Fuzzy Simultaneous Congruences

We introduce a very natural generalization of the well-known problem of simultaneous congruences. Instead of searching for a positive integer $s$ that is specified by $n$ fixed remainders modulo integer divisors $a_1,\dots,a_n$ we consider remainder intervals $R_1,\dots,R_n$ such that $s$ is feasible if and only if $s$ is congruent to $r_i$ modulo $a_i$ for some remainder $r_i$ in interval $R_i$ for all $i$. This problem is a special case of a 2-stage integer program with only two variables per constraint which is is closely related to directed Diophantine approximation as well as the mixing set problem. We give a hardness result showing that the problem is NP-hard in general. By investigating the case of harmonic divisors, i.e. $a_{i+1}/a_i$ is an integer for all $i<n$, which was heavily studied for the mixing set problem as well, we also answer a recent algorithmic question from the field of real-time systems. We present an algorithm to decide the feasibility of an instance in time $\mathcal{O}(n^2)$ and we show that if it exists even the smallest feasible solution can be computed in strongly polynomial time $\mathcal{O}(n^3)$

Scheduling with Many Shared Resources

Consider the many shared resource scheduling problem where jobs have to be scheduled on identical parallel machines with the goal of minimizing the makespan. However, each job needs exactly one additional shared resource in order to be executed and hence prevents the execution of jobs that need the same resource while being processed. Previously a $(2m/(m+1))$-approximation was the best known result for this problem. Furthermore, a $6/5$-approximation for the case with only two machines was known as well as a PTAS for the case with a constant number of machines. We present a simple and fast 5/3-approximation and a much more involved but still reasonable 1.5-approximation. Furthermore, we provide a PTAS for the case with only a constant number of machines, which is arguably simpler and faster than the previously known one, as well as a PTAS with resource augmentation for the general case. The approximation schemes make use of the N-fold integer programming machinery, which has found more and more applications in the field of scheduling recently. It is plausible that the latter results can be improved and extended to more general cases. Lastly, we give a $5/4 - \varepsilon$ inapproximability result for the natural problem extension where each job may need up to a constant number (in particular $3$) of different resources

A practical approach to the sensitivity analysis for kinetic Monte Carlo simulation of heterogeneous catalysis

Lattice kinetic Monte Carlo simulations have become a vital tool for predictive quality atomistic understanding of complex surface chemical reaction kinetics over a wide range of reaction conditions. In order to expand their practical value in terms of giving guidelines for the atomic level design of catalytic systems, it is very desirable to readily evaluate a sensitivity analysis for a given model. The result of such a sensitivity analysis quantitatively expresses the dependency of the turnover frequency, being the main output variable, on the rate constants entering the model. In the past, the application of sensitivity analysis, such as degree of rate control, has been hampered by its exuberant computational effort required to accurately sample numerical derivatives of a property that is obtained from a stochastic simulation method. In this study, we present an efficient and robust three-stage approach that is capable of reliably evaluating the sensitivity measures for stiff microkinetic models as we demonstrate using the CO oxidation on RuO2(110) as a prototypical reaction. In the first step, we utilize the Fisher information matrix for filtering out elementary processes which only yield negligible sensitivity. Then we employ an estimator based on the linear response theory for calculating the sensitivity measure for non- critical conditions which covers the majority of cases. Finally, we adapt a method for sampling coupled finite differences for evaluating the sensitivity measure for lattice based models. This allows for an efficient evaluation even in critical regions near a second order phase transition that are hitherto difficult to control. The combined approach leads to significant computational savings over straightforward numerical derivatives and should aid in accelerating the nano-scale design of heterogeneous catalysts

Evaluation of the impact of telementoring using ECHO© technology on healthcare professionals' knowledge and self-efficacy in assessing and managing pain for people with advanced dementia nearing the end of life

Abstract Background Pain assessment and management in advanced and end-stage dementia are challenging; patients are at risk of under-diagnosis, under-assessment and under-treatment. Previous research has highlighted the importance of needs-driven training and development in this area for physicians, nurses and healthcare assistants (HCAs) across specialties, disciplines and care settings. This study used teleconferencing technology to connect healthcare professionals across multiple settings and disciplines in real-time clinics, based on the Project ECHO© model. This paper reports the evaluation of the clinics by physicians, nurses and HCAs, including their knowledge and self-efficacy in pain assessment and management for patients with advanced and end-stage dementia. Methods A mixed method evaluation comprising quantitative survey of self-reported knowledge and self-efficacy pre- and post-ECHO clinic participation, and qualitative exploration of experiences of the clinics using focus group interviews. A census approach to sampling was undertaken. Pre- and post-ECHO evaluations were administered electronically using Survey Monkey software. Mann-Whitney U tests were used to explore differences in knowledge and self-efficacy scores pre- and post-ECHO clinic participation. Statistical significance was set a-priori at p = 0.05. Focus groups were video- and audio-recorded, transcribed verbatim and analysed using Braun & Clarke’s model of thematic analysis. Results Eighteen healthcare professionals [HCPs] (physicians [n = 7], nurses [n = 10], HCA [n = 1]) and twenty HCPs (physicians [n = 10], nurses [n = 10]) completed pre- and post-ECHO evaluations respectively, reporting improvements in knowledge and self-efficacy on participation in ECHO clinics and perceived utility of the clinics. Seven HCPs (physicians [n = 2], nurses [n = 5]) participated in two focus groups. Four themes emerged: knowledge and skills development and dissemination; protected time; areas for improvement; and the future of ECHO. Conclusions Telementoring clinics for HCP education and training in pain assessment and management in advanced and end-stage dementia demonstrate a positive impact on knowledge and self-efficacy of HCPs and highlight the value of a cross-specialty network of practice which spans across disciplines/HCP types, care settings and geographical areas. Further development of ECHO services in this and in other clinical areas, shows significant potential to support delivery of high-quality care to complex patient populations

Rest-Frame Optical Spectra of Three Strongly Lensed Galaxies at z~2

We present Keck II NIRSPEC rest-frame optical spectra for three recently discovered lensed galaxies: the Cosmic Horseshoe (z = 2.38), the Clone (z = 2.00), and SDSS J090122.37+181432.3 (z = 2.26). The boost in signal-to-noise ratio (S/N) from gravitational lensing provides an unusually detailed view of the physical conditions in these objects. A full complement of high S/N rest-frame optical emission lines is measured, spanning from rest-frame 3600 to 6800AA, including robust detections of fainter lines such as H-gamma, [SII]6717,6732, and in one instance [NeII]3869. SDSS J090122.37+181432.3 shows evidence for AGN activity, and therefore we focus our analysis on star-forming regions in the Cosmic Horseshoe and the Clone. For these two objects, we estimate a wide range of physical properties, including star-formation rate (SFR), metallicity, dynamical mass, and dust extinction. In all respects, the lensed objects appear fairly typical of UV-selected star-forming galaxies at z~2. The Clone occupies a position on the emission-line diagnostic diagram of [OIII]/H-beta vs. [NII]/H-alpha that is offset from the locations of z~0 galaxies. Our new NIRSPEC measurements may provide quantitative insights into why high-redshift objects display such properties. From the [SII] line ratio, high electron densities (~1000 cm^(-3)) are inferred compared to local galaxies, and [OIII]/[OII] line ratios indicate higher ionization parameters compared to the local population. Building on previous similar results at z~2, these measurements provide further evidence (at high S/N) that star-forming regions are significantly different in high-redshift galaxies, compared to their local counterparts (abridged).Comment: 16 pages, 8 figures. Accepted for publication in the Astrophysical Journa