Neural Network Method for Solving Partial Differential Equations

A method is presented to solve partial differential equations (pde's) and its boundary and/or initial conditions by using neural networks. It uses the fact that multiple input, single output, single hidden layer feedforward networks with a linear output layer with no bias are capable of arbitrarily well approximating arbitrary functions and its derivatives, which is proven by a number of authors and well known in literature. Knowledge about the pde and its boundary and/or initial conditions is incorporated into the structures and the training sets of several neural networks. In this way we obtain networks of which some are specifically structured. To find the solution of the pde and its boundary and/or initial conditions we have to train all obtained networks simultaneously. Therefore we use an evolutionary algorithm to train the networks. We demonstrate the working of our method by applying it to two problems.     

Parameterization for reconstruction of 3D freeform objects from laser-scanned data based on a PDE method

Published online: 19 July 2001     

Comparative study of the pharmacokinetics of amitriptyline oxide and trimipramine after single administration in healthy male probands and patients with renal failure

The pharmacokinetics of the antidepressants amitriptyline oxide and trimipramine and their major metabolites amitriptyline, nor-triptyline and desmethyltrimipramine, were studied in twelve healthy male subjects (aged from 22 to 62 years) and twelve patients (aged from 25 to 73 years) with severe renal impairment (glomerular filtration rate < 10 ml/min). Oral single doses of 60 mg amitriptyline oxide and 50 mg trimipramine, separated by a washout period, were administered to all study participants. Blood and urine samples were collected up to 120 hours after administration. For trimipramine and desmethyltrimipramine, a new HPLC method was developed. The "Fischer Somatic and Undesired Effects Check List" was used for the assessment of adverse events. The mean plasma half-life and AUC of amitriptyline oxide and its metabolites were significantly higher in patients than in healthy adults. For trimipramine the AUC was significantly higher in patients. The plasma half-life of trimipramine was longer in patients, but statistically not significant. The maximum plasma concentrations for both drugs and metabolites were at an average distinctly higher in patients. Clearance rate of amitroptylinoxide and trimipramine also differed between the two groups. Correlating with these results a high incidence and a longer persistence (in most cases > 12 hours) and more pronounced adverse effects were noted in the patient group, whereas in volunteers adverse events were only observed up to approximately eight hours.     

Energy sensitive detection of heavy ions with transition edge calorimeters

Status and results of a research project are reported, which aims at developing calorimetric low temperature detectors for heavy ions. The special conditions for the detection of energetic heavy ions are discussed. The response of an aluminium transition edge calorimeter, operated at about1.5K, to the impact of heavy ions was investigated. The observed energy resolutions E/E=3.9×10^–3for5.9MeV/u ²⁰⁸ Pb-ions, E/E=1.6×10^–3for4.8MeV/u ⁵⁸ Ni-ions and E/E=4.3×10^–3for100MeV/u ²⁰ Ne-ions are most probably not yet limited by the intrinsic detector resolution. The present results already represent an improvement over conventional solid state detectors and ionization chambers.     

Just how insoluble are monoterpenes?

Prior generalizations about the ecological roles of monoterpenes may be misleading if based on the presumed insolubility of monoterpenes in water. We determined the aqueous solubility of 31 biologically active monoterpenes by gas chromatography. While hydrocarbons were of low solubility (< 35 ppm), oxygenated monoterpenes exhibited solubilities one or two orders of magnitude higher, with ranges of 155–6990 ppm for ketones and of 183–1360 ppm for alcohols. Many monoterpenes are phytotoxic in concentrations under 100 ppm, well below the saturated aqueous concentrations of oxygenated monoterpenes. Therefore, even dilute, unsaturated solutions of monoterpenes, occurring naturally in plant tissues and soil solutions, may act as potent biological inhibitors.     

Chemical doping of single-wall carbon nanotubes

Single-wall carbon nanotubes can be doped, or intercalated, with electron donors or acceptors, similar to graphite and some conjugated polymers. The resulting materials show many of the same features: enhanced electrical conductivity, conduction electron paramagnetism, partial or complete reversibility, and cyclability. Reactions may be carried out in vapor or liquid phase, or electrochemically. Structural information is sketchy at best, due to the limited quality of currently available materials and solvent-related effects. Recent developments in coagulation-based fiber extrusion and partially aligned materials offer new opportunities for novel material modifications by chemical doping.     

Neural computing models for prediction of permeability coefficient of coarse-grained soils

Correlations are very significant from the earliest days; in some cases, it is essential as it is difficult to measure the amount directly, and in other cases it is desirable to ascertain the results with other tests through correlations. Soft computing techniques are now being used as alternate statistical tool, and new techniques such as artificial neural networks, fuzzy inference systems, genetic algorithms, and their hybrids were employed for developing the predictive models to estimate the needed parameters, in the recent years. Determination of permeability coefficient (k) of soils is very important for the definition of hydraulic conductivity and is difficult, expensive, time-consuming, and involves destructive tests. In this paper, use of some soft computing techniques such as ANNs (MLP, RBF, etc.) and ANFIS (adaptive neuro-fuzzy inference system) for prediction of permeability of coarse-grained soils was described and compared. As a result of this paper, it was obtained that the all constructed soft computing models exhibited high performance for predicting k. In order to predict the permeability coefficient, ANN models having three inputs, one output were applied successfully and exhibited reliable predictions. However, all four different algorithms of ANN have almost the same prediction capability, and accuracy of MLP was relatively higher than RBF models. The ANFIS model for prediction of permeability coefficient revealed the most reliable prediction when compared with the ANN models, and the use of soft computing techniques will provide new approaches and methodologies in prediction of some parameters in soil mechanics.     

Relationships between psychophysically acceptable and maximum voluntary hand force capacity in the context of underlying biomechanical limitations

This research investigated if proportional relationships between psychophysically acceptable and maximum voluntary hand forces are dependent on the underlying biomechanical factor (i.e. whole body balance or joint strength) that limited the maximum voluntary hand force. Eighteen healthy males completed two unilateral maximal exertions followed by a 30 min psychophysical load-adjust protocol in each of nine pre-defined standing scenarios. Center of pressure (whole body balance) and joint moments (joint strength) were calculated to evaluate whether balance or joint strength was most likely limiting maximum voluntary hand force. The ratio of the psychophysically acceptable force to the maximal force was significantly different depending on the underlying biomechanical factor. Psychophysically acceptable hand forces were selected at 86.3 ± 19.7% of the maximum voluntary hand force when limited by balance (pulling exertions), 67.5 ± 15.2% when limited by joint strength (downward pressing) and 78 ± 23% when the limitation was undefined in medial exertions.     

Thermochemische Kennwerte für die Reaktion,Mo + O2 ⇌ MoO2 sowie in Eisenschmelzen

Zusammenstellung von Schrifttumsangaben für die Änderung der freien Standardenthalpien der Reaktionen , Mo + O₂ ? MoO₂ und in Eisenschmelzen. Neubestimmung der Temperaturabhängigkeiten der Größen ΔG^oCr₂O₃, ΔG^oMoO₂ und ΔG^o_O im Eisen bei Temperaturen zwischen 1460 bzw. 1530 und 1725 °C. Nachweis der Anwendbarkeit der neu ermittelten thermodynamischen Funktionen durch EMK-Parallelmessungen an ThO₂ (Y₂O₃)- und ZrO₂ (MgO)-Festelektrolytzellen mit Cr-Cr₂O₃- und Mo-MoO₂-Referenzelektroden in Reineisenschmelzen bei 1600 °C. Ermittlung des Parameters p_e′ der Elektronenteilleitfähigkeit für einen teilstabilisierten ZrO₂-Festelektrolyten mit einem Stoffmengengehalt von 5% MgO.     

A new version of AAKF (Reduced Tensor Matrix Elements) adapted to spectroscopic notation

Title of program: REDUCED TENSOR MATRIX ELEMENTS 2 Catalogue number: AAKP Program obtainable from: CPC Program Library, Queen's University of Belfast N. Ireland (see application form in this issue) Computer: Installation: IBM 360/75 University of Waterloo, Waterloo, Ont. Canada Operating system: OS/360 HASP II Programming languages used: FORTRAN IV High speed store required: 102 K bytes No. of bits per byte: 8 Overlay structure: None Other peripherals used: Card reader, line printer No. of cards in combined program and test deck: 1524 Card punching code: EBCDIC 029CPC Library subprograms used:

     

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Cat. numbers	Titles	Refs. in C.P.C.
ACQB	P SHELL CFP	1 (1969) 15
ACRN	A NEW D SHELL CFP	6 (1973) 88
AAGD	NJSYM	1 (1970) 241, 2 (1971) 173
AAGD0001	ADAPT NJSYM FOR WEIGHTS		2 (1971) 180
AAGD0002		ADAPT TO INTEGER ARITHMETIC	5 (1973) 161