Antiviral Resistance against Viral Mutation: Praxis and Policy for SARS CoV-2
Robert PENNER - 2021-02-25 (M/21/04)
New tools developed by Moderna, BioNTech/Pfizer and Oxford/Astrazeneca provide universal solutions to previously problematic aspects of drug or vaccine delivery, uptake and toxicity, portending new tools across the medical sciences. A novel method is presented based on estimating protein backbone free energy via geometry to predict effective antiviral targets, antigens and vaccine cargoes that are resistant to viral mutation. This method, partly described in earlier work of the author, is reviewed and reformulated here in light of the profusion of recent structural data on the SARS CoV-2 spike glycoprotein and its latest mutations. Scientific and regulatory challenges to nucleic acid therapeutic and vaccine development and deployment are also discussed.
Conditional distributions for quantum systems
Arthur PARZYGNAT - 2021-02-02 (P/21/03)
Conditional distributions, as defined by the Markov category framework, are studied in the setting of matrix algebras (quantum systems). Their construction as linear unital maps are obtained via a categorical Bayesian inversion procedure. Simple criteria establishing when such linear maps are positive are obtained. Several examples are provided, including the standard EPR scenario, where the EPR correlations are reproduced in a purely compositional (categorical) manner. A comparison between the Bayes map and the Petz recovery map is provided, illustrating some key differences.
Superselection of the weak hypercharge and the algebra of the Standard Model
Ivan TODOROV - 2021-01-28 (P/21/02)
Restricting the $\mathbb{Z}_2$-graded tensor product of Clifford algebras $C\ell_4\hat{$C\ell_4^1$. We emphasize the role of the exactly conserved weak hypercharge Y, promoted here to a superselection rule for both observables and gauge transformations. This yields a change of the definition of the particle subspace adopted in recent work with Michel Dubois-Violette \cite{DT20}; here we exclude the zero eigensubspace of Y consisting of the sterile (anti)neutrinos which are allowed to mix. One thus modifies the Lie superalgebra generated by the Higgs field. Equating the normalizations of $\Phi$ in the lepton and the quark subalgebras we obtain a relation between the masses of the W boson and the Higgs that fits the experimental values within one percent accuracy.
Sketch of a Program for Universal Automorphic Functions to Capture Monstrous Moonshine
Igor FRENKEL, Robert PENNER - 2021-01-05 (M/21/01)
We review and reformulate old and prove new results about the triad $ {\rm PPSL}_2({\mathbb Z})\subseteq{\rm PPSL}_2({\mathbb R})\circlearrowright ppsl_2({\mathbb R}) $, which provides a universal generalization of the classical automorphic triad ${\rm PSL}_2({\mathbb Z})\subseteq{\rm PSL}_2({\mathbb R})\circlearrowright psl_2({\mathbb R})$. The leading P or $p$ in the universal setting stands for $piecewise$, and the group ${\rm PPSL}_2({\mathbb Z})$ plays at once the role of universal modular group, universal mapping class group, Thompson group $T$ and Ptolemy group. We produce a new basis of the Lie algebra $ppsl_2({\mathbb R})$, compute its structure constants, define a central extension which is compared with the Weil-Petersson 2-form, and discuss its representation theory. We construct and study new framed holographic coordinates on the universal Teichmrm analogous to the invariant Eisenstein 1-form $E_2(z)dz$, which gives rise to the spin 1 representation of $psl_2({\mathbb R})$ extended by the trivial representation. This suggests the full program for developing the theory of universal automorphic functions conjectured to yield the bosonic CFT$_2$. Relaxing the automorphic condition to the commutant leads to our ultimate conjecture on realizing the Monster CFT$_2$ via the automorphic representation for the universal triad. This conjecture is als