Maria Colombo

Bio: Maria Colombo is an academic researcher from École Polytechnique Fédérale de Lausanne. The author has contributed to research in topics: Limit (mathematics) & Mathematics. The author has an hindex of 22, co-authored 106 publications receiving 2790 citations. Previous affiliations of Maria Colombo include Scuola Normale Superiore di Pisa & ETH Zurich.

Regularity for Double Phase Variational Problems

Abstract: We prove sharp regularity theorems for minimisers of a class of variational integrals whose integrand switches between two different types of degenerate elliptic phases, according to the zero set of a modulating coefficient \({a(\cdot)}\) The model case is given by the functional $$ w \mapsto \int (|Dw|^p + a(x)|Dw|^q) \, {\rm d}x,$$ where q > p and \({a(\cdot) \geqq 0}\)

Bounded Minimisers of Double Phase Variational Integrals

Abstract: Bounded minimisers of the functional $$w \mapsto \int (|Dw|^p+a(x)|Dw|^q)\,{\rm d}x,$$ where $${0 \leqq a(\cdot) \in C^{0, \alpha}}$$ and $${1 < p < q}$$ , are $${C^{1, \beta}}$$ -regular provided the sharp bound $${q \leqq p + \alpha}$$ holds.

Regularity for general functionals with double phase

Abstract: We prove sharp regularity results for a general class of functionals of the type $$\begin{aligned} w \mapsto \int F(x, w, Dw) \, dx, \end{aligned}$$ featuring non-standard growth conditions and non-uniform ellipticity properties. The model case is given by the double phase integral $$\begin{aligned} w \mapsto \int b(x,w)(|Dw|^p+a(x)|Dw|^q) \, dx,\quad 1

Harnack inequalities for double phase functionals

Abstract: We prove a Harnack inequality for minimisers of a class of non-autonomous functionals with non-standard growth conditions. They are characterised by the fact that their energy density switches between two types of different degenerate phases.

Regularity for general functionals with double phase

Abstract: We prove sharp regularity results for a general class of functionals of the type $$ w \mapsto \int F(x, w, Dw) \, dx\;, $$ featuring non-standard growth conditions and non-uniform ellipticity properties. The model case is given by the double phase integral $$ w \mapsto \int b(x,w)(|Dw|^p+a(x)|Dw|^q) \, dx\;,\quad 1

QM/MM Methods for Biomolecular Systems

Abstract: Combined quantum-mechanics/molecular-mechanics (QM/MM) approaches have become the method of choice for modeling reactions in biomolecular systems. Quantum-mechanical (QM) methods are required for describing chemical reactions and other electronic processes, such as charge transfer or electronic excitation. However, QM methods are restricted to systems of up to a few hundred atoms. However, the size and conformational complexity of biopolymers calls for methods capable of treating up to several 100,000 atoms and allowing for simulations over time scales of tens of nanoseconds. This is achieved by highly efficient, force-field-based molecular mechanics (MM) methods. Thus to model large biomolecules the logical approach is to combine the two techniques and to use a QM method for the chemically active region (e.g., substrates and co-factors in an enzymatic reaction) and an MM treatment for the surroundings (e.g., protein and solvent). The resulting schemes are commonly referred to as combined or hybrid QM/MM methods. They enable the modeling of reactive biomolecular systems at a reasonable computational effort while providing the necessary accuracy.

QM/MM: what have we learned, where are we, and where do we go from here?

Abstract: This paper briefly reviews the current status of the most popular methods for combined quantum mechanical/molecular mechanical (QM/MM) calculations, including their advantages and disadvantages There is a special emphasis on very general link-atom methods and various ways to treat the charge near the boundary Mechanical and electric embedding are contrasted We consider methods applicable to gas-phase organic chemistry, liquid-phase organic and organometallic chemistry, biochemistry, and solid-state chemistry Then we review some recent tests of QM/MM methods and summarize what we learn about QM/MM from these studies We also discuss some available software Finally, we present a few comments about future directions of research in this exciting area, where we focus on more intimate blends of QM with MM

Optimal Transport for Applied Mathematicians : Calculus of Variations, PDEs, and Modeling

Abstract: Preface.- Primal and Dual Problems.- One-Dimensional Issues.- L^1 and L^infinity Theory.- Minimal Flows.- Wasserstein Spaces.- Numerical Methods.- Functionals over Probabilities.- Gradient Flows.- Exercises.- References.- Index.

Copper binding to the prion protein: Structural implications of four identical cooperative binding sites (octarepeat peptidesynuclear magnetic resonanceycircular dichroismyelectron spin resonance)

Abstract: Evidence is growing to support a functional role for the prion protein (PrP) in copper metabolism. Copper ions appear to bind to the protein in a highly conserved octapeptide repeat region (sequence PHGGGWGQ) near the N terminus. To delineate the site and mode of binding of Cu(II) to the PrP, the copper-binding properties of peptides of varying lengths corresponding to 2-, 3-, and 4-octarepeat sequences have been probed by using various spectroscopic techniques. A two-octarepeat peptide binds a single Cu(II) ion with Kd ' 6 mM whereas a four-octarepeat peptide coopera- tively binds four Cu(II) ions. Circular dichroism spectra indicate a distinctive structuring of the octarepeat region on Cu(II) binding. Visible absorption, visible circular dichroism, and electron spin resonance spectra suggest that the coordi- nation sphere of the copper is identical for 2, 3, or 4 octare- peats, consisting of a square-planar geometry with three nitrogen ligands and one oxygen ligand. Consistent with the pH dependence of Cu(II) binding, proton NMR spectroscopy indicates that the histidine residues in each octarepeat are coordinated to the Cu(II) ion. Our working model for the structure of the complex shows the histidine residues in successive octarepeats bridged between two copper ions, with both the N«2 and Nd1 imidazole nitrogen of each histidine residue coordinated and the remaining coordination sites occupied by a backbone amide nitrogen and a water molecule. This arrangement accounts for the cooperative nature of complex formation and for the apparent evolutionary require- ment for four octarepeats in the PrP.