Phase-Sensitive Vibrational Sum and Difference Frequency-Generation Spectroscopy Enabling Nanometer-Depth Profiling at Interfaces

The unique physical and chemical properties of interfaces are governed by a finite depth that describes the transition from the topmost atomic layer to the properties of the bulk material. Thus, understanding the physical nature of interfaces requires detailed insight into the different structures, chemical compositions, and physical processes that form this interfacial region. Such insight has traditionally been difficult to obtain from experiments, as it requires a combination of structural and chemical sensitivity with spatial depth resolution on the nanometer scale. In this contribution, we present a vibrational spectroscopic approach that can overcome these limitations. By combining phase-sensitive sum and difference frequency-generation (SFG and DFG, respectively) spectroscopy and by selectively determining different nonlinear interaction pathways, we can extract precise depth information and correlate these to specific vibrationally resonant modes of interfacial species. We detail the mathematical framework behind this approach and demonstrate the performance of this technique in two sets of experiments on selected model samples. An analysis of the results shows an almost perfect match between experiment and theory, confirming the practicability of the proposed concept under realistic experimental conditions. Furthermore, in measurements with self-assembled monolayers of different chain lengths, we analyze the spatial accuracy of the technique and find that the precision can even reach the sub-nanometer regime. We also discuss the implications and the information content of such depth-sensitive measurements and show that the concept is very general and goes beyond the analysis of the depth profiles. The presented SFG/DFG technique offers new perspectives for spectroscopic investigations of interfaces in various material systems by providing access to fundamental observables that have so far been inaccessible by experiments. Here, we set the theoretical and experimental basis for such future investigations

Approximating Nash Equilibria and Dense Bipartite Subgraphs via an Approximate Version of Carathéodory's Theorem

We present algorithmic applications of an approximate version of Caratheodory's theorem. The theorem states that given a set of vectors X in R^d, for every vector in the convex hull of X there exists an ε-close (under the p-norm distance, for 2 ≤ p < ∞) vector that can be expressed as a convex combination of at most b vectors of X, where the bound b depends on ε and the norm p and is independent of the dimension d. This theorem can be derived by instantiating Maurey's lemma, early references to which can be found in the work of Pisier (1981) and Carl (1985). However, in this paper we present a self-contained proof of this result. Using this theorem we establish that in a bimatrix game with n x n payoff matrices A, B, if the number of non-zero entries in any column of A+B is at most s then an ε-Nash equilibrium of the game can be computed in time n^O(log s/ε^2}). This, in particular, gives us a polynomial-time approximation scheme for Nash equilibrium in games with fixed column sparsity s. Moreover, for arbitrary bimatrix games---since s can be at most n---the running time of our algorithm matches the best-known upper bound, which was obtained by Lipton, Markakis, and Mehta (2003). The approximate Carathéodory's theorem also leads to an additive approximation algorithm for the densest k-bipartite subgraph problem. Given a graph with n vertices and maximum degree d, the developed algorithm determines a k x k bipartite subgraph with density within ε (in the additive sense) of the optimal density in time n^O(log d/ε^2)

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

The JWST Resolved Stellar Populations Early Release Science Program VI. Identifying Evolved Stars in Nearby Galaxies

We present an investigation of evolved stars in the nearby star-forming galaxy WLM, using NIRCam imaging from the JWST resolved stellar populations early-release science (ERS) program. We find that various combinations of the F090W, F150W, F250M, and F430M filters can effectively isolate red supergiants (RSGs) and thermally-pulsing asymptotic giant branch (TP-AGB) stars from one another, while also providing a reasonable separation of the primary TP-AGB subtypes: carbon-rich C-type stars and oxygen-rich M-type stars. The classification scheme we present here agrees very well with the well-established Hubble Space Telescope (HST) medium-band filter technique. The ratio of C to M-type stars (C/M) is 0.8$\pm$0.1 for both the new JWST and the HST classifications, which is within one sigma of empirical predictions from optical narrow-band CN and TiO filters. The evolved star colors show good agreement with the predictions from the PARSEC$+$COLIBRI stellar evolutionary models, and the models indicate a strong metallicity dependence that makes stellar identification even more effective at higher metallicity. However, the models also indicate that evolved star identification with NIRCam may be more difficult at lower metallicies. We test every combination of NIRCam filters using the models and present additional filters that are also useful for evolved star studies. We also find that $\approx$90\% of the dusty evolved stars are carbon-rich, suggesting that carbonaceous dust dominates the present-day dust production in WLM, similar to the findings in the Magellanic Clouds. These results demonstrate the usefulness of NIRCam in identifying and classifying dust-producing stars without the need for mid-infrared data.Comment: 15 page, 12 figures, submitted to AAS Journal

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

The JWST Resolved Stellar Populations Early Release Science Program. II. Survey Overview

We present the JWST Resolved Stellar Populations Early Release Science (ERS) program. We obtained 27.5 hr of NIRCam and NIRISS imaging of three targets in the Local Group (Milky Way globular cluster M92, ultrafaint dwarf galaxy Draco II, and star-forming dwarf galaxy WLM), which span factors of similar to 10(5) in luminosity, similar to 10(4) in distance, and similar to 10(5) in surface brightness. We describe the survey strategy, scientific and technical goals, implementation details, present select NIRCam color-magnitude diagrams (CMDs), and validate the NIRCam exposure time calculator (ETC). Our CMDs are among the deepest in existence for each class of target. They touch the theoretical hydrogen-burning limit in M92 (&lt;0.08 M-circle dot; M-F090W similar to +13.6), include the lowest-mass stars observed outside the Milky Way in Draco II (0.09M(circle dot); M-F090W similar to +12.1), and reach similar to 1.5 mag below the oldest main-sequence turnoff in WLM (M-F090W similar to +4.6). The PARSEC stellar models provide a good qualitative match to the NIRCam CMDs, though they are similar to 0.05 mag too blue compared to M92 F090W - F150W data. Our CMDs show detector-dependent color offsets ranging from similar to 0.02 mag in F090W - F150W to similar to 0.1 mag in F277W - F444W; these appear to be due to differences in the zero-point calibrations among the detectors. The NIRCam ETC (v2.0) matches the signal-to-noise ratios based on photon noise in uncrowded fields, but the ETC may not be accurate in more crowded fields, similar to what is known for the Hubble Space Telescope. We release the point-source photometry package DOLPHOT, optimized for NIRCam and NIRISS, for the community

Latent variables and route choice behavior

In the last decade, a broad array of disciplines has shown a general interest in enhancing discrete choice models by considering the incorporation of psychological factors affecting decision making. This paper provides insight into the comprehension of the determinants of route choice behavior by proposing and estimating a hybrid model that integrates latent variable and route choice models. Data contain information about latent variable indicators and chosen routes of travelers driving regularly from home to work in an urban network. Choice sets include alternative routes generated with a branch and bound algorithm. A hybrid model consists of measurement equations, which relate latent variables to measurement indicators and utilities to choice indicators, and structural equations, which link travelers' observable characteristics to latent variables and explanatory variables to utilities. Estimation results illustrate that considering latent variables (i.e., memory, habit, familiarity, spatial ability, time saving skills) alongside traditional variables (e.g., travel time, distance, congestion level) enriches the comprehension of route choice behavior