The curse of dimensionality for the class of monotone functions and for the class of convex functions

We study the integration and approximation problems for monotone or convex bounded functions that depend on $d$ variables, where $d$ can be arbitrarily large. We consider the worst case error for algorithms that use finitely many function values. We prove that these problems suffer from the curse of dimensionality. That is, one needs exponentially many (in $d$) function values to achieve an error $\epsilon$.     

A theoretical description of elastic pillar substrates in biophysical experiments.

Arrays of elastic pillars are used in biophysical experiments as sensors for traction forces. The evaluation of the forces can be complicated if they are coupled to the pillar displacements over large distances. This is the case if many of the pillars are interconnected by elastic linkages as, for example, in fiber networks that are grown on top of pillars. To calculate the traction forces in such a network, we developed a set of nonlinear inhomogeneous equations relating the forces in the linking elements to the resulting pillar deflections. We chose a homogeneous, activated two-dimensional network of cytoskeletal actin filaments to illustrate that a pillar substrate is generally not a force sensor but a force-gradient sensor. In homogeneous networks the forces acting along the filaments can be approximated by analyzing only pillar deflections in the edge zones of the substrate and by integration over the corresponding force gradients.     

Automorphisms of split Cayley algebras over real closed fields

Research supported in part by NSERC Canada grant A7251.     

NLO event generation for chargino production at the ILC

We present a Monte Carlo event generator for simulating chargino pair production at the International Linear Collider (ILC) at next-to-leading order in the electroweak couplings. By properly resumming photons in the soft and collinear regions, we avoid negative event weights, so the program can simulate physical (unweighted) event samples. Photons are explicitly generated throughout the range where they can be experimentally resolved. Inspecting the dependence on the cutoffs separating the soft and collinear regions, we evaluate the systematic errors due to soft and collinear approximations. In the resummation approach, the residual uncertainty can be brought down to the per-mil level, coinciding with the expected statistical uncertainty at the ILC. PACS 12.15.Lk; 13.40.Ks; 13.66.Hk; 14.80.Ly     

Endliche projektive Ebenen gerader Ordnung mit Polaritäten

Ohne ZusammenfassungHerrn Herbert Zeitler zum 70. Geburtstag gewidmet