Lower bounds for on-line graph colorings

We propose two strategies for Presenter in on-line graph coloring games. The first one constructs bipartite graphs and forces any on-line coloring algorithm to use $2\log_2 n - 10$ colors, where $n$ is the number of vertices in the constructed graph. This is best possible up to an additive constant. The second strategy constructs graphs that contain neither $C_3$ nor $C_5$ as a subgraph and forces $\Omega(\frac{n}{\log n}^\frac{1}{3})$ colors. The best known on-line coloring algorithm for these graphs uses $O(n^{\frac{1}{2}})$ colors

Emergent quantum confinement at topological insulator surfaces

Bismuth-chalchogenides are model examples of three-dimensional topological insulators. Their ideal bulk-truncated surface hosts a single spin-helical surface state, which is the simplest possible surface electronic structure allowed by their non-trivial $\mathbb{Z}_2$ topology. They are therefore widely regarded ideal templates to realize the predicted exotic phenomena and applications of this topological surface state. However, real surfaces of such compounds, even if kept in ultra-high vacuum, rapidly develop a much more complex electronic structure whose origin and properties have proved controversial. Here, we demonstrate that a conceptually simple model, implementing a semiconductor-like band bending in a parameter-free tight-binding supercell calculation, can quantitatively explain the entire measured hierarchy of electronic states. In combination with circular dichroism in angle-resolved photoemission (ARPES) experiments, we further uncover a rich three-dimensional spin texture of this surface electronic system, resulting from the non-trivial topology of the bulk band structure. Moreover, our study reveals how the full surface-bulk connectivity in topological insulators is modified by quantum confinement.Comment: 9 pages, including supplementary information, 4+4 figures. A high resolution version is available at http://www.st-andrews.ac.uk/~pdk6/pub_files/TI_quant_conf_high_res.pd

Energy-Spin Trajectories in AdS_5 x S^5 from Semiclassical Vertex Operators

We study the relation between vertex operators in AdS_5 x S^5 and classical spinning string solutions. In the limit of large quantum numbers the treatment of vertex operators becomes semiclassical. In this regime, a given vertex operator carrying a certain set of quantum numbers defines a singular solution. We show in a number of examples that this solution coincides with the classical string solution with the same quantum numbers but written in a different two-dimensional coordinate system. The marginality condition imposed on an operator yields a relation between the energy and the other quantum numbers which is shown to coincide with that of the corresponding classical string solution. We also argue that in some cases vertex operators in AdS_5 x S^5 cannot be given by expressions similar to the ones in flat space and a more involved consideration is required.Comment: 23 pages, 1 Figur

On correlation functions of operators dual to classical spinning string states

We explore how to compute, classically at strong coupling, correlation functions of local operators corresponding to classical spinning string states. The picture we obtain is of `fattened' Witten diagrams, the evaluation of which turns out to be surprisingly subtle and requires a modification of the naive classical action due to a necessary projection onto appropriate wave functions. We examine string solutions which compute the simplest case of a two-point function and reproduce the right scaling with the anomalous dimensions corresponding to the energies of the associated spinning string solutions. We also describe, under some simplifying assumptions, how the spacetime dependence of a conformal three-point correlation function arises in this setup.Comment: 27 pages, 3 figures; v2: references and comments added

On the cubic interactions of massive and partially-massless higher spins in (A)dS

Cubic interactions of massive and partially-massless totally-symmetric higher-spin fields in any constant-curvature background of dimension greater than three are investigated. Making use of the ambient-space formalism, the consistency condition for the traceless and transverse parts of the parity-invariant interactions is recast into a system of partial differential equations. The latter can be explicitly solved for given s_1-s_2-s_3 couplings and the 2-2-2 and 3-3-2 examples are provided in detail for general choices of the masses. On the other hand, the general solutions for the interactions involving massive and massless fields are expressed in a compact form as generating functions of all the consistent couplings. The St\"uckelberg formulation of the cubic interactions as well as their massless limits are also analyzed.Comment: 42 pages, 2 tables, LaTex. Comments on two-derivative couplings involving partially-massless spin-2 fields added, typos corrected, references added. v2: final version to appear in JHEP. v3: formulae (3.4) and (3.9) correcte

The burden and risks of pediatric pneumonia in Nigeria: A desk‐based review of existing literature and data

Background: Pneumonia is a leading killer of children under‐5 years, with a high burden in Nigeria. We aimed to quantify the regional burden and risks of pediatric pneumonia in Nigeria, and specifically the states of Lagos and Jigawa. / Methods: We conducted a scoping literature search for studies of pneumonia morbidity and mortality in under‐5 children in Nigeria from 10th December 2018 to 26th April 2019, searching: Cochrane, PubMed, and Web of Science. We included grey literature from stakeholders' websites and information shared by organizations working in Nigeria. We conducted multivariable logistic regression using the 2016 to 2017 Multiple Cluster Indicators Survey data set to explore factors associated with pneumonia. Descriptive analyses of datasets from 2010 to 2019 was done to estimate trends in mortality, morbidity, and vaccination coverage. / Results: We identified 25 relevant papers (10 from Jigawa, 8 from Lagos, and 14 national data). None included data on pneumonia or acute respiratory tract infection burden in the health system, inpatient case‐fatality rates, severity, or age‐specific pneumonia mortality rates at state level. Secondary data analysis found that no household or caregiver socioeconomic indicators were consistently associated with self‐reported symptoms of cough and/or difficulty breathing, and seasonality was inconsistently associated, dependant on region. / Conclusion: There is a clear evidence gap around the burden of pediatric pneumonia in Nigeria, and challenges with the interpretation of existing household survey data. Improved survey approaches are needed to understand the risks of pediatric pneumonia in Nigeria, alongside the need for investment in reliable routine data systems to provide data on the clinical pneumonia burden in Nigeria

Health system challenges for improved childhood pneumonia case management in Lagos and Jigawa, Nigeria

Background: Case fatality rates for childhood pneumonia in Nigeria remain high. There is a clear need for improved case management of pneumonia, through the sustainable implementation of the Integrated Management of Childhood Illnesses (IMCI) diagnostic and treatment algorithms. We explored barriers and opportunities for improved case management of childhood pneumonia in Lagos and Jigawa states, Nigeria. / Methods: A mixed‐method analysis was conducted to assess the current health system capacity to deliver quality care. This was done through audits of 16 facilities in Jigawa and 14 facilities in Lagos, questionnaires (n = 164) and 13 focus group discussions with providers. Field observations provided context for data analysis and triangulation. / Results: There were more private providers in Lagos (4/8 secondary facilities) and more government providers in Jigawa (4/8 primary, 3/3 secondary, and 1/1 tertiary facilities). Oxygen and pulse oximeters were available in two of three in Jigawa and six of eight in Lagos of the sampled secondary care facilities. None of the eight primary facilities surveyed in Jigawa had oxygen or pulse oximetry available while in Lagos two of three primary facilities had oxygen and one of three had pulse oximeters. Other IMCI and emergency equipment were also lacking including respiratory rate timers, particularly in Jigawa state. Health care providers scored poorly on knowledge of IMCI, though previous IMCI training was associated with better knowledge. Key enabling factors in delivering pediatric care highlighted by health care providers included accountability procedures and feedback loops, the provision of free medication for children, and philanthropic acts. Common barriers to provide care included the burden of out‐of‐pocket payments, challenges in effective communication with caregivers, delayed presentation, and lack of clear diagnosis, and case management guidelines. / Conclusion: There is an urgent need to improve how the prevention and treatment of pediatric pneumonia is directed in both Lagos and Jigawa. Priority areas for reducing pediatric pneumonia burden are training and mentoring of health care providers, community health education, and introduction of oximeters and oxygen supply

R^4 counterterm and E7(7) symmetry in maximal supergravity

The coefficient of a potential R^4 counterterm in N=8 supergravity has been shown previously to vanish in an explicit three-loop calculation. The R^4 term respects N=8 supersymmetry; hence this result poses the question of whether another symmetry could be responsible for the cancellation of the three-loop divergence. In this article we investigate possible restrictions from the coset symmetry E7(7)/SU(8), exploring the limits as a single scalar becomes soft, as well as a double-soft scalar limit relation derived recently by Arkani-Hamed et al. We implement these relations for the matrix elements of the R^4 term that occurs in the low-energy expansion of closed-string tree-level amplitudes. We find that the matrix elements of R^4 that we investigated all obey the double-soft scalar limit relation, including certain non-maximally-helicity-violating six-point amplitudes. However, the single-soft limit does not vanish for this latter set of amplitudes, which suggests that the E7(7) symmetry is broken by the R^4 term.Comment: 33 pages, typos corrected, published versio

X-ray Absorption and Reflection in Active Galactic Nuclei

X-ray spectroscopy offers an opportunity to study the complex mixture of emitting and absorbing components in the circumnuclear regions of active galactic nuclei, and to learn about the accretion process that fuels AGN and the feedback of material to their host galaxies. We describe the spectral signatures that may be studied and review the X-ray spectra and spectral variability of active galaxies, concentrating on progress from recent Chandra, XMM-Newton and Suzaku data for local type 1 AGN. We describe the evidence for absorption covering a wide range of column densities, ionization and dynamics, and discuss the growing evidence for partial-covering absorption from data at energies > 10 keV. Such absorption can also explain the observed X-ray spectral curvature and variability in AGN at lower energies and is likely an important factor in shaping the observed properties of this class of source. Consideration of self-consistent models for local AGN indicates that X-ray spectra likely comprise a combination of absorption and reflection effects from material originating within a few light days of the black hole as well as on larger scales. It is likely that AGN X-ray spectra may be strongly affected by the presence of disk-wind outflows that are expected in systems with high accretion rates, and we describe models that attempt to predict the effects of radiative transfer through such winds, and discuss the prospects for new data to test and address these ideas.Comment: Accepted for publication in the Astronomy and Astrophysics Review. 58 pages, 9 figures. V2 has fixed an error in footnote