strong shocks are discontinuous within hydrodynamics and therefore probe the microscopics of the theory. In this paper we consider the case of the strongly coupled N=4 plasma whose microscopic description, applicable for scales smaller than the inverse temperature, is given in terms of gravity in an asymptotically $AdS_5$ space. In the gravity approximation, weak and strong shocks should be described by smooth metrics with no discontinuities. For weak shocks we find the dual metric in a derivative expansion and for strong shocks we use linearized gravity to find the exponential tail that determines the width of the shock. In particular we find that, when the velocity of the fluid relative to the shock approaches the speed of light $v\to 1$ the penetration depth $\ell$ scales as $\ell\sim (1-v^2)^{1/4}$. We compare the results with second order hydrodynamics and the Israel-Stewart approximation. Although they all agree in the hydrodynamic regime of weak shocks, we show that there is not even qualitative agreement for strong shocks. For the gravity side, the existence of shock waves implies that there are disturbances of constant shape propagating on the horizon of the dual black holes.Comment: 47 pages, 8 figures; v2:typos corrected, references adde

Bulk spectral function sum rule in QCD-like theories with a holographic dual

We derive the sum rule for the spectral function of the stress-energy tensor in the bulk (uniform dilatation) channel in a general class of strongly coupled field theories. This class includes theories holographically dual to a theory of gravity coupled to a single scalar field, representing the operator of the scale anomaly. In the limit when the operator becomes marginal, the sum rule coincides with that in QCD. Using the holographic model, we verify explicitly the cancellation between large and small frequency contributions to the spectral integral required to satisfy the sum rule in such QCD-like theories.Comment: 16 pages, 2 figure

Peak reduction technique in commutative algebra

The "peak reduction" method is a powerful combinatorial technique with applications in many different areas of mathematics as well as theoretical computer science. It was introduced by Whitehead, a famous topologist and group theorist, who used it to solve an important algorithmic problem concerning automorphisms of a free group. Since then, this method was used to solve numerous problems in group theory, topology, combinatorics, and probably in some other areas as well. In this paper, we give a survey of what seems to be the first applications of the peak reduction technique in commutative algebra and affine algebraic geometry.Comment: survey; 10 page

Cardiac Calcitropes, Myotropes, and Mitotropes: JACC Review Topic of the Week.

The term "inotrope" is familiar and intimately connected with pharmaceuticals clinically used for treatment of low cardiac output with cardiogenic shock. Traditional inotropic agents exert their effect by modulating calcium signaling in the myocardium. Their use is associated with poor long-term outcomes. Newer molecules in development intend to break from calcium mediation and the associated detrimental long-term effects by targeting distinct mechanisms of action to improve cardiac performance. Thus, "inotropy" does not sufficiently describe the range of potential novel pharmaceutical products. To enhance communication around and evaluation of current, emerging, and potential therapies, this review proposes a novel nuanced and holistic framework to categorize pharmacological agents that improve myocardial performance based on 3 myocardial mechanisms: calcitropes, which alter intracellular calcium concentrations; myotropes, which affect the molecular motor and scaffolding; and mitotropes, which influence energetics. Novel chemical entities can easily be incorporated into this structure, distinguishing themselves based on their mechanisms and clinical outcomes

An elementary stringy estimate of transport coefficients of large temperature QCD

Modeling QCD at large temperature with a simple holographic five dimensional theory encoding minimal breaking of conformality, allows for the calculation of all the transport coefficients, up to second order, in terms of a single parameter. In particular, the shear and bulk relaxation times are provided. The result follows by deforming the AdS background with a scalar dual to a marginally relevant operator, at leading order in the deformation parameter.Comment: 11 pages; v2: comments and references adde

Modelling-based evaluation of the costs, benefits and cost-effectiveness of multipathogen point-of-care tests for sexually transmitted infections in symptomatic genitourinary medicine clinic attendees

Objectives To quantify the costs, benefits and cost-effectiveness of three multipathogen point-of-care (POC) testing strategies for detecting common sexually transmitted infections (STIs) compared with standard laboratory testing. Design Modelling study. Setting Genitourinary medicine (GUM) services in England. Population A hypothetical cohort of 965 988 people, representing the annual number attending GUM services symptomatic of lower genitourinary tract infection. Interventions The decision tree model considered costs and reimbursement to GUM services associated with diagnosing and managing STIs. Three strategies using hypothetical point-of-care tests (POCTs) were compared with standard care (SC) using laboratory-based testing. The strategies were: A) dual POCT for Chlamydia trachomatis (CT) and Neisseria gonorrhoeae (NG); B) triplex POCT for CT-NG and Mycoplasma genitalium (MG); C) quadruplex POCT for CT-NG-MG and Trichomonas vaginalis (TV). Data came from published literature and unpublished estimates. Primary and secondary outcome measures Primary outcomes were total costs and benefits (quality-adjusted life years (QALYs)) for each strategy (2016 GB, £) and associated incremental cost-effectiveness ratios (ICERs) between each of the POC strategies and SC. Secondary outcomes were inappropriate treatment of STIs, onward STI transmission, pelvic inflammatory disease in women, time to cure and total attendances. Results In the base-case analysis, POC strategy C, a quadruplex POCT, was the most cost-effective relative to the other strategies, with an ICER of £36 585 per QALY gained compared with SC when using microcosting, and cost-savings of £26 451 382 when using tariff costing. POC strategy C also generated the most benefits, with 240 467 fewer clinic attendances, 808 fewer onward STI transmissions and 235 135 averted inappropriate treatments compared with SC. Conclusions Many benefits can be achieved by using multipathogen POCTs to improve STI diagnosis and management. Further evidence is needed on the underlying prevalence of STIs and SC delivery in the UK to reduce uncertainty in economic analyses

Quantum critical lines in holographic phases with (un)broken symmetry

All possible scaling IR asymptotics in homogeneous, translation invariant holographic phases preserving or breaking a U(1) symmetry in the IR are classified. Scale invariant geometries where the scalar extremizes its effective potential are distinguished from hyperscaling violating geometries where the scalar runs logarithmically. It is shown that the general critical saddle-point solutions are characterized by three critical exponents ($\theta, z, \zeta$). Both exact solutions as well as leading behaviors are exhibited. Using them, neutral or charged geometries realizing both fractionalized or cohesive phases are found. The generic global IR picture emerging is that of quantum critical lines, separated by quantum critical points which correspond to the scale invariant solutions with a constant scalar.Comment: v3: 32+29 pages, 2 figures. Matches version published in JHEP. Important addition of an exponent characterizing the IR scaling of the electric potentia

Drag force in a strongly coupled anisotropic plasma

We calculate the drag force experienced by an infinitely massive quark propagating at constant velocity through an anisotropic, strongly coupled N=4 plasma by means of its gravity dual. We find that the gluon cloud trailing behind the quark is generally misaligned with the quark velocity, and that the latter is also misaligned with the force. The drag coefficient $\mu$ can be larger or smaller than the corresponding isotropic value depending on the velocity and the direction of motion. In the ultra-relativistic limit we find that generically $\mu \propto p$. We discuss the conditions under which this behaviour may extend to more general situations.Comment: 25 pages, 13 figures; v2: minor changes, added reference

Fermions and Type IIB Supergravity On Squashed Sasaki-Einstein Manifolds

We discuss the dimensional reduction of fermionic modes in a recently found class of consistent truncations of type IIB supergravity compactified on squashed five-dimensional Sasaki-Einstein manifolds. We derive the lower dimensional equations of motion and effective action, and comment on the supersymmetry of the resulting theory, which is consistent with N=4 gauged supergravity in $d=5$, coupled to two vector multiplets. We compute fermion masses by linearizing around two $AdS_{5}$ vacua of the theory: one that breaks N=4 down to N=2 spontaneously, and a second one which preserves no supersymmetries. The truncations under consideration are noteworthy in that they retain massive modes which are charged under a U(1) subgroup of the $R$-symmetry, a feature that makes them interesting for applications to condensed matter phenomena via gauge/gravity duality. In this light, as an application of our general results we exhibit the coupling of the fermions to the type IIB holographic superconductor, and find a consistent further truncation of the fermion sector that retains a single spin-1/2 mode.Comment: 43 pages, 2 figures, PDFLaTeX; v2: added references, typos corrected, minor change