We present two matrix-free methods for solving exact penalty subproblems on product sets that arise when solving large-scale optimization problems. The first approach is a novel iterative reweighting algorithm (IRWA), which iteratively minimizes quadratic models of relaxed subproblems while automatically updating a relaxation vector. The second approach is based on alternating direction augment...

We define a finitary model of first-order Peano Arithmetic in which quantification is interpreted constructively in terms of Turing-computability, and show that it is inconsistent with the standard interpretation of PA. 1 Hilbert’s interpretation of quantification Hilbert interpreted quantification in terms of his ε-function as follows [Hi27]: IV. The logical ε-axiom 13. A(a)→ A(ε(A)) Here ε(A)...

Let F : X → X be a C 2 loc map in a Banach space X, and A be its Frèchet derivative at the element w := w ε , which solves the problem (*) ˙ w = −A −1 ε (F (w) + εw), w(0) = w 0 , where A ε := A + εI. Assume that A −1 ε ≤ cε −k , 0 < k ≤ 1, 0 < ε > ε 0. Then (*) has a unique global solution, w(t), there exists w(∞), and (* *) F (w(∞)) + εw(∞) = 0. Thus the DSM (Dynamical Systems Method) is just...

The object of this thesis is the study of high density discrete systems as variational limit of low density discrete energies indexed by the number of nodes of the system itself. In this context the term discreteness should be understood rather broadly as inferring to different scales from crystal lattice to grain structure while the low-to-high density limit refers to the discrete-to-continuum...

Nowak G, Bakajsova D, Samarel AM. Protein kinase C-ε activation induces mitochondrial dysfunction and fragmentation in renal proximal tubules. Am J Physiol Renal Physiol 301: F197–F208, 2011. First published February 2, 2011; doi:10.1152/ajprenal.00364.2010.—PKC-ε activation mediates protection from ischemia-reperfusion injury in the myocardium. Mitochondria are a subcellular target of these pr...

Protein kinase C ε (PKC ε ) signals through RhoA to modulate cell invasion and motility. In this study, the multifaceted interaction between PKC ε and RhoA was defined. Phosphopeptide mapping revealed that PKC ε phosphorylates RhoA at T127 and S188. Recombinant PKC ε bound to recombinant RhoA in the absence of ATP indicating that the association between PKC ε and RhoA does not require an active...

Distributed learning in expert referral networks is a new Active Learning paradigm where experts—humans or automated agents—solve problems if they can or refer said problems to others with more appropriate expertise. Recent work augmented the basic learning-to-refer method with proactive skill posting, where experts may report their top skills to their colleagues, and proposed a modified algori...