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GPCRLMD, a deep generative framework for efficient all-atom GPCR-ligand simulation, achieves state-of-the-art performance in GPCR-ligand dynamics simulation, faithfully reproducing ensemble observables and critical ligand-receptor interactions.
Let $\Omega(n)$ denote the number of prime factors of $n$, counted with multiplicity. We prove that if $A\subset\mathbb{N}^3$ has positive upper Banach density, then there are $(x,y,z)\in\mathbb{N}^3$ and $d\in\mathbb{N}$ such that $$(x,y,z),(x+d,y,z),(x,y+d,z),(x,y,z+\Omega(d))\in A.$$ To establish the above result, w...
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