A multipath analysis of biswapped networks.

Biswapped networks of the form $Bsw(G)$ have recently been proposed as interconnection networks to be implemented as optical transpose interconnection systems. We provide a systematic construction of $\kappa+1$ vertex-disjoint paths joining any two distinct vertices in $Bsw(G)$, where $\kappa\geq 1$ is the connectivity of $G$. In doing so, we obtain an upper bound of $\max\{2\Delta(G)+5,\Delta_\kappa(G)+\Delta(G)+2\}$ on the $(\kappa+1)$-diameter of $Bsw(G)$, where $\Delta(G)$ is the diameter of $G$ and $\Delta_\kappa(G)$ the $\kappa$-diameter. Suppose that we have a deterministic multipath source routing algorithm in an interconnection network $G$ that finds $\kappa$ mutually vertex-disjoint paths in $G$ joining any $2$ distinct vertices and does this in time polynomial in $\Delta_\kappa(G)$, $\Delta(G)$ and $\kappa$ (and independently of the number of vertices of $G$). Our constructions yield an analogous deterministic multipath source routing algorithm in the interconnection network $Bsw(G)$ that finds $\kappa+1$ mutually vertex-disjoint paths joining any $2$ distinct vertices in $Bsw(G)$ so that these paths all have length bounded as above. Moreover, our algorithm has time complexity polynomial in $\Delta_\kappa(G)$, $\Delta(G)$ and $\kappa$. We also show that if $G$ is Hamiltonian then $Bsw(G)$ is Hamiltonian, and that if $G$ is a Cayley graph then $Bsw(G)$ is a Cayley graph

Stack- and Queue-like Dynamics in Recurrent Neural Networks

What dynamics do simple recurrent networks (SRNs) develop to represent stack-like and queue-like memories? SRNs have been widely used as models in cognitive science. However, they are interesting in their own right as non-symbolic computing devices from the viewpoints of analogue computing and dynamical systems theory. In this paper, SRNs are trained oil two prototypical formal languages with recursive structures that need stack-like or queue-like memories for processing, respectively. The evolved dynamics are analysed, then interpreted in terms of simple dynamical systems, and the different ease with which SRNs aquire them is related to the properties of these simple dynamical Within the dynamical systems framework, it is concluded that the stack-like language is simpler than the queue-like language, without making use of arguments from symbolic computation theory

Quantum computation in semiconductor quantum dots of electron-spin asymmetric anisotropic exchange

The universal quantum computation is obtained when there exists asymmetric anisotropic exchange between electron spins in coupled semiconductor quantum dots. The asymmetric Heisenberg model can be transformed into the isotropic model through the control of two local unitary rotations for the realization of essential quantum gates. The rotations on each qubit are symmetrical and depend on the strength and orientation of asymmetric exchange. The implementation of the axially symmetric local magnetic fields can assist the construction of quantum logic gates in anisotropic coupled quantum dots. This proposal can efficiently use each physical electron spin as a logical qubit in the universal quantum computation.Comment: 4 pages, 1 figur

A single-shot line-scanning spatially dispersed short coherence interferometer using Fourier transform profilometry

Single-shot inspection at nanoscale resolution is a problematic challenge for providing on-line inspection of manufacturing techniques such as roll-to-roll processes where the measurand is constantly moving. An example of such a measurement challenge is defect detection on vapor barrier films formed by depositing an aluminum oxide layer several tens of nanometres thick on a flexible polymer substrate. Effective detection and characterisation of defects in this layer requires a single-shot approach with nanometre scale vertical resolution. This paper describes a line-scanning interferometer where a short coherence light source having a 25 nm linewidth source is spatially dispersed across the measurand thus encoding spatial position along a profile by wavelength. Phase shift interferometry (PSI) can be used to decode phase and thus height information, but requires multiple image captures. In order to realise single-shot measurement which is more suitable for online applications, a Fourier transform profilometry (FTP) approach is necessary. This paper explores the implementation of the FTP approach and presents a comparison of the measurement capability of FTP with the previously reported PSI method