In this short note, we investigate the existence of universal relations between the gravimagnetic Love number of irrotational stars and the dimensionless moment of inertia. These Love numbers take into account the internal motion of the fluid, while the star is globally irrotational. The goal is to extend the so-called I-Love-Q relations - providing a strong correlation between the gravitoelectric Love number, the dimensionless moment of inertia and the dimensionless rotation-induced quadrupole - to the gravitomagnetic sector, where internal motion is taken into account. As a byproduct, we present for the first time this new gravitomagnetic Love number for realistic equations of state.

Markov decision processes (MDPs) with multi-dimensional weights are useful to analyze systems with multiple objectives that may be conflicting and require the analysis of trade-offs. We study the complexity of percentile queries in such MDPs and give algorithms to synthesize strategies that enforce such constraints. Given a multi-dimensional weighted MDP and a quantitative payoff function $f$, thresholds $v_i$ (one per dimension), and probability thresholds $\alpha_i$, we show how to compute a single strategy to enforce that for all dimensions $i$, the probability of outcomes $\rho$ satisfying $f_i(\rho) \geq v_i$ is at least $\alpha_i$. We consider classical quantitative payoffs from the literature (sup, inf, lim sup, lim inf, mean-payoff, truncated sum, discounted sum). Our work extends to the quantitative case the multi-objective model checking problem studied by Etessami et al. in unweighted MDPs.

We generalize the notion of kinematical Lie algebra introduced in physics for the classification of the various possible relativity algebras an isotropic spacetime can accommodate. We first give an elementary proof of the fact that such a generalized kinematical Lie algebra $\mathfrak{g}$ always carries a canonical structure of symplectic involutive Lie algebra (shortly ``siLa''). In other words, if $G$ is a connected Lie group admitting $\mathfrak{g}$ as Lie algebra, there always exists a Lie subgroup $H$ of $G$ constituted by the elements of $G$ that are fixed under an involutive automorphism of $G$ and such that the homogenenous space $M=G/H$ is a symplectic symmetric space. In particular, the manifold $M$ canonically carries a $G$-invariant linear torsionfree connection $\nabla$ whose geodesic symmetries centered at all points extend as global $\nabla$-affine transformations of $M$. The manifold $M$ is also canonically equipped with a symplectic structure $\omega$ which is invariant under every geodesic symmetry, implying in particular that it is parallel w.r.t the linear connection: $\nabla\omega=0$. In a second part, we give a complete description of the fine structure of our generalized siLa's. Our discussion yields a complete classification of such sila's.

In this note, we consider how the bundle geometry of field space interplays with the covariant phase space methods so as to allow to write results of some generality on the presymplectic structure of invariant gauge theories coupled to matter. We obtain in particular the generic form of Noether charges associated with field-independent and field-dependent gauge parameters, as well as their Poisson bracket. We also provide the general field-dependent gauge transformations of the presymplectic potential and 2-form, which clearly highlight the problem posed by boundaries in generic situations. We then conduct a comparative analysis of two strategies recently considered to evade the boundary problem and associate a modified symplectic structure to a gauge theory over a bounded regions: namely the use of edge modes on the one hand, and of variational connections on the other. To do so, we first try to give the clearest geometric account of both, showing in particular that edge modes are a special case of differential geometric tool of gauge symmetry reduction known as the "dressing field method". Applications to Yang-Mills theory and General Relativity reproduce or generalise several results of the recent literature.