In this short note, we present some evidence towards the existence of an algebra of BPS $G_2$ instantons. These are instantonic configurations that govern the partition functions of 7d SYM theories on local $G_2$ holonomy manifolds $mathcal X$. To sh
ed light on such structure, we begin investigating the relation with parent 4d $mathcal N=1$ theories obtained by geometric engineering M-theory on $mathcal X$. The main point of this paper is to substantiate the following dream: the holomorphic sector of such theories on multi-centered Taub-NUT spaces gives rise to an algebra whose characters organise the $G_2$ instanton partition function. As a first step towards this program, we argue by string duality that a multitude of geometries $mathcal X$ exist that are dual to well-known 4d SCFTs arising from D3 branes probes of CY cones: all these models are amenable to analysis along the lines suggested by Dijkgraaf, Gukov, Neitzke and Vafa in the context of topological M-theory. Moreover, we discuss an interesting relation to Costellos twisted M-theory, which arises at local patches, and is a key ingredient in identifying the relevant algebras.
This project explores public opinion on the Supplemental Nutrition Assistance Program (SNAP) in news and social media outlets, and tracks elected representatives voting records on issues relating to SNAP and food insecurity. We used machine learning,
sentiment analysis, and text mining to analyze national and state level coverage of SNAP in order to gauge perceptions of the program over time across these outlets. Results indicate that the majority of news coverage has negative sentiment, more partisan news outlets have more extreme sentiment, and that clustering of negative reporting on SNAP occurs in the Midwest. Our final results and tools will be displayed in an on-line application that the ACFB Advocacy team can use to inform their communication to relevant stakeholders.
