Filtrations, mixed complexes, and cyclic homology in mixed characteristic

We describe an approach to computing cyclic homology suited to ground rings of characteristicp or mixed characteristic. We illustrate the method by computing HC for coordinate rings of affine plane curves and for maximal orders of semisimple algebras.Partially supported by NSF Grant No. DMS-8807203 and NSA Grant No. MDA 904-92-H-3026.     

Optimizing neural network architectures using generalization error estimators

This paper addresses the optimization of neural network architectures. It is suggested to optimize the architecture by selecting the model with minimal estimated averaged generalization error. We consider a least-squares (LS) criterion for estimating neural network models, i.e., the associated model weights are estimated by minimizing the LS criterion. The quality of a particular estimated model is measured by the average generalization error. This is defined as the expected squared prediction error on a novel input-output sample averaged over all possible training sets. An essential part of the suggested architecture optimization scheme is to calculate an estimate of the average generalization error. We suggest using the GEN-estimator [9, 10] which allows for dealing with nonlinear, incomplete models, i.e., models which are not capable of modeling the underlying nonlinear relationship perfectly. In most neural network applications, it is impossible to suggest a perfect model, and consequently the ability to handle incomplete models is urgent. A concise derivation of the GEN-estimator is provided, and its qualities are demonstrated by comparative numerical studies.The Computational Neural Network Center, Electronics Institute, The Technical University of Denmark, Building 349. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 9, pp. 1131–1147, September, 1994.     

A column switching technique for the determination of lidocaine and its metabolites in horse urine

Summary A rapid method is described for the determination of lidocaine and its metabolites in horse urine using a column switching technique and HPLC analysis. This procedure offers a sensitive assay without the need for time consuming extractions.     

Alternating-Sign Matrices and Domino Tilings (Part II)

We continue the study of the family of planar regions dubbed Aztec diamonds in our earlier article and study the ways in which these regions can be tiled by dominoes. Two more proofs of the main formula are given. The first uses the representation theory of GL(n). The second is more combinatorial and produces a generating function that gives not only the number of domino tilings of the Aztec diamond of order n but also information about the orientation of the dominoes (vertical versus horizontal) and the accessibility of one tiling from another by means of local modifications. Lastly, we explore a connection between the combinatorial objects studied in this paper and the square-ice model studied by Lieb.     

Breather trapping and breather transmission in a DNA model with an interface

We study the dynamics of moving discrete breathers in an interfaced piecewise DNA molecule. This is a DNA chain in which all the base pairs are identical and there exists an interface such that the base pairs dipole moments at each side are oriented in opposite directions. The Hamiltonian of the Peyrard-Bishop model is augmented with a term that includes the dipole-dipole coupling between base pairs. Numerical simulations show the existence of two dynamical regimes. If the translational kinetic energy of a moving breather launched towards the interface is below a critical value, it is trapped in a region around the interface collecting vibrational energy. For an energy larger than the critical value, the breather is transmitted and continues travelling along the double strand with lower velocity. Reflection phenomena never occur. The same study has been carried out when a single dipole is oriented in opposite direction to the other ones. When moving breathers collide with the single inverted dipole, the same effects appear. These results emphasize the importance of this simple type of local inhomogeneity as it creates a mechanism for the trapping of energy. Finally, the simulations show that, under favorable conditions, several launched moving breathers can be trapped successively at the interface region producing an accumulation of vibrational energy. Moreover, an additional colliding moving breather can produce a saturation of energy and a moving breather with all the accumulated energy is transmitted to the chain.     

High-performance size-exclusion chromatographic procedure for the determination of fluoresceinyl isothiocyanate dextrans of various molecular masses in biological media

A high-performance size-exclusion chromatographic procedure, using Nucleosil Diol, for the quantitative analysis of fluoresceinyl isothiocyanate dextrans of various molecular masses (10,000-150,000) in biological media was developed. The influence of the molecular mass and the degree of substitution of the conjugates on the chromatographic behaviour are discussed. In addition to quantitation, the molecular mass of the conjugates with degree of substitution below 1.6 could be estimated from the chromatograms. Linear standard calibration curves were obtained at concentrations down to 0.050 micrograms ml-1 in rabbit plasma and urine and homogenates of rabbit liver, lymph node and muscle when the derivative (degree of substitution 0.85) was monitored by fluorescence detection (lambda ex = 493 nm, lambda em = 520 mm). The fluoresceinyl isothiocyanate dextrans were found to be stable for more than three days at 37 degrees in all biological media under investigation. A pH-rate profile for the alkaline hydrolysis of fluoresceinyl isothiocyanate dextrans was constructed. The applicability of the method to pharmacokinetic studies was demonstrated by recording the plasma concentration-time profile of a fluoresceinyl isothiocyanate dextran T-70 conjugate following intravenous injection to a rabbit. In relation to future pharmacokinetic investigations on dextran conjugates, the results reported indicate that labelling of the parent dextran with fluoresceinyl isothiocyanate and monitoring of the fluoresceinyl isothiocyanate dextran conjugate throughout the organism using the described method is a promising development.     

High-resolution infrared and theoretical study of four fundamental bands of gaseous 1,3,4-oxadiazole between 800 and 1600 cm

The Fourier transform infrared spectrum of gaseous 1,3,4-oxadiazole, C₂H₂N₂O, has been recorded in the 800–1600 cm⁻¹ wavenumber region with a resolution around 0.0030 cm⁻¹. The four fundamental bands ν₉(B₁; 852.5 cm⁻¹), ν₁₄(B₂; 1078.5 cm⁻¹), ν₄(A₁; 1092.6 cm⁻¹), and ν₂(A₁; 1534.9 cm⁻¹) are analyzed by the standard Watson model. Ground state rotational and quartic centrifugal distortion constants are obtained from a simultaneous fit of ground state combination differences from three of these bands and previous microwave transitions. Upper state spectroscopic constants are obtained for all four bands from single band fits using the Watson model. The ν₄ and ν₁₄ bands form a c-Coriolis interacting dyad, and the two bands are analyzed simultaneously by a model including first and second order Coriolis resonance using the ab initio predicted Coriolis coupling constant . An extended local resonance in ν₂ is explained as higher order b-Coriolis type resonance with ν₆ + ν₁₀, which is further perturbed globally by the ν₁₅ + ν₁₀ level. A fit of selected low-J transitions to a triad model including ν₂(A₁), ν₆ + ν₁₀(B₁), and ν₁₅ + ν₁₀(A₂) using an ab initio calculated Coriolis coupling constant is performed.The rotational constants, ground state quartic centrifugal distortion constants, anharmonic frequencies, and vibration–rotational constants (α-constants) predicted by quantum chemical calculations using a cc-pVTZ and TZ2P basis with B3LYP methodology, are compared with the present experimental data, where there is generally good agreement. A complete set of anharmonic frequencies and α-constants for all fundamental levels of the molecule is given.