Consensus in non-commutative spaces

Convergence analysis of consensus algorithms is revisited in the light of the Hilbert distance. The Lyapunov function used in the early analysis by Tsitsiklis is shown to be the Hilbert distance to consensus in log coordinates. Birkhoff theorem, which proves contraction of the Hilbert metric for any positive homogeneous monotone map, provides an early yet general convergence result for consensus algorithms. Because Birkhoff theorem holds in arbitrary cones, we extend consensus algorithms to the cone of positive definite matrices. The proposed generalization finds applications in the convergence analysis of quantum stochastic maps, which are a generalization of stochastic maps to non-commutative probability spaces. ©2010 IEEE.

Efficient decoding with generative score-spaces using the expectation semiring

State-of-the-art speech recognisers are usually based on hidden Markov models (HMMs). They model a hidden symbol sequence with a Markov process, with the observations independent given that sequence. These assumptions yield efficient algorithms, but limit the power of the model. An alternative model that allows a wide range of features, including word- and phone-level features, is a log-linear model. To handle, for example, word-level variable-length features, the original feature vectors must be segmented into words. Thus, decoding must find the optimal combination of segmentation of the utterance into words and word sequence. Features must therefore be extracted for each possible segment of audio. For many types of features, this becomes slow. In this paper, long-span features are derived from the likelihoods of word HMMs. Derivatives of the log-likelihoods, which break the Markov assumption, are appended. Previously, decoding with this model took cubic time in the length of the sequence, and longer for higher-order derivatives. This paper shows how to decode in quadratic time. © 2013 IEEE.

Growth-Parameter Spaces and Optical Properties of Cubic Boron Nitride Films on Si(001)

Cubic boron nitride (c-BN) films were deposited on Si(001) substrates in an ion beam assisted deposition (IBAD) system under various conditions, and the growth parameter spaces and optical properties of c-BN films have been investigated systematically. The results indicate that suitable ion bombardment is necessary for the growth of c-BN films, and a well defined parameter space can be established by using the P/a-parameter. The refractive index of BN films keeps a constant of 1.8 for the c-BN content lower than 50%, while for c-BN films with higher cubic phase the refractive index increases with the c-BN content from 1.8 at chi(c) = 50% to 2.1 at chi(c) = 90%. Furthermore, the relationship between n and rho for BN films can be described by the Anderson-Schreiber equation, and the overlap field parameter gamma is determined to be 2.05.

Storage of photoexcited electron-hole pairs in an AlAs/GaAs heterostructure created by electron transfer in real and kappa spaces

The storage of photoexcited electron-hole pairs is experimentally carried out and theoretically realized by transferring electrons in both real and k spaces through resonant Gamma - X in an AlAs/GaAs heterostructure. This is proven by the peculiar capacitance jump and hysteresis in the measured capacitance-voltage curves. Our structure may be used as a photonic memory cell with a long storage time and a fast retrieval of photons as well.

Formalizing Triggers: A Learning Model for Finite Spaces

In a recent seminal paper, Gibson and Wexler (1993) take important steps to formalizing the notion of language learning in a (finite) space whose grammars are characterized by a finite number of parameters. They introduce the Triggering Learning Algorithm (TLA) and show that even in finite space convergence may be a problem due to local maxima. In this paper we explicitly formalize learning in finite parameter space as a Markov structure whose states are parameter settings. We show that this captures the dynamics of TLA completely and allows us to explicitly compute the rates of convergence for TLA and other variants of TLA e.g. random walk. Also included in the paper are a corrected version of GW's central convergence proof, a list of "problem states" in addition to local maxima, and batch and PAC-style learning bounds for the model.

The potential risk from 222radon posed to archaeologists and earth scientists: reconnaissance study of radon concentrations, excavations and archaeological shelters in the Great cave of Niah, Sarawak, Malaysia

Gillmore, G. Gilbertson, D. Grattan, J. Hunt, C. McLaren, S. Pyatt, B. Banda, R. Barker, G. Denman, A. Phillips, P. Reynolds, T. The potential risk from 222radon posed to archaeologists and earth scientists: reconnaissance study of radon concentrations, excavations and archaeological shelters in the Great cave of Niah, Sarawak, Malaysia. Ecotoxicology and Environmental Safety. 2005. 60 pp 213-227.