Detailed balance in ion channels: Application of Feinberg’s theorem

Detailed balance helps reduce the number of necessary measurements on ion channel models. Even imprecise formulations may lead to correct conditions because of the special structure of these models.     

Discrepancy of Arithmetic Progressions in Higher Dimensions

K. F. Roth (1964, Acta. Arith.9, 257-260) proved that the discrepancy of arithmetic progressions contained in [1, N]={1, 2, …, N} is at least cN^1/4, and later it was proved that this result is sharp. We consider the d-dimensional version of this problem. We give a lower estimate for the discrepancy of arithmetic progressions on [1, N]^d and prove that this result is nearly sharp. We use our results to give an upper estimate for the discrepancy of lines on an N×N lattice, and we also give an estimate for the discrepancy of a related random hypergraph.     

Electron-phonon interaction in carbon schwarzites

The recent synthesis of random schwarzites has stimulated the present ab initio calculation of the electronic structure and electron-phonon interaction in two different periodic D-type schwarzites, fcc-(C₂₈)₂ (made of 24 seven-membered rings per unit cell) and fcc-(C₆₄)₂ (made of 12 eight membered and 48 six-membered rings per unit cell). Like in fullerenes, also in schwarzites the electron-phonon interaction potential is found to increase with the absolute Gauss curvature, though it remains smaller than for doped fullerenes. Received 19 December 2002 Published online 1st April 2003 RID="a" ID="a"e-mail: marco.bernasconi@unimib.it     

Interface control of emergent ferroic order in Ruddlesden-Popper Sr(n+1)Ti(n)O(3n+1)

We discovered from first principles an unusual polar state in the low n Sr(n+1)Ti(n)O(3n+1) Ruddlesden-Popper (RP) layered perovskites in which ferroelectricity is nearly degenerate with antiferroelectricity, a relatively rare form of ferroic order. We show that epitaxial strain plays a key role in tuning the "perpendicular coherence length" of the ferroelectric mode, and does not induce ferroelectricity in these low-dimensional RP materials as is well known to occur in SrTiO(3). These systems present an opportunity to manipulate the coherence length of a ferroic distortion in a controlled way, without disorder or a free surface.     

Highly enantioselective conjugate addition of nitromethane to chalcones using bifunctional cinchona organocatalysts

Cinchona alkaloid-derived chiral bifunctional thiourea organocatalysts were synthesized and applied in the Michael addition between nitromethane and chalcones with high ee and chemical yields.     

Random trees and general branching processes

We consider a tree that grows randomly in time. Each time a new vertex appears, it chooses exactly one of the existing vertices and attaches to it. The probability that the new vertex chooses vertex x is proportional to w(deg(x)), a weight function of the actual degree of x. The weight function w : ℕ → ℝ₊ is the parameter of the model. In 4 and 11 the authors derive the asymptotic degree distribution for a model that is equivalent to the special case, when the weight function is linear. The proof therein strongly relies on the linear choice of w. Using well‐established results from the theory of general branching processes we give the asymptotical degree distribution for a wide range of weight functions. Moreover, we provide the asymptotic distribution of the tree itself as seen from a randomly selected vertex. The latter approach gives greater insight to the limiting structure of the tree. Our proof is robust and we believe that the method may be used to answer several other questions related to the model. It relies on the fact that considering the evolution of the random tree in continuous time, the process may be viewed as a general branching process, this way classical results can be applied. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007