International audience We conjecture two combinatorial interpretations for the symmetric function ∆eken, where ∆f is an eigenoperator for the modified Macdonald polynomials defined by Bergeron, Garsia, Haiman, and Tesler. Both interpretations can be seen as generalizations of the Shuffle Conjecture, a statement originally conjectured by Haglund, Haiman, Remmel, Loehr, and Ulyanov and recently proved by Carlsson and Mellit. We show how previous work of the second and third authors on Tesler matrices and ordered set partitions can be used to verify several cases of our conjectures. Furthermore, we use a reciprocity identity and LLT polynomials to prove another case. Finally, we show how our conjectures inspire 4-variable generalizations of the Catalan numbers, extending work of Garsia, Haiman, and the first author.

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In a recent preprint, Carlsson and Oblomkov (2018) obtain a long sought after monomial basis for the ring DR n of diagonal coinvariants. Their basis is closely related to the "schedules" formula for the Hilbert series of DR n which was conjectured by the first author and Loehr (2005) and first proved by Carlsson and Mellit (2018), as a consequence of their proof of the famous Shuffle Conjecture. In this article we obtain a schedules formula for the combinatorial side of the Delta Conjecture, a conjecture introduced by the first author, Remmel and Wilson (2018) which contains the Shuffle Conjecture as a special case. Motivated by the Carlsson-Oblomkov basis for DR n and our Delta schedules formula, we introduce a (conjectural) basis for the module SDR n of super-diagonal coinvariants, an S n module generalizing DR n introduced recently by Zabrocki (2019) which conjecturally corresponds to the Delta Conjecture. arXiv:1908.04732v1 [math.CO]

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Relating macromolecular “structure to function” is considered a foundational skill in biochemistry and molecular biology course curriculums. The molecular visualization skills necessary to interpret information in 3D models of biological macromolecules, however, are often lacking. Moreover, current technologies aimed at spanning this skills gap often require varying degrees of prior knowledge, training, and/or hardware requirements that can make implementation difficult. To address this we have developed a simple classroom activity using augmented reality technology that allows students to quickly and easily interact with high‐resolution images of a 3D macromolecule. The activity was implemented in a junior/senior level biochemistry course as part of a class discussion on the structure and function of the potassium channel. The 3D images were integrated as an iPad application in which a 3D virtual image of the molecule would appear superimposed on the real world on the iPad screen when the iPad camera was directed towards a printed QR code. Students were able to rotate, translate, and zoom in on the molecule by physically moving either the iPad or the QR code sheet. The activity was also accompanied with worksheet questions aimed at developing an interpretation of the 3D structure. Student attitudes were assessed using a pre/post survey analysis. Results indicate increases in student confidence towards visualizing the 3D structures of biological macromolecules, as well as an increase in positive student perceptions of the helpfulness of looking at 3D structures for learning protein biochemistry. This abstract is from the Experimental Biology 2018 Meeting. There is no full text article associated with this abstract published in The FASEB Journal.