Error control in the perfectly matched layer based multilevel fast multipole algorithm

The development of efficient algorithms to analyze complex electromagnetic structures is of topical interest. Application of these algorithms in commercial solvers requires rigorous error controllability. In this paper we focus on the perfectly matched layer based multilevel fast multipole algorithm (PML-MLFMA), a dedicated technique constructed to efficiently analyze large planar structures. More specifically the crux of the algorithm, viz. the pertinent layered medium Green functions, is under investigation. Therefore, particular attention is paid to the plane wave decomposition for 2-D homogeneous space Green functions in very lossy media, as needed in the PML-MLFMA. The result of the investigations is twofold. First, upper bounds expressing the required number of samples in the plane wave decomposition as a function of a preset accuracy are rigorously derived. These formulas can be used in 2-D homogeneous (lossy) media MLFMAs. Second, a more heuristic approach to control the error of the PML-MLFMA’s Green functions is presented. The theory is verified by means of several numerical experiments.     

Single-cell recording and stimulation with a 16k micro-nail electrode array integrated on a 0.18 μm CMOS chip

To cope with the growing needs in research towards the understanding of cellular function and network dynamics, advanced micro-electrode arrays (MEAs) based on integrated complementary metal oxide semiconductor (CMOS) circuits have been increasingly reported. Although such arrays contain a large number of sensors for recording and/or stimulation, the size of the electrodes on these chips are often larger than a typical mammalian cell. Therefore, true single-cell recording and stimulation remains challenging. Single-cell resolution can be obtained by decreasing the size of the electrodes, which inherently increases the characteristic impedance and noise. Here, we present an array of 16,384 active sensors monolithically integrated on chip, realized in 0.18 μm CMOS technology for recording and stimulation of individual cells. Successful recording of electrical activity of cardiac cells with the chip, validated with intracellular whole-cell patch clamp recordings are presented, illustrating single-cell readout capability. Further, by applying a single-electrode stimulation protocol, we could pace individual cardiac cells, demonstrating single-cell addressability. This novel electrode array could help pave the way towards solving complex interactions of mammalian cellular networks.     

Player splitting in extensive form games

By a player splitting we mean a mechanism that distributes the information sets of a player among so-called agents. A player splitting is called independent if each path in the game tree contains at most one agent of every player. Following Mertens (1989), a solution is said to have the player splitting property if, roughly speaking, the solution of an extensive form game does not change by applying independent player splittings. We show that Nash equilibria, perfect equilibria, Kohlberg-Mertens stable sets and Mertens stable sets have the player splitting property. An example is given to show that the proper equilibrium concept does not satisfy the player splitting property. Next, we give a definition of invariance under (general) player splittings which is an extension of the player splitting property to the situation where we also allow for dependent player splittings. We come to the conclusion that, for any given dependent player splitting, each of the above solutions is not invariant under this player splitting. The results are used to give several characterizations of the class of independent player splittings and the class of single appearance structures by means of invariance of solution concepts under player splittings. Received: December 1996/Revised Version: January 2000     

Transformations of Gibbs measures

We study local transformations of Gibbs measures. We establish sufficient conditions for the quasilocality of the images and obtain results on the existence and continuity properties of their relative energies. General results are illustrated by simple examples. Received: 11 November 1997 / Revised version: 20 February 1998     

Elementary equivalence and codimension in p-adic fields

We give examples of fields elementarily equivalent to a given finite extension of the p-adic numbers but not containing a subfield of finite codimension elementarily equivalent to the p-adics.     

Logarithmic-Exponential Power Series

We use generalized power series to construct algebraically anonstandard model of the theory of the real field with exponentiation.This model enables us to show the undefinability of the zetafunction and certain non-elementary and improper integrals.We also use this model to answer a question of Hardy by showingthat the compositional inverse to the function (log x) (loglog x) is not asymptotic as x+ to a composition of semialgebraicfunctions, log and exp.     

Solving the linear matroid parity problem as a sequence of matroid intersection problems

In this paper, we present an O(r ⁴ n) algorithm for the linear matroid parity problem. Our solution technique is to introduce a modest generalization, the non-simple parity problem, and identify an important subclass of non-simple parity problems called easy parity problems which can be solved as matroid intersection problems. We then show how to solve any linear matroid parity problem parametrically as a sequence of easy parity problems.In contrast to other algorithmic work on this problem, we focus on general structural properties of dual solutions rather than on local primal structures. In a companion paper, we develop these ideas into a duality theory for the parity problem.     

(E,E)‐2,5‐Di­methoxy‐1,4‐bis­[2‐(3,4,5‐tri­methoxy­phenyl)­ethenyl]­benzene

In the title compound, C₃₀H₃₄O₈, molecular symmetry is coincident with crystallographic inversion symmetry. A three‐dimensional network is generated containing both C—H·π and C—H·n(O) interactions. A comparison of the geometry of this mol­ecule and the structure of a number of 2,4,6‐tri­methoxy‐substituted analogues is provided.     

The approximability of three-dimensional assignment problems with bottleneck objective

We discuss two special cases of the three-dimensional bottleneck assignment problem where a certain underlying cost function satisfies the triangle inequality. We present polynomial time 2-approximation algorithms for the broadest class of these special cases, and we prove that (unless P = NP) this factor 2 is best possible even in the highly restricted setting of the Euclidean plane.