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The BMS$_3$ Lie algebra belongs to a one-parameter family of Lie algebras obtained by centrally extending abelian extensions of the Witt algebra by a tensor density representation. In this paper we call such Lie algebras $\hat{\mathfrak{g}}_\lambda$, with BMS$_3$ corresponding to the universal central extension of $\lambda = -1$. We construct the BRST complex for $\hat{\mathfrak{g}}_\lambda$ in two different ways: one in the language of semi-infinite cohomology and the other using the formalism of vertex operator algebras. We pay particular attention to the case of BMS$_3$ and discuss some natural field-theoretical realisations. We prove two theorems about the BRST cohomology of $\hat{\mathfrak{g}}_\lambda$. The first is the construction of a quasi-isomorphic embedding of the chiral sector of any Virasoro string as a $\hat{\mathfrak{g}}_\lambda$ string. The second is the isomorphism (as Batalin--Vilkovisky algebras) of any $\hat{\mathfrak{g}}_\lambda$ BRST cohomology and the chiral ring of a topologically twisted $N{=}2$ superconformal field theory.

We investigate how to efficiently set up work groups to boost group productivity, individual satisfaction, and learning. Therefore, we conduct a natural field experiment in a compulsory undergraduate course and study differences between self-selected and randomly assigned groups. We find that self-selected groups perform significantly worse on group assignments. Yet, students in self-selected groups learn more and are more satisfied than those in randomly assigned groups. The effect of allowing students to pick group members dominates the effect of different group compositions in self-selected groups: When controlling for the skill, gender, and home region composition of groups, the differences between self-selected and randomly formed groups persist almost unaltered. The distribution of GitHub commits per group reveals that the better average performance of randomly assigned groups is mainly driven by highly skilled individuals distributed over more groups due to the assignment mechanism. Moreover, these highly skilled individuals contribute more to the group in randomly formed groups. We argue that this mechanism explains why self-selected groups perform worse on the projects but acquire more knowledge than randomly formed groups. These findings are relevant for setting up workgroups in academic, business, and governmental organizations when tasks are not constrained to the skill set of specific individuals.

This paper introduces a geometric framework for classical cohomological field theories based on $G^{\star}$-algebras and gauge natural field theories. A BV-BFV extension of the framework is provided, which incorporates the cotangent lift of the Donaldson-Witten theory as an illustrative example., Comment: 46 pages

In viticulture, there are several applications where bud detection in vineyard images is a necessary task, susceptible of being automated through the use of computer vision methods. A common and effective family of visual detection algorithms are the scanning-window type, that slide a (usually) fixed size window along the original image, classifying each resulting windowed-patch as containing or not containing the target object. The simplicity of these algorithms finds its most challenging aspect in the classification stage. Interested in grapevine buds detection in natural field conditions, this paper presents a classification method for images of grapevine buds ranging 100 to 1600 pixels in diameter, captured in outdoor, under natural field conditions, in winter (i.e., no grape bunches, very few leaves, and dormant buds), without artificial background, and with minimum equipment requirements. The proposed method uses well-known computer vision technologies: Scale-Invariant Feature Transform for calculating low-level features, Bag of Features for building an image descriptor, and Support Vector Machines for training a classifier. When evaluated over images containing buds of at least 100 pixels in diameter, the approach achieves a recall higher than 0.9 and a precision of 0.86 over all windowed-patches covering the whole bud and down to 60% of it, and scaled up to window patches containing a proportion of 20%-80% of bud versus background pixels. This robustness on the position and size of the window demonstrates its viability for use as the classification stage in a scanning-window detection algorithms., Comment: 21 pages, 7 figures, 2 tables

Carrollian conformal field theories (carrollian CFTs) are natural field theories on null infinity of an asymptotically flat spacetime or, in general, geometries with conformal carrollian structure. Using a basis transformation, gravitational S-matrix elements can be brought into the form of correlators of a carrollian CFT. Therefore, it has been suggested that carrollian CFTs could provide a co-dimension one dual description to gravity in asymptotically flat spacetimes. In this work, we construct an embedding space formalism for three-dimensional carrollian CFTs and use it to determine two- and three-point correlators. These correlators are fixed by the global subgroup ISO(3,1) of the carrollian conformal symmetries, i.e., the Bondi--van der Burg--Metzner--Sachs symmetries (BMS). The correlators coincide with well-known two- and three-point scattering amplitudes in Minkowski space written with respect to a basis of asymptotic position states., Comment: 45 pages; v2 appendix expanded, agrees with published version

We describe a general procedure for mapping arbitrary $n$-qubit states to two-dimensional (2D) vector fields. The mappings use complex rational function representations of individual qubits, producing classical vector field configurations that can be interpreted in terms of 2D inviscid fluid flows or electric fields. Elementary qubits are identified with localized defects in 2D harmonic vector fields, and multi-qubit states find natural field representations via complex superpositions of vector field products. In particular, separable states appear as highly symmetric flow configurations, making them both dynamically and visually distinct from entangled states. The resulting real-space representations of entangled qubit states enable an intuitive visualization of their transformations under quantum logic operations. We demonstrate this for the quantum Fourier transform and the period finding process underlying Shor's algorithm, along with other quantum algorithms. Due to its generic construction, the mapping procedure suggests the possibility of extending concepts such as entanglement or entanglement entropy to classical continuum systems, and thus may help guide new experimental approaches to information storage and non-standard computation.