Prolongation Approach to B\"{a}cklund Transformation of Zhiber-Mikhailov-Shabat Equation

The prolongation structure of Zhiber-Mikhailov-Shabat (ZMS) equation is studied by using Wahlquist-Estabrook's method. The Lax-pair for ZMS equation and Riccati equations for pseudopotentials are formulated respectively from linear and nonlinear realizations of the prolongation structure. Based on nonlinear realization of the prolongation structure, an auto-B$\ddot{a}$cklund transformation of ZMS equation is obtained.Comment: Revtex, no figures, to appear in J. Math. Phys. (1996

Two Polyak-Type Step Sizes for Mirror Descent

We propose two Polyak-type step sizes for mirror descent and prove their convergences for minimizing convex locally Lipschitz functions. Both step sizes, unlike the original Polyak step size, do not need the optimal value of the objective function.Comment: 13 page

Mutation in Bruton Tyrosine Kinase (BTK) A428D confers resistance To BTK-degrader therapy in chronic lymphocytic leukemia.

Targeting BTK has profoundly changed the face of CLL treatment over the past decade. Iterative advances in the cat and mouse game of resistance and redesign have moved BTK inhibitors from covalent to non-covalent and now targeted protein degraders. However, contrary to the presumption that protein degraders may be impervious to mutations in BTK, we now present clinical evidence that a mutation in the kinase domain of BTK, namely A428D, can confer disease resistance to a BTK degrader currently in clinical trials, that is BGB-16673. Modeling of a BTK A428D mutation places a negatively charged aspartic acid in place of the hydrophobic side chain of alanine within the binding pocket of another BTK-degrader in clinical development, namely NX-2127, suggesting that CLL cells with BTK A428D also may be resistant to NX-2127, as they already are known to be with either non-covalent or covalent inhibitors of BTK. Consequently, the two BTK degraders furthest advanced in clinical trials potentially may select for CLL cells with BTK A428D that are resistant to all approved BTKis