Algebraic methods for inferring biochemical networks: A maximum likelihood approach

We present a novel method for identifying a biochemical reaction network based on multiple sets of estimated reaction rates in the corresponding reaction rate equations arriving from various (possibly different) experiments. The current method, unlike some of the graphical approaches proposed in the literature, uses the values of the experimental measurements only relative to the geometry of the biochemical reactions under the assumption that the underlying reaction network is the same for all the experiments. The proposed approach utilizes algebraic statistical methods in order to parametrize the set of possible reactions so as to identify the most likely network structure, and is easily scalable to very complicated biochemical systems involving a large number of species and reactions. The method is illustrated with a numerical example of a hypothetical network arising from a “mass transfer”-type model.     

A Note on Toeplitz Operators in Schatten-Herz Classes Associated with Rearrangement-invariant Spaces

In recent papers, B. Choe, H. Koo, K. Na (see [3]) and Loaiza, M. Lopez-Garcia e S. Perez-Esteva (see [5]) studied conditions in order to a Toeplitz operator, acting on the harmonic Bergman space over the unit ball in and on analytic Bergman space on the unit disk in the complex plane, respectively, belong to the so-called Schaten-Herz class. The purpose of this note is to prove necessary and sufficient conditions in order to a Toeplitz operator T _μ with positive symbol, acting on the harmonic Bergman space on the unit ball in belong to a Schatten-Herz class S ^F _E , associated with a pair of rearrangement invariant sequence spaces E and F. The conditions involve the Berezin transform of its symbol and the average function. on some euclidian discs. The main point is the characterization of Toeplitz operators, that belong to Schatten ideals S _E associated with an arbitrary rearrangement invariant sequence space E.      

Nonlinear Multigrid Methods for Numerical Solution of the Variably Saturated Flow Equation in Two Space Dimensions

The need of accurate and efficient numerical schemes to solve Richards’ equation is well recognized. This study is carried out to examine the numerical performances of the nonlinear multigrid method for numerical solving of the two-dimensional Richards’ equation modeling water flow in variably saturated porous media. The numerical approach is based on an implicit, second-order accurate time discretization combined with a vertex centered finite volume method for spatial discretization. The test problems simulate infiltration of water in 2D saturated–unsaturated soils with hydraulic properties described by van Genuchten–Mualem models. The numerical results obtained are compared with those provided by the modified Picard–preconditioned conjugated gradient (Krylov subspace) approach.     

Poly(alkylene-H-phosphonate)s obtained by direct esterification and oxidation of hypophosphorous acid with ethylene glycol

This paper presents for the first time the synthesis of poly(alkylene-H-phosphonate)s by one-pot tandem reaction of hypophosphorous acid and ethylene glycol. Zirconium oxychloride was used as esterification catalyst, Nickel vinylphosphonate, Nickel sulfate, Nickel chloride hexahydrate were used as transfer hydrogenation catalyst. Nickel vinylphosphonate was synthesized in our laboratory and used for the first time as catalyst in this process. The compounds were characterized by ¹H-NMR, ¹³C-NMR and ³¹P-NMR spectroscopy. Molar masses were determined by SEC-MALLS technique and depend on the catalyst used. The obtained poly(alkylene-H-phosphonate)s have molar masses between 1.50 and 11.85 kDa, higher than those obtained by other methods mentioned in the literature.     

Two‐Photon Absorption and Time‐Resolved Stimulated Emission Depletion Spectroscopy of a New Fluorenyl Derivative

The synthesis, comprehensive linear photophysical characterization, two‐photon absorption (2PA), steady‐state and time‐resolved stimulated emission depletion properties of a new fluorene derivative, (E)‐1‐(2‐(di‐p‐tolylamino)‐9,9‐diethyl‐9H‐fluoren‐7‐yl)‐3‐(thiophen‐2‐yl)prop‐2‐en‐1‐one ( 1 ), are reported. The primary linear spectral properties, including excitation anisotropy, fluorescence lifetimes, and photostability, were investigated in a number of aprotic solvents at room temperature. The degenerate 2PA spectra of 1 were obtained with open‐aperture Z‐scan and two‐photon induced fluorescence methods, using a 1 kHz femtosecond laser system, and maximum 2PA cross‐sections of ～400–600 GM were obtained. The nature of the electronic absorption processes in 1 was investigated by DFT‐based quantum chemical methods implemented in the Gaussian 09 program. The one‐ and two‐photon stimulated emission spectra of 1 were measured over a broad spectral range using a femtosecond pump–probe‐based fluorescence quenching technique, while a new methodology for time‐resolved fluorescence emission spectroscopy is proposed. An effective application of 1 in fluorescence bioimaging was demonstrated by means of one‐ and two‐photon fluorescence microscopy images of HCT 116 cells containing dye encapsulated micelles.     

Transient excited-state absorption and gain spectroscopy of a two-photon absorbing probe with efficient superfluorescent properties

The synthesis, linear photophysical properties, two-photon absorption (2PA), excited-state transient absorption, and gain spectroscopy of a new fluorene derivative tert-butyl 4,4'-(4,4' (1E,1'E)-2,2'-(9,9-bis(2- (2-ethoxyethoxy)ethyl)-9H-fluorene-2,7-diyl)bis(ethene-2,1-diyl)bis(4,1 phenylene)]dipiperazine-1-carboxylate (1) are reported. The steady-state linear absorption and fluorescence spectra, along with excitation anisotropy, fluorescence lifetimes, and photochemical stability of 1 were investigated in a number of organic solvents at room temperature. The 2PA spectra of 1 with a maximum cross-section of ~ 300 GM were obtained with a 1 kHz femtosecond laser system using open-aperture Z-scan and two-photon-induced fluorescence methods. The transient excited-state absorption (ESA) and gain kinetics of 1 were investigated by a femtosecond pump-probe methodology. Fast relaxation processes (~1-2 ps) in the gain and ESA spectra of 1 were revealed in ACN solution, attributable to symmetry-breaking effects in the first excited state. Efficient superfluorescence properties of 1 were observed in a nonpolar solvent under femtosecond excitation. One- and two-photon fluorescence microscopy imaging of HCT 116 cells incubated with probe 1 was accomplished, suggesting the potential of this new probe in two-photon fluorescence microscopy bioimaging.     

Electronic excitations and lattice dynamics of coordinatively "unsaturated" complex transition metal compounds

Single crystal polarized Raman and infrared spectra of the series Na(5)[MO(2)][X] with M = Co(I), Ni(I), and Cu(I) and X = S(2-) and CO(3)(2-), are reported. All phonon modes are assigned to the lattice eigenmodes based on the group theory analysis and first principles lattice dynamics calculations. The energies of the fundamental symmetric and asymmetric vibrations of the [MO(2)](3-) complex are discussed on the basis of their electronic structure and variation in M-O interatomic distances. Electronic Raman scattering and luminescence are observed for the magnetic members of the series (Co(I), d(8), and Ni(I), d(9)). Ligand field theory is employed to account for the electronic effects which originate from states split by spin-orbit coupling.     

Hankel operators in Schatten ideals

We study membership to Schatten ideals S _E , associated with a monotone Riesz–Fischer space E, for the Hankel operators H _f defined on the Hardy space H ²(∂D). The conditions are expressed in terms of regularity of its symbol: we prove that H _f ∈S _E if and only if f∈B _E , the Besov space associated with a monotone Riesz–Fischer space E(dλ) over the measure space (D,dλ) and the main tool is the interpolation of operators. Received: December 17, 1999; in final form: September 25, 2000?Published online: July 13, 2001     

Surface properties of some carotenoids spread in monolayers at the air/water interface. Experimental and computational approach

The surface pressure versus molecular area isotherms of some carotenoids: β,β-carotene-4-one (echinenone, ECH), β,β-carotene-4,4′-dione (canthaxanthin, CAN) and 4,4′-diapo-ω,ω-carotene-4,4′-dial (APO), spread at the air/water interface, are reported. A van der Waals type state equation is used to describe the high molecular area portions of the compression isotherms and interaction parameters within monolayers are derived. Quantum chemical semi-empirical SCF MO calculations (AM1 and PM3) are performed for the optimized geometries of molecules and dipole moments are calculated. Similar theoretical magnitudes are obtained by both methods. Surface properties, like collapse pressure, surface compressional modulus and interaction parameters are discussed in terms of dipole-dipole interactions, and correlations with the calculated quantities for the carotenoid molecules are analyzed. The orientation of the different carotenoid molecules in the monolayer is discussed.