We propose a continuous normalizing flow for sampling from the high-dimensional probability distributions of Quantum Field Theories in Physics. In contrast to the deep architectures used so far for this task, our proposal is based on a shallow design and incorporates the symmetries of the problem. We test our model on the $\phi^4$ theory, showing that it systematically outperforms a realNVP baseline in sampling efficiency, with the difference between the two increasing for larger lattices. On the largest lattice we consider, of size $32\times 32$, we improve a key metric, the effective sample size, from 1% to 66% w.r.t. the realNVP baseline.

We study the quantum modular properties of $\widehat Z{}^G$-invariants of closed three-manifolds. Higher depth quantum modular forms are expected to play a central role for general three-manifolds and gauge groups $G$. In particular, we conjecture that for plumbed three-manifolds whose plumbing graphs have $n$ junction nodes with definite signature and for rank $r$ gauge group $G$, that $\widehat Z{}^G$ is related to a quantum modular form of depth $nr$. We prove this for $G={\rm SU}(3)$ and for an infinite class of three-manifolds (weakly negative Seifert with three exceptional fibers). We also investigate the relation between the quantum modularity of $\widehat Z{}^G$-invariants of the same three-manifold with different gauge group $G$. We conjecture a recursive relation among the iterated Eichler integrals relevant for $\widehat Z{}^G$ with $G={\rm SU}(2)$ and ${\rm SU}(3)$, for negative Seifert manifolds with three exceptional fibers. This is reminiscent of the recursive structure among mock modular forms playing the role of Vafa-Witten invariants for ${\rm SU}(N)$. We prove the conjecture when the three-manifold is moreover an integral homological sphere.

The first images of the jet and low velocity component (LVC) from the strongly accreting classical T Tauri star RU Lupi are presented. Adaptive optics assisted spectro-imaging of forbidden emission lines was used. The main aim of the observations was to test the conclusion from a recent spectro-astrometric study that the narrow component of the LVC is tracing an MHD disk wind, and to estimate the mass loss rate in the wind. The structure and morphology of the component supports a wind origin for the NC. An upper limit to the launch radius and semi-opening angle of the wind in [O I]{\lambda}6300 emission are estimated to be 2 au and 19° in agreement with MHD wind models for high accretors. The height of the [O I]{\lambda}6300 wind emitting region, a key parameter for the derivation of the mass loss rate, is estimated for the first time at approximately 35 au giving M_out = 2.6 x 10^-11 M_sun/yr. When compared to the derived mass accretion rate of M_acc = 1.6 x 10^-7 M_sun/yr, the efficiency in the wind is too low for the wind to be significantly contributing to angular momentum removal.

One of the fundamental results in graph minor theory is that for every planar graph~$H$, there is a minimum integer~$f(H)$ such that graphs with no minor isomorphic to~$H$ have treewidth at most~$f(H)$. The best known bound for an arbitrary planar $H$ is ${O(|V(H)|^9\operatorname{poly~log} |V(H)|)}$. We show that if $H$ is the disjoint union of cycles, then $f(H)$ is $O(|V(H)|\log^2 |V(H)|)$, which is a$\log|V(H)|$ factor away being optimal.

One of the fundamental results in graph minor theory is that for every planar graph~$H$, there is a minimum integer~$f(H)$ such that graphs with no minor isomorphic to~$H$ have treewidth at most~$f(H)$. The best known bound for an arbitrary planar $H$ is ${O(|V(H)|^9\operatorname{poly~log} |V(H)|)}$. We show that if $H$ is the disjoint union of cycles, then $f(H)$ is $O(|V(H)|\log^2 |V(H)|)$, which is a $\log|V(H)|$ factor away being optimal.