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We study the growth of representations of the Lie algebra of vector fields on the affine space that admit a compatible action of the polynomial algebra. We establish the Bernstein inequality for these representations, enabling us to focus on modules with minimal growth, known as holonomic modules. We show that simple holonomic modules are isomorphic to the tensor product of a holonomic module over the Weyl algebra and a finite-dimensional $\mathfrak{gl}_n$-module. We also prove that holonomic modules have a finite length and that the representation map associated with a holonomic module is a differential operator. Finally, we present examples illustrating our results.

For a finitely generated integral super domain $A$, we prove the Lie superalgebra $\mathcal{V} = Der(A)$ of super derivations is a simple Lie superalgebra.

There is increasing interest in the study of nonperturbative aspects of three-dimensional quantum field theories (QFT). They appear as holographic dual to theories of (strongly coupled) gravity. For instance, in Holographic Cosmology, the two-point function of the Energy-Momentum Tensor (EMT) of a particular class of three-dimensional QFTs can be mapped into the power spectrum of the Cosmic Microwave Background in the gravitational theory. However, the presence of divergent contact terms poses challenges in extracting a renormalised EMT two-point function on the lattice. Using a $\phi^4$ theory of adjoint scalars valued in the $\mathfrak{su}(N)$ Lie Algebra as a proof-of-concept motivated by Holographic Cosmology, we apply a novel method for filtering out such contact terms by making use of infinitely differentiable "bump" functions which enforce a smooth window that excludes contributions at zero spatial separation. The process effectively removes the local contact terms and allows us to extract the continuum limit behaviour of the renormalised EMT two-point function., Comment: Proceedings for the 39th International Symposium on Lattice Field Theory

For a smooth algebraic variety $X$, we study the category of finitely generated modules over the ring of function of $X$ that has a compatible action of the Lie algebra $\mathcal{V}$ of polynomials vector fields on $X$. We show that the associated representation of $\mathcal{V}$ is given by a differential operator of order depending on the rank of the module. The order of the differential operator provides a natural measure of the complexity of the representation, with the simplest case being that of $D$-modules.

In collaborative social development platforms such as GitHub, forking a repository is a common activity. A variant fork wants to split the development from the original repository and grow towards a different direction. In this preliminary exploratory research, we analyze the possible reasons for creating a variant fork in blockchain-oriented software. By collecting repositories in GitHub, we created a dataset with repositories and their variants, from which we manually analyzed 86 variants. Based on the variants we studied, the main reason to create a variant in blockchain-oriented software is to support a different blockchain platform (65%)., Comment: Accepted for the 5th International Workshop on Blockchain Oriented Software Engineering 2022

In the holographic approach to cosmology, cosmological observables are described in terms of correlators of a three-dimensional boundary quantum field theory. As a concrete model, we study the $3D$ massless $SU(N)$ scalar matrix field theory with a $\phi^4$ interaction. On the lattice, the energy-momentum tensor (EMT) in this theory can mix with the operator $\phi^2$. We utilize the Wilson Flow to renormalize the EMT on the lattice, and present numerical results for the mixing coefficient for $N = 2$. Obtaining the renormalized EMT will allow us to make predictions for the CMB power spectra in the regime where the dual QFT is non-perturbative., Comment: 10 pages, 3 figures, presented at the 38th International Symposium on Lattice Field Theory - LATTICE2021 - 26-30 July, 2021, Massachusetts Institute of Technology

Some test amplification tools extend a manually created test suite with additional test cases to increase the code coverage. The technique is effective, in the sense that it suggests strong and understandable test cases, generally adopted by software engineers. Unfortunately, the current state-of-the-art for test amplification heavily relies on program analysis techniques which benefit a lot from explicit type declarations present in statically typed languages. In dynamically typed languages, such type declarations are not available and as a consequence test amplification has yet to find its way to programming languages like Smalltalk, Python, Ruby and Javascript. We propose to exploit profiling information --readily obtainable by executing the associated test suite-- to infer the necessary type information creating special test inputs with corresponding assertions. We evaluated this approach on 52 selected test classes from 13 mature projects in the Pharo ecosystem containing approximately 400 test methods. We show the improvement in killing new mutants and mutation coverage at least in 28 out of 52 test classes (53%). Moreover, these generated tests are understandable by humans: 8 out of 11 pull-requests submitted were merged into the main code base (72%). These results are comparable to the state-of-the-art, hence we conclude that test amplification is feasible for dynamically typed languages.

We obtain a classification of simple modules with finite weight multiplicities over basic classical map superalgebras. Any such module is parabolic induced from a simple cuspidal bounded module over a cuspidal map superalgebra. Further on, any simple cuspidal bounded module is isomorphic to an evaluation module. As an application, we obtain a classification of all simple Harish-Chandra modules for basic classical loop superalgebras. Extending these results to affine Kac-Moody Lie superalgebras obtained by adding the degree derivation, we construct a family of bounded simple modules of level zero, and conjecture that all bounded simple cuspidal modules belong to this family. Finally, we show that for affine Kac-Moody Lie superalgebras of type I the Kac induction functor reduces the classification of all simple bounded modules to the classification of the same class of modules over the even part, whose classification is claimed by Dimitrov and Grantcharov.

We present a study of the IR behaviour of a three-dimensional super-renormalisable quantum field theory (QFT) consisting of a scalar field in the adjoint of $SU(N)$ with a $\varphi^4$ interaction. A bare mass is required for the theory to be massless at the quantum level. In perturbation theory the critical mass is ambiguous due to infrared (IR) divergences and we indeed find that at two-loops in lattice perturbation theory the critical mass diverges logarithmically. It was conjectured long ago in [Jackiw 1980, Appelquist 1981] that super-renormalisable theories are nonperturbatively IR finite, with the coupling constant playing the role of an IR regulator. Using a combination of Markov-Chain-Monte-Carlo simulations of the lattice-regularised theory, both frequentist and Bayesian data analysis, and considerations of a corresponding effective theory we gather evidence that this is indeed the case., Comment: Version accepted for publication in PRL, added references, updated plots, extended discussion of IR behaviour in perturbation theory and EFT

A nonperturbative determination of the energy-momentum tensor is essential for understanding the physics of strongly coupled systems. The ability of the Wilson flow to eliminate divergent contact terms makes it a practical method for renormalizing the energy-momentum tensor on the lattice. In this paper, we utilize the Wilson flow to define a procedure to renormalize the energy-momentum tensor for a three-dimensional massless scalar field in the adjoint of $SU(N)$ with a $\varphi^4$ interaction on the lattice. In this theory the energy-momentum tensor can mix with $\varphi^2$ and we present numerical results for the mixing coefficient for the $N=2$ theory., Comment: 29 pages, 9 figures

Estimating future events is a difficult task. Unlike humans, machine learning approaches are not regularized by a natural understanding of physics. In the wild, a plausible succession of events is governed by the rules of causality, which cannot easily be derived from a finite training set. In this paper we propose a novel theoretical framework to perform causal future prediction by embedding spatiotemporal information on a Minkowski space-time. We utilize the concept of a light cone from special relativity to restrict and traverse the latent space of an arbitrary model. We demonstrate successful applications in causal image synthesis and future video frame prediction on a dataset of images. Our framework is architecture- and task-independent and comes with strong theoretical guarantees of causal capabilities., Comment: Includes supplement

Microservices architectures have become largely popular in the last years. However, we still lack empirical evidence about the use of microservices and the practices followed by practitioners. Thereupon, in this paper, we report the results of a survey with 122 professionals who work with microservices. We report how the industry is using this architectural style and whether the perception of practitioners regarding the advantages and challenges of microservices is according to the literature., Comment: Accepted at 6th Brazilian Workshop on Software Visualization, Evolution and Maintenance (VEM), p. 1-8, 2018