Fundamental insights into the properties of a function come from the study of its Moreau envelopes and Proximal point mappings. In this paper we examine the stability of these two objects under several types of perturbations. In the simplest case, we consider tilt-perturbations, i.e. perturbations which correspond to adding a linear term to the objective function. We show that for functions tha...

Amaç: Lenfödem (LE), aksiller lenf nodu diseksiyonu ve radyoterapi ile tedavi edilen meme kanserli olgularda yaygın gelişen iyatrojenik bir komplikasyondur. Bu çalışmada lenfödemli hastalarda kanseri tedavisi sonrası, lenfatik sistem endotelinden salınan, homeobox transkripsiyon faktörü (Prox-1), damar endotel reseptörü-1 (LVYE-1) podoplanin (PDPN) belirteçlerinin serum düzeylerini araştırmayı ...

Proximal gradient descent (PGD) and stochastic proximal gradient descent (SPGD) are popular methods for solving regularized risk minimization problems in machine learning and statistics. In this paper, we propose and analyze an accelerated variant of these methods in the mini-batch setting. This method incorporates two acceleration techniques: one is Nesterov’s acceleration method, and the othe...

Prox is a stochastic method to map the local and global structures of real-world complex networks which are called Small Worlds. Prox transforms a graph into a Markov chain, the states of which are the nodes of the graph in question. Particles wander from one node to another within the graph by following the graph‟s edges. It is the dynamics of the particles‟ trajectories that map the structura...

We provide tight upper and lower bounds on the complexity of minimizing the average of m convex functions using gradient and prox oracles of the component functions. We show a significant gap between the complexity of deterministic vs randomized optimization. For smooth functions, we show that accelerated gradient descent (AGD) and an accelerated variant of SVRG are optimal in the deterministic...

In this paper, we derive a randomized version of the Mirror-Prox method for solving some structured matrix saddle-point problems, such as the maximal eigenvalue minimization problem. Deterministic first-order schemes, such as Nesterov’s Smoothing Techniques or standard Mirror-Prox methods, require the exact computation of a matrix exponential at every iteration, limiting the size of the problem...

One key factor in stabilization of protein drugs in liquid formulations is the choice of appropriate excipients at optimum concentrations that provide extended shelf life while also ensuring highest safety to the patient. Although general principles of stabilization have emerged from the literature over the past decade, the mechanisms by which excipients can improve the stability of a protein d...

Active Pt-based catalysts at low temperature towards the preferential oxidation of carbon monoxide in hydrogen-rich stream reaction (CO-PROX) are great importance for H2-fueled fuel cells, but still remain a challenge. Herein, we propose simple approach to synthesize highly active Pt20Fe/CeO2 catalyst employing borohydride reduction process. Transmission electronic microscopy revealed monodispe...