Parameter estimation in water-distribution systems by least squares

The weighted-least-squares method using sensitivity-analysis technique is proposed for the estimation of parameters in water-distribution systems. The parameters considered are the Hazen-Williams coefficients for the pipes. The objective function used is the sum of the weighted squares of the differences between the computed and the observed values of the variables. The weighted-least-squares method can elegantly handle multiple loading conditions with mixed types of measurements such as heads and consumptions, different sets and number of measurements for each loading condition, and modifications in the network configuration due to inclusion or exclusion of some pipes affected by valve operations in each loading condition. Uncertainty in parameter estimates can also be obtained. The method is applied for the estimation of parameters in a metropolitan urban water-distribution system in India.

A modified least squares algorithm to treat associations in liquid alloys

The associated model for binary systems has been modified to include volume effects and excess entropy arising from preferential interactions between the associate and the free atoms or between the free atoms. Equations for thermodynamic mixing functions have been derived. An optimization procedure using a modified conjugate gradient method has been used to evaluate the enthalpy and entropy interaction energies, the free energy of dissociation of the complex, its temperature dependance and the size of the associate. An expression for the concentration—concentration structure factor [Scc (0)] has been deduced from the modified associated solution model. The analysis has been applied to the thermodynamic mixing functions of liquid Ga-Te alloys at 1120 K, believed to contain Ga2Te3 associates. It is observed that the modified associated solution model incorporating volume effects and terms for the temperature dependance of interaction energies, describes the thermodynamic properties of Ga-Te system satisfactorily.

Least squares QR-based decomposition provides an efficient way of computing optimal regularization parameter in photoacoustic tomography

A computationally efficient approach that computes the optimal regularization parameter for the Tikhonov-minimization scheme is developed for photoacoustic imaging. This approach is based on the least squares-QR decomposition which is a well-known dimensionality reduction technique for a large system of equations. It is shown that the proposed framework is effective in terms of quantitative and qualitative reconstructions of initial pressure distribution enabled via finding an optimal regularization parameter. The computational efficiency and performance of the proposed method are shown using a test case of numerical blood vessel phantom, where the initial pressure is exactly known for quantitative comparison. (C) 2013 Society of Photo-Optical Instrumentation Engineers (SPIE)

WLS method for parameter estimation in water distribution networks

The weighted-least-squares method based on the Gauss-Newton minimization technique is used for parameter estimation in water distribution networks. The parameters considered are: element resistances (single and/or group resistances, Hazen-Williams coefficients, pump specifications) and consumptions (for single or multiple loading conditions). The measurements considered are: nodal pressure heads, pipe flows, head loss in pipes, and consumptions/inflows. An important feature of the study is a detailed consideration of the influence of different choice of weights on parameter estimation, for error-free data, noisy data, and noisy data which include bad data. The method is applied to three different networks including a real-life problem.

Probabilistic least squares approach to ordinal regression

This paper proposes a novel approach to solve the ordinal regression problem using Gaussian processes. The proposed approach, probabilistic least squares ordinal regression (PLSOR), obtains the probability distribution over ordinal labels using a particular likelihood function. It performs model selection (hyperparameter optimization) using the leave-one-out cross-validation (LOO-CV) technique. PLSOR has conceptual simplicity and ease of implementation of least squares approach. Unlike the existing Gaussian process ordinal regression (GPOR) approaches, PLSOR does not use any approximation techniques for inference. We compare the proposed approach with the state-of-the-art GPOR approaches on some synthetic and benchmark data sets. Experimental results show the competitiveness of the proposed approach.

x-ray studies on crystalline complexes involving amino-acids and peptides .10. head-to-tail sequences in the crystal-structure of l-lysine acetate

l-Lysine acetate crystallises in the monoclinic space group P21 with a = 5.411 (1), b = 7.562(1), c= l2.635(2) Å and β = 91.7(1). The crystal structure was solved by direct methods and refined to an R value of 0.049 using the full matrix least squares method. The conformation and the aggregation of lysine molecules in the structure are similar to those found in the crystal structure of l-lysine l-aspartate. A conspicuous similarity between the crystal structures of l-arginine acetate and l-lysine acetate is that in both cases the strongly basic side chain, although having the largest pK value, interacts with the weakly acidic acetate group leaving the α-amino and the α-carboxylate groups to take part in head-to-tail sequences. These structures thus indicate that electrostatic effects are strongly modulated by other factors so as to give rise to head-to-tail sequences which have earlier been shown to be an almost universal feature of amino acid aggregation in the solid state.

Approximate solutions of Fredholm integral equations of the second kind

This note is concerned with the problem of determining approximate solutions of Fredholm integral equations of the second kind. Approximating the solution of a given integral equation by means of a polynomial, an over-determined system of linear algebraic equations is obtained involving the unknown coefficients, which is finally solved by using the least-squares method. Several examples are examined in detail. (c) 2009 Elsevier Inc. All rights reserved.

Isonicotinic acid hydrazide - a reinvestigation

C6HvN30, orthorhombic, P2~2121, a = 14.915 (15), b=ll.400 (10), c=3.835 (5) A, Din= 1"417 (7), De= 1"395 g cm -3 and Z=4. The structure was refined by the least-squares method to an R of 0.072 for 699 observed reflexions. The angle between the mean planes of the pyridine ring and the acid hydrazide moiety is 18.1 °. The molecules are held together in the crystal by a network of N-H...N hydrogen bonds.

Star Camera Calibration Combined with Independent Spacecraft Attitude Determination

A methodology for determining spacecraft attitude and autonomously calibrating star camera, both independent of each other, is presented in this paper. Unlike most of the attitude determination algorithms where attitude of the satellite depend on the camera calibrating parameters (like principal point offset, focal length etc.), the proposed method has the advantage of computing spacecraft attitude independently of camera calibrating parameters except lens distortion. In the proposed method both attitude estimation and star camera calibration is done together independent of each other by directly utilizing the star coordinate in image plane and corresponding star vector in inertial coordinate frame. Satellite attitude, camera principal point offset, focal length (in pixel), lens distortion coefficient are found by a simple two step method. In the first step, all parameters (except lens distortion) are estimated using a closed-form solution based on a distortion free camera model. In the second step lens distortion coefficient is estimated by linear least squares method using the solution of the first step to be used in the camera model that incorporates distortion. These steps are applied in an iterative manner to refine the estimated parameters. The whole procedure is faster enough for onboard implementation.

Fracture process zone size and true fracture energy of concrete using acoustic emission

Acoustic emission (AE) energy, instead of amplitude, associated with each of the event is used to estimate the fracture process zone (FPZ) size. A steep increase in the cumulative AE energy of the events with respect to time is correlated with the formation of FPZ. Based on the AE energy released during these events and the locations of the events, FPZ size is obtained. The size-independent fracture energy is computed using the expressions given in the boundary effect model by least squares method since over-determined system of equations are obtained when data from several specimens are used. Instead of least squares method a different method is suggested in which the transition ligament length, measured from the plot of histograms of AE events plotted over the un-cracked ligament, is used directly to obtain size-independent fracture energy. The fracture energy thus calculated seems to be size-independent.

Process variability-aware statistical hybrid modeling of dynamic power dissipation in 65 nm CMOS designs

A generalized technique is proposed for modeling the effects of process variations on dynamic power by directly relating the variations in process parameters to variations in dynamic power of a digital circuit. The dynamic power of a 2-input NAND gate is characterized by mixed-mode simulations, to be used as a library element for 65mn gate length technology. The proposed methodology is demonstrated with a multiplier circuit built using the NAND gate library, by characterizing its dynamic power through Monte Carlo analysis. The statistical technique of Response. Surface Methodology (RSM) using Design of Experiments (DOE) and Least Squares Method (LSM), are employed to generate a "hybrid model" for gate power to account for simultaneous variations in multiple process parameters. We demonstrate that our hybrid model based statistical design approach results in considerable savings in the power budget of low power CMOS designs with an error of less than 1%, with significant reductions in uncertainty by atleast 6X on a normalized basis, against worst case design.

Crystal structure of L-lysyl-L-glutamic acid dihydrate

L-Lysyl-L-glutamic acid dihydrate, C11N3O5H21·2H2O, crystallizes in the monoclinic space group P21 with a = 12.474(2), b = 5.020(1), c = 13.157(2) Å, β= 114.69(1)° and Z = 2. The crystal structure was solved by direct methods and refined to an R value of 0.037 using full matrix least-squares method. The molecule exists as a double zwitterion with both the amino and carboxyl groups ionised. The peptide has a folded conformation with its Lys residue trans and Glu residue gauche−gauche+. The side chains of the Lys and Glu residues correspond to all trans and folded (g−g−g−) conformations respectively. The terminal carboxyl group forms hydrogen bonds with the ξ-amino group of the lysine side chain. The head-to-tail interaction often seen in peptide crystals is absent in the present structure. In the extended crystal structure water molecules form channels along the b direction and are enclosed within helically arranged hydrogen bonds formed by the lysine side chain and the peptide backbone.

Crystal and molecular structure of l-valyl-l-lysine hydrochloride

l-Valyl-l-lysine hydrochloride, C11N3O3H23 HCl, rystallizes in the monoclinic space group P2, with a = 5.438(5), b = 14.188(5), c = 9.521(5) Å, β= 95.38(2)° and Z = 2. The crystal structure, solved by direct methods, refined to R = 0.036, using full matrix least-squares method. The peptide exists in a zwitterionic form, with the N atom of the lysine side-chain protonated. The two γ-carbons of the valine side-chain have positional disorder, giving rise to two conformations, χ111= -67.3 and 65.9°, one of which (65.9°) is sterically less favourable and has been found to be less popular amongst residues branching at β-C. The lysine side-chain has the geometry of g− tgt, not seen in crystal structures of the dipeptides reported so far. Interestingly, χ32 (63.6°) of lysine side-chain has a gauche+ conformation unlike in most of the other tructures, where it is trans. The neighbouring peptide molecules are hydrogen bonded in a head-to-tail fashion, a rather uncommon interaction in lysine peptide structures. The structure shows considerable similarity with that of l-Lys-l-Val HO in conformational angles and H-bond interactions [4].

1, 2-Bis (diphenylphosphino) etane bridged dinuclear copper (I) complexes: Investigations of solid state and solution structures by CP/MAS31P NMR spectroscopy, X-ray crystallography, IR spectroscopy and solution 31P NMR and 63Cu NMR spectroscopy

Three different complexes of copper (I) with bridging 1, 2-bis(diphenylphosphino)ethane (dppe), namely [Cu2 (mu-dppe) (CH3CN)6] (ClO4)2 (1), [Cu2 (mu-dppe)2 (CH3 CN)2] (ClO4)2 (2), and [Cu2 (mu-dppe) (dppe)2 (CH3CN)2] (ClO4)2 (3) have been prepared. The structure of [Cu2 (mu-dppe) (dPPe)2 (CH3CH)2] (ClO4)2 has been determined by X-ray crystallography. It crystallizes in the space group PT with a=12.984(6) angstrom, b=13.180(6) angstrom, c=14.001(3) angstrom, alpha=105.23(3), beta=105.60(2), gamma=112.53 (4), V=1944 (3) angstrom3, and Z=1. The structure was refined by least-squares method with R=0.0365; R(w)=0.0451 for 6321 reflections with F0 greater-than-or-equal-to 3 sigma (F0). The CP/MAS P-31 and IR spectra of the complexes have been analysed in the light of available crystallographic data. IR spectroscopy is particularly helpful in identifying the presence of chelating dppe. P-31 chemical shifts observed in solid state are very different from those observed in solution, and change significantly with slight changes in structure. In solution, complex 1 remains undissociated but complexes 2 and 3 undergo extensive dissociation. With a combination of room temperature H-1, Cu-63, and variable temperature P-31 NMR spectra, it is possible to understand the various processes occurring in solution.

Reactions of copper(I) aryloxides with phenyl isothiocyanate: steric and ligand control in the oligomerization of [N-phenylimino(aryloxy)methanethiolato]copper(I) complexes

The preparation of five different copper(I) complexes [CuSC(=NPh)(OAr)}L(n)]m (1-5) formed by the insertion of PhNCS into the Cu-OAr bond and the crystal structure analyses of three of them have been carried out. A monomeric species 1 (OAr = 2,6-dimethylphenoxide) is formed in the presence of excess PPh3 (n = 2, m = 1) and crystallizes as triclinic crystals with a = 12.419(4) angstrom, b = 13.298(7) angstrom, c = 15.936(3) angstrom, alpha = 67.09(3)-degrees, beta = 81.63(2)-degrees, gamma = 66.54(3)-degrees, V = 2224(2) angstrom3, and Z = 2. The structure was refined by the least-squares method to final R and R(w) values of 0.038 and 0.044, respectively, for 7186 unique reflections. Copper(I) 2,5-di-tert-butyl-4-methylphenoxide results in the formation of a dimeric species 2 in the presence of P(OMe)3 (n = 1, m = 2), where the coordination around Cu is trigonal. Crystals of 2 were found to be orthorhombic with a = 15.691(2) angstrom, b = 18.216(3) angstrom, c = 39.198(5) angstrom, v = 11204(3) angstrom3, and Z = 8. Least-squares refinement gave final residuals of R = 0.05 and R(w) = 0.057 with 6866 unique reflections. A tetrameric species 3 results when PPh3 is replaced by P(OMe)3 in the coordination sphere of copper(I) 2,6-dimethylphenoxide. It crystallizes in the space group P1BAR with a = 11.681 (1) angstrom, b = 13.373(2) angstrom, c = 20.127(1) angstrom, a = 88.55(l)-degrees, beta = 89.65(l)-degrees, gamma = 69.28(1)-degrees, V = 2940(l) angstrom3, and Z = 2. Least-squares refinement of the structure gave final values of 0.043 and 0.05 for R and R(w) respectively using 12214 unique reflections. In addition, a dimeric species 4 is formed when 1 equiv of PPh3 is added to the copper(I) 4-methylphenoxide, while with an excess of PPh3 a monomeric species 5 is isolated. Some interconversions among these complexes are also reported.