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...

Abstract. This paper is concerned with a biharmonic equation under the Navier boundary condition (P∓ε) : ∆u = u n+4 n−4 , u > 0 in Ω and u = ∆u = 0 on ∂Ω, where Ω is a smooth bounded domain in R, n ≥ 5, and ε > 0. We study the asymptotic behavior of solutions of (P−ε) which are minimizing for the Sobolev quotient as ε goes to zero. We show that such solutions concentrate around a point x0 ∈ Ω a...

We show that every n-point tree metric admits a (1 + ε)-embedding into ` C(ε) logn 1 , for every ε > 0, where C(ε) ≤ O ( ( 1ε ) 4 log 1ε ) ) . This matches the natural volume lower bound up to a factor depending only on ε. Previously, it was unknown whether even complete binary trees on n nodes could be embedded in ` O(logn) 1 with O(1) distortion. For complete d-ary trees, our construction ach...

We consider a Gaussian diffusion Xt (Ornstein-Uhlenbeck process) with drift coefficient γ and diffusion coefficient σ, and an approximating process Y ε t converging to Xt in L2 as ε → 0. We study estimators γ̂ε, σ̂ ε which are asymptotically equivalent to the Maximum likelihood estimators of γ and σ, respectively. We assume that the estimators are based on the available N = N(ε) observations extr...

We are interested in (ε)-regular bipartite graphs which are the central objects in the regularity lemma of Szemerédi for sparse graphs. A bipartite graph G = (A]B,E) with density p = |E|/(|A||B|) is (ε)-regular if for all sets A′ ⊆ A and B′ ⊆ B of size |A′| ≥ ε|A| and |B ′| ≥ ε|B|, it holds that |eG(A, B′)/(|A′||B′|) − p| ≤ εp. In this paper we prove a characterization for (ε)-regularity. That ...