Minimal Diagnosis and Diagnosability of Discrete-Event Systems Modeled by Automata

In the last several decades, the model-based diagnosis of discrete-event systems (DESs) has increasingly become an active research topic in both control engineering and artificial intelligence. However, in contrast with the widely applied minimal diagnosis of static systems, in most approaches to the diagnosis of DESs, all possible candidate diagnoses are computed, including nonminimal candidates, which may cause intractable complexity when the number of nonminimal diagnoses is very large. According to the principle of parsimony and the principle of joint-probability distribution, generally, the minimal diagnosis of DESs is preferable to a nonminimal diagnosis. To generate more likely diagnoses, the notion of the minimal diagnosis of DESs is presented, which is supported by a minimal diagnoser for the generation of minimal diagnoses. Moreover, to either strongly or weakly decide whether a minimal set of faulty events has definitely occurred or not, two notions of minimal diagnosability are proposed. Necessary and sufficient conditions for determining the minimal diagnosability of DESs are proven. The relationships between the two types of minimal diagnosability and the classical diagnosability are analysed in depth

Electron spin relaxation in GaAs1−x_{1-x}Bix_x: Effects of spin-orbit tuning by Bi incorporation

The electron spin relaxation in $n$-type and intrinsic GaAs$_{1-x}$Bi$_x$ with Bi composition $0\le x \le 0.1$ is investigated from the microscopic kinetic spin Bloch equation approach. The incorporation of Bi is shown to markedly decrease the spin relaxation time as a consequence of the modification of the spin-orbit interaction. We demonstrate that the density and temperature dependences of spin relaxation time in GaAs$_{1-x}$Bi$_x$ resemble the ones in GaAs. Meanwhile, the Bir-Aronov-Pikus mechanism is found to be negligible compared to the D'yakonov-Perel' mechanism in intrinsic sample. Due to the absence of direct measurement of the electron effective mass in the whole compositional range under investigation, we further explore the effect of a possible variation of electron effective mass on the electron spin relaxation.Comment: 4 pages, 3 figure

Angle-Resolved X-Ray Circular and Magnetic Circular Dichroisms: Definitions and Applications

We introduce definitions of angle-resolved x-ray circular dichroism (ARXCD) and magnetic x-ray circular dichroism (ARMXCD). As defined, the much larger effect of circular dichroism (ARXCD) is separated from the smaller magnetic (ARMXCD) effect. In all materials, ARXCD is zero along mirror planes while nonzero elsewhere. ARMXCD is nonzero only in magnetic materials. The measurement and analysis of ARMXCD allow element specific surface magnetism and surface structure as well as their inter-relationship to be studied as functions of the outgoing electron\u27s direction