We provide a proximal average with repect to $1$-coercive Legendre function. In the sense of Bregman distance, envelope is convex combination envelopes individual functions. The mapping convexified mappings Techniques from variational analysis keys for average.

We introduce a new method for training generative adversarial networks by applying the Wasserstein-2 metric proximal on generators. The approach is based Wasserstein information geometry. It defines parametrization invariant natural gradient pulling back optimal transport structures from probability space to parameter space. obtain easy-to-implement iterative regularizers updates of implicit de...

Bauschke, Lucet, and Trienis [SIAM Rev., 50 (2008), pp. 115–132] developed the concept of the proximal average of two convex functions. In this work we show the relationship between the proximal average and the Moreau envelope and exploit this relationship to develop stability theory for a generalized proximal average function. This approach allows us to extend the concept of the proximal avera...

INTRODUCTION Different arterial inflow sites have been reported to date for particularly challenging cardiac operations. The ascending aorta, femoral artery, and subclavian artery are the most commonly used sites. Although its use has been reported, the aortic arch has not gained popularity in the performance of cannulation. According to a search performed in the PubMed database, aortic arch ca...

PURPOSE To review short-term outcomes of proximal femoral locking compression plate (PF-LCP) fixation for proximal femoral fractures in terms of postoperative complications and failure rates. METHODS Medical records of 21 men and 5 women aged 22 to 85 (mean, 49.7) years who underwent internal fixation with the PF-LCP for proximal femoral fractures were reviewed. Younger patients (mean age, 38...

Proximal focal femoral deficiency (PFFD) is a rare skeletal condition characterized by development failure of the subtrochanteric region of the femoral axis, with several degrees of shortening of the proximal region. There are no case reports of patients with this condition associated with a subtrochanteric fracture. We therefore describe herein the case of a newborn patient with clinical and r...