The cardinality of manifold atlases

It is shown that any finite dimensionalC ⁰ manifold (connected and Hausdorff but otherwise unrestricted) has an atlas of cardinality not greater than that of the continuum; while if it has a Hölder continuous pseudo-Riemannian metric then there is a countable atlas.     

Isolation of mitogenic substance from sclerotia of Sclerotinia sclerotiorum IFO 9395 extracted with phosphate buffer.

The buffer extracts (3S) of sclerotia of Sclerotinia sclerotiorum IFO 9395 contained mitogenic substance(s) to murine splenocytes (Shinohara et al. Chem. Pharm. Bull., 38, 2219 (1990)). Although the native 3S was slightly mitogenic, heating of 3S induced significant mitogenic activity. To isolate the mitogen, we separated 3S by ion-exchange and gel filtration chromatographies. The isolated mitogen, named sclerogen, has a molecular mass of 32 kilodaltons (kDa) on sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) and the isoelectric point (pI) of 5.9 by chromatofocusing. Sclerogen was significantly mitogenic in vitro against murine splenocytes after heat denaturation, and also showed the augmentation of the primary mixed lymphocyte reaction (MLR) in vitro. However, sclerogen did not show the activation of an alternative pathway of complement and hemagglutination activity. These results suggest that sclerogen is a unique mitogen which differs from lectins and shows mitogenicity after heat denaturation.     

Rb saturation spectroscopy with an optically narrowed FM diode laser

A fast-frequency modulated (FM) diode laser has been optically narrowed using the technique of resonant optical feedback, to provide linewidths in each FM mode of ≈ 200 kHz peak-to-peak. With a drive frequency of 50 MHz and modulation index of 0.2, the FM laser has been used for the first time to obtain Doppler-free FM spectra of the Rb D₁ line at 795 nm. The potential use of this system for laser frequency stabilisation is discussed.     

Large fault-tolerant interconnection networks

This paper deals with reliability and fault-tolerant properties of networks. We first survey general reliability properties of networks, in particular those concerning diameter vulnerability. Then we study in details reliability properties of some families of networks in particular de Bruijn and Kautz networks and their generalizations which appear as very good fault-tolerant networks.     

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Electron traps and positive DLTS signals in VPE GaAs MESFETs

Capacitance DLTS measurements have been performed in VPE GaAs MESFETs prepared on Bridgman Cr-doped and LEC undoped semi-insulating substrates. A band of electron traps not intrinsically related to the VPE growth process and accumulating near the metal (gate) — semiconductor interface was detected in all the samples. Deeper regions into the channel were free from any detectable trap. Near pinch-off conditions, a positive capacitance signal was found to dominate the DLTS spectra only in the case of samples prepared on Cr-doped substrates. The hypothesis of this positive transient being related to changes in the occupation of surface states in the ungated surface access regions has been checked by comparing experimental and calculated dependencies of the signal amplitude on reverse gate voltage. Unexplained discrepancies, together with the absence of positive signal in MESFETs prepared on LEC undoped substrates, suggest the possibility of hole emission from hole traps within the bulk of the device.     

Truncated Newton method for sparse unconstrained optimization using automatic differentiation

When solving large complex optimization problems, the user is faced with three major problems. These are (i) the cost in human time in obtaining accurate expressions for the derivatives involved; (ii) the need to store second derivative information; and (iii), of lessening importance, the time taken to solve the problem on the computer. For many problems, a significant part of the latter can be attributed to solving Newton-like equations. In the algorithm described, the equations are solved using a conjugate direction method that only needs the Hessian at the current point when it is multiplied by a trial vector. In this paper, we present a method that finds this product using automatic differentiation while only requiring vector storage. The method takes advantage of any sparsity in the Hessian matrix and computes exact derivatives. It avoids the complexity of symbolic differentiation, the inaccuracy of numerical differentiation, the labor of finding analytic derivatives, and the need for matrix store. When far from a minimum, an accurate solution to the Newton equations is not justified, so an approximate solution is obtained by using a version of Dembo and Steihaug's truncated Newton algorithm (Ref. 1).This paper was presented at the SIAM National Meeting, Boston, Massachusetts, 1986.