Optimal data fitting on lie groups: A coset approach

This work considers the problem of fitting data on a Lie group by a coset of a compact subgroup. This problem can be seen as an extension of the problem of fitting affine subspaces in n to data which can be solved using principal component analysis. We show how the fitting problem can be reduced for biinvariant distances to a generalized mean calculation on an homogeneous space. For biinvariant Riemannian distances we provide an algorithm based on the Karcher mean gradient algorithm. We illustrate our approach by some examples on SO(n). © 2010 Springer -Verlag Berlin Heidelberg.

Capacity approaching codes for non-coherent orthogonal modulation

This paper describes a curve-fitting approach for the design of capacity approaching coded modulation for orthogonal signal sets with non-coherent detection. In particular, bit-interleaved coded modulation with iterative decoding is considered. Decoder metrics are developed that do not require knowledge of the signal-to-noise ratio, yet still offer very good performance. © 2007 IEEE.

Temporally adaptive estimation of logistic classifiers on data streams

Modern technology has allowed real-time data collection in a variety of domains, ranging from environmental monitoring to healthcare. Consequently, there is a growing need for algorithms capable of performing inferential tasks in an online manner, continuously revising their estimates to reflect the current status of the underlying process. In particular, we are interested in constructing online and temporally adaptive classifiers capable of handling the possibly drifting decision boundaries arising in streaming environments. We first make a quadratic approximation to the log-likelihood that yields a recursive algorithm for fitting logistic regression online. We then suggest a novel way of equipping this framework with self-tuning forgetting factors. The resulting scheme is capable of tracking changes in the underlying probability distribution, adapting the decision boundary appropriately and hence maintaining high classification accuracy in dynamic or unstable environments. We demonstrate the scheme's effectiveness in both real and simulated streaming environments. © Springer-Verlag 2009.

Nucleated polymerization with secondary pathways. I. Time evolution of the principal moments.

Self-assembly processes resulting in linear structures are often observed in molecular biology, and include the formation of functional filaments such as actin and tubulin, as well as generally dysfunctional ones such as amyloid aggregates. Although the basic kinetic equations describing these phenomena are well-established, it has proved to be challenging, due to their non-linear nature, to derive solutions to these equations except for special cases. The availability of general analytical solutions provides a route for determining the rates of molecular level processes from the analysis of macroscopic experimental measurements of the growth kinetics, in addition to the phenomenological parameters, such as lag times and maximal growth rates that are already obtainable from standard fitting procedures. We describe here an analytical approach based on fixed-point analysis, which provides self-consistent solutions for the growth of filamentous structures that can, in addition to elongation, undergo internal fracturing and monomer-dependent nucleation as mechanisms for generating new free ends acting as growth sites. Our results generalise the analytical expression for sigmoidal growth kinetics from the Oosawa theory for nucleated polymerisation to the case of fragmenting filaments. We determine the corresponding growth laws in closed form and derive from first principles a number of relationships which have been empirically established for the kinetics of the self-assembly of amyloid fibrils.

Identification of damping: Part 4, error analysis

In previous papers (S. Adhikari and J. Woodhouse 2001 Journal of Sound and Vibration 243, 43-61; 63-88; S. Adhikari and J. Woodhouse 2002 Journal of Sound and Vibration 251, 477-490) methods were proposed to obtain the coefficient matrix for a viscous damping model or a non-viscous damping model with an exponential relaxation function, from measured complex natural frequencies and modes. In all these works, it has been assumed that exact complex natural frequencies and complex modes are known. In reality, this will not be the case. The purpose of this paper is to analyze the sensitivity of the identified damping matrices to measurement errors. By using numerical and analytical studies it is shown that the proposed methods can indeed be expected to give useful results from moderately noisy data provided a correct damping model is selected for fitting. Indications are also given of what level of noise in the measured modal properties is needed to mask the true physical behaviour.

A unified circuit model for the polysilicon thin film transistor

This paper describes a unified approach to modelling the polysilicon thin film transistor (TFT) for the purposes of circuit design. The approach uses accurate methods of predicting the channel conductance and then fitting the resulting data with a polynomial. Two methods are proposed to find the channel conductance: a device model and measurement. The approach is suitable because the TFT does not have a well defined threshold voltage. The polynomial conductance is then integrated generally to find the drain current and channel charge, necessary for a complete circuit model. © 1991 The Japan Society of Applied Physics.

Real time feature-based facial tracking using Lie algebras

We have developed a novel human facial tracking system that operates in real time at a video frame rate without needing any special hardware. The approach is based on the use of Lie algebra, and uses three-dimensional feature points on the targeted human face. It is assumed that the roughly estimated facial model (relative coordinates of the three-dimensional feature points) is known. First, the initial feature positions of the face are determined using a model fitting technique. Then, the tracking is operated by the following sequence: (1) capture the new video frame and render feature points to the image plane; (2) search for new positions of the feature points on the image plane; (3) get the Euclidean matrix from the moving vector and the three-dimensional information for the points; and (4) rotate and translate the feature points by using the Euclidean matrix, and render the new points on the image plane. The key algorithm of this tracker is to estimate the Euclidean matrix by using a least square technique based on Lie algebra. The resulting tracker performed very well on the task of tracking a human face.

The modelling of soil plasticity

The modeling of the soil plasticity was discussed and it was shown that the grain breakage is an important factor of the plastic soil behaviour. A reduction of internal coefficient of friction was observed when stress-level was increased. The yield paths of all stress path tests determined by curve fitting were presented.

Vibration-assisted bone-graft compaction in impaction bone grafting of the femur

The complications of impaction bone grafting in revision hip replacement includes fracture of he femur and subsidence of the prosthesis. In this in vitro study we aimed to investigate whether the use of vibration, combined with a perforated tamp during the compaction of morsellised allograft would reduce peak loads and hoop strains in the femur as a surrogate marker of the risk of fracture and whether it would also improve graft compaction and prosthetic stability. We found that the peak loads and hoop strains transmitted to the femoral cortex during graft compaction and subsidence of the stem in subsequent mechanical testing were reduced. This innovative technique has the potential to reduce the risk of intra-operative fracture and to improve graft compaction and therefore prosthetic stability. © 2007 British Editorial Society of Bone and Joint Surgery.