Metabolism of xanthohumol and isoxanthohumol, prenylated flavonoids from hops (Humulus lupulus L.), by human liver microsomes

The female flowers of hops (Humulus lupulus L.) used to flavor beer contain the prenylated flavonoids xanthohumol (XN) and isoxanthohumol (IX). IX is moderately estrogenic in vitro and XN has pharmacological properties that might make it useful as a cancer chemopreventive agent. The metabolism of these dietary flavonoids was investigated in vitro using human liver microsomes. Hydroxylation of a prenyl methyl group was the primary route of oxidative metabolism forming either cis or trans hydroxylated metabolites of IX but only the trans isomer of XN. The double bond on the prenyl group of both compounds formed an epoxide which was opened by an intramolecular reaction with the neighboring hydroxyl group. The potent phytoestrogen 8-prenylnaringenin (8-PN) was detected as a demethylation product of IX. However, the analogous demethylation reaction was not observed for XN. Since XN can be converted to IX through acid-catalyzed cyclization in the stomach, XN might contribute to the in vivo levels of estrogenic 8-PN following consumption of hops extracts.     

Hybrid cross approximation of integral operators

The efficient treatment of dense matrices arising, e.g., from the finite element discretisation of integral operators requires special compression techniques. In this article we use the -matrix representation that approximates the dense stiffness matrix in admissible blocks (corresponding to subdomains where the underlying kernel function is smooth) by low-rank matrices. The low-rank matrices are assembled by a new hybrid algorithm (HCA) that has the same proven convergence as standard interpolation but also the same efficiency as the (heuristic) adaptive cross approximation (ACA).     

New Coins From Old: Computing With Unknown Bias

Suppose that we are given a function f : (0, 1)→(0,1) and, for some unknown p∈(0, 1), a sequence of independent tosses of a p-coin (i.e., a coin with probability p of “heads”). For which functions f is it possible to simulate an f(p)-coin? This question was raised by S. Asmussen and J. Propp. A simple simulation scheme for the constant function f(p)≡1/2 was described by von Neumann (1951); this scheme can be easily implemented using a finite automaton. We prove that in general, an f(p)-coin can be simulated by a finite automaton for all p ∈ (0, 1), if and only if f is a rational function over ℚ. We also show that if an f(p)-coin can be simulated by a pushdown automaton, then f is an algebraic function over ℚ; however, pushdown automata can simulate f(p)-coins for certain nonrational functions such as . These results complement the work of Keane and O’Brien (1994), who determined the functions f for which an f(p)-coin can be simulated when there are no computational restrictions on the simulation scheme. * Supported by a Miller Fellowship. † Supported in part by NSF Grant DMS-0104073 and by a Miller Professorship. ‡ This work is supported under a National Science Foundation Graduate Research Fellowship.     

A New Partition Identity Coming from Complex Dynamics

We present a new identity involving compositions (i.e., ordered partitions of natural numbers). The formula has its origin in complex dynamical systems and appears when counting, in the polynomial family periodic critical orbits with equivalent itineraries. We give two different proofs of the identity; one following the original approach in dynamics and another with purely combinatorial methods. Received October 1, 2004     

A Brunn-Minkowski inequality for the Monge-Ampère eigenvalue

We prove a Brunn-Minkowski-type inequality for the eigenvalue Λ of the Monge-Ampère operator: Λ^-1/2n is concave in the class of domains in Rⁿ endowed with Minkowski addition. The equality case is explicitly described too. The main device of the proof is a notion of addition for convex functions, called infimal convolution, which corresponds to the Minkowski addition of the graphs of the involved functions.     

The gas phase structures of the isomers of benzene: IV. Hexafluoro-dewar-benzene

Gas phase electron diffraction data for HFDB were analyzed, following conventional procedures, and a structure was deduced for the perfluoro-bicyclo-[2.2.0]hexa-2,5-diene consistent with its C_2v symmetry. A least squares analysis of the molecular scattering function gave the following r_g values: [-C-C-] = 1.597 ± 0.006 Å, [C-C-] = 1.503 ± 0.002 Å, [-C-C-] = 1.356 ± 0.007 Å, [-C-F](bridge) = 1.331 ± 0.008 Å, [-C-F] (terminal) = 1.323 ± 0.004 Å. The flap angle between the rings is 115.3( ± .7)°. The terminal fluorines are in the planes of the corresponding rings.The most notable feature of the structure is the long C-C bridge bond, which was also observed in hexamethyl-Dewar-benzene. The geometrical features of HFDB are compared with corresponding ones in HMDB, and with perfluoro- cyclobutene as well as with theoretical estimates.     

A disjoint disks property for 3-manifolds

We show that the map separation property (MSP), a concept due to H.W. Lambert and R.B. Sher, is an appropriate analogue of J.W. Cannon’s disjoint disks property (DDP) for the class $\text{C}$ of compact generalized 3-manifolds with zero-dimensional singular set, modulo the Poincaré conjecture. Our main result is that the Poincaré conjecture (in dimension three) is equivalent to the conjecture that every X?$\text{C}$ with the MSP is a topological 3-manifold.