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Perfect Roman Domination and Unique Response Roman Domination

The idea of enumeration algorithms with polynomial delay is to polynomially bound the running time between any two subsequent solutions output by the enumeration algorithm. While it is open for more than four decades if all minimal dominating sets of a graph can be enumerated in output-polynomial time, it has recently been proven that pointwise-minimal Roman dominating functions can be enumerated even with polynomial delay. The idea of the enumeration algorithm was to use polynomial-time solvable extension problems. We use this as a motivation to prove that also two variants of Roman dominating functions studied in the literature, named perfect and unique response, can be enumerated with polynomial delay. This is interesting since Extension Perfect Roman Domination is W[1]-complete if parameterized by the weight of the given function and even W[2]-complete if parameterized by the number vertices assigned 0 in the pre-solution, as we prove. Otherwise, efficient solvability of extension problems and enumerability with polynomial delay tend to go hand-in-hand. We achieve our enumeration result by constructing a bijection to Roman dominating functions, where the corresponding extension problem is polynomimaltime solvable. Furthermore, we show that Unique Response Roman Domination is solvable in polynomial time on split graphs, while Perfect Roman Domination is NP-complete on this graph class, which proves that both variations, albeit coming with a very similar definition, do differ in some complexity aspects. This way, we also solve an open problem from the literature

Extracurricular activities to enhance the employment outcomes of Mathematics graduates

The employability skills of Mathematics graduates have been an area of concern for the mathematics community, employers and stake holders nationwide. Higher education institutions are addressing these skills in many ways, embarking on different strategies, to enhance the employment outcomes of their graduates. Although this topic has received a good deal of attention lately, it is useful to explore different ways to enhance students’ employability skills as they can impact positively on their employment outcomes. This may take the form of specific employability initiatives at department level, appropriate for the programme portfolio, to complement traditional careers advice services provided centrally by the university. This paper describes how the employability skills of Mathematics students can be enhanced by providing relevant extracurricular activities throughout their degree programmes, and discusses the implementation at our institution. Student feedback on the activities has been very positive and the implementation appears to have enhanced our graduates’ employability outcomes

STL: Surprisingly Tricky Logic (for System Validation)

Much of the recent work developing formal methods techniques to specify or learn the behavior of autonomous systems is predicated on a belief that formal specifications are interpretable and useful for humans when checking systems. Though frequently asserted, this assumption is rarely tested. We performed a human experiment (N = 62) with a mix of people who were and were not familiar with formal methods beforehand, asking them to validate whether a set of signal temporal logic (STL) constraints would keep an agent out of harm and allow it to complete a task in a gridworld capture-the-flag setting. Validation accuracy was $45\% \pm 20\%$ (mean $\pm$ standard deviation). The ground-truth validity of a specification, subjects' familiarity with formal methods, and subjects' level of education were found to be significant factors in determining validation correctness. Participants exhibited an affirmation bias, causing significantly increased accuracy on valid specifications, but significantly decreased accuracy on invalid specifications. Additionally, participants, particularly those familiar with formal methods, tended to be overconfident in their answers, and be similarly confident regardless of actual correctness. Our data do not support the belief that formal specifications are inherently human-interpretable to a meaningful degree for system validation. We recommend ergonomic improvements to data presentation and validation training, which should be tested before claims of interpretability make their way back into the formal methods literature

The Mass-Radius Relation Of Young Stars. I. Usco 5, An M4.5 Eclipsing Binary In Upper Scorpius Observed By K2

We present the discovery that UScoCTIO 5, a known spectroscopic binary in the Upper Scorpius star-forming region (P = 34 days, M-tot sin(i) = 0.64M(circle dot)), is an eclipsing system with both primary and secondary eclipses apparent in K2 light curves obtained during Campaign 2. We have simultaneously fit the eclipse profiles from the K2 light curves and the existing RV data to demonstrate that UScoCTIO 5 consists of a pair of nearly identical M4.5 stars with M-A = 0.329 +/- 0.002 M-circle dot, R-A = 0.834 +/- 0.006 R-circle dot, M-B = 0.317 +/- 0.002 M-circle dot, and R-B = 0.810 +/- 0.006 R-circle dot. The radii are broadly consistent with pre-main-sequence ages predicted by stellar evolutionary models, but none agree to within the uncertainties. All models predict systematically incorrect masses at the 25%-50% level for the HR diagram position of these mid-M dwarfs, suggesting significant modifications to mass-dependent outcomes of star and planet formation. The form of the discrepancy for most model sets is not that they predict luminosities that are too low, but rather that they predict temperatures that are too high, suggesting that the models do not fully encompass the physics of energy transport (via convection and/or missing opacities) and/or a miscalibration of the SpT-T-eff scale. The simplest modification to the models (changing T-eff to match observations) would yield an older age for this system, in line with the recently proposed older age of Upper Scorpius (tau similar to 11 Myr).NASA Science Mission directorateW. M. Keck FoundationAstronom

Offensive Alliances in Signed Graphs

Signed graphs have been introduced to enrich graph structures expressing relationships between persons or general social entities, introducing edge signs to reflect the nature of the relationship, e.g., friendship or enmity. Independently, offensive alliances have been defined and studied for undirected, unsigned graphs. We join both lines of research and define offensive alliances in signed graphs, hence considering the nature of relationships. Apart from some combinatorial results, mainly on k-balanced and k-anti-balanced signed graphs (where the latter is a newly introduced family of signed graphs), we focus on the algorithmic complexity of finding smallest offensive alliances, looking at a number of parameterizations. While the parameter solution size leads to an FPT result for unsigned graphs, we obtain W[2]-completeness for the signed setting. We introduce new parameters for signed graphs, e.g., distance to weakly balanced signed graphs, that could be of independent interest. We show that these parameters yield FPT results. Here, we make use of the recently introduced parameter neighborhood diversity for signed graphs

Numerical and experimental comparison of confinement effects on a fully-passive oscillating-foil turbine

A numerical and experimental comparison of a fully-passive oscillating-foil turbine operating in different confinement levels is conducted to assert how well CFD-based FSI simulations can predict the performances of the turbine. It is found the present 3D URANS simulations match reasonably well the experimental observations, especially in terms of pitch angles and power extraction. Indeed, the results confirm that confinement increases the extracted power and the efficiency of the fully-passive blade. At low confinement level, the main flow features are shown to be well captured by the simulations. At large confinement levels, some issues with lateral walls interactions are discussed as possible explanation for the observed discrepancies