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

Eine Arbeitslosenversicherung für den Euroraum als automatischer Stabilisator: Grenzen und Möglichkeiten. Endbericht: Gutachten im Auftrag des Bundesministeriums für Arbeit, Soziales und Konsumentenschutz der Republik Österreich

Die vorliegende Studie analysiert die makroökonomischen Stabilisierungs- und mikroökonomischen Verteilungswirkungen der Einführung einer Europäischen Arbeitslosenversicherung. Auf Grundlage dynamischer makroökonomischer Simulationen wird gezeigt, dass ein solches Transfersystem innerhalb des Euroraums - je nach Ausgestaltung - zu einer merklichen Stabilisierung der wirtschaftlichen Entwicklung geführt hätte. Dies gilt selbst für eine gemessen am Transferumfang relativ kleine Europäische Arbeitslosenversicherung mit einer maximalen Bezugszeit von sechs Monaten und einer Nettoersatzquote von 30 Prozent; mit größerem Leistungsumfang steigt die Stabilisierungswirkung, aber im Gegenzug auch die möglicherweise unerwünschten Wirkungen auf Arbeitsanreize und das Ausmaß der Umverteilung zwischen den Mitgliedsländern. Die Verteilungswirkungen dürften insgesamt aus politischer Sicht unproblematisch sein; tendenziell finden sich leicht progressive bis neutrale Effekte auf die Einkommensverteilung, Haushalte mit niedrigeren Einkommen profitieren also überproportional von der Einführung einer Europäischen Arbeitslosenversicherung. [...]The present study analyzes the stabilization and distributional effects of the establishment of a European unemployment insurance. Using dynamic macroeconomic simulations it is shown that, depending on the design, such a transfer system within the Eurozone would lead to a sizeable stabilization of output and employment. This is also true for an insurance scheme of relatively small size (in terms of the respective transfers to the unemployed), with a maximum period of entitlement to unemployment benefits of six months and a net replacement rate of 30 percent. A larger scheme would have greater stabilizing effects but would be coupled with potentially undesirable consequences for work incentives and fiscal redistribution between member states. From a policy perspective, the distributional effects within a country can be expected to be limited, with slightly progressive or neutral effects on income inequality. As a result, households with lower incomes are expected to disproportionately benefit from the introduction of a European unemployment insurance. [...

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