Quasiregular maps on Carnot groups

In this paper we initiate the study of quasiregular maps in a sub-Riemannian geometry of general Carnot groups. We suggest an analytic definition for quasiregularity and then show that nonconstant quasiregular maps are open and discrete maps on Carnot groups which are two-step nilpotent and of Heisenberg type; we further establish, under the same assumption, that the branch set of a nonconstant quasiregular map has Haar measure zero and, consequently, that quasiregular maps are almost everywhere differentiable in the sense of Pansu. Our method is that of nonlinear potential theory. We have aimed at an exposition accessible to readers of varied background. Dedicated to Seppo Rickman on his sixtieth birthday J.H. was partially supported by NSF, the Academy of Finland, and the A. P. Sloan Foundation. I.H. was partially supported by the EU HCM contract no. CHRX-CT92-0071.     

A general screening method for doping agents in human urine by solid phase extraction and liquid chromatography/time-of-flight mass spectrometry

A general screening method based on solid phase extraction (SPE) and liquid chromatography/time-of-flight mass spectrometry (LC/TOFMS) was developed and investigated with 124 different doping agents, including stimulants, -blockers, narcotics, -adrenergic agonists, agents with anti-estrogenic activity, diuretics and cannabinoids. Mixed mode cation exchange/C8 cartridges were applied to SPE, and chromatography was based on gradient elution on a C18 column. Ionization of the analytes was achieved with electrospray ionization in the positive mode. Identification by LC/TOFMS was based on retention time, accurate mass and isotopic pattern. Validation of the method consisted of analysis of specificity, analytical recovery, limit of detection and repeatability. The minimum required performance limit (MRPL), established by World Anti-Doping Agency (WADA), was attained to 97 doping agents. The extraction recoveries varied between 33 and 98% and the median was 58%. Mass accuracy was always better than 5 ppm, corresponding to a maximum mass error of 0.7 mDa. The repeatability of the method for spiked urine samples, expressed as median of relative standard deviations (RSD%) at concentrations of MRPL and 10 times MRPL, were 14% and 9%, respectively. The suitability of the LC/TOFMS method for doping control was demonstrated with authentic urine samples.     

Determination of Backbone Angle ψ in Proteins Using a TROSY-Based α/β-HN(CO)CA-J Experiment

Transverse relaxation-optimized NMR experiment (TROSY) for the measurement of three-bond scalar coupling constant between ¹H^α_i−1 and ¹⁵N_i defining the dihedral angle ψ is described. The triple-spin-state-selective experiment allows measurement of ³J_H^αN from ¹³C^α, ¹⁵N, and ¹H^N correlation spectra H₂O with minimum resonance overlap. Transverse relaxation of ¹³C^α spin is minimized by using spin-state-selective filtering and by acquiring a signal longer in ¹⁵N-dimension in a manner of semi-constant-time TROSY evolution. The ³J_H^αN values obtained with the proposed α/β-HN(CO)CA-J TROSY scheme are in good agreement with the values measured earlier from ubiquitin in D₂O using the HCACO[N] experiment.     

Polymer translocation through a nanopore under an applied external field

We investigate the dynamics of polymer translocation through a nanopore under an externally applied field using the two-dimensional fluctuating bond model with single-segment Monte Carlo moves. We concentrate on the influence of the field strength E, length of the chain N, and length of the pore L on forced translocation. As our main result, we find a crossover scaling for the translocation time tau with the chain length from tau approximately N2nu for relatively short polymers to tau approximately N1+nu for longer chains, where nu is the Flory exponent. We demonstrate that this crossover is due to the change in the dependence of the translocation velocity v on the chain length. For relatively short chains v approximately N-nu, which crosses over to v approximately N(-1) for long polymers. The reason for this is that with increasing N there is a high density of segments near the exit of the pore, which slows down the translocation process due to slow relaxation of the chain. For the case of a long nanopore for which R parallel, the radius of gyration Rg along the pore, is smaller than the pore length, we find no clear scaling of the translocation time with the chain length. For large N, however, the asymptotic scaling tau approximately N1+nu is recovered. In this regime, tau is almost independent of L. We have previously found that for a polymer, which is initially placed in the middle of the pore, there is a minimum in the escape time for R parallel approximately L. We show here that this minimum persists for weak fields E such that EL is less than some critical value, but vanishes for large values of EL.     

Isotopic pattern and accurate mass determination in urine drug screening by liquid chromatography/time-of-flight mass spectrometry

An efficient method was developed for toxicological drug screening in urine by liquid chromatography coupled with electrospray ionization time-of-flight mass spectrometry. The method relies on a large target database of exact monoisotopic masses representing the elemental formulae of reference drugs and their metabolites. Mass spectral identification is based on matching measured accurate mass and isotopic pattern (SigmaFit) of a sample component with those in the database. Data post-processing software was developed for automated reporting of findings in an easily interpretable form. The mean and median of SigmaFit for true-positive findings were 0.0066 and 0.0051, respectively. The mean and median of mass error absolute values for true-positive findings were 2.51 and 2.17 ppm, respectively, corresponding to 0.65 and 0.60 mTh. For routine screening practice, a SigmaFit tolerance of 0.03 and a mass tolerance of 10 ppm were chosen. Ion abundance differences from urine extracts did not affect the accuracy of the automatically acquired SigmaFit or mass values. The results show that isotopic pattern matching by SigmaFit is a powerful means of identification in addition to accurate mass measurement.     

Langevin dynamics simulations of polymer translocation through nanopores

We investigate the dynamics of polymer translocation through a nanopore using two-dimensional Langevin dynamics simulations. In the absence of an external driving force, we consider a polymer which is initially placed in the middle of the pore and study the escape time tau(e) required for the polymer to completely exit the pore on either side. The distribution of the escape times is wide and has a long tail. We find that tau(e) scales with the chain length N as tau(e) approximately N(1+2nu), where nu is the Flory exponent. For driven translocation, we concentrate on the influence of the friction coefficient xi, the driving force E, and the length of the chain N on the translocation time tau, which is defined as the time duration between the first monomer entering the pore and the last monomer leaving the pore. For strong driving forces, the distribution of translocation times is symmetric and narrow without a long tail and tau approximately E(-1). The influence of xi depends on the ratio between the driving and frictional forces. For intermediate xi, we find a crossover scaling for tau with N from tau approximately N(2nu) for relatively short chains to tau approximately N(1+nu) for longer chains. However, for higher xi, only tau approximately N(1+nu) is observed even for short chains, and there is no crossover behavior. This result can be explained by the fact that increasing xi increases the Rouse relaxation time of the chain, in which case even relatively short chains have no time to relax during translocation. Our results are in good agreement with previous simulations based on the fluctuating bond lattice model of polymers at intermediate friction values, but reveal additional features of dependency on friction.     

p-harmonic functions on graphs and manifolds

We show that the LiouvilleD _p -property is invariant under rough isometries between a Riemannian manifold of bounded geometry and a graph of bounded degree. The first author was supported partly by the EU HCM contract No. CHRX-CT92-0071. This article was processed by the author using the Springer-Verlag TEX P Jourlg macro package 1991.