Strong and weak interactions of rational vector rogue waves and solitons to any n -component nonlinear Schrödinger system with higher-order effects

The higher-order effects play an important role in the wave propagations of ultrashort (e.g. subpicosecond or femtosecond) light pulses in optical fibres. In this paper, we investigate any n -component fourth-order nonlinear Schrödinger ( n -FONLS) system with non-zero backgrounds containing the n -Hirota equation and the n -Lakshmanan–Porsezian–Daniel equation. Based on the loop group theory, we find the multi-parameter family of novel rational vector rogue waves (RVRWs) of the n -FONLS equation starting from the plane-wave solutions. Moreover, we exhibit the weak and strong interactions of some representative RVRW structures. In particular, we also find that the W-shaped rational vector dark and bright solitons of the n -FONLS equation as the second- and fourth-order dispersion coefficients satisfy some relation. Furthermore, we find the higher-order RVRWs of the n -FONLS equation. These obtained rational solutions will be useful in the study of RVRW phenomena of multi-component nonlinear wave models in nonlinear optics, deep ocean and Bose–Einstein condensates.

Exploring the low $$\tan \beta $$ region of two Higgs doublet models at the LHC

Current interpretations of the LHC results on two Higgs doublet models (2HDM) underestimate the sensitivity due to neglecting higher order effects. In this work, we revisit the impact of these effects using the current cross-section times branching ratio limits of the $$A\rightarrow hZ, H \rightarrow VV$$ A → h Z , H → V V and $$H\rightarrow hh$$ H → h h channels. With a degenerate heavy Higgs mass $$m_\varPhi $$ m Φ , we find that the LHC searches gain sensitivity to the small $$\tan \beta $$ tan β region after including loop corrections, even close to $$\cos (\beta -\alpha )=0$$ cos ( β - α ) = 0 which is not reachable at tree level for all types of 2HDM. For a benchmark point with $$m_\varPhi =300$$ m Φ = 300 GeV, $$\tan \beta <1.8(1.2)$$ tan β < 1.8 ( 1.2 ) can be probed for the Type-I(II) 2HDM model for $$\cos (\beta -\alpha )=0$$ cos ( β - α ) = 0 . When the deviation from $$\cos (\beta -\alpha )=0$$ cos ( β - α ) = 0 is larger, the region for which current searches have exclusion potential becomes larger.

Responsible innovation, anticipation and responsiveness: case studies of algorithms in decision support in justice and security, and an exploration of potential, unintended, undesirable, higher-order effects

The collection and use of personal data on citizens in the design and deployment of algorithms in the domain of justice and security is a sensitive topic. Values like fairness, autonomy, privacy, accuracy, transparency and property are at stake. Negative examples of algorithms that propagate or exacerbate biases, inequalities or injustices have received ample attention, both in academia and in popular media. To supplement this view, we will discuss two positive examples of Responsible Innovation (RI): the design and deployment of algorithms in decision support, with good intentions and careful approaches. We then explore potential, unintended, undesirable, higher-order effects of algorithms—effects that may occur despite good intentions and careful approaches. We do that by engaging with anticipation and responsiveness, two key dimensions of Responsible Innovation. We close the paper with proposing a framework and a series of tentative recommendations to promote anticipation and responsiveness in the design and deployment of algorithms in decision support in the domain of justice and security.

Reputations for Resolve and Higher-Order Beliefs in Crisis Bargaining

Reputations for resolve are said to be one of the few things worth fighting for, yet they remain inadequately understood. Discussions of reputation focus almost exclusively on first-order belief change— A stands firm, B updates its beliefs about A’s resolve. Such first-order reputational effects are important, but they are not the whole story. Higher-order beliefs—what A believes about B’s beliefs, and so on—matter a great deal as well. When A comes to believe that B is more resolved, this may decrease A’s resolve, and this in turn may increase B’s resolve, and so on. In other words, resolve is interdependent. We offer a framework for estimating higher-order effects, and find evidence of such reasoning in a survey experiment on quasi-elites. Our findings indicate both that states and leaders can develop potent reputations for resolve, and that higher-order beliefs are often responsible for a large proportion of these effects (40 percent to 70 percent in our experimental setting). We conclude by complementing the survey with qualitative evidence and laying the groundwork for future research.