Zermelo Navigation and a Speed Limit to Quantum Information Processing

We use a specific geometric method to determine speed limits to the implementation of quantum gates in controlled quantum systems that have a specific class of constrained control functions. We achieve this by applying a recent theorem of Shen, which provides a connection between time optimal navigation on Riemannian manifolds and the geodesics of a certain Finsler metric of Randers type. We use the lengths of these geodesics to derive the optimal implementation times (under the assumption of constant control fields) for an arbitrary quantum operation (on a finite dimensional Hilbert space), and explicitly calculate the result for the case of a controlled single spin system in a magnetic field, and a swap gate in a Heisenberg spin chain

Subtended angles

The first is partially supported by NSF grant DMS 1301614. The second author is partially supported by NSF grant DMS 1301614 and MULTIPLEX no. 317532. The third author’s research supported in part by the Hungarian National Science Foundation OTKA 104343, by the Simons Foundation Collaboration Grant #317487, and by the European Research Council Advanced Investigators Grant 267195

Low-density star cluster formation: Discovery of a young faint fuzzy on the outskirts of the low-mass spiral galaxy NGC 247

The classical globular clusters found in all galaxy types have half-light radii of rh ~2-4 pc, which have been tied to formation in the dense cores of giant molecular clouds. Some old star clusters have larger sizes, and it is unclear if these represent a fundamentally different mode of low-density star cluster formation. We report the discovery of a rare, young \u27faint fuzzy\u27 star cluster, NGC 247-SC1, on the outskirts of the low-mass spiral galaxy NGC 247 in the nearby Sculptor group, and measure its radial velocity using Keck spectroscopy. We use Hubble Space Telescope imaging to measure the cluster half-light radius of rh ≃ 12 pc and a luminosity of LV ≃ 4 × 105Lθ. We produce a colour-magnitude diagram of cluster stars and compare to theoretical isochrones, finding an age of ≃300 Myr, a metallicity of [Z/H] ~-0.6 and an inferred mass of M∗ ≃ 9 × 104Mθ. The narrow width of blue-loop star magnitudes implies an age spread of ≲50 Myr, while no old red-giant branch stars are found, so SC1 is consistent with hosting a single stellar population, modulo several unexplained bright \u27red straggler\u27 stars. SC1 appears to be surrounded by tidal debris, at the end of an ∼2 kpc long stellar filament that also hosts two low-mass, low-density clusters of a similar age. We explore a link between the formation of these unusual clusters and an external perturbation of their host galaxy, illuminating a possible channel by which some clusters are born with large sizes

Extendibility of bilinear forms on banach sequence spaces

[EN] We study Hahn-Banach extensions of multilinear forms defined on Banach sequence spaces. We characterize c(0) in terms of extension of bilinear forms, and describe the Banach sequence spaces in which every bilinear form admits extensions to any superspace.The second author was supported by MICINN Project MTM2011-22417.DANIEL CARANDO; Sevilla Peris, P. (2014). Extendibility of bilinear forms on banach sequence spaces. Israel Journal of Mathematics. 199(2):941-954. https://doi.org/10.1007/s11856-014-0003-9S9419541992F. Albiac and N. J. Kalton, Topics in Banach Space Theory, Graduate Texts in Mathematics, Vol. 233, Springer, New York, 2006.R. Arens, The adjoint of a bilinear operation, Proceedings of the American Mathematical Society 2 (1951), 839–848.R. Arens, Operations induced in function classes, Monatshefte für Mathematik 55 (1951), 1–19.R. M. Aron and P. D. Berner, A Hahn-Banach extension theorem for analytic mappings, Bulletin de la Société Mathématique de France 106 (1978), 3–24.S. Banach, Sur les fonctionelles linéaires, Studia Mathematica 1 (1929), 211–216.S. Banach, Théorie des opérations linéaires, (Monogr. Mat. 1) Warszawa: Subwncji Funduszu Narodowej. VII, 254 S., Warsaw, 1932.D. Carando, Extendible polynomials on Banach spaces, Journal of Mathematical Analysis and Applications 233 (1999), 359–372.D. Carando, Extendibility of polynomials and analytic functions on l p, Studia Mathematica 145 (2001), 63–73.D. Carando, V. Dimant and P. Sevilla-Peris, Limit orders and multilinear forms on lp spaces, Publications of the Research Institute for Mathematical Sciences 42 (2006), 507–522.J. M. F. Castillo, R. García, A. Defant, D. Pérez-García and J. Suárez, Local complementation and the extension of bilinear mappings, Mathematical Proceedings of the Cambridge Philosophical Society 152 (2012), 153–166.J. M. F. Castillo, R. García and J. A. Jaramillo, Extension of bilinear forms on Banach spaces, Proceedings of the American Mathematical Society 129 (2001), 3647–3656.P. Cembranos and J. Mendoza, The Banach spaces ℓ ∞(c 0) and c 0(ℓ ∞) are not isomorphic, Journal of Mathematical Analysis and Applications 367 (2010), 461–463.A. Defant and K. Floret, Tensor Norms and Operator Ideals, North-Holland Mathematics Studies, Vol. 176, North-Holland Publishing Co., Amsterdam, 1993.A. Defant and C. Michels, Norms of tensor product identities, Note di Matematica 25 (2005/06), 129–166.J. Diestel, H. Jarchow and A. Tonge, Absolutely Summing Operators, Cambridge Studies in Advanced Mathematics, Vol. 43, Cambridge University Press, Cambridge, 1995.D. J. H. Garling, On symmetric sequence spaces, Proceedings of the London Mathematical Society (3) 16 (1966), 85–106.A. Grothendieck, Résumé de la théorie métrique des produits tensoriels topologiques, Bol. Soc. Mat. São Paulo 8 (1953), 1–79.H. Hahn, Über lineare Gleichungssysteme in linearen Räumen, Journal für die Reine und Angewandte Mathematik 157 (1927), 214–229.R. C. James, Bases and reflexivity of Banach spaces, Annals of Mathematics (2) 52 (1950), 518–527.H. Jarchow, C. Palazuelos, D. Pérez-García and I. Villanueva, Hahn-Banach extension of multilinear forms and summability, Journal of Mathematical Analysis and Applications 336 (2007), 1161–1177.W. B. Johnson and L. Tzafriri, On the local structure of subspaces of Banach lattices, Israel Journal of Mathematics 20 (1975), 292–299.P. Kirwan and R. A. Ryan, Extendibility of homogeneous polynomials on Banach spaces, Proceedings of the American Mathematical Society 126 (1998), 1023–1029.J. Lindenstrauss and A. Pełczyński, Absolutely summing operators in Lp-spaces and their applications, Studia Mathematica 29 (1968), 275–326.J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces. II, Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas], Vol. 97, Springer-Verlag, Berlin, 1979. Function spaces.G. Pisier, Factorization of Linear Operators and Geometry of Banach Spaces, CBMS Regional Conference Series in Mathematics, Vol. 60, Published for the Conference Board of the Mathematical Sciences, Washington, DC, 1986.M. Fernndez-Unzueta and A. Prieto, Extension of polynomials defined on subspaces, Mathematical Proceedings of the Cambridge Philosophical Society 148 (2010), 505–518.W. L. C. Sargent, Some sequence spaces related to the lp spaces, Journal of the London Mathematical Society 35 (1960), 161–171.N. Tomczak-Jaegermann, Banach-Mazur Distances and Finite-Dimensional Operator Ideals, Pitman Monographs and Surveys in Pure and Applied Mathematics, Vol. 38, Longman Scientific & Technical, Harlow, 1989

How much time do nurses have for patients? a longitudinal study quantifying hospital nurses' patterns of task time distribution and interactions with health professionals

<p>Abstract</p> <p>Background</p> <p>Time nurses spend with patients is associated with improved patient outcomes, reduced errors, and patient and nurse satisfaction. Few studies have measured how nurses distribute their time across tasks. We aimed to quantify how nurses distribute their time across tasks, with patients, in individual tasks, and engagement with other health care providers; and how work patterns changed over a two year period.</p> <p>Methods</p> <p>Prospective observational study of 57 nurses for 191.3 hours (109.8 hours in 2005/2006 and 81.5 in 2008), on two wards in a teaching hospital in Australia. The validated Work Observation Method by Activity Timing (WOMBAT) method was applied. Proportions of time in 10 categories of work, average time per task, time with patients and others, information tools used, and rates of interruptions and multi-tasking were calculated.</p> <p>Results</p> <p>Nurses spent 37.0%[95%CI: 34.5, 39.3] of their time with patients, which did not change in year 3 [35.7%; 95%CI: 33.3, 38.0]. Direct care, indirect care, medication tasks and professional communication together consumed 76.4% of nurses' time in year 1 and 81.0% in year 3. Time on direct and indirect care increased significantly (respectively 20.4% to 24.8%, P < 0.01;13.0% to 16.1%, P < 0.01). Proportion of time on medication tasks (19.0%) did not change. Time in professional communication declined (24.0% to 19.2%, P < 0.05). Nurses completed an average of 72.3 tasks per hour, with a mean task length of 55 seconds. Interruptions arose at an average rate of two per hour, but medication tasks incurred 27% of all interruptions. In 25% of medication tasks nurses multi-tasked. Between years 1 and 3 nurses spent more time alone, from 27.5%[95%CI 24.5, 30.6] to 39.4%[34.9, 43.9]. Time with health professionals other than nurses was low and did not change.</p> <p>Conclusions</p> <p>Nurses spent around 37% of their time with patients which did not change. Work patterns were increasingly fragmented with rapid changes between tasks of short length. Interruptions were modest but their substantial over-representation among medication tasks raises potential safety concerns. There was no evidence of an increase in team-based, multi-disciplinary care. Over time nurses spent significantly less time talking with colleagues and more time alone.</p

Parental perceptions of barriers and facilitators to preventing child unintentional injuries within the home: a qualitative study

Background Childhood unintentional injury represents an important global health problem. Most of these injuries occur at home, and many are preventable. The main aim of this study was to identify key facilitators and barriers for parents in keeping their children safe from unintentional injury within their homes. A further aim was to develop an understanding of parents’ perceptions of what might help them to implement injury prevention activities. Methods Semi-structured interviews were conducted with sixty-four parents with a child aged less than five years at parent’s homes. Interview data was transcribed verbatim, and thematic analysis was undertaken. This was a Multi-centre qualitative study conducted in four study centres in England (Nottingham, Bristol, Norwich and Newcastle). Results Barriers to injury prevention included parents’ not anticipating injury risks nor the consequences of some risk-taking behaviours, a perception that some injuries were an inevitable part of child development, interrupted supervision due to distractions, maternal fatigue and the presence of older siblings, difficulties in adapting homes, unreliability and cost of safety equipment and provision of safety information later than needed in relation to child age and development. Facilitators for injury prevention included parental supervision and teaching children about injury risks. This included parents’ allowing children to learn about injury risks through controlled risk taking, using “safety rules” and supervising children to ensure that safety rules were adhered to. Adapting the home by installing safety equipment or removing hazards were also key facilitators. Some parents felt that learning about injury events through other parents’ experiences may help parents anticipate injury risks. Conclusions There are a range of barriers to, and facilitators for parents undertaking injury prevention that would be addressable during the design of home safety interventions. Addressing these in future studies may increase the effectiveness of interventions

Pointwise estimates to the modified Riesz potential

In a smooth domain a function can be estimated pointwise by the classical Riesz potential of its gradient. Combining this estimate with the boundedness of the classical Riesz potential yields the optimal Sobolev-Poincar, inequality. We show that this method gives a Sobolev-Poincar, inequality also for irregular domains whenever we use the modified Riesz potential which arise naturally from the geometry of the domain. The exponent of the Sobolev-Poincar, inequality depends on the domain. The Sobolev-Poincar, inequality given by this approach is not sharp for irregular domains, although the embedding for the modified Riesz potential is optimal. In order to obtain the results we prove a new pointwise estimate for the Hardy-Littlewood maximal operator.Peer reviewe