On-line learning in radial basis functions networks

An analytic investigation of the average case learning and generalization properties of Radial Basis Function Networks (RBFs) is presented, utilising on-line gradient descent as the learning rule. The analytic method employed allows both the calculation of generalization error and the examination of the internal dynamics of the network. The generalization error and internal dynamics are then used to examine the role of the learning rate and the specialization of the hidden units, which gives insight into decreasing the time required for training. The realizable and over-realizable cases are studied in detail; the phase of learning in which the hidden units are unspecialized (symmetric phase) and the phase in which asymptotic convergence occurs are analyzed, and their typical properties found. Finally, simulations are performed which strongly confirm the analytic results.

Characterization of time-resolved laser differential phase using 3D complementary cumulative distribution functions

An experimental method for characterizing the time-resolved phase noise of a fast switching tunable laser is discussed. The method experimentally determines a complementary cumulative distribution function of the laser's differential phase as a function of time after a switching event. A time resolved bit error rate of differential quadrature phase shift keying formatted data, calculated using the phase noise measurements, was fitted to an experimental time-resolved bit error rate measurement using a field programmable gate array, finding a good agreement between the time-resolved bit error rates.

Enhancing SPH using moving least-squares and radial basis functions

In this paper we consider two sources of enhancement for the meshfree Lagrangian particle method smoothed particle hydrodynamics (SPH) by improving the accuracy of the particle approximation. Namely, we will consider shape functions constructed using: moving least-squares approximation (MLS); radial basis functions (RBF). Using MLS approximation is appealing because polynomial consistency of the particle approximation can be enforced. RBFs further appeal as they allow one to dispense with the smoothing-length - the parameter in the SPH method which governs the number of particles within the support of the shape function. Currently, only ad hoc methods for choosing the smoothing-length exist. We ensure that any enhancement retains the conservative and meshfree nature of SPH. In doing so, we derive a new set of variationally-consistent hydrodynamic equations. Finally, we demonstrate the performance of the new equations on the Sod shock tube problem.

Energy and structure of dilute hard- and soft-sphere gases

The energy and structure of dilute hard- and soft-sphere Bose gases are systematically studied in the framework of several many-body approaches, such as the variational correlated theory, the Bogoliubov model, and the uniform limit approximation, valid in the weak-interaction regime. When possible, the results are compared with the exact diffusion Monte Carlo ones. Jastrow-type correlation provides a good description of the systems, both hard- and soft-spheres, if the hypernetted chain energy functional is freely minimized and the resulting Euler equation is solved. The study of the soft-sphere potentials confirms the appearance of a dependence of the energy on the shape of the potential at gas paremeter values of x~0.001. For quantities other than the energy, such as the radial distribution functions and the momentum distributions, the dependence appears at any value of x. The occurrence of a maximum in the radial distribution function, in the momentum distribution, and in the excitation spectrum is a natural effect of the correlations when x increases. The asymptotic behaviors of the functions characterizing the structure of the systems are also investigated. The uniform limit approach is very easy to implement and provides a good description of the soft-sphere gas. Its reliability improves when the interaction weakens.

Monte Carlo thermodynamic and structural properties of the TIP4P water model: dependence on the computational conditions

Classical Monte Carlo simulations were carried out on the NPT ensemble at 25°C and 1 atm, aiming to investigate the ability of the TIP4P water model [Jorgensen, Chandrasekhar, Madura, Impey and Klein; J. Chem. Phys., 79 (1983) 926] to reproduce the newest structural picture of liquid water. The results were compared with recent neutron diffraction data [Soper; Bruni and Ricci; J. Chem. Phys., 106 (1997) 247]. The influence of the computational conditions on the thermodynamic and structural results obtained with this model was also analyzed. The findings were compared with the original ones from Jorgensen et al [above-cited reference plus Mol. Phys., 56 (1985) 1381]. It is notice that the thermodynamic results are dependent on the boundary conditions used, whereas the usual radial distribution functions g(O/O(r)) and g(O/H(r)) do not depend on them.

Termodinâmica estatística de líquidos com o método de Monte Carlo. II. O líquido clorofórmio

Thermodynamic properties and radial distribution functions for liquid chloroform were calculated using the Monte Carlo method implemented with Metropolis algorithm in the NpT ensemble at 298 K and 1 atm. A five site model was developed to represent the chloroform molecules. A force field composed by Lennard-Jones and Coulomb potential functions was used to calculate the intermolecular energy. The partial charges needed to represent the Coulombic interactions were obtained from quantum chemical ab initio calculations. The Lennard-Jones parameters were adjusted to reproduce experimental values for density and enthalpy of vaporization for pure liquid. All thermodynamic results are in excelent agreement with experimental data. The correlation functions calculated are in good accordance with theoretical results avaliable in the literature. The free energy for solvating one chloroform molecule into its own liquid at 298 K and 1 atm was computed as an additional test of the potential model. The result obtained compares well with the experimental value. The medium effects on cis/trans convertion of a hypotetical solute in water TIP4P and chloroform solvents were also accomplished. The results obtained from this investigation are in agreement with estimates of the continuous theory of solvation.

C-H...O hydrogen bonding in 4-phenyl-benzaldehyde: a comprehensive crystallographic, spectroscopic and computational study

The crystal structure of 4-phenyl-benzaldehyde reveals the presence of a dimer linked by the C=O and C( 9)-H groups of adjacent molecules. In the liquid phase, the presence of C-(HO)-O-... bonded forms is revealed by both vibrational and NMR spectroscopy. A Delta H value of - 8.2 +/- 0.5 kJ mol(-1) for the dimerisation equilibrium is established from the temperature-dependent intensities of the bands assigned to the carbonyl-stretching modes. The NMR data suggest the preferential engagement of the C(2,6)-H and C(10/12)/C(11)-H groups as hydrogen bond donors, instead of the C(9)-H group. While ab initio calculations for the isolated dimers are unable to corroborate these NMR results, the radial distribution functions obtained from molecular dynamics simulations show a preference for C(2,6)-H and C(10/12)/C(11)-(HO)-O-... contacts relative to the C(9)-(HO)-O-... ones.

Complex formation in solutions of oppositely charged polyelectrolytes at different polyion compositions and salt content

The formation of complexes in solutions containing positively charged polyions (polycations) and a variable amount of negatively charged polyions (polyanions) has been investigated by Monte Carlo simulations. The polyions were described as flexible chains of charged hard spheres interacting through a screened Coulomb potential. The systems were analyzed in terms of cluster compositions, structure factors, and radial distribution functions. At 50% charge equivalence or less, complexes involving two polycations and one polyanion were frequent, while closer to charge equivalence, larger clusters were formed. Small and neutral complexes dominated the solution at charge equivalence in a monodisperse system, while larger clusters again dominated the solution when the polyions were made polydisperse. The cluster composition and solution structure were also examined as functions of added salt by varying the electrostatic screening length. The observed formation of clusters could be rationalized by a few simple rules.

A Monte Carlo study of solutions of oppositely charged polyelectrolytes

The formation of complexes appearing in solutions containing oppositely charged polyelectrolytes has been investigated by Monte Carlo simulations using two different models. The polyions are described as flexible chains of 20 connected charged hard spheres immersed in a homogenous dielectric background representing water. The small ions are either explicitly included or their effect described by using a screened Coulomb potential. The simulated solutions contained 10 positively charged polyions with 0, 2, or 5 negatively charged polyions and the respective counterions. Two different linear charge densities were considered, and structure factors, radial distribution functions, and polyion extensions were determined. A redistribution of positively charged polyions involving strong complexes formed between the oppositely charged polyions appeared as the number of negatively charged polyions was increased. The nature of the complexes was found to depend on the linear charge density of the chains. The simplified model involving the screened Coulomb potential gave qualitatively similar results as the model with explicit small ions. Finally, owing to the complex formation, the sampling in configurational space is nontrivial, and the efficiency of different trial moves was examined.

Monte Carlo investigations of intermolecular interactions in water-amide mixtures

Monte Carlo simulations of water-amides (amide=fonnamide-FOR, methylfonnamide-NMF and dimethylformamide-DMF) solutions have been carried out in the NpT ensemble at 308 K and 1 atm. The structure and excess enthalpy of the mixtures as a function of the composition have been investigated. The TIP4P model was used for simulating water and six-site models previously optimized in this laboratory were used for simulating the liquid amides. The intermolecular interaction energy was calculated using the classical 6-12 Lennard-Jones potential plus a Coulomb term. The interaction energy between solute and solvent has been partitioned what leads to a better understanding of the behavior of the enthalpy of mixture obtained for the three solutions experimentally. Radial distribution functions for the water-amides correlations permit to explore the intermolecular interactions between the molecules. The results show that three, two and one hydrogen bonds between the water and the amide molecules are formed in the FOR, NMF and DMF-water solutions, respectively. These H-bonds are, respectively, stronger for DMF-water, NMF-water and FOR-water. In the NMF-water solution, the interaction between the methyl group of the NMF and the oxygen of the water plays a role in the stabilization of the aqueous solution quite similar to that of an H-bond in the FOR-water solution. (c) 2005 Elsevier B.V. All rights reserved.

Monte Carlo thermodynamic and structural properties of the TIP4P water model: dependence on the computational conditions

Classical Monte Carlo simulations were carried out on the NPT ensemble at 25°C and 1 atm, aiming to investigate the ability of the TIP4P water model [Jorgensen, Chandrasekhar, Madura, Impey and Klein; J. Chem. Phys., 79 (1983) 926] to reproduce the newest structural picture of liquid water. The results were compared with recent neutron diffraction data [Soper; Bruni and Ricci; J. Chem. Phys., 106 (1997) 247]. The influence of the computational conditions on the thermodynamic and structural results obtained with this model was also analyzed. The findings were compared with the original ones from Jorgensen et al [above-cited reference plus Mol. Phys., 56 (1985) 1381]. It is notice that the thermodynamic results are dependent on the boundary conditions used, whereas the usual radial distribution functions g(O/O(r)) and g(O/H(r)) do not depend on them.

C-H center dot center dot center dot O and N-H center dot center dot center dot O hydrogen bonds in liquid amides investigated by Monte Carlo simulation

Monte Carlo simulations of liquid formamide, N-methylformamide (MF), and N,N-dimethylformamide (DMF) have been performed in the isothermal and isobaric ensemble at 298 K and 1 atm, aiming to investigate the C-H ... O and N-H ... O hydrogen bonds. The interaction energy was calculated using the classical 6-12 Lennard-Jones pairwise potential plus a Coulomb term on a rigid six-site molecular model with the potential parameters being optimized in this work. Theoretical values obtained for heat of vaporization and liquid densities are in good agreement with the experimental data. The radial distribution function [RDF, g(r)] obtained compare well with R-X diffraction data available. The RDF and molecular mechanics (MM2) minimization show that the C-H ... O interaction has a significant role in the structure of the three liquids. These results are supported by ab initio calculations. This Interaction is particularly important in the structure of MF. The intensity of the N-H ... O hydrogen bond is greater in the MF than formamide. This could explain some anomalous properties verified in MF. (C) 1997 John Wiley & Sons, Inc.

Theoretical studies of liquids by computer simulations: the water-acetone mixture.

Monte Carlo simulation results for pure liquid acetone and water-acetone mixtures calculated in the isothermal and isobaric (NPT) ensemble at T=298K and p=1.0atm are presented. The TIP4P model was used for water and optimized potential for liquid simulation (OPLS) force field parameters used for acetone. The results obtained for the average configurational energy as a function of the mole fraction are in good accord with experimental data. Energy partitioning and co-ordination numbers results calculated for equimolar water-acetone solution are compared to similar data obtained for other water-organic liquid mixtures. These results show an increase in water-water interaction energy and co-ordination numbers when the interaction between water and organic liquid molecules decrease. Distribution functions for pure liquid acetone and water-acetone mixtures are presented. Dipole-dipole angular correlation functions obtained for pure liquid acetone show a predominance of dimers with parallel alignment of dipole moments. Radial distribution functions from water-acetone interaction show characteristic features of hydrogen bonded liquids. Radial and angular distribution functions for water-water correlation calculated in pure water and in equimolar water-acetone mixture are compared, showing very similar features in both systems. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Application of a new reverse Monte Carlo algorithm to polyatomic molecular systems. I. Liquid water

Using a new reverse Monte Carlo algorithm, we present simulations that reproduce very well several structural and thermodynamic properties of liquid water. Both Monte Carlo, molecular dynamics simulations and experimental radial distribution functions used as input are accurately reproduced using a small number of molecules and no external constraints. Ad hoc energy and hydrogen bond analysis show the physical consistency and limitations of the generated RMC configurations. (C) 2001 American Institute of Physics.

X-ray diffraction investigation of Co(II) ions in borosilicate glasses

The radial distribution functions of cobalt glasses with 6%, 8%, and 14% CoO are compared with those of suitable cobalt-free borosilicate matrices leading to difference distribution curves representative of the cobalt structural arrangement. Analysis of the curves indicates that cobalt ions are surrounded by approximately four oxygen neighbors at the distance expected for fourfold coordination. © 1986 American Institute of Physics.