‎In this paper‎, ‎we define and study the notion of zero elements in topoframes; a topoframe is a pair‎ ‎$(L‎, ‎tau)$‎, ‎abbreviated $L_{ tau}$‎, ‎consisting of a frame $L$ and a‎ ‎subframe $ tau $ all of whose elements are complemented elements in‎ ‎$L$‎. ‎We show that‎ ‎the $f$-ring $ mathcal{R}(L_tau)$‎, ‎the set of $tau$-real continuous functions on $L$‎, ‎is uniformly complete‎. ‎Also‎, ‎t...

‎In this paper‎, ‎we generalize the proximal point algorithm to complete CAT(0) spaces and show‎ ‎that the sequence generated by the proximal point algorithm‎ $w$-converges to a zero of the maximal‎ ‎monotone operator‎. ‎Also‎, ‎we prove that if $f‎: ‎Xrightarrow‎ ‎]-infty‎, +‎infty]$ is a proper‎, ‎convex and lower semicontinuous‎ ‎function on the complete CAT(0) space $X$‎, ‎then the proximal...

Abstract Funding Acknowledgements Type of funding sources: None. Background Catheter ablation has become an established treatment option for premature ventricular complexes (PVCs). It is well known that the use fluoroscopy exposes patients and medical staff to potentially harmful stochastic deterministic effects ionising radiations. Purpose We sought analyse procedural outcomes in terms safety ...

Masked language models (MLMs) have contributed to drastic performance improvements with regard zero anaphora resolution (ZAR). To further improve this approach, in study, we made two proposals. The first is a new pretraining task that trains MLMs on anaphoric relations explicit supervision, and the second proposal finetuning method remedies notorious issue, pretrain-finetune discrepancy. Our ex...