Coherent optical neural networks and the generalization characteristic

Coherent optical neural-network systems are presented by which we are to realize (1) control of optical neural-network behavior by carrier frequency modulation and (2) frequency-domain multiplexing as a new degree of neural parallelism. In the coherent optical neural network, lightwave carries amplitude, phase, and frequency signals which are processed through optical neural connections consisting of transparency, delay, and optical nonlinear neurons. The neural learning process is realized by adjusting the delay time and the transpar-ency of the optical connections by regarding the carrier frequency as a learning parameter. A simulation experiment demonstrates that the proposed system learns desired output signals depending on the optical carrier frequencies, which leads to the above advantages. It is also found that the generalization characteristics depends on built-in input delays. The generalization quality is discussed from the viewpoint of function approximation or synthesis using sinusoidal basis functions.     

Development of spatial light modulators with nonlinear organic materials

An electrically addressable spatial light modulator is designed using nonlinear organic materials for optical information processing and display. One candidates for spatial light modulator (SLM) material is a nonlinear organic polymer of poly-methyl-methacrylate doped with disperse red 1. The measured electrooptic coefficient r₃₃ is 2.9 pm/V at the wavelength of 633 nm. Resonator structure for a material is discussed with the goal of increasing electrooptic effects for SLM applications.     

Link Homology in 4-Manifolds

We define link homology in 4-manifolds, and show that it hasa close connection to linking numbers and intersection matricesof 4-manifolds. We also define null-homologous links in 4-manifolds.We give a necessary and sufficient condition for links to benull-homologous in 4-manifolds. This condition implies thatfor any 4-manifold with second Betti number n, there are (n+ 2)-component links which are not nullhomologous in the 4-manifold.     

On a first-passage problem for a cumulative process with exponential decay

A first-passage problem for a cumulative process is investigated. The cumulative process is assumed to be generated by a Poisson process, and the amplitude generated by an event is assumed to decay exponentially. An integral equation for the probability density of the first-passage time until the total amplitude exceeds a pre-specified threshold level is derived. The Laplace transform of the probability density of the first-passage time is obtained explicity when each amplitude generated by an event is distributed exponentially. The mean first-passage times are given in a closed form and plotted versus the threshold level.     

The theorem for semisimple Hopf algebras

We give an algebraic version of a result of G. I. Kac, showing that a semisimple Hopf algebra of dimension , where is a prime and , over an algebraically closed field of characteristic 0 contains a non-trivial central group-like. As an application we prove that, if , is isomorphic to a group algebra.

     

Fan-type theorem for path-connectivity

A graphG is said to bek-path-connected if every pair of distinct vertices inG are joined by a path of length at leastk. We prove that if max{deg _G ^x , deg _G ^y }k for every pair of verticesx,y withd _G (x,y)=2 in a 2-connected graphG, whered _G (x,y) is the distance betweenx andy inG, thenG isk-path-connected.     

Performance at 10–50 K of Bi-2212/Ag multilayer tape fabricated by using pre-annealing and intermediate rolling process

High-transport critical current density (J_c-oxide)>500 kA/cm² at 4.2 K, 10 T can be obtained for Bi-2212/Ag tapes fabricated by using pre-annealing and intermediate rolling (PAIR) and melt-solidification process. In this paper, we report high-temperature properties of PAIR-processed Bi-2212/Ag multilayer tape in order to show their potential for practical applications operated at cryocooling temperatures. Magnetic field dependence and angular dependence of critical current (I_c) are investigated at temperatures ranging 10–50 K by using helium gas cooling and liquid neon. Field-temperature curves for I_c=0.2 and 2.0 A are also determined in order to show the approximation of the irreversible field. High-temperature performance of the tape is attractive to consider future applications. For example, the best sample carries I_c=267 A (engineering-J_c=303 A/mm², J_c-oxide=151 kA/cm²) and 92 A (104 A/mm², 52 kA/cm²) at 27.1 K (in liquid neon), in magnetic fields (parallel to the tape surface) of 2 and 10 T, respectively. Engineering-J_c of 100 A/mm² is obtained even in the perpendicular field of 0.5 T at 27.1 K.